Fundamentals of Biomechanics

Duane Knudson

Fundamentalsof Biomechanics

Second Edition

Duane KnudsonDepartment of KinesiologyCalifornia State University at ChicoFirst & Normal StreetChico, CA [email protected]

Library of Congress Control Number: 2007925371

ISBN 978-0-387-49311-4 e-ISBN 978-0-387-49312-1

Printed on acid-free paper.

© 2007 Springer Science+Business Media, LLCAll rights reserved. This work may not be translated or copied in whole or in part without the written permission of thepublisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerptsin connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval,electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed isforbidden.The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified assuch, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.

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Preface ix

Acknowledgments xi

PART I

INTRODUCTION

CHAPTER 1

INTRODUCTION TO BIOMECHANICSOF HUMAN MOVEMENT

WHAT IS BIOMECHANICS? 3

WHY STUDY BIOMECHANICS? 5Improving Performance 5Preventing and Treating Injury 9Qualitative and Quantitative Analysis 11

WHERE CAN I FIND OUT ABOUT

BIOMECHANICS? 12Scholarly Societies 13Computer Searches 14Biomechanics Textbooks 15

BIOMECHANICAL KNOWLEDGE VERSUS

INFORMATION 16Kinds of Sources 16Evaluating Sources 18A Word About Right and

Wrong Answers 1

SUMMARY 20

REVIEW QUESTIONS 21

KEY TERMS 21

SUGGESTED READING 21

WEB LINKS 22

CHAPTER 2

FUNDAMENTALS OF BIOMECHANICSAND QUALITATIVE ANALYSIS

KEY MECHANICAL CONCEPTS 23Mechanics 23Basic Units 25

NINE FUNDAMENTALS OF BIOMECHANICS 29Principles and Laws 29Nine Principles for Application of

Biomechanics 30

QUALITATIVE ANALYSIS 35

SUMMARY 36

REVIEW QUESTIONS 36

KEY TERMS 37


WEB LINKS 37

PART II

BIOLOGICAL/STRUCTURAL BASES

CHAPTER 3

ANATOMICAL DESCRIPTION ANDITS LIMITATIONS

REVIEW OF KEY ANATOMICAL CONCEPTS 41Directional Terms 42Joint Motions 43Review of Muscle Structure 46

MUSCLE ACTIONS 49Active and Passive Tension of Muscle 51Hill Muscle Model 51

THE LIMITATIONS OF FUNCTIONAL

ANATOMICAL ANALYSIS 53Mechanical Method of Muscle

Action Analysis 53The Need for Biomechanics to

Understand Muscle Actions 56Sports Medicine and Rehabilitation

Applications 60

RANGE-OF-MOTION PRINCIPLE 60

FORCE–MOTION PRINCIPLE 63

SUMMARY 65

REVIEW QUESTIONS 66

KEY TERMS 66


WEB LINKS 67

v

Contents

9

CHAPTER 4

MECHANICS OF THEMUSCULOSKELETAL SYSTEM

TISSUE LOADS 69

RESPONSE OF TISSUES TO FORCES 69Stress 70Strain 70Stiffness and Mechanical Strength 71Viscoelasticity 72

BIOMECHANICS OF THE PASSIVE

MUSCLE–TENDON UNIT (MTU) 75

BIOMECHANICS OF BONE 76

BIOMECHANICS OF LIGAMENTS 77

THREE MECHANICAL CHARACTERISTICS

OF MUSCLE 79Force–Velocity Relationship 79Force–Length Relationship 84Force–Time Relationship 86

STRETCH-SHORTENING CYCLE (SSC) 88

FORCE–TIME PRINCIPLE 92

NEUROMUSCULAR CONTROL 94The Functional Unit of Control:

Motor Units 94Regulation of Muscle Force 95Proprioception of Muscle Action

and Movement 99

SUMMARY 100

REVIEW QUESTIONS 101

KEY TERMS 101


WEB LINKS 103

PART III

MECHANICAL BASES

CHAPTER 5

LINEAR AND ANGULARKINEMATICS

LINEAR MOTION 107Speed and Velocity 109Acceleration 113Uniformly Accelerated Motion 115

OPTIMAL PROJECTION PRINCIPLE 117

ANGULAR MOTION 121Angular Velocity 122Angular Acceleration 123

COORDINATION CONTINUUM PRINCIPLE 128

SUMMARY 130


KEY TERMS 131


WEB LINKS 132

CHAPTER 6

LINEAR KINETICS

LAWS OF KINETICS 133

NEWTON'S LAWS OF MOTION 133Newton's First Law and First

Impressions 133Newton's Second Law 136Newton's Third Law 137

INERTIA PRINCIPLE 139

MUSCLE ANGLE OF PULL:QUALITATIVE AND QUANTITATIVE

ANALYSIS OF VECTORS 141Qualitative Vector Analysis of

Muscle Angle of Pull 141Quantitative Vector Analysis of

Muscle Angle of Pull 143

CONTACT FORCES 145

IMPULSE–MOMENTUM RELATIONSHIP 147

FORCE–TIME PRINCIPLE 149

WORK–ENERGY RELATIONSHIP 151

Mechanical Energy 151Mechanical Work 155Mechanical Power 157

SEGMENTAL INTERACTION PRINCIPLE 160

SUMMARY 164


KEY TERMS 166


WEB LINKS 167

VI FUNDAMENTALS OF BIOMECHANICS

CHAPTER 7

ANGULAR KINETICS

TORQUE 169SUMMING TORQUES 173ANGULAR INERTIA (MOMENT OF INERTIA) 174NEWTON'S ANGULAR ANALOGUES 178EQUILIBRIUM 179CENTER OF GRAVITY 180PRINCIPLE OF BALANCE 183SUMMARY 189REVIEW QUESTIONS 190KEY TERMS 190SUGGESTED READING 191WEB LINKS 191

CHAPTER 8

FLUID MECHANICS

FLUIDS 193FLUID FORCES 193

Buoyancy 193Drag 195Lift 200The Magnus Effect 203

PRINCIPLE OF SPIN 208SUMMARY 210KEY TERMS 210REVIEW QUESTIONS 210SUGGESTED READING 210WEB LINKS 211

PART IV

APPLICATIONS OF BIOMECHANICSIN QUALITATIVE ANALYSIS

CHAPTER 9

APPLYING BIOMECHANICS INPHYSICAL EDUCATION

QUALITATIVE ANALYSIS OF KICKING

TECHNIQUE 215QUALITATIVE ANALYSIS OF BATTING 218QUALITATIVE ANALYSIS OF THE

BASKETBALL FREE THROW 219EXERCISE/ACTIVITY PRESCRIPTION 220QUALITATIVE ANALYSIS OF CATCHING 222

SUMMARY 224DISCUSSION QUESTIONS 224SUGGESTED READING 224WEB LINKS 225

CHAPTER 10

APPLYING BIOMECHANICS INCOACHING

QUALITATIVE ANALYSIS OF

THROWING TECHNIQUE 227QUALITATIVE ANALYSIS OF

DRIBBLING TECHNIQUE 228QUALITATIVE ANALYSIS OF

CONDITIONING 230RECRUITMENT 231QUALITATIVE ANALYSIS OF CATCHING 233SUMMARY 234DISCUSSION QUESTIONS 234SUGGESTED READING 234WEB LINKS 235

CHAPTER 11

APPLYING BIOMECHANICS INSTRENGTH AND CONDITIONING


SQUAT TECHNIQUE 237QUALITATIVE ANALYSIS OF

DROP JUMPS 239EXERCISE SPECIFICITY 240INJURY RISK 242EQUIPMENT 244SUMMARY 244DISCUSSION QUESTIONS 245SUGGESTED READING 246WEB LINKS 246

CHAPTER 12

APPLYING BIOMECHANICS IN SPORTSMEDICINE AND REHABILITATION

INJURY MECHANISMS 247EXERCISE SPECIFICITY 248EQUIPMENT 250

CONTENTS VII

READINESS 251

INJURY PREVENTION 252

SUMMARY 253

DISCUSSION QUESTIONS 254


WEB LINKS 255

REFERENCES 257

APPENDIX A

GLOSSARY 283

APPENDIX B

CONVERSION FACTORS 297

APPENDIX C

SUGGESTED ANSWERS TO SELECTED


APPENDIX D

RIGHT-ANGLE TRIGONOMETRY

REVIEW 305

APPENDIX E


BIOMECHANICAL PRINCIPLES 307

INDEX 309

LAB ACTIVITIES

1 FINDING BIOMECHANICAL SOURCES L-2

2 QUALITATIVE AND QUANTITATIVE

ANALYSIS OF RANGE OF MOTION L-4

3 FUNCTIONAL ANATOMY? L-6

4 MUSCLE ACTIONS AND THE STRETCH-

SHORTENING CYCLE (SSC) L-8

5A VELOCITY IN SPRINTING L-10

5B ACCURACY OF THROWING

SPEED MEASUREMENTS L-12

6A TOP GUN KINETICS:FORCE–MOTION PRINCIPLE L–14

6B IMPULSE–MOMENTUM:FORCE–TIME PRINCIPLE L-16

7A ANGULAR KINETICS OF EXERCISE L-18

7B CALCULATING CENTER OF GRAVITY

USING ANGULAR KINETICS L-20

8 MAGNUS EFFECT IN BASEBALL

PITCHING L-22

9 QUALITATIVE ANALYSIS OF

LEAD-UP ACTIVITIES L-24

10 COMPARISON OF SKILLED AND

NOVICE PERFORMANCE L-26

11 COMPARISON OF TRAINING

MODES L-28

12 QUALITATIVE ANALYSIS OF

WALKING GAIT L-30

VIII FUNDAMENTALS OF BIOMECHANICS

This second edition of Fundamentals ofBiomechanics was developed primarily toupdate a well-received text. The unique-ness of integrating biological and mechani-cal bases in analyzing and improving hu-man movement has been expanded withmore examples, figures, and lab activities.Citations to the latest research and weblinks help students access primary sources.Students and instructors will appreciate theCD with lab activities, answers to reviewquestions, sample questions, and graphicsfiles of the illustrations.

This book is written for students takingthe introductory biomechanics course inKinesiology/HPERD. The book is designedfor majors preparing for all kinds of humanmovement professions and therefore uses awide variety of movement examples to il-lustrate the application of biomechanics.While this approach to the application ofbiomechanics is critical, it is also importantthat students be introduced to the scientificsupport or lack of support for these qualita-tive judgments. Throughout the text exten-sive citations are provided to support theprinciples developed and give students ref-erences for further study. Algebraic levelmathematics is used to teach mechanicalconcepts. The focus of the mathematical ex-amples is to understand the mechanicalvariables and to highlight the relationshipbetween various biomechanical variables,rather than to solve quantitative biome-chanical word problems. It is obvious fromresearch in physics instruction that solvingquantitative word problems does not in-crease the conceptual understanding of im-portant mechanical laws (Elby, 2001;

Lawson & McDermott, 1987; Kim & Pak,2002).

So why another textbook on the biome-chanics of human motion? There are plentyof books that are really anatomy bookswith superficial mechanics, that teach me-chanics with sport examples, or are sportbooks that use some mechanics to illustratetechnique points. Unfortunately, there arenot many books that truly integrate the bi-ological and mechanical foundations of hu-man movement and show students how toapply and integrate biomechanical knowl-edge in improving human movement. Thisbook was written to address these limita-tions in previous biomechanics texts. Thetext presents a clear conceptual under-standing of biomechanics and builds nineprinciples for the application of biomechan-ics. These nine principles form the appliedbiomechanics tools kinesiology profession-als need. The application of these biome-chanical principles is illustrated in qualita-tive analysis of a variety of human move-ments in several contexts for the kinesiolo-gy professional: physical education, coach-ing, strength and conditioning, and sportsmedicine. This qualitative analysis ap-proach meets the NASPE Guidelines andStandards (Kinesiology Academy, 1992) foran introductory biomechanics course, andclearly shows students how biomechanicalknowledge must be applied when kinesiol-ogy professionals improve human move-ment.

The text is subdivided into four parts:Introduction, Biological/Structural Bases,Mechanical Bases, and Applications ofBiomechanics in Qualitative Analysis. Each

ix

Preface

part opener provides a concise summary ofthe importance and content of that sectionof text. The text builds from familiar ana-tomical knowledge, to new biomechanicalprinciples and their application.

This book has several features that aredesigned to help students link personal ex-perience to biomechanical concepts andthat illustrate the application of biome-chanics principles. First, nine general prin-ciples of biomechanics are proposed anddeveloped throughout the text. These prin-ciples are the application link for the bio-mechanical concepts used to improvemovement or reduce injury risk. Some textshave application chapters at the end of thebook, but an application approach and ex-amples are built in throughout Funda-mentals of Biomechanics. Second, there areactivity boxes that provide opportunities forstudents to see and feel the biomechanicalvariables discussed. Third, there are practi-cal application boxes that highlight the appli-cations of biomechanics in improvingmovement and in treating and preventinginjury. Fourth, the interdisciplinary issuesboxes show how biomechanics is integratedwith other sport sciences in addressing hu-man movement problems. Fifth, all chap-ters have associated lab activities (located atthe end of the book, after the index) that usesimple movements and measurements toexplore concepts and principles. These labactivities do not require expensive labequipment, large blocks of time, or dedicat-ed lab space. Finally, Part IV (chapters 9through 12) provides real-life case studies

of how the biomechanical principles can bequalitatively applied to improve humanmovement in a variety of professions. Noother text provides as many or as thoroughguided examples of applying biomechani-cal principles in actual human movementsituations. These application chapters alsoprovide discussion questions so that studentsand instructors can extend the discussionand debate on professional practice usingspecific examples.

There are also features that make it easyfor students to follow the material andstudy for examinations. Extensive use ofgraphs, photographs, and illustrations areincorporated throughout. Aside from visualappeal, these figures illustrate importantpoints and relationships between biome-chanical variables and performance. Thebook provides an extensive glossary of keyterms and biomechanics research terminolo-gy so that students can read original biome-chanical research. Each chapter provides asummary, extensive citations of importantbiomechanical research, and suggested read-ings. The chapters in Parts I, II, and III con-clude with review questions for student studyand review. The lists of web links offer stu-dents the internet addresses of significantwebsites and professional organizations.

I hope that you master the fundamen-tals of biomechanics, integrate biomechan-ics into your professional practice, and arechallenged to continuously update yourbiomechanical toolbox. Some of you willfind advanced study and a career in biome-chanics exciting opportunities.

X FUNDAMENTALS OF BIOMECHANICS

The author would like to thank the manypeople who have contributed to the secondedition of this book. I am indebted to manybiomechanics colleagues who have sharedtheir expertise with me, given permissionto share their work, and contributed somuch to students and our profession. Iwould like to thank Tim Oliver for his ex-pert editing, formatting, design, and art ed-iting of the book, Katherine Hanley-

Knutson for many fine illustrations, andAaron Johnson of Springer for his vision tomake this book happen.

To the ones I truly love—Lois, Josh,and Mandy—thanks for being such greatpeople and for sharing the computer.Finally, I would like to thank God for knit-ting all of us so “fearfully and wonderfullymade.”

xi

Acknowledgments

PARTIINTRODUCTION

Kinesiology is the scholarly study of humanmovement, and biomechanics is one of themany academic subdisciplines of kinesiol-ogy. Biomechanics in kinesiology involvesthe precise description of human movementand the study of the causes of human move-ment. The study of biomechanics is relevantto professional practice in many kinesiologyprofessions. The physical educator or coachwho is teaching movement technique andthe athletic trainer or physical therapisttreating an injury use biomechanics to quali-tatively analyze movement. The chapters inpart I demonstrate the importance of biome-chanics in kinesiology and introduce you tokey biomechanical terms and principles thatwill be developed throughout the text. Thelab activities associated with part I relate tofinding biomechanical knowledge and iden-tifying biomechanical principles in action.

1

Most people are extremely skilled in manyeveryday movements like standing, walk-ing, or climbing stairs. By the time childrenare two, they are skilled walkers with littleinstruction from parents aside from emo-tional encouragement. Unfortunately, mod-ern living does not require enough move-ment to prevent several chronic diseasesassociated with low physical activity (USD-HHS, 1996). Fortunately, many humanmovement professions help people to par-ticipate in beneficial physical activities.Physical Educators, coaches, athletic train-ers, strength & conditioning coaches, per-sonal trainers, and physical therapists allhelp people reap the benefits of physical ac-tivity. These human movement professionsrely on undergraduate training in kinesiol-ogy, and typically require coursework inbiomechanics. Kinesiology is the term re-ferring to the whole scholarly area of hu-man movement study, while biomechanicsis the study of motion and its causes in liv-ing things. Biomechanics provides key in-formation on the most effective and safestmovement patterns, equipment, and rele-vant exercises to improve human move-ment. In a sense, kinesiology professionalssolve human movement problems everyday, and one of their most important toolsis biomechanics. This chapter outlines thefield of biomechanics, why biomechanics issuch an important area to the kinesiologyprofessional, and where biomechanics in-formation can be found.

WHAT IS BIOMECHANICS?

Biomechanics has been defined as the studyof the movement of living things using the sci-ence of mechanics (Hatze, 1974). Mechanics isa branch of physics that is concerned withthe description of motion and how forcescreate motion. Forces acting on livingthings can create motion, be a healthy stim-ulus for growth and development, or over-load tissues, causing injury. Biomechanicsprovides conceptual and mathematicaltools that are necessary for understandinghow living things move and how kinesiol-ogy professionals might improve move-ment or make movement safer.

Most readers of this book will be ma-jors in departments of Kinesiology, HumanPerformance, or HPERD (Health, PhysicalEducation, Recreation, and Dance). Kinesi-ology comes from two Greek verbs thattranslated literally means “the study ofmovement.” Most American higher educa-tion programs in HPERD now use “kinesi-ology” in the title of their department be-cause this term has come to be known asthe academic area for the study of humanmovement (Corbin & Eckert, 1990). Thischange in terminology can be confusing be-cause “kinesiology” is also the title of afoundational course on applied anatomythat was commonly required for a physicaleducation degree in the first half of thetwentieth century. This older meaning ofkinesiology persists even today, possibly

CHAPTER 1

Introduction to Biomechanicsof Human Movement

3

because biomechanics has only recently(since 1970s) become a recognized special-ization of scientific study (Atwater, 1980;Wilkerson, 1997).

This book will use the term kinesiologyin the modern sense of the whole academicarea of the study of human movement.Since kinesiology majors are pursuing ca-reers focused on improving human move-ment, you and almost all kinesiology stu-dents are required to take at least onecourse on the biomechanics of humanmovement. It is a good thing that you arestudying biomechanics. Once your friendsand family know you are a kinesiology ma-jor, you will invariably be asked questionslike: should I get one of those new rackets,why does my elbow hurt, or how can I stopmy drive from slicing? Does it sometimesseem as if your friends and family have re-gressed to that preschool age when everyother word out of their mouth is “why”?What is truly important about this commonexperience is that it is a metaphor for thelife of a human movement professional.Professions require formal study of theoret-ical and specialized knowledge that allowsfor the reliable solution to problems. This isthe traditional meaning of the word “pro-fessional,” and it is different than its com-mon use today. Today people refer to pro-fessional athletes or painters becausepeople earn a living with these jobs, but Ibelieve that kinesiology careers shouldstrive to be more like true professions suchas medicine or law.

People need help in improving humanmovement and this help requires knowl-edge of “why” and “how” the human bodymoves. Since biomechanics gives the kine-siology professional much of the knowl-edge and many of the skills necessary to an-swer these “what works?” and “why?”questions, biomechanics is an importantscience for solving human movement prob-lems. However, biomechanics is but one of

many sport and human movement sciencetools in a kinesiology professional's tool-box. This text is also based on the philoso-phy that your biomechanical tools must becombined with tools from other kinesiologysciences to most effectively deal with hu-man movement problems. Figure 1.1a illus-trates the typical scientific subdisciplines ofkinesiology. These typically are the core sci-ences all kinesiology majors take in theirundergraduate preparations. This overviewshould not be interpreted to diminish theother academic subdisciplines common inkinesiology departments like sport history,sport philosophy, dance, and sport admin-istration/management, just to name a few.

The important point is that knowledgefrom all the subdisciplines must be inte-grated in professional practice since prob-lems in human movement are multifaceted,with many interrelated factors. For themost part, the human movement problemsyou face as a kinesiology professional willbe like those “trick” questions professorsask on exams: they are complicated bymany factors and tend to defy simple, dual-istic (black/white) answers. While the ap-plication examples discussed in this textwill emphasize biomechanical principles,readers should bear in mind that this bio-mechanical knowledge should be inte-grated with professional experience and theother subdisciplines of kinesiology. It is thisinterdisciplinary approach (Figure 1.1b)that is essential to finding the best interven-tions to help people more effectively andsafely. Dotson (1980) suggests that true ki-nesiology professionals can integrate themany factors that interact to affect move-ment, while the layman typically looks atthings one factor at time. Unfortunately,this interdisciplinary approach to kinesiol-ogy instruction in higher education hasbeen elusive (Harris, 1993). Let's look atsome examples of human movement prob-lems where it is particularly important to

4 FUNDAMENTALS OF BIOMECHANICS

integrate biomechanical knowledge intothe qualitative analysis.

WHY STUDY BIOMECHANICS?

Scientists from many different areas (e.g.,kinesiology, engineering, physics, biology,zoology) are interested in biomechanics.Why are scholars from so many differentacademic backgrounds interested in animalmovement? Biomechanics is interesting be-cause many people marvel at the abilityand beauty in animal movement. Somescholars have purely theoretical or aca-demic interests in discovering the lawsand principles that govern animal move-ment. Within kinesiology, many biomech-anists have been interested in the applica-tion of biomechanics to sport and exercise.The applications of biomechanics to human

movement can be classified into two mainareas: the improvement of performanceand the reduction or treatment of injury(Figure 1.2).

Improving Performance

Human movement performance can be en-hanced many ways. Effective movementinvolves anatomical factors, neuromuscu-lar skills, physiological capacities, and psy-chological/cognitive abilities. Most kinesi-ology professionals prescribe techniquechanges and give instructions that allow aperson to improve performance. Biome-chanics is most useful in improving per-formance in sports or activities where tech-nique is the dominant factor rather thanphysical structure or physiological capac-ity. Since biomechanics is essentially the

CHAPTER 1: INTRODUCTION TO BIOMECHANICS OF HUMAN MOVEMENT 5

Figure 1.1. (a) The major academic subdisciplines or sciences of kinesiology. (b) Schematic of the integration of allthe sciences in an interdisciplinary approach to solving human movement problems in kinesiology.

science of movement technique, biome-chanics is the main contributor to one of themost important skills of kinesiology profes-sionals: the qualitative analysis of humanmovement (Knudson & Morrison, 2002).

Imagine a coach is working with agymnast who is having problems with herback handspring (Figure 1.3). The coach ob-serves several attempts and judges that theangle of takeoff from the round off and

body arch are performed poorly. Thecoach's experience tells him that this athleteis strong enough to perform this skill, butthey must decide if the gymnast shouldconcentrate on her takeoff angle or moreback hyperextension in the block. Thecoach uses his knowledge of biomechanicsto help in the qualitative analysis of this sit-uation. Since the coach knows that a betterarch affects the force the gymnast createsagainst the mat and affects the angle oftakeoff of the gymnast, he decides to helpthe gymnast work on her “arch” followingthe round off.

Biomechanics research on sports tech-niques sometimes tends to lag behind thechanges that are naturally occurring insports. Athletes and coaches experimentwith new techniques all the time. Studentsof biomechanics may be surprised to findthat there are often limited biomechanical


Figure 1.2. The two major applications of biomechan-ics are to improve human movement and the treat-ment or prevention of injury.

Figure 1.3. Biomechanics principles must be inte-grated with other kinesiology sciences to solve humanmovement problems, like in the qualitative analysis around off and back handspring.

studies on many techniques in many popu-lar sports. The vast number of techniques,their variations, and their high rates ofchange and innovation tend to outdistancebiomechanics research resources. Sport bio-mechanics research also lags behind thecoaches and athletes because scientific re-search takes considerable time to conductand report, and there is a lack of fundingfor this important research. There is lessfunding for biomechanical studies aimed atimproving performance compared to stud-ies focused on preventing and treating in-juries. Students looking for biomechanicalresearch on improving sports technique of-ten will have fewer sources than studentsresearching the biomechanics of injury.

While technique is always relevant inhuman movement, in some activities thepsychological, anatomical, or physiologicalfactors are more strongly related to success.Running is a good example of this kind ofmovement. There is a considerable amountof research on the biomechanics of runningso coaches can fine tune a runner's tech-nique to match the profile of elite runners(Cavanagh, Andrew, Kram, Rogers, San-derson, & Hennig, 1985; Buckalew, Barlow,Fischer, & Richards, 1985; Williams, Ca-vanagh, & Ziff, 1987). While these tech-nique adjustments make small improve-ments in performance, most of runningperformance is related to physiologicalabilities and their training. Studies that pro-vide technique changes in running basedon biomechanical measurements havefound minimal effects on running economy(Cavanagh, 1990; Lake & Cavanagh, 1996;Messier & Cirillo, 1989). This suggests thattrack coaches can use biomechanics to re-fine running technique, but they shouldonly expect small changes in performancefrom these modifications.

Human performance can also be en-hanced by improvements in the design ofequipment. Many of these improvementsare related to new materials and engineer-

ing designs. When these changes areintegrated with information about thehuman performer, we can say the improve-ments in equipment were based on biome-chanics. Engineers interested in sportsequipment often belong to the Intern-ational Sports Engineering Association(http://www.sportsengineering.org/) andpublish research in ISEA proceedings(Subic & Haake, 2000) or the Sports Engi-neering journal. Research on all kinds ofequipment is conducted in biomechanicslabs at most major sporting goods manu-facturers. Unfortunately, much of the re-sults of these studies are closely guardedtrade secrets, and it is difficult for thelayperson to determine if marketing claimsfor “improvements” in equipment designare real biomechanical innovations or justcreative marketing.

There are many examples of how ap-plying biomechanics in changing equip-ment designs has improved sports per-formance. When improved javelin designsin the early 1980s resulted in longer throwsthat endangered other athletes and specta-tors, redesigns in the weight distribution ofthe “new rules” javelin again shortenedthrows to safer distances (Hubbard & Al-aways, 1987). Biomechanics researchers (El-liott, 1981; Ward & Groppel, 1980) weresome of the first to call for smaller tennisrackets that more closely matched the mus-cular strength of young players (Figure 1.4).Chapter 8 will discuss how changes insports equipment are used to change fluidforces and improve performance.

While breaking world records usingnew equipment is exciting, not all changesin equipment are welcomed with openarms by sport governing bodies. Someequipment changes are so drastic theychange the very nature of the game and arequickly outlawed by the rules committee ofthe sport. One biomechanist developed away to measure the stiffness of basketballgoals, hoping to improve the consistency of


their response but found considerable re-sistance from basketball folks who likedtheir unique home court advantages. An-other biomechanist recently developed anew “klap” speed skate that increased thetime and range of motion of each push offthe ice, dramatically improving times andbreaking world records (de Koning, Hou-dijk, de Groot, & Bobbert, 2000). This gavequite an advantage to the country wherethese skates were developed, and there wascontroversy over the amount of time otherskaters were able to practice with the newskates before competition. These dramaticequipment improvements in many sportshave some people worried that winningOlympic medals may be more in the hands

of the engineers than athletes (Bjerklie,1993).

Another way biomechanics researchimproves performance is advances in exer-cise and conditioning programs. Bio-mechanical studies of exercise movementsand training devices serve to determine themost effective training to improve perform-ance (Figure 1.5). Biomechanical researchon exercises is often compared to researchon the sport or activity that is the focus oftraining. Strength and conditioning profes-sionals can better apply the principle ofspecificity when biomechanical research isused in the development of exercise pro-grams. Computer-controlled exercise andtesting machines are another example ofhow biomechanics contributes to strengthand conditioning (Ariel, 1983). In the nextsection the application of biomechanics inthe medical areas of orthotics and prosthet-ics will be mentioned in relation to prevent-ing injury, but many prosthetics are nowbeing designed to improve the performanceof disabled athletes.


Figure 1.4. The design of sports equipment must beappropriate for an athlete, so rackets for children areshorter and lighter than adult rackets. Photo used withpermission from Getty Images.

Figure 1.5. A computerized testing and exercise dy-namometer by Biodex. The speed, muscle actions (iso-metric, concentric, eccentric), and pattern of loading(isokinetic, isotonic) can be selected. Image courtesy ofBiodex Medical Systems.

Preventing and Treating Injury

Movement safety, or injury prevention/treatment, is another primary area wherebiomechanics can be applied. Sports medi-cine professionals have traditionally stud-ied injury data to try to determine thepotential causes of disease or injury (epi-demiology). Biomechanical research is apowerful ally in the sports medicine questto prevent and treat injury. Biomechanicalstudies help prevent injuries by providinginformation on the mechanical propertiesof tissues, mechanical loadings duringmovement, and preventative or rehabilita-tive therapies. Biomechanical studies pro-vide important data to confirm potential in-jury mechanisms hypothesized by sportsmedicine physicians and epidemiologicalstudies. The increased participation of girlsand women in sports has made it clear thatfemales are at a higher risk for anterior cru-ciate ligament (ACL) injuries than malesdue to several biomechanical factors (Bo-den, Griffin, & Garrett, 2000). Continuedbiomechanical and sports medicine studiesmay help unravel the mystery of this highrisk and develop prevention strategies (seeChapter 12).

Engineers and occupational therapistsuse biomechanics to design work tasks andassistive equipment to prevent overuse in-juries related to specific jobs. Combiningbiomechanics with other sport sciences hasaided in the design of shoes for specificsports (Segesser & Pforringer, 1989), espe-cially running shoes (Frederick, 1986; Nigg,1986). Since the 1980s the design and engi-neering of most sports shoes has includedresearch in company biomechanics labs.The biomechanical study of auto accidentshas resulted in measures of the severity ofhead injuries, which has been applied inbiomechanical testing, and in design ofmany kinds of helmets to prevent head in-jury (Calvano & Berger, 1979; Norman,1983; Torg, 1992). When accidents result in

amputation, prosthetics or artificial limbscan be designed to match the mechanicalproperties of the missing limb (KluteKallfelz, & Czerniecki, 2001). Preventingacute injuries is also another area of biome-chanics research. Forensic biomechanics in-volves reconstructing the likely causes ofinjury from accident measurements andwitness testimony.

Biomechanics helps the physical thera-pist prescribe rehabilitative exercises, assis-tive devices, or orthotics. Orthotics aresupport objects/braces that correct defor-mities or joint positioning, while assistivedevices are large tools to help patient func-tion like canes or walkers. Qualitativeanalysis of gait (walking) also helps thetherapist decide whether sufficient muscu-lar strength and control have been regainedin order to permit safe or cosmetically nor-mal walking (Figure 1.6). An athletic trainermight observe the walking pattern forsigns of pain and/or limited range of mo-tion in an athlete undergoing long-termconditioning for future return to the field.An athletic coach might use a similar quali-


Figure 1.6. Qualitative analysis of gait (walking) is ofimportance in physical therapy and the treatment ofmany musculoskeletal conditions.

tative analysis of the warm-up activities ofthe same athlete several weeks later tojudge their readiness for practice or compe-tition. Many biomechanists work in hospi-tals providing quantitative assessments ofgait function to document the effectivenessof therapy. The North American group in-terested in these quantitative assessmentsfor medical purposes is the Gait and Clini-cal Movement Analysis Society (GCMAS)at http://www.gcmas.net/cms/index.php.Good sources for the clinical and biome-chanical aspects of gait are Kirtley (2006),Perry (1992), Whittle (1996), and the clini-cal gait analysis website: http://guardian.curtin.edu.au/cga/.

Dramatic increases in computer mem-ory and power have opened up new areasof application for biomechanists. Many ofthese areas are related to treating and pre-venting human injury. Biomechanical stud-ies are able to evaluate strategies for pre-venting falls and fractures in the elderly(Robinovitch, Hsiao, Sandler, Cortez, Liu, &Paiement, 2000). Biomechanical computermodels can be used to simulate the effect ofvarious orthopaedic surgeries (Delp, Loan,Hoy, Zajac, & Rosen, 1990) or to educatewith computer animation. Some biomech-anists have developed software used toadapt human movement kinematic data so

that computer game animations have thelook of truly human movement, but withthe superhuman speed that makes gamesexciting (Figure 1.7). Some people use bio-mechanics to perform forensic examina-tions. This reconstruction of events fromphysical measurements at the scene is com-bined with medical and other evidence todetermine the likely cause of many kinds ofaccidents.


Figure 1.7. Biomechanical measurements and soft-ware can be used to make accurate animations of hu-man motion that can be used for technique improve-ment, cinema special effects, and computer games.Drawing based on image provided by Vicon MotionSystems.

Application

A variety of professions are interested in using biomechanics to modify human movement.A person thatfabricates prosthetics (artificial limbs) would use biomechanics to understand the normal functioning ofjoints, the loadings the prosthetic must withstand, and how the prosthetic can be safely attached to theperson. List possible questions biomechanics could answer for a(n):

Athletic Coach?Orthopaedic Surgeon?Physical Educator?Physical Therapist?Athletic Trainer?Strength & Conditioning Professional?Occupational Fitness Consultant?

You? What question about human movement technique are you curious about?

Qualitative and QuantitativeAnalysis

Biomechanics provides information for avariety of kinesiology professions to ana-lyze human movement to improve effec-tiveness or decrease the risk of injury. Howthe movement is analyzed falls on a contin-uum between a qualitative analysis and aquantitative analysis. Quantitative analy-sis involves the measurement of biome-chanical variables and usually requires acomputer to do the voluminous numericalcalculations performed. Even short move-ments will have thousands of samples ofdata to be collected, scaled, and numeri-cally processed. In contrast, qualitativeanalysis has been defined as the “system-atic observation and introspective judg-ment of the quality of human movement forthe purpose of providing the most appro-priate intervention to improve perform-ance” (Knudson & Morrison, 2002, p. 4).Analysis in both quantitative and qualita-tive contexts means identification of thefactors that affect human movement per-formance, which is then interpreted usingother higher levels of thinking (synthesis,evaluation) in applying the information tothe movement of interest. Solving problemsin human movement involves high levels ofcritical thinking and an interdisciplinaryapproach, integrating the many kinesiologysciences.

The advantages of numerical measure-ments of quantitative over those of qualita-tive analysis are greater accuracy, consis-tency, and precision. Most quantitativebiomechanical analysis is performed in re-search settings; however, more and moredevices are commercially available that in-expensively measure some biomechanicalvariables (e.g., radar, timing lights, timingmats, quantitative videography systems).Unfortunately, the greater accuracy ofquantitative measures comes at the cost oftechnical skills, calibration, computational

and processing time, as well as dangers ofincreasing errors with the additional com-putations involved. Even with very fastmodern computers, quantitative biome-chanics is a labor-intensive task requiringconsiderable graduate training and experi-ence. For these reasons and others, qualita-tive analysis of human movement remainsthe main approach kinesiology profession-als use in solving most human movementproblems. Qualitative analysis will be themain focus of the applications of biome-chanics presented in this book. Whetheryour future jobs use qualitative or quantita-tive biomechanical analysis, you will needto be able to access biomechanical knowl-edge. The next section will show you manysources of biomechanical knowledge.


Activity:Videotape Replay

Tape a sporting event from a TV broadcast ona VCR. Find a sequence in the video wherethere is a movement of interest to you andwhere there is a good close-up shot of the ac-tion.You could also video yourself performinga movement using a camcorder.Watch the re-play at real-time speed and try to estimatethe percentage of time taken up by the majorphases of the movement. Most skills can bebroken down into three phases—prepara-tion, action, and follow-through—but you canhave as many phases as you think apply to themovement of interest. Rewind the tape anduse the “pause” and “frame” advance func-tions to count the number of video frames inthe skill and calculate the times and percent-ages for each phase of the skill. Most VCRsshow every other field, giving you a video“clock” with 30 pictures per second. Note,however, that some VCRs show you everyfield (half of interlaced video) so your clockwill be accurate to 1/60th of a second. Howcould you check what your or the classes'VCR does in frame advance mode? Howclose was your qualitative judgment to themore accurate quantitative measure of time?

WHERE CAN I FIND OUTABOUT BIOMECHANICS?

This text provides a general introduction tothe biomechanics of human movement inkinesiology. Many students take advancedcourses in biomechanics and do library re-search for term projects. This text will pro-vide quite a few references on many topicsthat will help students find original sourcesof biomechanical data. The relative youth ofthe science of biomechanics and the manydifferent academic areas interested in bio-mechanics (among others, biology, engi-neering, medicine, kinesiology, physics)makes the search for biomechanical knowl-edge challenging for many students. Thissection will give you a brief tour of some ofthe major fields where biomechanics re-search is of interest.

Where you find biomechanics researchdepends on the kind of data you are inter-ested in. Many people are curious abouthuman movement, but there are also manyscholars who are interested in the biome-chanics of a wide variety of animals. An ex-cellent way to study the theoretical aspectsof biomechanics is to study animals that

have made adaptations to be good at cer-tain kinds of movements: like fish, kanga-roos, or frogs. Much of this biomechanicalresearch on animals is relevant to the studyof human movement.

Professionals from many fields are in-terested in human movement, so there isconsiderable interest and research in hu-man biomechanics. As a science biome-chanics is quite young (infant), but biome-chanics is more like the middle child withinthe subdisciplines of kinesiology. Biome-chanics is not as mature as Exercise Physiol-ogy or Motor Learning but is a bit olderthan Sport Psychology and other subdisci-plines. Basic biomechanics research onmany popular sport techniques will havebeen conducted in the early to mid-20thcentury. Biomechanics research in kinesiol-ogy since the 1970s has tended to becomemore narrowly focused and specialized,and has branched into areas far beyondsport and education. As a result, studentswith basic sport technique interests nowhave to integrate biomechanics researchover a 50-year period.

Depending on the depth of analysisand the human movement of interest, a stu-


Application

Even though qualitative and quantitative analyses are not mutually exclusive, assume that qual-itative-versus-quantitative biomechanical analysis is an either/or proposition in the followingexercise. For the sports medicine and athletics career areas, discuss with other students whatkind of analysis is most appropriate for the questions listed. Come to a consensus and be pre-pared to give your reasons (cost, time, accuracy, need, etc.) for believing that one approachmight be better than another.

Sport Medicine

1. Is the patient doing the lunge exercise correctly?2. Is athlete “A” ready to play following rehab for their injured ACL?

Athletics

1. Should pole vaulter “B” change to a longer pole?2. Is athlete “A” ready to play following rehab for their injured ACL?

dent of biomechanics may find himselfreading literature in biomechanical, med-ical, physiological, engineering, or otherspecialized journals. The smaller and morenarrow the area of biomechanical interest(for example, specific fibers, myofibrils,ligaments, tendons), the more likely therewill be very recent research on the topic.Research on the effect of computerized re-tail check-out scanners would likely befound in recent journals related to engineer-ing, human factors, and ergonomics. A stu-dent interested in a strength and condition-ing career might find biomechanical studieson exercises in medical, physical education,physiology, and specialized strength andconditioning journals. Students with clini-cal career interests who want to know ex-actly what muscles do during movementmay put together data from studies dealingwith a variety of animals. Clues can comefrom classic research on the muscles of thefrog (Hill, 1970), the cat (Gregor & Abelew,1994) and turkeys (Roberts, Marsh,Weyand, & Taylor, 1997), as well as humanmuscle (Ito, Kawakami, Ichinose, Fuka-shiro, & Fukunaga, 1998). While muscleforce-measuring devices have been im-

planted in humans, the majority of the in-vasive research to determine the actions ofmuscles in movement is done on animals(Figure 1.8).

Scholarly Societies

There are scholarly organizations exclu-sively dedicated to biomechanics. Scholarlysocieties typically sponsor meetings andpublications to promote the developmentof their fields. Students of sport biome-chanics should know that the InternationalSociety of Biomechanics in Sports (ISBS) isdevoted to promotion of sport biomechan-ics research and to helping coaches applybiomechanical knowledge in instruction,training, and conditioning for sports. TheISBS publishes scholarly papers on sportsbiomechanics that are accepted from paperspresented at their annual meetings and thejournal Sports Biomechanics. Their website(http://isbs.org/) provides links to a vari-ety of information on sport biomechanics.The websites for the societies discussed inthis section are listed at the end of thischapter and in a file on the CD.


Figure 1.8. Schematic of a buckle transducer for in vivo measurement of muscle forces in animal locomotion.Adapted with permission from Biewener and Blickhan (1988).

The International Society of Biome-chanics (ISB) is the international society ofscholars interested in biomechanics from allkinds of academic fields. The ISB hosts in-ternational meetings and sponsors journals.Some examples of regional biomechanicssocieties include the American Society ofBiomechanics (ASB), the Canadian Societyof Biomechanics, and the European Soci-ety of Biomechanics. The ASB website hasseveral links, including a list of graduateprograms and papers accepted for presen-tation at ABS annual meetings. Another re-lated scholarly society is the InternationalSociety for Electrophysiology and Kinesiol-ogy (ISEK), which promotes the elec-tromyographic (EMG) study of humanmovement. Engineers interested in equip-ment design, sport, and human movementhave founded the ISEA mentioned earlier.There are other scholarly organizations thathave biomechanics interest groups relatedto the parent disciplines of medicine, biol-ogy, or physics.

Aside from the many specialized bio-mechanics societies, there are biomechanicsinterest groups in various scholarly/pro-fessional organizations that have an interestin human movement. Two examples arethe American Alliance for Health, PhysicalEducation, Recreation, and Dance (AAH-PERD) and the American College of SportsMedicine (ACSM). AAHPERD is the origi-nal physical education scholarly/profes-sional organization, founded in 1885. Bio-mechanists in HPERD can be active in theBiomechanics Academy of the National As-sociation for Sport and Physical Education(NASPE is one of the HPERD associationswithin the alliance). The American Collegeof Sports Medicine was founded in 1954 byphysicians and exercise scientists to be ascholarly society interested in promotion ofthe study and application of exercise, sportsmedicine, and sports science. The ACSMsubstructure interested in biomechanics is

the biomechanics interest group (BIG).Other professional organizations in medi-cine, physical therapy, athletic training,and/or strength and conditioning sponsorbiomechanics programs related to theirunique interests. Whatever career path youselect, it is important that you join and par-ticipate in the related scholarly and profes-sional organizations.

Computer Searches

One of the best ways to find information onhuman biomechanics is to use computer-ized bibliographies or databases of books,chapters, and articles. Some of the best elec-tronic sources for kinesiology students areSportDiscus, MEDLINE, and EMBASE.SportDiscus is the CD-ROM version of thedatabase compiled by the Sport Infor-mation Resource Center (SIRC) in Ontario,Canada (http://www.sirc.ca/). SIRC hasbeen compiling scholarly sources on sportand exercise science since 1973. Many uni-versities buy access to SportDiscus and Med-line for faculty and student research. Sport-Discus is quite helpful in locating researchpapers in the ISBS edited proceedings.

Medical literature has been well cata-loged by Index Medicus and the searchabledatabases MEDLINE and EMBASE. Thesedatabases are quite extensive but do not listall published articles so a search of both isadvisable (Minozzi, Pistotti, & Forni, 2000)for literature searches related to sportsmedicine. Besides access from your univer-sity library, the national library of medicineprovides free searching of Medline athttp://www.ncbi.nlm.nih.gov/entrez/query.fcgi. Very large databases like Sport-Discus, Medline, and EMBASE are great re-search tools if searched intelligently. Thesedatabases and others (e.g., Biological Ab-stracts, Science Citation Index) should be


searched by the careful linking of keywordsand Boolean (logic: and, or) operators. Re-member that much of the power of index-ing is the cross-referencing as well as the di-rect listings for your search items.

Many journals now publish keywordswith articles to facilitate the searching forthe articles with similar terms. The searchrequest for “biomechanics” in some data-bases will return all items (probably toomany) beginning with these letters in the ti-tle, abstract, or keywords including biome-chanics or biomechanical. Searching for“kinematic and ankle” will find sourcesdocumenting the motion at the ankle joint.Even better would be “kinematic or ankleor subtalar,” because any one of the threesearch terms matching would select a re-source. You miss very little with this search,but it is necessary to go through quite afew sources to find the most relevant ones.Be persistent in your search and let yourreadings refine your search strategy. A stu-dent interested in occupational overuse in-juries (sports medicine term) will find thatthe human factors field may refer to thistopic as “cumulative trauma disorder,”“work-related musculoskeletal disorders,”or “occupational overuse syndrome” just toname a few (Grieco, Molteni, DeVito, &Sias, 1998).

There are bibliographies of literaturethat are in print that list sources relevant to

biomechanics. The President's Council onPhysical Fitness and Sports publishes Phys-ical Fitness/Sports Medicine. The Physical Ed-ucation Index is a bibliographic service forEnglish language publications that is pub-lished quarterly by BenOak Publishing.The PE Index reviews more than 170 maga-zines and journals, provides some citationsfrom popular press magazines, and this in-dex can be used to gather “common knowl-edge.” Early sport and exercise biomechan-ics research has been compiled in severalbibliographies published by the Universityof Iowa (Hay, 1987).

Biomechanics Textbooks

Good sources for knowledge and links (nothyperlinks) to sources commonly missedby students are biomechanics textbooks.Biomechanics students should look up sev-eral biomechanics textbooks and reviewtheir coverage of a research topic. Scholarsoften write textbooks with research inter-ests that are blended into their texts, andmany authors make an effort to provide ex-tensive reference lists for students. Remem-ber that writing books takes considerabletime, so references in a particular text maynot be totally up-to-date, but they do givestudents leads and clues on many good


Interdisciplinary Issue:Collaborative Biomechanics

Finding biomechanics information is like a scavenger hunt that will lead students all over a li-brary.We have seen that biomechanics research can be found in biology, engineering, medical,and other specialized journals. “Interdisciplinary” means using several different disciplines si-multaneously to solve a problem. Do some preliminary research for sources (journals and ed-ited proceedings/books) on a human movement of interest to you. Do the titles and abstractsof the sources you found suggest scholars from different disciplines are working together tosolve problems, or are scholars working on a problem primarily from their own area or dis-cipline? What have other students found in their research?

sources. The quality of a biomechanicalsource will be difficult for many students tojudge, so the next section will coach you inevaluating biomechanical sources.

BIOMECHANICAL KNOWLEDGEVERSUS INFORMATION

Knowledge is different from information.Knowledge is contextual, theory-based,and data-supported ideas that make thebest current explanation for reality. Scien-tific knowledge is a theoretical structure oflaws and principles that is built on the con-sensus of experimental evidence by scien-tists in that field. Students often fail to real-ize that knowledge is a structure that isconstantly being constructed and remod-eled as new theories and evidence are ex-amined, and transitions in the structure areoften controversial.

Biomechanical knowledge is built by aconsensus of scientists from a variety of dis-ciplines interested in human movement(e.g., biology, engineering, kinesiology,medicine). Most real-world human move-ment problems have only partial answersbecause of limited biomechanical researchor knowledge that is specifically related tothe context of the person and problem of in-terest. Although the stack of biomechanicalknowledge is not perfect, a critical reviewof this will be the best guide and closest tothe truth.

The modification of human movementbased on biomechanical knowledge is diffi-cult because movement is a multifacetedproblem, with many factors related to theperformer and activity all interacting to af-fect the outcome. The next chapter willpresent nine general principles of biome-chanical knowledge that are useful in ap-plying biomechanics in general to improvehuman movement. There will be a few bitsof the knowledge puzzle that are well

known and rise to the level of scientific law.While most biomechanical knowledge isnot perfect and can only be organized intosome general principles, it is much better atguiding professional practice than merelyusing information or trail and error.

Living in an information age, it is easyfor people to become insensitive to the im-portant distinction between informationand knowledge. The most important differ-ence is that information has a much higherchance of being incorrect than knowledge.Information is merely access to opinions ordata, with no implied degree of accuracy.Information is also much easier to access inthe age of the Internet and wireless commu-nications. Do not confuse ease of accesswith accuracy or value. This distinction isclearer as you look at the hierarchy of thekinds of sources used for scholarly researchand a simple strategy for the evaluation ofthe quality of a source.

Kinds of Sources

When searching for specific biomechanicalknowledge it is important to keep in mindthe kind of source you are reading. There isa definite hierarchy of the scholarly or aca-demic rigor of published research and writ-ing. Figure 1.9 illustrates typical examplesof this hierarchy. Although there are excep-tions to most rules, it is generally true thatthe higher up a source on the hierarchy thebetter the chance that the information pre-sented is closer to the current state ofknowledge and the truth. For this reasonprofessionals and scholars focus their atten-tion on peer-reviewed journals to maintaina knowledge base for practice. Some pub-lishers are now “publishing” electronic ver-sions of their journals on the world wideweb (WWW) for subscribers or make pa-pers available for free after a certain wait-ing period.

Most scholarly journals publish origi-nal research that extends the body of


knowledge, or review papers that attemptto summarize a body of knowledge. Manyjournals also publish supplements that con-tain abstracts (short summaries of a re-search study) of papers that have been ac-cepted for presentation at a scholarlymeeting or were published in another jour-nal. While the review of these abstracts isnot as rigorous as a full journal article, ab-stracts do provide students with cluesabout what the most recent research is fo-

cusing on. Reading biomechanics researchwill be challenging for most undergradu-ates. Appendix A provides a comprehen-sive glossary of biomechanics terms thatwill help you when reading the biomechan-ics literature related to your professional in-terests.

In the middle of academic rigor are ed-ited proceedings, edited books, and profes-sional journals. These publications havevarying degrees of peer review before pub-


Figure 1.9. The many kinds of biomechanics sources of information and the hierarchy of their academic rigor.

lication, as well as varying rules on whatconstitutes acceptable evidence. At the bot-tom of the credibility chain are popularpress publications (magazines/newspa-pers) and hypertext on the worldwide web.While these sources are appropriate formore subjective observations of laypersons,there are serious threats to the validity ofthe observations from these sources. Themajor problems with webpages are theirimpermanence (unlike archival research lit-erature) and the lack of review (anyone canpost a webpage). Another good exampleis the teaching and coaching tips pub-lished by the Physical Education Digest(http://www.pedigest.com). Most of tipsand cues are opinions of coaches and teach-ers in popular press magazines that havenot been tested by scientific research. It ispossible that some of these opinions arecorrect and useful, but there is little evi-dence used to verify the advice, so kinesiol-ogy professionals should verify with otherprimary sources before using the advice.The next section will summarize a quickmethod for checking the credibility of vari-ous sources for biomechanical knowledge.

Evaluating Sources

The previous section clearly suggests thatcertain sources and kinds of evidence aremore likely to be accurate. When evaluat-ing the credibility of sources that fall at sim-ilar levels of rigor, the “me” test can be eas-ily applied to judge the chance of the advicebeing a good and balanced representationof reality. The “m” stands for motivation.What is the motivation for the person orsource providing the information? Sourceswith little financial interest in to making theobservations/claims and who are dedi-cated to advancing a body of knowledge orhuman potential (scholarly journals) aremuch more likely to provide accurate infor-mation. The motivation of the popularpress (TV, newspapers, magazines) and the

internet (WWW) involves profit and self-promotion based on numbers of viewersand, therefore, is more prone to sensational-ize and to not weigh all the evidence.

The “e” in the acronym stands for thekey element of all science: evidence. Scienceis based on logical analysis and the balanceof many controlled studies. This weighingof all the evidence stands in stark contrastto the more emotional claims of the popularpress. The more emotional and sensationalthe language, even if it talks about “the lat-est study,” the more likely you are readingonly part of the whole picture. Rememberthat the structure of knowledge is a compli-cated structure built over time using manysmall pieces. The “latest” piece of theknowledge puzzle may be in error (see thenext section) or will be rejected by mostscholars as having flaws that make it lessvaluable as other research.

This simple “me” strategy is just thefirst step in learning more professionalstrategies for weighing evidence. In medi-cine and allied health there are formalmethods for classifying the strength of sci-entific evidence called “evidence-basedpractice” to assist in diagnosis and treat-ment (Hadorn et al., 1996; Sackett et al.,1996). Authors have called the sports medi-cine and kinesiology professions to moreconsistently focus on using critical reviewof evidence to support practice (Faulkner etal., 2006; Knudson, 2005; Shrier, 2006).

One formidable barrier to a kinesiologyprofessional's ability to weigh biomechani-cal evidence is the technical and specializedterminology employed in most studies.Throughout this text many of these meas-urement systems and mechanical terms arecovered. Appendix A provides an extensiveglossary of biomechanical terms and quan-titative measurement systems. Two papersthat provide good summaries of biome-chanical and exercise science terms areavailable (Knuttgen & Kraemer, 1987;Rogers & Cavanagh, 1984). Students re-


viewing biomechanical studies should asktheir instructor for assistance when the textor these sources do not clear up their un-derstanding.

A Word About Right andWrong Answers

The increasing amount and complexity ofresearch and technology tends to givemany people a false sense of the correctnessof numbers. Few people will question ameasurement if some machine output num-bers on a printout, unless they are very fa-miliar with the measurement. Like ourknowledge-versus-information discussion,it is very important for kinesiology profes-sionals to understand that the process of re-viewing and weighing the evidence is oftenmore important than finding the perfect or“right” answer. Such absolutes in a compli-cated world are quite rare, usually only oc-curring when a technique change wouldrun against a law of physics or one of ourprinciples of biomechanics. These princi-ples (and laws) of mechanics are the appli-cation tools developed throughout thisbook.

So the good news is that biomechanicshelps kinesiology professionals solve prob-lems, while the bad news is that most of

these everyday questions/problems do nothave easy, dichotomous (right/wrong) an-swers. There are many factors that affectmost phenomena and there is variation innearly all phenomena. In fact, all true sci-ence is written using statistics to accountfor this variation. Statistics use estimates ofdata variation to attach a probability to anyyes/no decision about the data. If you reada study that says an observation was signif-icant at the 0.05 level, this only means thatthe result is not likely a fluke or observationdue to chance variation alone. It is possiblethat chance alone created this “difference,”and p < 0.05 means that in the long runthere is about a 1-in-20 chance that the ob-servation or decision about the data iswrong. Since most studies use this errorstandard (p < 0.05), this means that, out oftwenty studies on a particular topic, onelikely reports an incorrect observation fromchance variation alone. A common miscon-ception among laypersons is that statisticsin a scientific study “proves” things. Statis-tics only provide tools that allow scientiststo place probability values about yes/nodecisions on the numbers observed in theirresearch. Proof is a long-term process re-quiring critical review of the whole body ofresearch on the issue. Remember this whentelevision news broadcasts sensationalizethe results of the “latest” study on somehealth issue or you are tempted to believe


Application

On your next trip to a physician or other medical professional's waiting room, evaluate thenature of the articles and advertisements in the magazines and displays you encounter. Do ad-vertisements related to claims in the articles appear near the article? Do the articles talkabout several studies, their relative merits, as well as the percentage of subjects with variousresponses? Does the professional you are visiting sell supplements or products to patients? Ifso, what does this tell you about motivation and potential conflicts of interest between prac-tice and profits? The biomechanics of most health and human performance problems in hu-man movement are classic examples of complicated problems, with many interrelated factorsand variability in the response of individuals to treatment.

that one biomechanical study settles a par-ticular issue.

Biomechanical knowledge is constantlychanging and usually cannot be easily clas-sified into always right or wrong answers,so there are two important professionaltools you must not forget to use. These toolswill work quite well with the biomechani-cal tools (nine principles) developed in thistext. These two tools are the Swiss ArmyKnives™ or Leathermen™ of your profes-sional toolbox because of they are so flexi-ble and important. One is your ability to

access biomechanical knowledge, and the otheris the critical thinking necessary to evaluateand integrate knowledge so it can be ap-plied in solving human movement prob-lems. You are not likely going to remembereverything in this book (though you wouldbe wise to), but you should have the knowl-edge to access, and critical thinking toolsthat allow you to find, evaluate, and applybiomechanics to human movement. Therest of this text will illustrate and explicatethe nine principles of biomechanics, whichare tools you would do well to never forgetwhen helping people improve their move-ment.

SUMMARY

Kinesiology is the scholarly study of hu-man movement. A core science in the aca-demic discipline of kinesiology is biome-chanics. Biomechanics in kinesiology is thestudy of motion and its causes in humanmovement. The field of biomechanics is rel-atively new and only has a few principlesand laws that can be used to inform profes-sional practice. Kinesiology professionalsoften use biomechanical knowledge in thequalitative analysis of human movement todecide on how to intervene to improvemovement and prevent or remediate injury.Applying biomechanics in qualitativeanalysis is most effective when a profes-sional integrates biomechanical knowledgewith professional experience and the othersubdisciplines of kinesiology. Biomechani-cal knowledge is found in a wide variety ofjournals because there are many academicand professional areas interested in themovement of living things. Students study-ing human biomechanics might find rele-vant biomechanical knowledge in booksand journals in applied physics, biology,engineering, ergonomics, medicine, physi-ology, and biomechanics.


Interdisciplinary Issue:Too Much Performance?

Recent controversies about sport per-formance enhancement through steroidsand genetics parallel the issues related tobiomechanics and improvements in equip-ment. Engineers and biomechanists haveused advances in technology to improvethe materials and design of sports equip-ment, although the use of tools in sporthas a long history (Minetti, 2004). Jenkins(2004) presents a nice review of how im-provements in equipment materials hasdramatically affected performance in sev-eral sports. These are truly interdiscipli-nary controversies because there are eth-ical, safety, athlete, coaching, and sport/his-torical perspectives on performance. Oneexample of technology correcting toomuch performance is the new rules forthe javelin in the mid-1980s.The center ofgravity of the the javelin was moved for-ward to decrease throwing distances be-cause many athletes were throwing theold javelin over 100 m.Advances in biome-chanics and computer technologies havealso been used to modify technique, train-ing, and equipment for the Olympics(Legwold, 1984; Sheppard, 2006).

REVIEW QUESTIONS

1. What is biomechanics and how is itdifferent from the two common meaningsof kinesiology?

2. Biomechanical knowledge is usefulfor solving what kinds of problems?

3. What are the advantages and disad-vantages of a qualitative biomechanicalanalysis?

4. What are the advantages and disad-vantages of a quantitative biomechanicalanalysis?

5. What kinds of journals publish bio-mechanics research?

6. What is the difference betweenknowledge and information?

7. Why should biomechanical knowl-edge be integrated with other sport and ex-ercise sciences in solving human movementproblems?

KEY TERMS

biomechanicselectromyography (EMG)informationinterdisciplinarykinesiologyknowledgeorthoticsprostheticsqualitative analysisquantitative analysis

SUGGESTED READING

Bartlett, R. M. (1997). Current issues in the me-chanics of athletic activities: A position paper.Journal of Biomechanics, 30, 477–486.

Cavanagh, P. R. (1990). Biomechanics: A bridgebuilder among the sport sciences. Medicine andScience in Sports and Exercise. 22, 546–557.

Chaffin, D., & Andersson, G. (1991). Occupa-tional biomechanics (2nd ed.). New York: Wiley.

Elliott, B. (1999). Biomechanics: An integralpart of sport science and sport medicine.Journal of Science and Medicine and Sport, 2,299–310.

Knudson, D. V., & Morrison, C. M. (2002).Qualitative analysis of human movement (2nded.). Champaign, IL: Human Kinetics.

Kumar, S. (1999). Biomechanics in ergonomics.London: Taylor & Francis.

Lees, A. (1999). Biomechanical assessment ofindividual sports for improved performance.Sports Medicine, 28, 299–305.

Sheppard, L. M. (2006). Visual effects andvideo analysis lead to Olympics victories. IEEEComputer Graphics and Applications, 26(2), 6–11.

LeVeau, B. (1992). Williams and Lissner's:Biomechanics of human motion (3rd ed.).Philadelphia: W. B. Sanders.

Segesser, B., & Pforringer, W. (Eds.) (1989). Theshoe in sport. Chicago: Year Book MedicalPublishers.

Yeadon, M. R., & Challis, J. H. (1994). Thefuture of performance-related sports biome-chanics research. Journal of Sports Sciences, 12,3–32.



WEB LINKS

AAHPERD—American Alliance for Health, Physical Education, Recreation, and Danceis the first professional HPERD organization in the United States.

http://www.aahperd.org/

Biomechanics Academy—A biomechanics interest area within AAHPERD and NASPE(National Association for Sport and Physical Education).

http://www.aahperd.org/naspe/template.cfm?template=specialinterests-biomechanics.html

AAKPE—American Academy of Kinesiology and Physical Education is the premier,honorary scholarly society in kinesiology.

http://www.aakpe.org/

ACSM—American College of Sports Medicine is a leader in the clinical and scientificaspects of sports medicine and exercise. ACSM provides the leading professional certi-fications in sports medicine.

http://acsm.org/

ISB—International Society of Biomechanics was the first biomechanics scholarly society.http://www.isbweb.org/

ASB—American Society of Biomechanics posts meeting abstracts from a variety of bio-mechanical scholars.

http://www.asbweb.org/

ISEA—International Sports Engineering Association hosts international meetings andpublishes the journal Sports Engineering.

http://www.sportsengineering.co.uk/

ISBS—International Society of Biomechanics in Sports hosts annual conferences andindexes papers published in their proceedings and journal (Sports Biomechanics).

http://www.isbs.org/

ISEK—International Society of Electrophysiological Kinesiology is the scholarly societyfocusing on applied electromyography (EMG) and other electrophysiological phenomena.

http://isek-online.org/

ISI—The Institute for Scientific Information (Thompson Scientific) provides a variety ofservices, including rating scholarly journals and authors.

http://www.isinet.com/isi/

Medline—Free searching of this medical database provided by the National Library ofMedicine.

http://www.ncbi.nlm.nih.gov/entrez/query.fcgi/

SIRC—The Sport Information Resource Center provides several database services forsport and kinesiology literature like SportDiscus. Many college libraries have subscrip-tions to SportDiscus.

http://www.sirc.ca/

In Chapter 1 we found that biomechanicsprovides tools that are needed to analyzehuman motion, improve performance, andreduce the risk of injury. In order to facili-tate the use of these biomechanical tools,this text will emphasize the qualitative un-derstanding of mechanical concepts. Manychapters, however, will include some quan-titative examples using the algebraic defi-nitions of the mechanical variables beingdiscussed. Mathematical formulas are aprecise language and are most helpful inshowing the importance, interactions, andrelationships between biomechanical vari-ables. While more rigorous calculus formsof these equations provide the most accu-rate answers commonly used by scientists(Beer & Johnson, 1984; Hamill & Knutzen,1995; Zatsiorsky, 1998, 2002), the majorityof kinesiology majors will benefit mostfrom a qualitative understanding of thesemechanical concepts. So this chapter beginswith key mechanical variables and termi-nology essential for introducing other bio-mechanical concepts. This chapter will em-phasize the conceptual understanding ofthese mechanical variables and leave moredetailed development and quantitative ex-amples for later in the text. Next, nine gen-eral principles of biomechanics are intro-duced that will be developed throughoutthe rest of the text. These principles use lesstechnical language and are the tools for ap-plying biomechanical knowledge in thequalitative analysis of human movement.The chapter concludes by summarizing amodel of qualitative analysis that is used inthe application section of the book.

KEY MECHANICAL CONCEPTS

Mechanics

Before we can begin to understand how hu-mans move, there are several mechanicalterms and concepts that must be clarified.Mechanics is the branch of physics thatstudies the motion of objects and the forcesthat cause that motion. The science of me-chanics is divided into many areas, but thethree main areas most relevant to biome-chanics are: rigid-body, deformable-body,and fluids.

In rigid-body mechanics, the object be-ing analyzed is assumed to be rigid and thedeformations in its shape so small they canbe ignored. While this almost never hap-pens in any material, this assumption isquite reasonable for most biomechanicalstudies of the major segments of the body.The rigid-body assumption in studies savesconsiderable mathematical and modelingwork without great loss of accuracy. Somebiomechanists, however, use deformable-body mechanics to study how biologicalmaterials respond to external forces thatare applied to them. Deformable-body me-chanics studies how forces are distributedwithin a material, and can be focused atmany levels (cellular to tissues/organs/system) to examine how forces stimulategrowth or cause damage. Fluid mechanicsis concerned with the forces in fluids (liq-uids and gasses). A biomechanist would usefluid mechanics to study heart valves,swimming, or adapting sports equipmentto minimize air resistance.

CHAPTER 2

23

Fundamentals of Biomechanicsand Qualitative Analysis

Most sports biomechanics studies arebased on rigid-body models of the skeletalsystem. Rigid-body mechanics is dividedinto statics and dynamics (Figure 2.1). Sta-tics is the study of objects at rest or in uni-form (constant) motion. Dynamics is thestudy of objects being accelerated by the ac-tions of forces. Most importantly, dynamicsis divided into two branches: kinematicsand kinetics. Kinematics is motion de-scription. In kinematics the motions of ob-jects are usually measured in linear (meters,feet, etc.) or angular (radians, degrees, etc.)terms. Examples of the kinematics of run-ning could be the speed of the athlete, thelength of the stride, or the angular velocityof hip extension. Most angular mechanical

variables have the adjective “angular” be-fore them. Kinetics is concerned with de-termining the causes of motion. Examplesof kinetic variables in running are the forcesbetween the feet and the ground or theforces of air resistance. Understandingthese variables gives the track coach knowl-edge of the causes of running performance.Kinetic information is often more powerfulin improving human motion because thecauses of poor performance have beenidentified. For example, knowing that thetiming and size of hip extensor action isweak in the takeoff phase for a long jumpermay be more useful in improving perform-ance than knowing that the jump wasshorter than expected.


Figure 2.1. The major branches of mechanics used in most biomechanical studies.

Basic Units

The language of science is mathematics. Bio-mechanics often uses some of the most com-plex kinds of mathematical calculations, es-pecially in deformable-body mechanics.Fortunately, most of the concepts and lawsin classical (Newtonian) rigid-body me-chanics can be understood in qualitativeterms. A conceptual understanding of bio-mechanics is the focus of this book, but alge-braic definitions of mechanical variableswill be presented and will make your under-standing of mechanical variables and theirrelationships deeper and more powerful.

First, let's look at how even conceptsseemingly as simple as numbers can differ

in their complexity. Scalars are variablesthat can be completely represented by anumber and the units of measurement. Thenumber and units of measurement (10 kg,100 m) must be reported to completelyidentify a scalar quantity. It makes no sensefor a track athlete to call home and say,“Hey mom, I did 16 and 0”; they need tosay, “I made 16 feet with 0 fouls.” The num-ber given a scalar quantity represents themagnitude or size of that variable.

Vectors are more complicated quanti-ties, where size, units, and direction must bespecified. Figure 2.2 shows several scalarsand the associated vectors common in bio-mechanics. For example, mass is the scalarquantity that represents the quantity of

CHAPTER 2: FUNDAMENTALS OF BIOMECHANICS AND QUALITATIVE ANALYSIS 25

Figure 2.2. Comparison of various scalar and vector quantities in biomechanics. Vector quantities must specifymagnitude and direction.

matter for an object. That same object'sweight is the gravitational force of attrac-tion between the earth and the object. Thedifference between mass and weight isdramatically illustrated with pictures of as-tronauts in orbit about the earth. Theirmasses are essentially unchanged, but theirweights are virtually zero because of themicrogravity when far from earth.

Biomechanics commonly uses direc-tions at right angles (horizontal/vertical,longitudinal/transverse) to mathematical-ly handle vectors. Calculations of velocityvectors in a two-dimensional (2D) analysisof a long jump are usually done in onedirection (e.g., horizontal) and then theother (vertical). The directions chosendepend on the needs of the analysis. Sym-bols representing vector quantities likevelocity (v) in this text will be identifiedwith bold letters. Physics and mechanicsbooks also use underlining or an arrowover the symbol to identify vector quanti-ties. These and other rules for vector calcu-lations will be summarized in chapter 6.These rules are important because whenadding vectors, one plus one is often nottwo because the directions of the vectorswere different. When adding scalars withthe same units, one plus one is alwaysequal to two. Another important point re-lated to vectors is that the sign (+ or –) cor-responds to directions. A –10 lb force is notless than a +10 lb force; they are the samesize but in opposite directions. The additionof vectors to determine their net effect iscalled the resultant and requires right-an-gle trigonometry. In chapter 6 we will alsosubtract or break apart a vector into right-angle components, to take advantage ofthese trigonometry relationships to solveproblems and to “see” other importantpushes/pulls of a force.

There are two important vector quanti-ties at the root of kinetics: force and torque.A force is a straight-line push or pull, usu-ally expressed in pounds (lbs) or Newtons

(N). The symbol for force is F. Rememberthat this push or pull is an interactional ef-fect between two bodies. Sometimes this“push” appears obvious as in a ball hittinga bat, while other times the objects are quitedistant as with the “pull” of magnetic orgravitational forces. Forces are vectors, andvectors can be physically represented ordrawn as arrows (Figure 2.3). The impor-tant characteristics of vectors (size and di-rection) are directly apparent on the figure.The length of the arrow represents the sizeor magnitude (500 N or 112 lbs) and the ori-entation in space represents its direction (15degrees above horizontal).

The corresponding angular variable toforce is a moment of force or torque. A mo-ment is the rotating effect of a force and willbe symbolized by an M for moment of forceor T for torque. This book will use the term“torque” synonymously with “moment offorce.” This is a common English meaningfor torque, although there is a more specificmechanics-of-materials meaning (a torsionor twisting moment) that leads some scien-tists to prefer the term “moment of force.”When a force is applied to an object that isnot on line with the center of the object, theforce will create a torque that tends to rotatethe object. In Figure 2.3 the impact forceacts below the center of the ball and wouldcreate a torque that causes the soccer ball toacquire backspin. We will see later that theunits of torque are pound-feet (lb•ft) andNewton-meters (N•m).

Let's look at an example of how kine-matic and kinetic variables are used in atypical biomechanical measurement of iso-metric muscular strength. “Isometric” is amuscle research term referring to muscleactions performed in constant (iso) length(metric) conditions. The example of a springis important for learning how mathematicsand graphs can be used to understand therelationship between variables. This exam-ple will also help to understand how mus-cles, tendons, and ligaments can be said to


have spring-like behavior. Figure 2.4 illus-trates the force–displacement graph for thespring in a handgrip dynamometer. A dy-namometer is a force-measuring device. Asa positive force (F) pulls on the spring, thespring is stretched a positive linear distance(displacement = d). Displacement is a kine-matic variable; force is a kinetic variable.

Therapists often measure a person'sgrip strength in essentially isometric condi-tions because the springs in hand dyna-mometers are very stiff and only elongatevery small distances. The force–displace-ment graph in Figure 2.4 shows a very sim-ple (predictable) and linear relationshipbetween the force in the spring (F) and theresulting elongation (d). In other words,there is a uniform increase (constant slope

of the line) in force with increasing springstretch. We will see later on in chapter 4that biological tissues have much morecomplex (curved) mechanical behaviorswhen loaded by forces, but there will be lin-ear regions of their load–deformationgraphs that are representative of their elas-tic properties.

Let's extend our example and see howanother mechanical variable can be derivedfrom force and displacement. Many simpleforce measuring devices (e.g., bathroomand fishing scales) take advantage of theelastic behavior of metal springs that arestretched or compressed short distances.This relationship is essentially the mathe-matical equation (F = k • d) of the calibra-tion line illustrated in Figure 2.4, and iscalled Hooke's Law. Hooke's Law is validfor small deformations of highly elasticmaterials like springs. The stiffness (elas-ticity) of the spring is symbolized as k,which represents the slope of the line. Inchapter 4 we will look at the stiffness of bi-ological tissues as the slope of the linear re-gion of a graph like this. If we plug in thelargest force and displacement (700 = k •0.01), we can solve for the stiffness of thespring, and find it to be 70,000 N/m. This


Figure 2.3. Vector representation of the force appliedby a foot to a soccer ball. The magnitude and directionproperties of a vector are both apparent on the dia-gram: the length of the arrow represents 500 Newtonsof force, while the orientation and tip of the arrow rep-resent the direction (15º above horizontal) of the force.

Figure 2.4. A graph (solid line) of the relationshipbetween the force (F) required to stretch a spring agiven displacement (d). The elasticity of the spring isthe slope of the line. The slope is the constant (k) inHooke's Law: (F = k • d).

says that the spring force will increase70,000 Newtons every meter it is stretched.This is about 15,730 pounds of tension if thespring were stretched to about 1.1 yards!Sounds pretty impressive, but rememberthat the springs are rarely elongated thatmuch, and you might be surprised howstiff muscle-tendon units can get whenstrongly activated.

Engineers measure the stiffness or elas-ticity of a material with special machinesthat simultaneously record the force anddeformation of the material. The slope ofthe load–deformation graph (force/length)in the linear region of loading is used to de-fine stiffness. Stiffness is the measure ofelasticity of the material, but this definitionoften conflicts with most people's commonunderstanding of elasticity. People often in-correctly think elasticity means an objectthat is easily deformed with a low force,which is really compliance (length/force),the opposite of stiffness. An engineerwould say that there was less stiffness orgreater compliance in the second spring il-lustrated as a dashed line.

Can you find the stiffness (spring con-stant, k) that corresponds to the dashed cal-ibration line in Figure 2.4? Remember thatthe stiffness, k, corresponds to the slope ofthe line illustrated in the figure and repre-sents the change in force for a given changein length. The slope or rate of change of avariable or graph will be an important con-cept repeated again and again in biome-chanics. Remember that forces and dis-placements are vectors, so directions are in-dicated by the sign (+ or –) attached to thenumber. What do you think the graphwould look like if the force were reversed,i.e., to push and compress the spring ratherthan stretching it? What would happen tothe sign of F and d?

It is also important to know that theprevious example could also be measuredusing angular rather than linear measure-ments. There are isokinetic dynamometers

that simultaneously measure the torque (T)and rotation (Figure 1.5). These angularmeasurements have been used to describethe muscular strength of muscle groups atvarious positions in the range of motion.

There are many other mechanical vari-ables that help us understand how humanmovement is created. These variables (e.g.,impulse, angular momentum, kinetic ener-gy) often have special units of measure-ment. What all these mechanical variablesand units have in common is that they canbe expressed as combinations of only fourbase units. These base units are length,mass, and time. In the International System(SI) these units are the second (s), kilogram(kg), meter (m), and radian (rad). Scientificresearch commonly uses SI units becausethey are base 10, are used throughout theworld, and move smoothly between tradi-tional sciences. A Joule of mechanical ener-gy is the same as a Joule of chemical energy


Activity: Elasticity

Take a rubber band and loop it betweenthe index fingers of your hands. Slowlystretch the rubber band by moving onehand away from the other.The tension inthe rubber band creates a torque thattends to abduct the metacarpophalangealjoints of your index finger. Does the ten-sion your fingers sense resisting thetorque from the rubber band uniformlyincrease as the band is stretched? Does aslightly faster stretch feel different? Ac-cording to Hooke's Law, elastic materialslike springs and rubber bands createforces directly proportional to the defor-mation of the material, but the timing ofthe stretch does not significantly affectthe resistance. Chapter 4 will deal withthe mechanical responses of biological tis-sues, which are not perfectly elastic, sothe rate of stretch affects the mechanicalresponse of the tissue.

stored in food. When this book uses mathe-matics to teach a conceptual understandingof mechanics in human movement (like inFigure 2.4), the SI system will usually beused along with the corresponding Englishunits for a better intuitive feel for many stu-dents. The symbols used are based on therecommendations of the International Soci-ety of Biomechanics (ISB, 1987).

These many biomechanical variablesare vitally important to the science of bio-mechanics and the integration of biome-chanics with other kinesiological sciences.Application of biomechanics by kinesiolo-gy professionals does not have to involvequantitative biomechanical measurements.The next section will outline biomechanicalprinciples based on the science and special-ized terminology of biomechanics.

NINE FUNDAMENTALSOF BIOMECHANICS

Biomechanists measure all kinds of linearand angular mechanical variables to docu-ment and find the causes of human motion.While these variables and studies are ex-tremely interesting to biomechanists, somekinesiology students and professionals maynot find them quite so inherently stimulat-ing. Most kinesiology professionals want toknow the basic rules of biomechanics thatthey can apply in their jobs. This sectionproposes nine such principles of biome-chanics and demonstrates how they relateto scientific laws. These biomechanicaltools must be combined with other toolsfrom your kinesiology toolbox to most ef-fectively solve movement problems. Be-cause these principles are the applicationrules for kinesiology professionals, theyhave usually been given less-scientificnames so that we can communicate effec-tively with our clients.

Principles and Laws

The nine principles of biomechanics thatfollow take the form of general principlesrelated to human movement. It is importantto realize that principles for application arenot the same as scientific laws. Science is asystematic method for testing hypotheseswith experimental evidence for the pur-pose of improving our understanding of re-ality. Science uses a process, know as thescientific method, for testing a theory abouta phenomenon with measurements, thenreevaluating the theory based on the data.Ultimately, science is interested in findingthe truth, facts, or laws of nature that pro-vide the best understanding of reality.When experimentation shows data alwaysconsistent with a theory (given certain con-ditions), then the theory becomes a law. Sci-entists must always be open to new dataand theories that may provide a more accu-rate description or improved understand-ing of a phenomenon. True scientific revo-lutions that throw out long-held and majortheories are not as common as most peoplethink. Though news reporters often heraldscientific “breakthroughs,” they are usuallyexaggerating the importance of a small stepin what is a very slow process of weighinga great deal of evidence.

Note that science is not defined as amethod for making practical applications ofknowledge. Technology is the term usuallyused to refer to the tools and methods ofapplying scientific knowledge to solveproblems or perform tasks. Remember thatin chapter 1 we noted the belief of somescholars that studying academic disciplinesand doing theoretical research are worthyenterprises without any need to show anypractical application of knowledge. Even in“applied” fields like kinesiology, there is along history of a theory-to-practice, or a sci-ence-to-profession gap (Harris, 1993). Whydoes this gap exist? It might exist becausesome scholars are hesitant to propose appli-


cation based on what is often less-than-con-clusive data, or they might be concernedabout receiving less recognition for appliedscholarship. Practitioners contribute to thisgap as well by refusing to recognize the the-oretical nature of science, by not readingwidely to compile the necessary evidencefor practice, and by demanding simple“how-to” rules of human movements whenthese simple answers often do not exist.

This text is based on the philosophythat the best use of the science of biome-chanics is in its translation to principles forimproving human movement. These prin-ciples are general rules for the applicationof biomechanics that are useful for most allhuman movements. Some of the principlesare based on major laws of mechanics,many of which are hundreds of years old.For example, Newton's Laws of Motion arestill used at NASA because they accuratelymodel the motion of spacecraft, eventhough there are more recent advance-ments in theoretical physics that are only animprovement in very extreme conditions(high-energy or near the speed of light).Unfortunately, the human body is a muchmore complicated system than the spaceshuttle, and biomechanists have not hadhundreds of years to make progress on the-ories of human movement. For these rea-sons, these nine principles of applicationshould be viewed as general rules that cur-rently fit what we currently know about thebiomechanics of human movement.

Nine Principles for Applicationof Biomechanics

The nine principles of biomechanics pro-posed in this text were selected becausethey constitute the minimum number orcore principles that can be applied to all hu-man movements and because they providea simple paradigm or structure to applybiomechanical knowledge. The names of

the principles are put in the common lan-guage of application; however, each can bedirectly linked to the concepts and laws ofbiomechanics. Special attention has beenpaid to make application of these principlesboth friendly and consistent with the spe-cialized terminology of mechanics. As kine-siology professionals you will know thenames of the biomechanical laws and theo-ries behind these principles, but you willneed to use more applied terminologywhen communicating with clients. This sec-tion will provide a description of each prin-ciple, and the application of these princi-ples will be developed throughout the text.The principles can be organized (Figure 2.5)into ones dealing primarily with the cre-ation of movement (process) and ones deal-ing with the outcome of various projectiles(product).

I want to point out that these principlesare based primarily on work of several bio-mechanists (Norman, 1975; Hudson, 1995)who have developed generic biomechani-cal principles for all human movements.Many biomechanics books have proposedgeneral principles for all movements(Meinel & Schnabel, 1998); various cate-gories of human movements like throwing,catching, and running (e.g., Broer & Zer-nicke, 1979; Dyson, 1986; Kreighbaum &Barthels, 1996; Luttgens & Wells, 1982); orspecific movements (e.g., Bunn, 1972;Groves & Camaione, 1975). Some biomech-anists believe that general principles appli-cable to all sports are difficult to identifyand have limited practical application dueto unique goals and environmental contextsof skills (Hochmuch & Marhold, 1978). Thisbook is based on the opposite philosophy.Kinesiology professionals should keep inmind the specific goals and contextual fac-tors affecting a movement, but the nineprinciples of biomechanics are importanttools for improving all human movements.

The first principle in biomechanics isthe Force–Motion principle. Force–motion



Figure 2.5. The nine principles of biomechanics can be classified into those related to movement of the body or aprojectile. The human body can be a projectile, so all nine principles can be applied to the human body.

says that unbalanced forces are acting onour bodies or objects when we either createor modify movement. In quiet standing theforce of gravity is balanced by ground reac-tion forces under our feet (Figure 2.6), so tomove from this position a person createslarger horizontal and vertical forces withtheir legs. This simple illustration of the

body is our first example of what in me-chanics is called a free-body diagram. Afree-body diagram is a simplified model ofany system or object drawn with the signif-icant forces acting on the object. The com-plexity and detail of the free-body diagramdepends on the purpose of the analysis. In-

spection of Figure 2.6 should make it quali-tatively obvious that the addition of the twovertical forces illustrated would cancel eachother out, keeping the person essentiallymotionless in the vertical direction. TheForce–Motion principle here correctly pre-dicts no change in motion, since there is nounbalanced force acting on the person. Lat-er on in the text we will use free-bodydiagrams to actually calculate the effect offorces and torques on the motion of thehuman body, and we will study the effectsof forces acting over time to change the mo-tion of the human body. We will also cometo see later that this principle is based onNewton's three laws of motion. The appli-cation of the Force–Motion principle inqualitative analysis will be exploredthroughout the text.

An important thing to notice in thisprinciple is the sequence of events. Forcesmust act first, before changes in motion canoccur. Detailed study of kinematics will il-lustrate when the motion occurred relativeto the acceleration and force causing it.Suppose a person is running on a sidewalkand a small child darts directly in the run-ner's path to grab a bouncing ball. In orderto avoid the child, the runner must changethe state of motion. The Force–Motion prin-ciple tells the kinesiology professional thatthe runner's sideward movement (a changein direction and speed) had to be created bylarge forces applied by the leg to theground. The force applied by the leg comesfirst and the sideward motion to avoid thecollision was the result.

Substantial changes in motion do notinstantly occur but are created over time,which leads us to the next principle ofForce–Time. It is not only the amount offorce that can increase the motion of an ob-ject; the amount of time over which forcecan be applied also affects the resulting mo-tion. A person using a longer approach inbowling has more time to apply forces toincrease ball speed. Increasing the time to


Figure 2.6. A free-body diagram of a person quietlystanding. The major vertical forces acting on the per-son (gravity and ground reaction force) are illustrated,while horizontal forces are small enough to ignore.

apply force is also an important techniquein slowing down objects (catching) andlanding safely. The impulse–momentum re-lationship, the original language of New-ton's second law, is the mathematical expla-nation of this important principle.

Another important principle to under-stand in the modification of motion is Iner-tia. Inertia can be defined as the property ofall objects to resist changes in their state ofmotion. Newton's first law of motion out-lines the principle of inertia. The Newton-ian view of inertia as a fundamental prop-erty of motion was a major conceptual leap,rejecting the old Aristotelian view that con-stant application of force was required formotion. The linear and angular measures ofinertia are mass (m) and moment of inertia(I). We will see that inertia can be viewed asa resistance to motion in the traditionalsense, but this property can also be used toan advantage when modifying motion ortransferring energy from one body segmentto another.

The next principle involves the Rangeof Motion the body uses in movement.Range of Motion is the overall motion usedin a movement and can be specified by lin-ear or angular motion of the body seg-ments. The purpose of some movementsmight require that some body segmentslimit range of motion, while others requir-ing maximum speed or force might requirelarger ranges of motion. Increasing therange of motion in a movement can be aneffective way to increase speed or to gradu-ally slow down from a high speed. A base-ball pitcher taking a longer stride (Figure2.7) is increasing the range of motion of theweight shift. Since moving through a rangeof motion takes time, this principle is relat-ed to the force–time principle.

The next biomechanical principle isBalance. Balance is a person's ability tocontrol their body position relative to somebase of support. Stability and mobility ofbody postures are inversely related, and

several biomechanical factors are involvedin manipulating a person's stability andmobility. A handstand is a difficult gymnas-tic skill not only because of the muscularstrength required, but also because of thesmall base of support in the anterior andposterior directions. Athletes in the startingblocks for sprints choose body postureswith less stability in favor of increased mo-bility in the direction of the race.

How the muscle actions and body seg-ment motions are timed in a human move-ment is usually referred to as coordination.The Coordination Continuum principlesays that determining the optimal timing ofmuscle actions or segmental motionsdepends on the goal of the movement. Ifhigh forces are the goal of the movement,


Figure 2.7. The forward stride of a pitcher increasesthe range of motion used to accelerate the body andeventually the baseball.

more simultaneous muscle actions andjoints rotations are usually observed, whilelow-force and high-speed movements tendto have more sequential muscle and jointactions (Hudson, 1995; Kreighbaum & Bar-thels, 1996). These two strategies (simulta-neous/sequential) can be viewed as a con-tinuum, with the coordination of most mo-tor skills falling somewhere between thesetwo strategies.

The principle of Segmental Interactionsays that the forces acting in a system oflinked rigid bodies can be transferredthrough the links and joints. Muscles nor-mally act in short bursts to produce torquesthat are precisely coordinated to comple-ment the effects of torques created by forcesat the joints. A wide variety of terms havebeen used to describe this phenomenon(transfer, summation, sequential) becausethere are many ways to study humanmovement. This variety of approaches hasalso created a confusing array of terminolo-gy classifying movements as either open orclosed (kinematic or kinetic) chains. We willsee that the exact mechanism of this princi-ple of biomechanics is not entirely clear,and common classification of movementsas open or closed chains is not clear or use-ful in analyzing movement (Blackard,Jensen, & Ebben, 1999; di Fabio, 1999; Dill-man, Murray, & Hintermeister, 1994).

The biomechanical principle of Opti-mal Projection says that for most humanmovements involving projectiles there is anoptimal range of projection angles for a spe-cific goal. Biomechanical research showsthat optimal angles of projection providethe right compromise between vertical ve-locity (determines time of flight) and hori-zontal velocity (determines range given thetime of flight) within the typical conditionsencountered in many sports. For example,in throwing most sport projectiles for hori-zontal distance, the typical air resistanceand heights of release combine to make itbeneficial for an athlete to use projection

angles below 45 degrees. Chapter 5 willgive several examples of how biomechani-cal studies have determined desirablerelease angles for various activities. Thisresearch makes it easier for coaches todetermine if athletes are optimizing theirperformance.

The last principle involves the Spin orrotations imparted to projectiles, and partic-ularly sport balls. Spin is desirable onthrown and struck balls because it stabilizesflight and creates a fluid force called lift.This lift force is used to create a curve or tocounter gravity, which affects the trajectoryand bounce of the ball. A volleyball playerperforming a jump serve should strikeabove the center of the ball to impart top-spin to the ball. The topspin creates a down-ward lift force, making the ball dive steeplyand making it difficult for the opponent topass. The spin put on a pass in Americanfootball (Figure 2.8) stabilizes the orienta-tion of the ball, which ensures aerodynami-cally efficient flight. The natural application


Figure 2.8. The spin imparted to a football during aforward pass serves to stabilize ball flight, to provideaerodynamically efficient flight.

of these biomechanical principles is in qual-itative analysis of human movement.

QUALITATIVE ANALYSIS

The examples that illustrate the applicationof the principles of biomechanics in the so-lution of human movement problems inthis book will be based on qualitative anal-yses. Research has shown that general prin-ciples of biomechanics provide a usefulstructure for qualitative analysis of humanmovement (Johnson, 1990; Matanin, 1993;Nielsen & Beauchamp, 1992; Williams &Tannehill, 1999; Wilkinson, 1996). Quantita-tive biomechanical analysis can also beused, but most kinesiology professionalswill primarily be using qualitative analysesof movement rather than quantitative bio-mechanical analyses.

There are several models of qualitativeanalysis of human movement. Tradition-ally, kinesiology professionals have used asimple error detection and correction ap-proach to qualitative analysis. Here the an-alyst relies on a mental image of the correcttechnique to identify “errors” in the per-formance and provide a correction. Thisapproach has several negative conse-quences and is too simplistic a model forprofessional judgments (Knudson & Mor-rison, 2002). The application of the princi-ples of biomechanics is illustrated in thepresent book using a more comprehensivevision of qualitative analysis than the sim-ple error detection/correction of the past.This text uses the Knudson and Morrison(2002) model of qualitative analysis (Figure2.9). This model provides a simple four-task structure: preparation, observation,evaluation/diagnosis, and intervention.This model of qualitative analysis is equal-ly relevant to athletic or clinical applica-tions of biomechanics to improving humanmovement.

In the preparation task of qualitativeanalysis the professional gathers relevantkinesiology knowledge about the activity,the performer, and then selects an observa-tional strategy. In the observation task theanalyst executes the observational strategy


Interdisciplinary Issue:The Vertical Jump

Now that the principles are out of the bag,let's use them to look at a common sportmovement, the vertical jump. Imagine anathlete is doing a standing vertical jump test.Which principles of biomechanics would beof most interest to scholars from motor de-velopment, motor learning, exercise physiol-ogy, or sport psychology studying the verti-cal jump test? What combinations of thesport sciences are most relevant to theconcept of skill in vertical jumping? Whatsports science provides the most relevantinformation to the physical determinants ofjumping ability? How could someone deter-mine if the success of elite jumpers is morestrongly related to genetics (nature/physi-cal) than coaching (nurture/training)? Howcould a strength coach integrate jump train-ing studies with biomechanical studies ofjumping techniques?

Figure 2.9. The four-task model of qualitative analy-sis. Adapted from Knudson and Morrison (2002).

to gather all relevant sensory informationabout the performance of the movement.The third task of qualitative analysis hastwo difficult components: evaluation andthen diagnosis of performance. In evalua-tion the analyst identifies strengths andweaknesses of performance. Diagnosis in-volves the prioritizing of the potential in-terventions to separate causes of poor per-formance from minor or symptomaticweaknesses. Intervention is the last task ofqualitative analysis. In this task the profes-sional executes some action on behalf of theperformer. Often in live qualitative analy-sis, the analyst will return immediately tothe observation task to monitor the inter-vention and the mover's progress.

SUMMARY

Most biomechanical research has beenbased on rigid-body models of the skeletal

system. Kinematics involves the descrip-tion of the motion, while kinetics focuses onthe forces that created the motion. There aremany biomechanical variables and they canbe classified as either scalars or vectors. De-spite the precision of quantitative biome-chanics, most kinesiology professionals ap-ply biomechanics at a qualitative or concep-tual level. The nine principles of biome-chanics that can be used to apply biome-chanics knowledge in professional practiceare Force–Motion, Force–Time, Inertia,Range of Motion, Balance, CoordinationContinuum, Segmental Interaction, Op-timal Projection, and Spin. These nine prin-ciples can be applied using a comprehen-sive model (Knudson & Morrison, 2002) ofqualitative analysis.

REVIEW QUESTIONS

1. What are major branches of mechan-ics, and which are most commonly used inperforming biomechanical analyses of hu-man movement?

2. What are the specific foci of kinemat-ic and kinetic analyses, and provide someexamples?

3. How are vector variables differentfrom scalar variables?

4. How is a scientific principle differentfrom a law?

5. The nine principles of biomechanicscan be classified into which two areas of in-terest?

6. What are the nine principles of bio-mechanics?

7. What are some other factors that af-fect human movement and the applicationof the principles of biomechanics?

8. List as many reasons as possible forthe apparent theory-to-practice gap be-tween scholars and practitioners.


Application: Quantitative Analysis

An athletic trainer is planning a qualitativeanalysis of the lower-extremity muscularfunction of an athlete finishing up an ante-rior cruciate ligament (ACL) rehabilitationprogram. The trainer has run the athletethrough the rehabilitation program, butwants a more functional evaluation of theathlete's ability and readiness for play.Theathlete will be doing several drills, includingmultiple one-legged hops and squats, shut-tle runs, landings, jumps, and lateral cuttingmovements. For the preparation task ofqualitative analysis, give examples of re-search or biomechanical principles thatyou think would be relevant to analyzingthe athlete's ability to prevent damage tothe ACL. Is there a task of qualitative analy-sis that more heavily relies on biomechan-ics than other sport sciences?

KEY TERMS

componentsdeformable bodydynamicsdynamometerfluidfree-body diagramisometrickinematicskineticsmassmechanicsresultantscalarsciencestrength (muscular)stiffnesstechnologytorque/moment of forcevectorweight

SUGGESTED READING

Hudson, J. L. (1995). Core concepts in kinesiol-ogy. JOPERD, 66(5), 54–55, 59–60.

Knudson, D., & Morrison, C. (2002). Qualitativeanalysis of human movement (2nd ed.).Champaign, IL: Human Kinetics.

Knuttgen, H. G., & Kraemer, W. J. (1987).Terminology and measurement in exerciseperformance. Journal of Applied Sport ScienceResearch, 1, 1–10.

Kreighbaum, E., & Bartels, K. M. (1996).Biomechanics: A qualitative approach to studyinghuman movement. Boston: Allyn & Bacon.

Norman, R. (1975). Biomechanics for the com-munity coach. JOPERD, 46(3), 49–52.

Rogers, M. M., & Cavanagh, P. R. (1984).Glossary of biomechanical terms, concepts,and units. Physical Therapy, 64, 82–98.


WEB LINKS

Physics and Mathematics Review provided by the physics department of the Universityof Guelph in Canada.

http://www.physics.uoguelph.ca/tutorials/tutorials.html

Knudson & Morrison (2002)—A link to the only book on the qualitative analysis ofhuman movement.

http://www.humankinetics.com/products/showproduct.cfm?isbn=0736034625

PARTIIBIOLOGICAL/STRUCTURAL BASES

The study of biomechanics requires anunderstanding of the structure of muscu-loskeletal systems and their mechanicalproperties. The three-dimensional comput-er model depicted here provides a goodrepresentation of the main structures ofthe ankle, but the response of these tissuesto forces and the subsequent movementallowed requires an understanding ofmechanics. The chapters in part II reviewkey concepts of anatomy used in biome-chanics and summarize key mechanicalproperties of the skeletal and neuromuscu-lar systems. Part II lab activities show howbiomechanics identifies the fascinatingactions of muscles and joints in humanmovement.

Image courtesy of Scott Barker, ATC.

39

In order to understand the origins of hu-man movement, it is essential to under-stand anatomy. Anatomy is the study of thestructure of the human body. Anatomy pro-vides essential labels for musculoskeletalstructures and joint motions relevant to hu-man movement. Knowledge of anatomy al-so provides a common “language” of thehuman body and motions for kinesiologyand medical professionals. Anatomy is animportant prerequisite for kinesiology pro-fessionals trying to improve movement,prevent or treat injury. Anatomy is primari-ly a descriptive field of study and is not, byitself, enough to explain the function of themusculoskeletal system in movement.Knowledge of anatomy must be combinedwith biomechanics to accurately determinethe musculoskeletal causes or the “how”human movement is created. This chapterreviews key anatomical concepts, showshow functional anatomy traditionally clas-sifies muscle actions, shows how biome-chanics is needed to determine musclefunction in movement, and discusses thefirst two of the nine principles of biome-chanics: Range of Motion and Force–Mo-tion.

REVIEW OF KEYANATOMICAL CONCEPTS

This section reviews several key conceptsfrom human anatomy. A course in grossanatomy (macroscopic structures) is a typi-

cal prerequisite for the introductory biome-chanics course. This section does not re-view all the bones, muscle, joints, andterms. Students and kinesiology profes-sionals must continuously review and re-fresh their knowledge of anatomy. Ana-tomy describes the human body relative tothe anatomical position. The anatomical posi-tion is approximated in Figure 3.1. Thethree spatial dimensions of the body corre-spond to the three anatomical planes:frontal, sagittal, and transverse. Recall thata plane of motion is a particular spatial di-rection or dimension of motion, and an axisis an imaginary line about which a body ro-tates. The anatomical axes associated withmotion in each of these planes are the an-tero-posterior, medio-lateral, and longitudi-nal axes. Knowing these planes and axes isimportant to understanding medical de-scriptions of motion or movements. Evenmore important may be the functional im-plications of the orientation of these axes tothe planes of motion they create. Note thatmotion in a particular plane (for example,sagittal) occurs by rotation about an axisoriented 90º (medio-lateral axis) to thatplane. A person supinating their forearm toillustrate the anatomical position is creatingmotion in a transverse plane about a longi-tudinal axis roughly along the forearm.Functional anatomy applies knowledge ofjoint axes of rotation and muscle positionsto hypothesize which muscles contribute tomotion in an anatomical plane.

CHAPTER 3

Anatomical Description andIts Limitations

41

Directional Terms

In addition to planes and axes, anatomy us-es several directional terms to help describethe position of structures relative to theanatomical position. Toward the head iscalled superior, while toward the feet is in-ferior. Body parts toward the front of thebody are anterior and objects to the backare in the posterior direction. Parts or mo-tion toward the midline of the body are saidto be medial, while motion or position to-ward the sides of the body are lateral. Thereare many other anatomical terms that havesimilar meanings as these but retain theoriginal Latin or Greek form of classical

anatomy. For example, superior is synony-mous with cephalic, while inferior is thesame a caudal. This book will use the morefamiliar English anatomical terms whenev-er possible.

Students with interests in sports medi-cine careers would do well to keep a med-ical dictionary handy and become familiarwith the variety of classical anatomicalterms used in medicine. Careful use of ter-minology is important in science and pro-fessions to prevent confusion. One exampleof the confusion that can occur with usingunfamiliar Greek or Latin terms is the de-bate over the directional terms valgus andvarus. The original Greek meanings of these


Figure 3.1. The major anatomical planes of motion, and axes of rotation.

terms (valgus [bowlegged] and varus[knock-kneed]) can be at odds with theirtypical use in orthopaedic medicine. Medi-cine usually defines genu (knee) valgus asan inward deviation of the knee joint, re-sulting in a knock-kneed appearance (Fig-ure 3.2). Genu varus or varum usually cor-responds to an outward deviating knee,which results in a bowlegged appearance.This leads to considerable confusion in de-scribing anatomical abnormalities, andsome have suggested that these terms bedropped or at least defined every time theyare used (Houston & Swischuk, 1980).Some would look at Figure 3.2 and say theknee deviates medially, while others wouldsay the lower leg deviates laterally. We will

see that this little problem of anatomical de-scription is very similar to the multiplekinematic frames of reference (chapter 5)that are all correct descriptions of a singlemotion and the different units of measure-ment that can be used. Mechanics andanatomy both share the minor problem thatthere are several standards that havegrown up with these sciences since peopleall over the world have been working onthese same problems. Students shouldstrive to read and write with special atten-tion to the meaning of professional/schol-arly terminology.

Joint Motions

Anatomy also has specific terminology de-scribing the major rotations of bones atjoints. “Flexion” refers to a decrease in jointangle in the sagittal plane, while “exten-sion” is motion increasing joint angle (Fig-ure 3.3a). Motion into the extremes of therange of motion are often noted as “hyper,”as in hyperextension. Motion of a segmentaway from the midline in the frontal planeis “abduction,” while movement back to-ward the midline is called “adduction”(Figure 3.3b). Joint motions in the trans-verse plane are usually called inward rota-tion (rotation of the anterior aspect of thesegment toward the midline) and outwardrotation (Figure 3.4). Some examples of spe-cial joint motion terms are “pronation,”which refers to internal rotation of the fore-arm at the radioulnar joint, or “horizontaladduction,” which is drawing the shoulder(glenohumeral joint) toward the midline ina transverse plane. Like the directionalterms, anatomical terminology related tothe rotations of joints is also used incorrect-ly. It is incorrect to say “a person is flexinga muscle” because flexion is a joint move-ment. It is important for kinesiology majorsto use anatomical terms correctly. Refer toyour anatomy book frequently to keep all

CHAPTER 3:ANATOMICAL DESCRIPTION AND ITS LIMITATIONS 43

Figure 3.2. Orthopedic and pediatric medicine oftencalls the lower extremity deviation in (a) genu (knee)valgus because the distal segment (lower leg) deviateslaterally from the midline of the body. Normal leg ori-entation in the frontal plane is illustrated in (b). Theuse of valgus and varus terminology is often inconsis-tent in the literature and should be clearly definedwhen used (Houston & Swischuk, 1980).

the joint motion terminology (this sectiondoes not review them all) fresh in yourmind.

While there are attempts to standardizeanatomical description throughout theworld (Federative Committee on Ana-tomical Terminology, 1998; Greathouse etal., 2004), there remain regional inconsisten-cies in terminology. For example, some re-fer to the frontal plane as the “coronal”plane. Applied sciences such as medicineoften develop specialized terms that areborrowed from anatomy, but that goagainst anatomical convention. A good ex-ample is related to how the foot acts duringthe stance phase of running. Medical andbiomechanical studies have adopted theterms “pronation” and “supination” to re-fer to the complex triplanar actions of thesubtalar joint. In normal running the foot

strikes the ground on the lateral aspect ofthe foot; the combined anatomical actionsof eversion, plantar flexion, and abductionin the first part of stance is called pronation.This pronation serves to absorb the shock ofthe collision of the foot with the ground(Figure 3.5). The opposite motion (supina-tion) stiffens the foot for the push off phaseof stance. Here is another example of howanatomical terms are not always used in aconsistent way. In your studies of biome-chanics and other kinesiology disciplines,remember that adaptations and variationsin anatomical terminology make it impor-tant to read carefully and often check back-ground information. Modern biomechani-cal studies often assume quite a bit aboutreader expertise in the area and may notcite sources giving necessary terminologyand background information. This saves


Figure 3.3. (a) Flexion and extension movements occur in a sagittal plane about a mediolateral axis; (b) adduc-tion/abduction of the hip joint occurs in a frontal plane about an anteroposterior axis.


Figure 3.4. Inward and outward rotation of the shoulder joint occurs in a transverse plane about a longitudinal axis.

Figure 3.5. Frontal plane view of rear-foot motion in the first half of the stance phase of running. The foot landsin a supinated position. The motion of the foot and ankle to accommodate to the surface and absorb shock is calledpronation.

journal space but places a burden on the ki-nesiology professional to be knowledgeableabout variations in descriptive terminology.

Review of Muscle Structure

The anatomical structure and micro-structure of skeletal muscle has consider-able functional importance. We will see lat-er that the function of the complex struc-tures of skeletal muscle can be easily mod-eled as coming from active and passivesources. This section will review a few ofthe structural components of skeletal mus-cle that are believed to be important inthese active and passive tissue properties.

Careful dissection of skeletal muscleshows that muscles are composed of manydistinct bundles of muscle fibers called fas-cicles. In cutting across a piece of beef or

chicken you may have noticed the tissue isin small bundles. The connective tissuesheath that surrounds the whole muscle,bundling the fascicles together, is calledepimysium (meaning over/above the mus-cle). Each fascicle is covered by connectivetissue called perimysium, meaning “aroundthe muscle.” There are hundreds of musclefibers within a fascicle, and an individualfiber is essentially a muscle cell. Musclefibers are also covered with connective tis-sue called endomysium (within the muscle).The gradual blending of these connectivetissue components of muscle forms a dis-tinct tendon or fuses with the calcified con-nective tissue, the periosteum of bones. Aschematic of the macrostructure of skeletalmuscle is shown in Figure 3.6.

The specific arrangement of fascicleshas a dramatic effect on the force andrange-of-motion capability of the muscle


Figure 3.6. The macroscopic structure of muscle includes several layers of connective tissue and bundles of mus-cle fibers called fascicles. Muscle fibers (cells) are multinucleated and composed of many myofibrils.

(Lieber & Friden, 2000). Anatomically, thisfiber arrangement has been classified as ei-ther parallel or pennate. A parallel ar-rangement means that the muscle fasciclesare aligned parallel to the long axis or lineof pull of the muscle. Muscles like the rec-tus abdominis, sartorius, and biceps brachiihave predominantly a parallel architecture(Figure 3.7a). Pennate muscles have fibersaligned at a small angle (usually less than15º) to a tendon or aponeurosis runningalong the long axis of the muscle. Anaponeurosis is a distinct connective tissueband within a muscle. This arrangement iscalled pennate because of the feathered ap-pearance. The tibialis posterior and semi-membranosus are primarily unipennate,while rectus femoris and gastrocnemius arebipennate (Figure 3.7b). An example of amultipennate muscle is the deltoid.

Muscles with parallel architecture fa-vor range of motion over force develop-ment. The greater muscle excursion and ve-locity of parallel muscles comes from thegreater number of sarcomeres aligned in se-

ries. The rectus abdominis can shorten from1/3 to 1/2 of its length because of the par-allel arrangement of fibers and fascicles.Small muscles may have a simple paralleldesign with fibers that run the length of themuscle, while larger parallel muscles havefibers aligned in series or end to end. Theseend-to-end connections and transverse con-nections within muscles make force trans-mission in muscle quite complex (Patel &Lieber, 1997; Sheard, 2000). Fiber architec-ture also interacts with the connective tis-sue within muscle to affect force or fibershortening. The fibers in the center of thebiceps do not shorten uniformly due to dif-ferences in the distal and proximal apo-neurosis (Pappas, Asakawa, Delp, Zajac, &Draceet, 2002). The amount of tendon amuscle has and the ratio of tendon to fibersalso affects the force and range-of-motionpotential of a muscle.

In essence, pennate muscles can createa greater tension because of a greater phys-iological cross-sectional area per anatomi-cal cross-sectional area, but have less range


Figure 3.7. (a) Parallel arrangement of muscle fibers with the tendon favors range of motion over force. (b) Pen-nate arrangement of fibers are angled into the tendon and create greater force but less range of motion.

(a) (b)

of shortening than a muscle with a parallelarchitecture. Physiological cross-sectionalarea is the total area of the muscle at rightangles to the muscle fibers.

Muscle fibers are some of the largestcells in the body and are long cylindricalstructures with multiple nuclei. A typicalmuscle cell is between 10 and 100 µm in di-ameter. The lengths of muscle fibers varieswidely from a few centimeters to 30 cmlong. Besides many nuclei there are hun-dreds to thousands of smaller protein fila-ments called myofibrils in every musclefiber. If a muscle cell were to be imaginedas a cylindrical straw dispenser, the my-ofibrils would be like the straws packed inthis dispenser. Figure 3.8 illustrates the mi-crostructure of a muscle fiber.

The microstructure of a muscle be-comes even more fascinating and complexas you pull out a straw (myofibril), only tonotice that there are even smaller threads orcylindrical structures within a myofibril.These many smaller fibers within each my-ofibril are all well organized and alignedwith other adjacent myofibrils in a fiber.This is why looking at skeletal muscle un-der a light microscope gives the appearance

of a consistent pattern of dark and lightbands. This is how skeletal muscle came tobe called striated muscle (Figure 3.8). Thesesmall sections of a myofibril between two Zlines (thin dark band) are called sarcom-eres. Sarcomeres are the basic contractilestructures of muscle.

Biomechanists model the active tensionof whole muscles based on the behavior ofthe interaction of two contractile proteins insarcomeres: actin and myosin. Actin is thethin protein filaments within the sarcom-eres of a myofibril, and myosin the thickerprotein filaments. Cross-bridges betweenmyosin and actin are attached and de-tached with the chemical energy stored inadenosine triphosphate (ATP). You may befamiliar with the names of the variouszones (Z line, A band, and I band) and oth-er substructures of a sarcomere.

While most biomechanists use simplemodels of the active tension of whole mus-cles, some biomechanists are interested inresearching the mechanical behavior of themicrostructures of myofibrils to increaseour understanding of where active and pas-sive forces originate. Considerable researchis being done to understand muscle actions


Figure 3.8. The microscopic structure of myofibril components of muscle fibers. Schematics of the sarcomere, aswell as of the actin and myosin filaments are illustrated.

at this microscopic level from variations inmyosin isoforms (Lutz & Lieber, 1999) toforce transmission throughout the musclefiber and muscle (Patel & Lieber, 1997;Sheard, 2000). Some muscle injuries couldbe due to this complex force production be-havior and to nonuniform stresses in thesarcomeres of fibers (Morgan, Whitehead,Wise, Gregory, & Proske, 2000; Talbot &Morgan, 1996).

Many kinesiology students are familiarwith muscular hypertrophy (increasedmuscle fiber diameter as a result of train-ing), but they are unaware that chronicelongation of muscles (like in stretching) in-creases the number of sarcomeres in serieswithin muscle fibers to increase their func-tional range of motion (Cox et al., 2000;Williams & Goldspink, 1978). The numberof sarcomeres and muscle fiber length areadaptable and strongly related to muscleperformance (Burkholder, Fingado, Baron,& Lieber, 1994).

It is clear that biomechanics plays a rolein understanding the functional signifi-cance of the gross and microstructural fac-tors of the muscletendon unit. Most gener-al concepts related to human movement,like muscular strength or range of motion,have many biomechanical factors and lev-els of structure that interact to determinehow the concept actually affects movement.This is our first example of the paradox oflearning: the more you know, the more youknow what you don't know. Now that wehave reviewed some of the major structuralfactors that affect muscle force and range ofmotion, let's define the kinds of actionsmuscles have.

MUSCLE ACTIONS

Muscle forces are the main internal motorsand brakes for human movement. Whilegravity and other external forces can beused to help us move, it is the torques cre-ated by skeletal muscles that are coordinat-

ed with the torques from external forces toobtain the human motion of interest. Whilesome biomechanists are interested in theforces and motions created by smooth (vis-ceral) or cardiac (heart) muscle, this textwill focus on the actions of skeletal musclethat create human movement.

The activation of skeletal muscle hastraditionally been called contraction. I willavoid this term because there are severalgood reasons why it is often inappropriatefor describing what muscles actually doduring movement (Cavanagh, 1988; Faulk-ner, 2003). Contraction implies shortening,which may only be accurate in describingthe general interaction of actin and myosinin activated muscle. Contraction also con-flicts with the many actions of muscles be-yond shortening to overcome a resistance.Saying “eccentric contraction” is essentiallysaying “lengthening shortening”! Ca-vanagh suggests that the term “action” ismost appropriate, and this book adopts thisterminology. Muscle action is the neuro-muscular activation of muscles that con-tributes to movement or stabilization of themusculoskeletal system. We will see thatmuscles have three major actions (eccentric,isometric, concentric) resulting from bothactive and passive components of muscletension. It could also be said that a fourthaction of muscle is inaction, not being acti-vated because their activation at that timewould be inefficient or counterproductiveto the task at hand.

Mechanically, the three kinds of actionsare based on the balance of the forces andtorques present at any given instant (Figure3.9). If the torque the activated muscles cre-ates is exactly equal to the torque of theresistance, an isometric action results. Abodybuilder's pose is a good example ofisometric muscle actions of opposing mus-cle groups. Recall that isometric literallymeans “same length.”

A concentric action occurs when thetorque the muscle group makes is larger


than the torque of a resistance, resultingin muscle shortening. The upward liftof a dumbbell in an arm curl is the concen-tric phase of the exercise. In essence aconcentric action occurs when a muscle ac-tivation results in shortening of the muscle-tendon unit. When the lifter gradually low-ers the weight in an arm curl, the torque themuscle group makes is less than the torqueof the resistance. This lowering of thedumbbell is an eccentric muscle action orthe lengthening of an activated muscle. Ineccentric actions muscles are used as brakeson external forces or motion like the brakesof your car.

The importance of these different mus-cle actions cannot be overemphasized.Functional anatomical analysis and mostpeople tend to focus primarily on the con-centric actions of muscles. This overempha-sis of what is usually in the minority ofmuscle actions for most movements gives afalse impression of how muscles create hu-man movement. The following section onthe limits of functional anatomy will ex-pand on this idea by showing that musclescreate movement in a variety of ways usingall three muscle actions, not just concentricaction.


Figure 3.9. The three kinds of muscle action are determined by the balance of torques (moments of force: M). Inconcentric action the torque of the abductors (MM) is greater than the torque of the resistance (MR), so the arm ris-es. In isometric conditions the joint angle does not change because MM and MR are equal. In eccentric action MMis less than MR, so the arm is lowered.

Application: Eccentric Actions and Muscle Injury

Eccentric actions are common to all muscles and virtually every human movement. Eccentric actions ofhigh intensity, repetitive nature, or during fatigue are associated with muscle injury.When eccentrically ac-tive muscles are rapidly overcome by external forces, a muscle strain injury can occur.When people per-form physical activity beyond typical levels, especially eccentric muscle actions, the result is usually delayed-onset muscle soreness.This is why it is important in conditioning to include both eccentric and concentricphases of exercises. Some athletic events would benefit from emphasis on eccentric training. For example,long jumpers and javelin throwers need strong eccentric strength in the takeoff and plant leg.

Active and PassiveTension of Muscle

Activated muscles create forces by pullingabout equally on all their attachments. Thistensile force really has two sources: activeand passive tension.

Active tension refers to the forces cre-ated between actin and myosin fibers in thesarcomeres of activated motor units. Soactive tension is the force created by thecontractile proteins (actin and myosin) us-ing chemical energy stored in ATP. Thisability of muscles to create active tensileforces is unique compared to the connectivetissue components (ligaments, tendons,bone) of the musculoskeletal system. Theshape of this active tension potential ofskeletal muscle is called the force–velocityrelationship of muscle and is summarizedin chapter 4.

Passive tension is the force that comesfrom an elongation of the connective tissuecomponents of the muscletendon unit.When a person does a stretching exercise,the tension she feels in the muscles is theinternal resistance of the muscletendon unitto the elongation of the stretch. This passivetension in stretching exercises can be quitelarge and may be responsible for the mus-cular weakness seen in muscles followingstretching (Knudson, McHugh, & Magnus-son, 2000). In the midranges of joint motion,passive tension does not significantly con-tribute to muscle forces in normal move-ment (Siegler & Moskowitz, 1984); howev-er, it is more a factor in low-force move-ments (Muraoka et al., 2005) and in variousneuromuscular disorders (Lamontagne,Malouin, & Richards, 2000). Muscle passivetension is a significant factor affectingmovement at the extremities of joint rangeof motion. The increase in passive tensionlimiting range of joint motion is quite ap-parent in multiarticular muscles and iscalled passive insufficiency. We will see inthe following chapter that passive tension

is an important component of theforce–length relationship of muscle. Thepassive insufficiency of poor hamstringflexibility could lead to poor performanceor risk of injury in activities that requirecombined hip flexion and knee extension,such as in a karate front kick (Figure 3.10).The passive tension in the hamstring mus-cles is high in Figure 3.10 because the mus-cle is simultaneously stretched across thehip and knee joint. We will learn later on inthis chapter that the concept of range ofmotion is a complicated phenomenon thatinvolves several mechanical variables.

Hill Muscle Model

One of the most widely used mechanicalmodels of muscle that takes into account


Figure 3.10. The combined hip flexion and knee exten-sion of a karate front kick may be limited by the pas-sive insufficiency of the hamstring muscles. This tech-nique requires excellent static and dynamic hamstringflexibility. Image courtesy of Master Steven J. Frey, 4th-Degree Black Belt.

both the active and passive components ofmuscle tension is the three-componentmodel developed by A. V. Hill in 1938 (Hill,1970). Hill was an English physiologist whomade substantial contributions to the un-derstanding of the energetics (heat andforce production) of isolated muscle ac-tions. Hill was also interested in muscularwork in athletics, and some of his experi-mental techniques represent ingenious ear-ly work in biomechanics (Hill, 1926, 1927).The Hill muscle model has two elements inseries and one element in parallel (Figure3.11). The contractile component (CC)represents the active tension of skeletalmuscle, while the parallel elastic compo-nent (PEC) and series elastic component(SEC) represent two key sources of passive

tension in muscle. The Hill muscle modelhas been the dominant theoretical modelfor understanding muscle mechanics and isusually used in biomechanical computermodels employed to simulate humanmovement.

We can make several functional gener-alizations about the mechanical behavior ofmuscle based on Figure 3.11. First, there iselasticity (connective tissue) in the produc-tion of active muscle tension modeled bythe series elastic component. The source ofthis series elasticity is likely a mixture of theactin/myosin filaments, cross bridge stiff-ness, sarcomere nonuniformity, and othersarcomere connective tissue components.Second, the passive tension of relaxed mus-cle that is easily felt in stretching exercisesor in passive insufficiency affects motion atthe extremes of joint range of motion. The“p” in the parallel elastic component is akey for students to remember this as theprimary source of passive tension in theHill muscle model. Third, muscle tensionresults from a complex interaction of activeand passive sources of tension. This thirdpoint can be generalized beyond the simpleHill muscle model as a result of recent re-search that has focused on the complextransmission of force within the connectivetissue components of muscle (Patel &Lieber, 1997). Muscles may not create equalforces at their attachments because of forcetransmitted to extramuscular connectivetissues (Huijing & Baan, 2001).

The separation of the passive tensioninto series and parallel components in theHill model and the exact equations used torepresent the elastic (springs) and contrac-tile components are controversial issues.Whatever the eventual source and com-plexity of elastic tension, it is important toremember that the stretch and recoil of elas-tic structures are an integral part of all mus-cle actions. It is likely that future researchwill increase our understanding of the in-teraction of active and passive components


Activity: Passive Tension

The effect of passive tension on joint mo-tions can be felt easily in multi-joint mus-cles when the muscles are stretchedacross multiple joints. This phenomenonis called passive insufficiency. Lie down in asupine (face upwards) position and notethe difference in hip flexion range of mo-tion when the knee is flexed and extend-ed.The hamstring muscle group limits hipflexion when the knee is extended be-cause these muscles cross both the hipand the knee joints. Clinical tests like thestraight-leg raise (Eksstrand,Wiktorsson,Oberg, & Gillquist, 1982), active knee ex-tension (Gajdosik & Lusin, 1983), and thesit-and-reach (Wells & Dillon, 1952) alluse passive insufficiency to evaluate ham-string static flexibility. Careful body posi-tioning is required in flexibility tests be-cause of passive insufficiency and othermechanical factors across several joints.Some aspects of this issue are exploredin Lab Activity 3.

of muscle tension in creating human move-ment. There are many other complexities inhow muscles create movement. The nextsection will briefly review the logic of func-tional anatomical analysis and how biome-chanics must be combined with anatomy tounderstand how muscles create movement.

THE LIMITATIONSOF FUNCTIONAL

ANATOMICAL ANALYSIS

Anatomy classifies muscles into functionalgroups (flexors/extensors, abductors/ad-ductors, etc.) based on hypothesized ac-tions. These muscle groups are useful gen-eral classifications and are commonly usedin fitness education, weight training, andrehabilitation. These hypothesized muscleactions in movements and exercises areused to judge the relevance of various exer-cise training or rehabilitation programs.This section will show that such qualitativeestimations of muscle actions are often in-correct. Similarly, many of the muscle ac-tions hypothesized by coaches and thera-

pists from subjective observation of move-ment are not correct (Bartlett, 1999; Herbert,Moore, Moseley, Schurr, & Wales, 1993).Kinesiology professionals can only deter-mine the true actions of muscle by examin-ing several kinds of biomechanical studiesthat build on anatomical information.

Mechanical Method of MuscleAction Analysis

Functional anatomy, while not an oxy-moron, is certainly a phrase that stretchesthe truth. Functional anatomy classifiesmuscles actions based on the mechanicalmethod of muscle action analysis. Thismethod essentially examines one muscle'sline of action relative to one joint axis of ro-tation, and infers a joint action based on ori-entation and pulls of the muscle in theanatomical position (Figure 3.12). In thesagittal plane, the biceps brachii is classi-fied as an elbow flexor because it is as-sumed that (1) the origins are at the shoul-der joint, (2) the insertion is on the radialtuberosity, and (3) the anterior orientation


Figure 3.11. The Hill model of muscle describes the active and passive tension created bythe MTU. Active tension is modeled by the contractile component, while passive tension ismodeled by the series and parallel elastic components.

and superior pull, as well as the superiororientation and posterior pull, would createelbow flexion. When a muscle is activated,however, it pulls both attachments approx-imately equally so that which end moves (ifone does at all) depends on many biome-chanical factors. Recall that there are threekinds of muscle actions, so that what the bi-ceps brachii muscle does at the elbow in aparticular situation depends on many bio-mechanical factors this book will explore.

Notice that the tension at both ends of amuscle often might not be the same becauseof the force transmitted to nearby musclesand extramuscular connective tissue (Hui-jing, 1999; Maas et al., 2004).

While the biceps is clearly an elbowflexor, this analysis assumes quite a bit anddoes not take into consideration other mus-cles, other external forces, and the biarticu-lar nature of the biceps. The long head ofthe biceps brachii crosses the shoulder joint.What if the movement of interest was theeccentric phase of the pull-over exercise(Figure 3.13), where the shoulder was theorigin because the elbow angle essentiallydid not change while shoulder flexion andextension were occurring? It is not entirelyclear if the long head of the biceps is in iso-metric or concentric action in this pull-overexercise example. Biomechanical data andanalysis are necessary to determine the ac-tual actions of muscles in movement. Thereare even cases where muscles accelerate a


Figure 3.12. The mechanical method of muscle actionanalysis applied to biceps and elbow flexion in thesagittal plane. It is assumed that in the anatomical po-sition the biceps pulls upward toward its anatomicalorigin from its anatomical insertion (radial tuberosity).The motion can be visualized using a bicycle wheelwith the axle aligned on the joint axis. If the the mus-cle were pulling on the wheel from its illustrated direc-tion and orientations relative to that joint axis (visual-ize where the line of action crosses the medial-lateraland superior-inferior axes of the sagittal plane), thewheel would rotate to the left, corresponding to elbowflexion. Unfortunately, the actions of other muscles,external forces, or other body positions are not ac-counted for in these analyses. More thorough andmathematical biomechanical analyses of the wholebody are required to determine the true actions ofmuscles.

Figure 3.13. In the eccentric phase of the pullover ex-ercise, the motion primarily occurs at the shoulderjoint, with the elbow angle remaining unchanged. Theisolated mechanical method of muscle action does nothelp in this situation to determine if the long head bi-ceps (crossing both the elbow and shoulder joints) isisometrically active, concentrically active, or inactive.Do you think a biarticular muscle like the biceps canbe doing two kinds of muscle actions at once? We willsee later that extensive kinetic biomechanical modelsand EMG research must be combined to determine theactual action of muscles in many movements. Imagecourtesy of VHI Kits, Tacoma, WA.

joint in the opposite direction to that in-ferred by functional anatomy (Zajac, 1991;Zajac & Gordon, 1989).

Rather invasive biomechanical meas-urements are usually required to determineexactly what muscle actions are occurringin normal movement. Many studies con-ducted on animals have shown that mus-cles often have surprising and complex ac-tions (see Biewener, 1998; Herzog, 1996a,b).One such study of the turkey (Roberts et al.,1997) gastrocnemius (plantar flexor) foundthe muscle acted in essentially an isometric

fashion in the stance phase of level running(Figure 3.14A), while concentric actionswere used running uphill (Figure 3.14B).The invasive nature of these kinds of meas-urements and the interesting variations inthe musculoskeletal structure of animals(fish, kangaroo rats, wallabies; Biewener,1998; Griffiths, 1989; Shadwick, Steffensen,Katz, & Knower, 1998) makes animal stud-ies a major area of interest for the biome-chanics of muscle function.

Similar complex behavior of muscle ac-tions has been observed in humans using


Figure 3.14. Simultaneous muscle force, length, and activation (EMG) measurements of the gastrocnemius of run-ning turkeys. (A) Note that in level running the muscle creates considerable force but the fibers do not shorten, sothe muscle is in isometric action and length changes are in the stretching and recoiling of the tendon. (B) in thestance phase of uphill running, the muscle fibers shorten (concentric action), doing mechanical work to lift theturkey's body. Reprinted with permission from Roberts et al. (1997). Copyright © 1997 American Association forthe Advancement of Science.

recent improvements in ultrasound imag-ing (Finni, Komi, & Lepola, 2000; Finni etal., 2001: Fukunaga, Ichinose, Ito, Kawaka-mi, & Fukashiro, 1997; Fukunaga, Kawaka-mi, Kubo, & Keneshisa, 2002; Kubo,Kawakami, & Fukunaga, 1999) and im-plantable fiberoptic force sensors (Komi,Belli, Huttunen, Bonnefoy, Geyssant, & La-cour, 1996). Recent studies of the humantibialis anterior have also documented non-linear and nonisometric behavior of themuscle (lengthening of tendon andaponeurosis while fibers shorten) in iso-metric actions (Maganaris & Paul, 2000; Itoet al., 1998). This is an area of intense re-search in biomechanics because the length-ening and shortening of muscle fibers,aponeurosis, and tendon from several dif-ferent muscles can all be documented in vi-vo during human movements (Finni, 2006;Fukashiro et al., 2006; Kawakami & Fuku-naga, 2006). It is clear now that muscle ac-tions in animal movements are more com-plicated than can be predicted by the con-centric, single-joint analysis of functionalanatomy.

Given these many examples of thecomplexity of muscle actions at the macroand microscopic levels, the hypothesizedmuscle actions from functional anatomy inmany human movements should be inter-preted with caution. Seemingly simplequestions of what muscles contribute mostto walking, jumping, or any movement rep-resent surprisingly complex biomechanicalissues. For example, should the word “ec-centric” be used as an adjective to describephases in weight training exercise (eccen-tric phase), when all the active muscles areclearly not in eccentric actions in the move-ment? If the active muscle group, body po-sition, and resistance are well defined, thisterminology is likely accurate. When thelifter “cheats” with other muscles in the ex-ercise, modifies exercise technique, or per-forms a similar sporting movement, the ec-centric adjective may not be accurate. The

actions of other muscles, external forces likegravity, and the complexity of the muscu-loskeletal system can make the isolatedanalyses of functional anatomy in theanatomical position inaccurate for dynamicmovement. Some biomechanical issues thatillustrate this point are summarized hereand developed throughout the book.

The Need for Biomechanics toUnderstand Muscle Actions

The traditional “kinesiological” analysis ofmovements of the early twentieth centuryessentially hypothesized how muscles con-tributed to motion in each phase of the skillby noting anatomical joint rotations and as-


Interdisciplinary Issue:Anthropometry

Anthropometry is the science concernedwith measurement of the physical properties(length, mass, density, moment of inertia, etc.)of a human body. Kinanthropometry is an areawithin kinesiology that studies how differ-ences in anthropometry affect sport perform-ance (see chapters 5 and 7 in Bloomfield,Ack-land, & Elliott, 1994).The main organization inthis area is the International Society for theAdvancement of Kinanthropometry (ISAK).Since humans move in a wide variety of activ-ities, many professionals use anthropometricdata. Engineers use these measurements todesign tools and workstations that fit mostpeople and decrease risk of overuse injuries.Prosthetic and orthotic manufacturers oftenmake anthropometric measurements on indi-viduals to customize the device to the individ-ual. Motor development scholars track thechanges in anthropometric characteristicswith growth and development. While peopleseem to have a wide variety of shapes andsizes, the relative (scaled to size) size of manyanthropometric variables is more consistent.Biomechanists use many of these averagephysical measurements to make quite accu-rate kinetic or center-of-gravity calculations.

suming muscles that create that joint rota-tion are active. Muscle actions in humanmovements, however, are not as simple asfunctional anatomy assumes (Bartlett,1999). Several kinds of biomechanical re-search bear this out, and show that the com-bination of several kinds of quantitativebiomechanical analysis are necessary to un-derstand the functions of muscles in move-ments.

First, electromyographic (EMG) stud-ies have documented general trends in acti-vation of muscles in a particular musclegroup, but with considerable potential vari-ation in that trend or in activation betweensubjects (Basmajian & De Luca, 1985). Theprimary source of this variation may bethe considerable redundancy (muscleswith the same joint actions) of the muscularsystem. Nearly identical movements can becreated by widely varying muscular forcesor joint torques (Hatze, 2000; Patla, 1987;Winter, 1984).

EMG studies show that the activationpatterns of individual muscles are not rep-resentative of all muscles in the same func-tional group (Arndt, Komi, Bruggemann, &Lukkariniemi, 1998; Bouisset, 1973), andthere are differences in how muscles withina muscle group respond to training (Rabitaet al., 2000). Even individual muscles arequite sophisticated, with different motorunit activation depending on the task ormuscle action (Babault, Pousson, Ballay, &Van Hoecke, 2001; Enoka, 1996; Gandevia,1999; Gielen, 1999). Muscles within a mus-cle group can alternate periods of activity inlow-level activities to minimize fatigue(Kouzaki, Shinohara, Masani, Kanehisa, &Fukunaga, 2002). Muscle activation canvary because of differences in joint angle,muscle action (Kasprisin & Grabiner, 2000;Nakazawa, Kawakami, Fukunaga, Yano, &Miyashita, 1993) or the degree of stabiliza-tion required in the task (Kornecki, Kebel,& Siemienski, 2001). For example, a manualmuscle test for the biceps used by physical

therapists uses isometric elbow flexion withthe forearm in supination to minimize bra-chioradialis activity and maximize bicepsactivity (Basmajian and De Luca, 1985). Re-cent EMG studies, however, have alsodemonstrated that some of these proce-dures used to isolate specific muscles inphysical therapy do not always isolate themuscle hypothesized as being tested (seeKelly, Kadrmas, & Speer, 1996; Rowlands,Wertsch, Primack, Spreitzer, Roberts, Spre-itzer, & Roberts, 1995).

The activation of many muscles to cre-ate a specific force or action is called a mus-cle synergy. A muscle synergy is a combi-nation of muscle actions that serves to opti-mally achieve a motor task. There is consid-erable recognition of the importance ofmuscle synergies and force sharing of mus-cles in biomechanical research (Arndt et al.,1998; Herzog, 1996b, 2000) and in currentrehabilitation and conditioning trends (seeInterdisciplinary Issue on training musclesversus movements). How individual mus-cles share the load is complicated, depend-ing on fiber type, contractile properties,cross-sectional area, moment arm, and an-tagonism (Ait-Haddou, Binding, & Herzog,2000). Motor control uses the term synergyto refer to underlying rules of the neuro-muscular system for using muscles to coor-dinate or create movements (Aruin, 2001;Bernstein, 1967).

Recent EMG research has in additionbegun to focus on different activation of


Activity: Muscle Synergy

Make a tight fist in your dominant hand asforcefully and quickly as you can. Observethe actions of the superficial muscles ofyour arm. Why do you think biceps andtriceps are isometrically activated in apower grip muscle synergy?

intramuscular sections within a muscle be-yond the traditional gross segmentation inclassical anatomy (Brown, et al., 2007; Mir-ka, Kelaher, Baker, Harrison, & Davis, 1997;Paton & Brown, 1994; Wickham & Brown,1998; Wickham et al., 2004). Wickham andBrown (1998) have confirmed different acti-vation of seven distinct segments of thedeltoid muscle, rather than the typicalthree sections (anterior, intermediate, pos-terior) of muscle fibers usually identified inanatomy. This line of research supports theEMG studies mentioned earlier which indi-cate that activation of muscles is muchmore complex than had been previouslythought. Further microanatomy and EMGresearch on muscles, particularly thosewith large attachments, will most likely in-crease our understanding of how parts ofthe muscles are activated differently to cre-ate movement.

Second, the descriptions of muscu-loskeletal anatomy often do not account forvariations in muscle attachment sites acrossindividuals. The numbers and sites of at-tachments for the rhomboid and scalenemuscles vary (Kamibayashi & Richmond,1998). A person born with missing middleand lower fibers of trapezius on one side oftheir body must primarily rely on rhom-boids for scapular retraction. Variations inskeletal structure are also hypothesized tocontribute to risk of injury. For example, theshape of the acromion process of the scapu-la is believed to be related to a risk of im-pingement syndrome (Whiting & Zernicke,1998). The role of anatomical variation ingross anatomy or in muscle architecture(Richmond, 1998) and their biomechanicaleffects of muscles actions and injury risk re-main an important area of study.

Third, the linked nature of the humanbody makes the isolated functional anatom-ical analysis incomplete. This linking ofbody segments means that muscle actionshave dramatic effects on adjacent and otherjoints quite distant from the ones the mus-

cles cross (Zajac, 1991; Zajac & Gordon,1989). This redistribution of mechanical en-ergy at distant joints may be more impor-tant to some movements than the tradition-al joint action hypothesized by functionalanatomy (Zajac, Neptune, & Kautz, 2002).Zajac and Gordon (1989), for example,showed how soleus activity in a sit-to-standmovement tends to extend the knee jointmore than it plantar flexes the ankle joint.Physical therapists know that the pectoralismajor muscle can be used to extend the el-bow in closed kinetic chain (see chapter 6)situations for patients with triceps paralysis(Smith, Weiss, & Lehmkuhl, 1996). Func-tional anatomy does not analyze how forcesand torques created by a muscle are distrib-uted throughout all the joints of the skeletalsystem or how these loads interact betweensegments. Zajac and Gordon (1989) haveprovided a convincing argument that theclassification of muscles as agonists or an-tagonists should be based on biomechani-cal models and joint accelerations, ratherthan torques the muscles create.

Dramatic examples of this wide varietyof effects of muscles can be seen in multiar-ticular muscles (van Ingen Schenau et al.,1989; Zajac, 1991). There is considerable in-terest in the topic of biarticular or multiar-ticular muscles, and it is known that theyhave different roles compared to similarmonoarticular muscles (Hof, 2001; Prilut-sky & Zatsiorsky, 1994; van Ingen Schenauet al., 1995). Another example of the com-plexity of movement is how small differ-ences in foot placement (angle of ankleplantar/dorsiflexion) dramatically affectswhich joint torques are used to cushion theshock in landing (DeVita & Skelly, 1992; Ko-vacs, Tihanyi, DeVita, Racz, Barrier, & Hor-tobagyi, 1999). A flat-footed landing mini-mizes a plantar flexor's ability to absorbshock, increasing the torque output of thehip and knee extensors. Small differences infoot angle in walking also affect the flexoror extensor dominance of the knee torque


(Simonsen, Dyhre-Poulsen, Voigt, Aagaard,& Fallentin, 1997), and the frontal planeknee torques that may be related to knee in-jury (Gregersen, Hull, & Hakansson, 2006;Teichtahl et al., 2006). The kinematics andkinetics chapters (5 and 6 & 7, respectively)will expand on the effects of the joints andsegment actions in human movement.

The fourth line of biomechanical re-search documenting the complexity ofmuscular actions creating movement aremodeling and simulation. Modeling in-volves the development of a mathematicalrepresentation of the biomechanical sys-tem, while simulation uses biomechanicalmodels to examine how changes in varioustechniques and parameters affect the move-ment or body. Biomechanical models of thehuman body can be used to simulate the ef-fects of changes in any of the parameters ofthe model. The more simple the model, theeasier the interpretation and application ofresults. For example, models of the motion

of body segments in airborne skills in gym-nastics and diving are quite effective in de-termining their effect on flight and rotation(Yeadon, 1998). As biomechanics modelsget more complicated and include more el-ements of the musculoskeletal system, themore difficult it is to validate the model. In-terpretation is even complicated because ofthe many interrelated factors and varia-tions in model parameters across subjects(Chow, Darling, & Ehrhardt, 1999; Hub-bard, 1993).

Despite the many controversial issuesin biomechanical modeling, these kinds ofstudies show that the actions of muscles inmovements are quite complex and are re-lated to segment and muscle geometry(Bobbert & van Ingen Schenau, 1988; Doo-renbosch, Veeger, van Zandwij, & van In-gen Schenau, 1997), muscle elasticity (An-derson & Pandy, 1993), coordination (Bob-bert & van Soest, 1994; Hatze, 1974; Nagano& Gerritsen, 2001), and accuracy or injury(Fujii & Hubbard, 2002; Thelen et al., 2006).One simulation found that non-extensormuscles of the legs could be used to im-prove jumping performance (Nagano et al.,2005), and it is also possible that coordina-tion in a movement even varies slightlyacross people because of differences inmuscle mechanics (Chowdhary & Challis,2001). Here we have the paradox of learn-ing again. What muscles do to create move-ment is quite complex, so kinesiologyscholars and professionals must decidewhat level of biomechanical system tostudy to best understand movement. Thestrength and conditioning field commonlygroups muscles into functional groups likethe knee extensors (quadriceps) or kneeflexors (hamstrings). Whatever movementsor level of analysis a kinesiology profes-sional chooses, biomechanics needs to beadded to anatomical knowledge to makevalid inferences about human movement.The next section briefly shows how thesports medicine professions have integrat-


Interdisciplinary Issue:Training Muscles vs. Movements

In the strength and conditioning field anarea of philosophical debate is related to agreater emphasis on training functionalmovements rather than training specificmuscle groups (Gambetta, 1995, 1997).Thisdebate is quite similar to the debate aboutthe relative benefits of training with freeweights or with machines.Training with freeweights can more easily simulate the bal-ance and stabilizing muscle actions in nor-mal and sport movements.The advantage ofmachines is that they provide more musclegroup-specific training with resistance thatis not as dependent on position relative togravity as free weights are. How might reha-bilitation and conditioning professionals usebiomechanics and EMG research to helpmatch training to the demands of normalmovement?

ed more biomechanical information intotheir professional practice.

Sports Medicine and RehabilitationApplications

Musculoskeletal anatomy and its motionterminology are important in kinesiologyand sports medicine, but it cannot be thesole basis for determining the function ofmuscles in human movement. Medical doc-tors specializing in sports medicine foundthat their extensive training in anatomywas not enough to understand injuries andmusculoskeletal function in the athletesthey treated (McGregor & Devereux, 1982).

This recognition by MDs that their strongknowledge of anatomy was incomplete tounderstand function and that they neededthe sciences of kinesiology was a factor inthe fusion of medical and kinesiology pro-fessionals that formed the American Col-lege of Sports Medicine (ACSM).

Today, many kinesiology students pre-pare for careers in medicine- and sportsmedicine-related careers (athletic training,physical therapy, orthotics, prosthetics,strength & conditioning). These professionsare concerned with analyzing the actions ofmuscles in movement. Where can sportsmedicine professionals (athletic trainers,physical therapists, physical medicine,strength and conditioning) get the most ac-curate information on the biomechanicalfunction of specific areas of the humanbody? Fortunately, there are several sourcesthat strive to weigh the anatomical/clinicalobservations with biomechanical research.These sources focus on both normal andpathomechanical function of the humanbody. The following sources are recom-mended since they represent this balancedtreatment of the subject, not relying solelyon experience or research (Basmajian &Wolf, 1990; Kendall, McCreary, & Provance,1993; Smith, Weiss, & Lehmkuhl, 1996).

It is important to remember that biome-chanics is an indispensable tool for all kine-siology professionals trying to understandhow muscles create movement, how to im-prove movement, and how problems in themusculoskeletal system can be compensat-ed for. The last two sections of this chapterillustrate how biomechanical principles canbe used to understand and improve humanmovement.

RANGE-OF-MOTIONPRINCIPLE

One area where anatomical description isquite effective is in the area of the range of


Application: Muscle Groups

If muscles create movement in complexsynergies that are adaptable, should kine-siology professionals abandon the com-mon practice of naming muscle groupsaccording to anatomical function (quads[knee extensors] or calf [ankle plantarflexors])? Such an extreme reaction tothe complexity of biomechanics is notnecessary. This common terminology islikely appropriate for prescribing generalstrength and conditioning exercises. Itmay even be an appropriate way to com-municate anatomical areas and move-ments in working with athletes knowl-edgeable and interested in performance.Kinesiology professionals do need toqualitatively analyze movements at adeeper level than their clients, and re-member that this simplified terminologydoes not always give an accurate pictureof how muscles really act in human move-ment. Biomechanical and other kinesiolo-gy research must be integrated with pro-fessional experience in qualitatively ana-lyzing movement.

motion used in movement. Movement canbe accurately described as combinations ofjoint angular motions. Remember that thebiomechanical principle of range of motion,however, can be more generally defined asany motion (both linear or angular) of thebody to achieve a certain movement goal.Specific joint motions can be of interest, butso too can the overall linear motions of thewhole body or an extremity. Coaches canspeak of the range of motion of a “stride” inrunning or an “approach” in the high jump.Therapists can talk about the range of mo-tion for a joint in the transverse plane.

In human movement the performer canmodify the number of joints, specific ana-tomical joint rotations, and amount of thoserotations to tailor range of motion. Range ofmotion in movement can be imagined on acontinuum from negligible motion to 100%of the physically possible motion. TheRange-of-Motion Principle states that lessrange of motion is most effective for low-ef-fort (force and speed) and high-accuracymovements, while greater range of motionfavors maximum efforts related to speedand overall force production (Hudson,1989). A person playing darts “freezes” orstabilizes most of the joints of the body withisometric muscle actions, and limits thedart throw to a small range of motion fo-cused on elbow and wrist. The javelinthrower uses a long running approach andtotal body action to use considerable rangeof motion to maximize the speed of javelinrelease. The great accuracy required in golfputting favors limiting range of motion byusing very few segments and limiting theirmotion to only what is needed to move theball near the hole (Figure 3.15).

The application of the range-of-motionprinciple is more complicated when the ef-fort of the movement is not maximal andwhen the load cannot be easily classified atthe extremes of the continuum. A baseballor softball seems pretty light, but where onthe range-of-motion continuum are these

intermediate load activities? How muchrange of motion should you use when theload is a javelin, a shot, or your bodyweight(vertical jump)? Biomechanical studies canhelp kinesiology professionals decide howmuch range of motion is “about right.” Inthe qualitative analysis of movement, thisapproach of identifying a range of correct-ness (like in range of motion) is quite usefulbecause the professional can either rein-force the performer's good performance, orsuggest less or more range of motion beused (Knudson & Morrison, 2002). The con-tinuum of range of motion can also be qual-itatively evaluated as a sliding scale (Knud-son, 1999c) or volume knob (Hudson, 1995)where the performer can be told to finetune range of motion by feedback (Figure3.16). Let's look at how biomechanical re-search can help professionals evaluate therange of motion in a vertical jump.

The amount and speed of counter-movement in a vertical jump is essential toa high jump. This range-of-motion variable


Figure 3.15. Very accurate movements like putting ingolf limit range of motion by freezing most segmentsand using only a few segments. Photo courtesy of Get-ty Images.

can be expressed as a linear distance (dropin center of mass as percentage of height) oras body configuration, like minimum kneeangle. We use the knee angle in this exam-ple because it is independent of a subject'sheight. One can hypothesize that maximiz-ing the drop (range of motion) with a smallknee angle in the countermovement wouldincrease the height of the jump; however,this is not the case. Skilled jumpers tend tohave minimum knee angles between 90 and110º (Ross & Hudson, 1997). The potentialbenefits of range of motion beyond thispoint seems to be lost because of poorermuscular leverage, change in coordination,or diminishing benefits of extra time to ap-ply force. The exact amount of counter-movement will depend on the strength andskill of the jumper, but coaches can general-ly expect the knee angles in this range.

Another example of the complexity ofapplying the range-of-motion principlewould be the overarm throw. In overarmthrowing the athlete uses range of motionfrom virtually the entire body to transferenergy from the ground, through the bodyand to the ball. The range of motion (kine-matics) of skilled overarm throwing hasbeen extensively studied. Early motor de-velopment studies show that one range-of-motion variable (the length of the forwardstride is usually greater than 50% of height)is important in a mature and forceful over-arm throw (Roberton & Halverson, 1984).Stride length in throwing is the horizontaldistance from the rear (push-off) foot to thefront foot. This linear range of motion fromleg drive tends to contribute 10 to 20% ofthe ball speed in skilled throwers (Miller,1980). The skill of baseball pitching uses


Figure 3.16. Range of motion can be evaluated and pictured as an analog scale or a volume knob. If a change inrange of motion is appropriate, the performer can be instructed to “increase” or “decrease” the range of motion intheir movement.

more stride range of motion, usually be-tween 75 and 90% of standing height, andhas been shown to significantly affect pitchspeed (Montgomery & Knudson, 2002).

The axial rotations of the hips andtrunk are the range-of-motion links be-tween stride and arm action. The differenti-ation of hip and trunk rotation is believedto be an important milestone in maturethrowing (Roberton & Halverson, 1984),and these movements contribute about 40to 50% of ball speed in skilled throwers. Incoaching high-speed throwing, coachesshould look for hip and trunk opposition(turning the non-throwing side toward thetarget) in preparation for the throw. The op-timal use of this range of motion is a coor-dination and segmental interaction issuethat will be discussed later. Students inter-ested in the skilled pattern of hip and trunkrange of motion should look at the researchon skilled pitchers (Fleisig, Barrentine,Zheng, Escamilla, & Andrews, 1999; Hong& Roberts, 1993; Stodden et al., 2005).

Arm action is the final contributor tothe range of motion used in overarm throw-ing. The complex joint actions of throwingcontribute significantly (30–50% of ball ve-locity) to skilled throwing (Miller, 1980). Totake advantage of the trunk rotation, theshoulder stays at roughly 90º of abductionto the spine (Atwater, 1979) and has beencalled the strong throwing position (Pla-genhoef, 1971). With initiation of the stride,the elbow angle stays near 90º to minimizeresistance to rotating the arm, so the majorincrease in ball speed is delayed until thelast 75 ms (a millisecond [ms] is a thou-sandth of a second) before release (Roberts,1991). Contrary to most coaching cues to“extend the arm at release,” the elbow istypically 20º short of complete extension atrelease to prevent injury (Fleisig et al.,1999). Inward rotation of the humerus, ra-dioulnar pronation, and wrist flexion alsocontribute to the propulsion of the ball(Roberts, 1991), but the fingers usually do

not flex to add additional speed to the ball(Hore, Watts, & Martin, 1996).

In overarm throwing it appears that therange-of-motion principle can be easily ap-plied in some motions like stride length us-ing biomechanical research as benchmarks;however, it is much more difficult to defineoptimal amounts of joint motions or bodyactions in complex movements like over-arm throwing. How range of motion mightbe changed to accommodate different levelof effort throws, more specific tasks/tech-niques (e.g., curveball, slider), or individ-ual differences is not clear. Currently, pro-fessionals can only use biomechanical stud-ies of elite and skilled performers as aguide for defining desirable ranges of mo-tion for movements. More data on a varietyof performers and advances in modeling orsimulation of movement are needed tomake better recommendations on howmodifications of range of motion may affectmovement.

FORCE–MOTION PRINCIPLE

Another way to modify human movementis to change the application of forces. TheForce–Motion Principle states that it takesunbalanced forces (and the subsequenttorques they induce) to create or modifyour motion. To know what size and direc-tion of force to change, recall that a free-body diagram of the biomechanical systemis usually employed. A major limitationof functional anatomical analysis was thelimited nature of the forces and structuresbeing considered. We are not in a positionto perform quantitative calculations to de-termine the exact motion created at thispoint in the text, but this section will pro-vide examples of the qualitative applicationof the Force–Motion Principle in improvinghuman movement. Later on, in chapters 6and 7, we will explore Newton's laws ofmotion and the major quantitative methods


used in biomechanics to explore the forcesthat create human movement.

Kinesiology professionals often workin the area of physical conditioning to im-prove function. Function can be high-levelsport performance or remediation of the ef-fects of an injury, disuse, or aging. If mus-cle forces are the primary motors (hip ex-tensors in running faster) and brakes (plan-tar flexors in landing from a jump), theForce–Motion Principle suggests that mus-cle groups that primarily contribute to themotion of interest should be trained. Re-member that this can be a more complextask than consulting your anatomy book.How can we know what exercises, tech-nique (speed, body position), or load toprescribe?

Imagine a physical education teacherworking with students on their upper bodymuscular strength. A particular student isworking toward improving his score on apull-up test in the fitness unit. The forces ina pull-up exercise can be simplified intotwo vertical forces: the downward gravita-tion force of bodyweight and an upwardforce created by concentric muscle actionsat the elbows, shoulders, and back. Theconsiderable isometric actions of the grip,shoulder girdle, and trunk do not appear tolimit this youngster's performance. Younote that this student's bodyweight is notexcessive, so losing weight is not an appro-priate choice. The teacher decides to workon exercises that train the elbow flexors, aswell as the shoulder adductors and exten-sors. The teacher will likely prescribe exer-cises like lat pulls, arm curls, and rowing toincrease the student's ability to pull down-ward with a force larger than his body-weight.

Suppose a coach is interested in help-ing a young gymnast improve her “splits”position in a cartwheel or other arm sup-port stunt (Figure 3.17). The gymnast caneasily overcome the passive muscular ten-sion in the hip adductors to create a split in

a seated position, but the downward forcecreating this static position is large (weightof the upper body) compared to the weightof the leg that assists the split in the invert-ed body position. The Force–Motion Princi-ple suggests that the balance of forces at thehips must be downward to create the splitin the dynamic action of the stunt. In otherwords, the forces of gravity and hip abduc-tors must create a torque equal to the up-ward torque created by the passive tensionin the hip adductors. If the gymnast is hav-ing trouble with this stunt, the two biome-chanical solutions that could be consideredare stretching the hip adductors (to de-crease passive muscle tension resistance)and increase the muscular strength or acti-vation of the hip abductors.

The examples of the Force–MotionPrinciple have been kept simple for severalreasons. First, we are only beginning ourjourney to an understanding of biomechan-ics. Second, the Force–Motion Principledeals with a complex and deeper level ofmechanics (kinetics) that explains the caus-es of motion. Third, as we saw in this chap-ter, the complexity of the biomechanical


Figure 3.17. The Force–Motion Principle can be ap-plied in a situation where a gymnast is having difficul-ty in performing inverted splits. The two forces thatmay limit the split are the passive tension resistance ofthe hip muscles or inadequate strength of the hip ab-ductors. The coach must decide which forces limit thisathlete's performance.

and neuromuscular system makes infer-ence of muscle actions complicated. Thevariability in the forces and kinematics ofhuman movement, therefore, have been ofinterest to a variety of scholars (see the In-terdisciplinary Issue on Variability). Therest of the book will provide challenges tothe perception that the causes of and solu-tions to human movement problems aresimple and introduce you to the main areasof biomechanics that are used to answerquestions about the causes of movement.

SUMMARY

Anatomy is the descriptive study of thestructure of the human body. This structur-al knowledge is an important prerequisitefor the study of human movement, butmust be combined with biomechanical

knowledge to determine how muscles cre-ate human movement. Kinesiology profes-sionals and students of biomechanics needto continually review their knowledge ofmusculoskeletal anatomy. Muscles tend tobe activated in synergies to cooperate or co-ordinate with other forces to achieve move-ment goals. Muscle tension is created fromactive or passive components, and the ac-tion muscles create are either eccentric,concentric, or isometric. Biomechanical re-search has shown that the actions of mus-cles in normal movement are more compli-cated than what is hypothesized by func-tional anatomy. The Range-of-Motion Prin-ciple of biomechanics can be used to im-prove human movement. Modifying rangeof motion in the countermovement of thevertical jump, as well as the stride andbody rotations in the overarm throw, were

Interdisciplinary Issue:Variability

Scientists from a variety of disciplineshave been interested in the variability ofhuman movement performance. Biome-chanical studies have often documentedvariability of kinematic and kinetic vari-ables to determine the number of trialsthat must be analyzed to obtain reliabledata (Bates, Osternig, Sawhill, & Janes,1983; Rodano & Squadrone, 2002;Win-ter, 1984). Motor learning studies havefocused on variability as a measure ofneuromuscular control (Davids et al.,2003; Slifkin & Newell, 2000).The studyof variability has also indicated that vari-ability may play a role in potential injury(James, Dufek, & Bates, 2000). Multiplebiomechanical measurements of kine-matics and kinetics may provide impor-tant contributions to interdisciplinarystudies of human movement variability.


Application: Decline Squats

Rehabilitation and conditioning profes-sionals often used incline and declinesupport surfaces to modify exercisesfor clients. People with limited ankledorsiflexion range of motion often dosquats with support under their heels.In rehabilitation, similar squat exercisesemphasizing the eccentric phase on de-cline surfaces are used in treating patel-lar tendinopathy (Kongsgaard et al.,2006). Apply the force-motion andrange of motion principles to study theexternal resistance relative to the bodyposition squatting on two different in-cline surfaces. How does the differentorientation of body to gravity and thejoint angles compare to a regular squatexercise? What other data or knowl-edge would help you in making thiscomparison or understanding the influ-ence of variations in the squat exercise?

examples discussed. The Force–MotionPrinciple was applied to exercise trainingand how passive tension affects gymnasticperformance.

REVIEW QUESTIONS

1. What are the major anatomical termsused in kinesiology and medicine to de-scribe the position and motion of the body?

2. What structural and functional prop-erties of muscle cells are different from oth-er body cells?

3. How do fiber properties andarrangement affect force and range-of-mo-tion potential of a muscle?

4. Name and define the three kinds ofmuscle actions.

5. What are the two major sources ofmuscle tension, and where in the range ofmotion are they most influential?

6. Explain the Hill three-componentmodel of muscle and how the componentsrelate to the sources of muscle tension.

7. What is an example of the Force– Mo-tion Principle in human movement?

8. Why is the mechanical method ofmuscle action analysis used in functionalanatomy inadequate to determine the ac-tions of muscles in human movement?

9. How does biomechanics help kinesi-ology professionals understand the causesand potential improvement of humanmovement?

10. What factors should a kinesiologistconsider when defining the appropriaterange of motion for a particular movement?

KEY TERMS

active tensionagonistantagonist

anatomyanthropometryactinconcentriccontractile componenteccentricfascicleHill muscle modelhypertrophyisometricmodelingmuscle actionmyofibrilmyosinparallel elastic componentpassive insufficiencypassive tensionpennationsarcomereseries elastic componentsimulationsynergy

SUGGESTED READING

Basmajian, J. V., & De Luca, C. J. (1985).Muscles alive: Their functions revealed by elec-tromyography (5th. ed.). Baltimore: Williams& Wilkins.

Cavanagh, P. R. (1988). On “muscle action”vs. “muscle contraction.” Journal of Biome-chanics, 21, 69.

Gielen, S. (1999). What does EMG tell usabout muscle function? Motor Control, 3,9–11.

Faulkner, J.A. (2003). Terminology for con-tractions of muscles during shortening,while isometric, and during lengthening.Journal of Applied Physiology, 95, 455–459.


Fitts, R. H., & Widrick, J. J. (1996). Musclemechanics: Adaptations in muscle resultingfrom exercise training. Exercise and SportSciences Reviews, 24, 427–473.

Hellebrandt, F. A. (1963). Living anatomy.Quest, 1, 43–58.

Herbert, R., Moore, S., Moseley, A., Schurr,K., & Wales, A. (1993). Making inferencesabout muscles forces from clinical observa-tions. Australian Journal of Physiotherapy, 39,195–202.

Herzog, W. (2000). Muscle properties andcoordination during voluntary movement.Journal of Sports Sciences, 18, 141–152.

Kleissen, R. F. M., Burke, J. H., Harlaar, J. &Zilvold, G. (1998). Electromyography in thebiomechanical analysis of human move-ment and its clinical application. Gait andPosture, 8, 143–158.

Lieber, R. L., & Bodine-Fowler, S. C. (1993).Skeletal muscle mechanics: Implications forrehabilitation. Physical Therapy, 73, 844–856.

Lieber, R. L., & Friden, J. (2000). Functionaland clinical significance of skeletal musclearchitecture. Muscle and Nerve, 23, 1647-1666.

Roberts, T. J., Marsh, R. L., Weyand, P. G., &Taylor, D. R. (1997). Muscular force in run-ning turkeys: The economy of minimizingwork. Science, 275, 1113–1115.

Soderberg, G. L., & Knutson, L.M. (2000). Aguide for use and interpretation of kinesio-logic electromyographic data. Physical Ther-apy, 80, 485-498.

Zajac, F. E. (2002). Understanding musclecoordination of the human leg with dynam-ical simulations. Journal of Biomechanics, 35,1011–1018.


WEB LINKS

Hypermuscle: Review of anatomical joint motion terminology from the University ofMichigan.

http://www.med.umich.edu/lrc/Hypermuscle/Hyper.html

PT Central Muscle Page: Comprehensive web muscle tableshttp://www.ptcentral.com/muscles/

Martindale's “Virtual” Medical Center-An electronic medical/anatomical libraryhosted by UC-Irvine.

http://www.martindalecenter.com/MedicalAnatomy.html

Body Worlds—von Hagens’ plastic-preserved human bodies.http://www.koerperwelten.de/en/pages/home.asp

Tour of Visible Human Project—Simple review of anatomical planes and structuresusing images from the NIH visible human project.

http://www.madsci.org/~lynn/VH/

Many professionals interested in humanmovement function need information onhow forces act on and within the tissues ofthe body. The deformations of muscles, ten-dons, and bones created by external forces,as well as the internal forces created bythese same structures, are relevant to un-derstanding human movement or injury.This chapter will provide an overview ofthe mechanics of biomaterials, specificallymuscles, tendons, ligaments, and bone. Theneuromuscular control of muscle forcesand the mechanical characteristics of mus-cle will also be summarized. The applica-tion of these concepts is illustrated usingthe Force–Time Principle of biomechanics.An understanding of mechanics of muscu-loskeletal tissues is important in under-standing the organization of movement, in-jury, and designing conditioning programs.

TISSUE LOADS

When forces are applied to a material, likehuman musculoskeletal tissues, they createloads. Engineers use various names to de-scribe how loads tend to change the shapeof a material. These include the principal oraxial loadings of compression, tension, andshear (Figure 4.1). Compression is when anexternal force tends to squeeze the mole-cules of a material together. Tension iswhen the load acts to stretch or pull apartthe material. For example, the weight of abody tends to compress the foot against theground in the stance phase of running,

which is resisted by tensile loading of theplantar fascia and the longitudinal liga-ment in the foot. Shear is a right-angleloading acting in opposite directions. Atrainer creates a shearing load across athlet-ic tape with scissor blades or their fingerswhen they tear the tape. Note that loads arenot vectors (individual forces) acting in onedirection, but are illustrated by two arrows(Figure 4.1) to show that the load resultsfrom forces from both directions.

When many forces are acting on a bodythey can combine to create combined loadscalled torsion and bending (Figure 4.2). Inbending one side of the material is loadedin compression while the other side experi-ences tensile loading. When a person is insingle support in walking (essentially aone-legged chair), the femur experiencesbending loading. The medial aspect of thefemur is in compression while the lateralaspect is in tension.

RESPONSE OF TISSUESTO FORCES

The immediate response of tissues to load-ing depends on a variety of factors. Thesize and direction of forces, as well asthe mechanical strength and shape ofthe tissue, affect how the material structurewill change. We will see in this sectionthat mechanical strength and muscularstrength are different concepts. This textwill strive to use “muscular” or “mechani-cal” modifiers with the term strength to

CHAPTER 4

Mechanics of theMusculoskeletal System

69

help avoid confusion. There are several im-portant mechanical variables that explainhow musculoskeletal tissues respond toforces or loading.

Stress

How hard a load works to change the shapeof a material is measured by mechanicalstress. Mechanical stress is symbolizedwith the Greek letter sigma (�) and is de-fined as the force per unit area within a ma-terial (� = F/A). Mechanical stress is similarto the concept of pressure and has the sameunits (N/m2 and lbs/in2). In the SI systemone Newton per meter squared is onePascal (Pa) of stress or pressure. As youread this book you are sitting in a sea of at-mospheric gases that typically exert a pres-sure of 1 atm, 101.3 KPa (kilopascals), or14.7 lbs/in2 on your body. Note that me-

chanical stress is not vector quantity, but aneven more complex quantity called a ten-sor. Tensors are generalized vectors thathave multiple directions that must be ac-counted for, much like resolving a force intoanatomically relevant axes like along a lon-gitudinal axis and at right angles (shear).The maximum force capacity of skeletalmuscle is usually expressed as a maximumstress of about 25–40 N/cm2 or 36–57lbs/in2 (Herzog, 1996b). This force poten-tial per unit of cross-sectional area is thesame across gender, with females tendingto have about two-thirds of the muscularstrength of males because they have abouttwo-thirds as much muscle mass a males.

Strain

The measure of the deformation of a materi-al created by a load is called strain. This de-


Figure 4.1. The principal axial loads of (a) compression, (b) tension, and (c) shear.

formation is usually expressed as a ratio ofthe normal or resting length (L0) of the ma-terial. Strain (�) can be calculated as achange in length divided by normal length:(L – L0)/ L0. Imagine stretching a rubberband between two fingers. If the band iselongated to 1.5 times its original length,you could say the band experiences 0.5 or50% tensile strain. This text will discuss thetypical strains in musculoskeletal tissues inpercentage units. Most engineers use muchmore rigid materials and typically talk interms of units of microstrain. Think aboutwhat can withstand greater tensile strain:the shaft of a tennis racket, the shaft of a golfclub, or the shaft of a fiberglass divingboard?

Stiffness and Mechanical Strength

Engineers study the mechanical behavior ofa material by loading a small sample in amaterials testing system (MTS), which si-multaneously measures the force and dis-placement of the material as it is deformedat various rates. The resulting graph iscalled a load-deformation curve (Figure4.3), which can be converted with othermeasurements to obtain a stress–straingraph. Load-deformation graphs have sev-eral variables and regions of interest. Theelastic region is the initial linear region ofthe graph where the slope corresponds tothe stiffness or Young's modulus of elastic-ity of the material. Stiffness or Young'smodulus is defined as the ratio of stress tostrain in the elastic region of the curve, butis often approximated by the ratio of load todeformation (ignoring the change in di-mension of the material). If the test werestopped within the elastic region the mate-rial would return to its initial shape. If thematerial were perfectly elastic, the force at agiven deformation during restitution (un-loading) would be the same as in loading.We will see later that biological tissues arenot like a perfectly elastic spring, so theylose some of the energy in restitution thatwas stored in them during deformation.

Beyond the linear region is the plasticregion, where increases in deformation oc-cur with minimal and nonlinear changes inload. The yield point or elastic limit is thepoint on the graph separating the elasticand plastic regions. When the material isdeformed beyond the yield point the mate-rial will not return to its initial dimensions.In biological materials, normal physiologi-cal loading occurs within the elastic region,and deformations near and beyond theelastic limit are associated with microstruc-tural damage to the tissue. Another impor-tant variable calculated from these meas-urements is the mechanical strength of thematerial.

CHAPTER 4: MECHANICS OF THE MUSCULOSKELETAL SYSTEM 71

Figure 4.2. Combined loads of (a) bending and (b) tor-sion. A bending load results in one side of the materi-al experiencing tension and the other compression.

The mechanical strength of a materialis the measurement of the maximum forceor total mechanical energy the material canabsorb before failure. The energy absorbedand mechanical work done on the materialcan be measured by the area under the loaddeformation graph. Within the plastic re-gion, the pattern of failure of the materialcan vary, and the definition of failure canvary based on the interest of the research.Conditioning and rehabilitation profession-als might be interested in the yield strength

(force at the end of the elastic region) ofhealthy and healing ligaments. Sports med-icine professionals may be more interestedin the ultimate strength that is largest forceor stress the material can withstand.Sometimes it is of interest to know the totalamount of strain energy (see chapter 6) thematerial will absorb before it breaks be-cause of the residual forces that remain af-ter ultimate strength. This is failurestrength and represents how much totalloading the material can absorb before it isbroken. This text will be specific in regardsto the term strength, so that when usedalone the term will refer to muscularstrength, and the mechanical strengths ofmaterials will be identified by their relevantadjective (yield, ultimate, or failure).

Viscoelasticity

Biological tissues are structurally complexand also have complex mechanical behav-ior in response to loading. First, biologicaltissues are anisotropic, which means thattheir strength properties are different foreach major direction of loading. Second, thenature of the protein fibers and amount ofcalcification all determine the mechanicalresponse. Third, most soft connective tissuecomponents of muscle, tendons, and liga-


Figure 4.3. The regions and key variables in a load–deformation graph of an elastic material.

Activity: Failure Strength

Two strong materials are nylon and steel.Nylon strings in a tennis racket can beelongated a great deal (high strain and alower stiffness) compared to steel strings.Steel is a stiff and strong material. Take apaper clip and apply a bending load. Didthe paper clip break? Bend it back the op-posite way and repeat counting the num-ber or bends before the paper clipbreaks. Most people cannot apply enoughforce in one shearing effort to break a pa-per clip, but over several loadings thesteel weakens and you can get a sense ofthe total mechanical work/energy youhad to exert to break the paper clip.

ments have another region in their load-de-formation graph. For example, when a sam-ple of tendon is stretched at a constant ratethe response illustrated in Figure 4.4 is typ-ical. Note that the response of the materialis more complex (nonlinear) than theHookean elasticity illustrated in Figure 2.4.The initial increase in deformation with lit-tle increase in force before the elastic regionis called the toe region. The toe region corre-sponds to the straightening of the wavy col-lagen fiber in connective tissue (Carlstedt &Nordin, 1989). After the toe region, theslope of the elastic region will vary depend-ing on the rate of stretch. This means thattendons (and other biological tissues) arenot perfectly elastic but are viscoelastic.

Viscoelastic means that the stress andstrain in a material are dependent on therate of loading, so the timing of the force

application affects the strain response of thematerial. Figure 4.5 illustrates the responseof a ligament that is stretched to a set lengthat two speeds, slow and fast. Note that ahigh rate of stretch results in a higher stiff-ness than a slow stretch. Muscles and ten-dons also have increasing stiffness with in-creasing rates of stretch. The viscoelasticityof muscles and tendons has great function-al significance. A slow stretch will result ina small increase in passive resistance (highcompliance) from the muscle, while themuscle will provide a fast increase in pas-sive resistance (high stiffness) to a rapidstretch. This is one of the reasons thatstretching exercises should be performedslowly, to minimize the increase in force inthe muscle–tendon unit (MTU) for a givenamount of stretch. The solid lines of thegraph represent the loading response of the


Figure 4.4. The typical load–deformation (elongation)curve for human tendon is more complex than formany materials. Initial elongation is resisted by smallforce increases in the toe region, followed by the elas-tic region. Much of the physiological loading of ten-dons in normal movement are likely within the toe re-gion (<5% strain: Maganaris & Paul, 2000), but elonga-tion beyond the elastic limit damages the tendon.

Figure 4.5. Load–deformation curves for tendonstretched at a fast and a slow rate to the same length.Force at any length in loading (solid line) are higherthan in unloading (dashed line). A viscoelastic materi-al has different stiffness at different rates of deforma-tion. A faster stretch results in greater force in the ten-don for a given length compared to a slow stretch.Hysteresis is the work and energy lost in the restitu-tion of the tendon and can be visualized as the area be-tween loading and unloading of the tendon.

ligament, while the dashed lines representthe mechanical response of the tissue as theload is released (unloading).

There are other important properties ofviscoelastic materials: creep, stress relax-ation, and hysteresis. Creep is the gradualelongation (increasing strain) of a materialover time when placed under a constanttensile stress. Stress relaxation is the de-crease in stress over time when a material iselongated to a set length. For example,holding a static stretch at a specific joint po-sition results in a gradual decrease in ten-sion in the muscle from stress relaxation. Ifyou leave a free weight hanging from a ny-lon cord, you might return several days lat-er to find the elongation (creep) in the cordhas stretched it beyond it initial length.Creep and stress relaxation are nonlinearresponses and have important implicationsfor stretching (see application box on flexi-bility and stretching) and risk of injury inrepetitive tasks. For example, work pos-

tures that stretch ligaments, reducing theirmechanical and proprioceptive effective-ness, increase joint laxity and likely increaserisk of injury (Solomonow, 2004).

Hysteresis is the property of viscoelas-tic materials of having a different unload-ing response than its loading response(Figure 4.5). Hysteresis also provides ameasure of the amount of energy lost be-cause the material is not perfectly elastic.The area between the loading and unload-ing is the energy lost in the recovery from


Activity:Viscoelasticity

An extreme example of viscoelastic behav-ior that serves as a good demonstration forteaching stretching exercises is the behav-ior of Silly Putty™. Roll the putty into acylinder, which serves as a model of mus-cle. The putty has low stiffness at slowstretching rates, so it gradually increases inlength under low force conditions and hasa plastic response. Now stretch the puttymodel quickly and note the much higherstiffness.This high stiffness makes the forcein the putty get quite high at short lengthsand often results in the putty breaking.Youmay be familiar with this complex (differ-ent) behavior of the material because theshape can be molded into a stable shapelike a ball, but when the ball is loaded quick-ly (thrown at a wall or the floor) it willbounce rather than flatten out.

Application: Stress Relaxation

Guitar players will know that steel stringsdo not lose tension (consequently theirtuning) as quickly as nylon strings; this phe-nomenon is not related to strength but toviscoelasticity. Steel guitar strings are muchmore elastic (stiffer) and have negligible vis-coelastic properties compared to nylonstrings. In a similar fashion, nylon tennisstrings lose tension over time. Skilled play-ers who prefer a higher tension to grab theball for making greater spin will often needto cut out and replace nylon strings beforethey break. Gut strings are more elasticthan nylon and tend to break before thereis substantial stress relaxation. Similarly,when a static stretch holds a muscle groupin an extended position for a long period oftime the tension in the stretched musclegroup decreases over time. This stress re-laxation occurs quickly (most within thefirst 15 seconds), with diminishing amountsof relaxation with longer amounts of time(see Knudson, 1998). How might a coachset up a stretching routine that maximizesstress relaxation of the athlete's muscles? Ifmany people dislike holding stretched posi-tions for a long period to time, how mightkinesiology professionals program stretch-ing to get optimal compliance and musclestress relaxation?

that stretch. We will learn in Chapter 6 thatenergy and work are related, and that me-chanical work is defined as force times dis-placement (F • d), so work can be visualizedas an area under a force-displacementgraph. If you want to visualize the failurestrength (work) of the material in Figure4.3, imagine or shade in the total area abovezero and below the load-deformationgraph.

All these mechanical response vari-ables of biological materials depend on pre-cise measurements and characteristics ofthe samples. The example mechanicalstrengths and strains mentioned in the nextsection represent typical values from the lit-erature. Do not assume these are exact val-ues because factors like training, age, anddisease all affect the variability of the me-chanical response of tissues. Methodologi-cal factors like how the human tissues werestored, attached to the machine, or precon-ditioned (like a warm-up before testing) allaffect the results. Remember that the rateof loading has a strong effect on the stiff-ness, strain, and strength of biological ma-terials. The following sections will empha-size more the strengths of tissues in differ-ent directions and how these are likely re-lated to common injuries.

BIOMECHANICS OF THE PASSIVEMUSCLE–TENDON UNIT (MTU)

The mechanical response of the MTU topassive stretching is viscoelastic, so the re-sponse of the tissue depends on the time orrate of stretch. At a high rate of passivestretch the MTU is stiffer than when it isslowly stretched. This is the primary reasonwhy slow, static stretching exercises arepreferred over ballistic stretching tech-niques. A slow stretch results in less passivetension in the muscle for a given amount ofelongation compared to a faster stretch. Theload in an MTU during other movementconditions is even more complicated be-

cause the load can vary widely with activa-tion, previous muscle action, and kind ofmuscle action. All these variables affecthow load is distributed in the active andpassive components of the MTU. Keep inmind that the Hill model of muscle has acontractile component that modulates ten-sion with activation, as well as two passivetension elements: the parallel elastic andthe series elastic components. The mechan-ical behavior of activated muscle is present-ed in the upcoming section on the “ThreeMechanical Characteristics of Muscle.”

Tendon is the connective tissue thatlinks muscle to bone and strongly affectshow muscles are used or injured in move-ment. Tendon is a well-vascularized tissuewhose mechanical response is primarily re-lated to the protein fiber collagen. The paral-lel arrangement of collagen fibers in tendonand cross-links between fibers makes ten-don about three times stronger in tensionthan muscle. The ultimate strength of ten-don is usually about 100 MPa (megapas-cals), or 14,500 lbs/in2 (Kirkendall & Gar-rett, 1997). Even though the diameter of ten-dons is often smaller than the associatedmuscle belly, their great tensile strengthmakes tendon rupture injuries rare. Acuteoverloading of the MTU usually results instrains (sports medicine term for over-stretched muscle, not mechanical strain)and failures at the muscletendon junction orthe tendon/bone interface (Garrett, 1996).

In creating movement, a long tendoncan act as an efficient spring in fast bounc-ing movements (Alexander, 1992) becausethe stiffness of the muscle belly can exceedtendon stiffness in high states of activa-tion. A muscle with a short tendon transfersforce to the bone more quickly becausethere is less slack to be taken out of the ten-don. The intrinsic muscles of the hand arewell suited to the fast finger movementsof a violinist because of their short tendons.The Achilles tendon provides shock absorp-tion and compliance to smooth out the


forces of the large calf muscle group (soleusand gastrocnemius).

BIOMECHANICS OF BONEUnlike muscle, the primary loads experi-enced by most bones are compressive. Themechanical response of bone to compres-sion, tension, and other complex loads de-pends on the complex structure of bones.Remember that bones are living tissueswith blood supplies, made of a high per-centage of water (25% of bone mass), andhaving considerable deposits of calcium

salts and other minerals. The strength ofbone depends strongly on its density ofmineral deposits and collagen fibers, and isalso strongly related to dietary habits andphysical activity. The loading of bones inphysical activity results in greater os-teoblast activity, laying down bone.Immobilization or inactivity will result indramatic decreases in bone density, stiff-ness, and mechanical strength. A Germanscientist is credited with the discovery thatbones remodel (lay down greater mineraldeposits) according to the mechanical stressin that area of bone. This laying down ofbone where it is stressed and reabsorptionof bone in the absence of stress is calledWolff's Law. Bone remodeling is well illus-trated by the formation of bone around thethreads of screws in the hip prosthetic inthe x-ray in Figure 4.6.

The macroscopic structure of boneshows a dense, external layer called cortical(compact) bone and the less-dense internalcancellous (spongy) bone. The mechanical


Figure 4.6. X-ray of a fractured femur with a metalplate repair. Note the remodeling of bone around thescrews that transfer load to the plate. Reprinted withpermission from Nordin & Frankel (2001).

Application: Osteoporosis

Considerable research is currently being direct-ed at developing exercise machines as counter-measures for the significant bone density loss inextended space flight. A microgravity environ-ment substantially decreases the loading of thelarge muscles and bones of the lower extremity,resulting in loss of bone and muscle mass.Thereis also interest in exercise as a preventative andremedial strategy for increasing the bone massof postmenopausal women. The strong link be-tween the positive stresses of exercise on bonedensity, however, is often complicated by suchother things like diet and hormonal factors. Inthe late 1980s researchers were surprised tofind that elite women athletes were at greaterrisk for stress fractures because they had thebone density of women two to three times theirage. Stress fractures are very small breaks inthe cortical (see below) bone that result fromphysical activity without adequate rest. Whatwas discovered was that overtraining and thevery low body fat that resulted in amenorrheaalso affected estrogen levels that tended to de-crease bone mass.This effect was stronger thanthe bone growth stimulus of the physical activi-ty. High-level women athletes in many sportsmust be careful in monitoring training, diet, andbody fat to maintain bone mass. Kinesiology pro-fessionals must be watchful for signs of a condi-tion called the female athlete triad. The femaleathlete triad is the combination of disorderedeating, amenorrhea, and osteoporosis that some-times occurs in young female athletes.

response of bone is dependent on this“sandwich” construction of cortical andcancellous bone. This design of a strongand stiff material with a weaker and moreflexible interior (like fiberglass) results ina composite material that is strong for agiven weight (Nordin & Frankel, 2001).This is much like a surf board constructedof fiberglass bonded over a foam core.Cortical bone is stiffer (maximum strainabout 2%), while cancellous bone is less stiffand can withstand greater strain (7%) be-fore failure. In general, this design results inultimate strengths of bone of about 200MPa (29,000 lbs/in2) in compression, 125MPa (18,000 lbs/in2) in tension, and 65 MPa(9,500 lbs/in2) in shear (Hayes, 1986). Thismeans that an excessive bending load onthe femur like in Figure 4.2 would mostlikely cause a fracture to begin on the later-al aspect that is under tensile loading.Using sports rules to protect athletes fromlateral blows (like blocking rules inAmerican football) is wise because bone isweakest under shearing loads.

It is also important to understand thatthe ultimate strength of bone depends onnutritional, hormonal, and physical activityfactors. Research done with an elite power-lifter found that the ultimate compressivestrength of a lumbar vertebral body (morethan 36,000 N or 4 tons) estimated frombone mineral measurements was twice thatof the previous maximal value. More re-cent studies of drop jump training in pre-pubescent children has demonstrated thatbone density can be increased, but it is un-clear if peak forces, rates of loading, or rep-etitions are the training stimulus for the in-creases in bone mass (Bauer, Fuchs, Smith,& Snow, 2001). More research on the os-teogenic effects of various kinds of loadingand exercise programs could help physicaleducators design programs that help schoolchildren build bone mass. The followingsection will outline the mechanical re-sponse of ligaments to loading.

BIOMECHANICS OFLIGAMENTS

Ligaments are tough connective tissues thatconnect bones to guide and limit joint mo-tion, as well as provide important proprio-ceptive and kinesthetic afferent signals(Solomonow, 2004). Most joints are not per-fect hinges with a constant axis of rotation,so they tend to have small accessory mo-tions and moving axes of rotation thatstress ligaments in several directions. Thecollagen fibers within ligaments are notarranged in parallel like tendons, but in avariety of directions. Normal physiologicalloading of most ligaments is 2–5% of tensilestrain, which corresponds to a load of �500N (112 lbs) in the human anterior cruciateligament (Carlstedt & Nordin, 1989), exceptfor “spring” ligaments that have a largepercentage of elastin fibers (ligamentumflavum in the spine), which can stretchmore than 50% of their resting length. Themaximum strain of most ligaments and ten-dons is about 8–10% (Rigby, Hirai, Spikes,& Eyring, 1959).

Like bone, ligaments and tendons re-model according to the stresses they aresubjected to. A long-term increase in themechanical strength of articular cartilagewith the loads of regular physical activityhas also been observed (Arokoski, Jurvelin,Vaatainen, & Helminen, 2000). Inactivity,however, results in major decreases in themechanical strength of ligaments and ten-don, with reconditioning to regain thisstrength taking longer than deconditioning(Carlstedt & Nordin, 1989). The ability ofthe musculoskeletal system to adapt tissuemechanical properties to the loads of phys-ical activity does not guarantee a low risk ofinjury. There is likely a higher risk of tissueoverload when deconditioned individualsparticipate in vigorous activity or whentrained individuals push the envelope,training beyond the tissue's ability to adaptduring the rest periods between training



Application: Flexibility and Stretching

A common health-related fitness component is flexibility. Flexibility is defined as “the intrinsic property ofbody tissues, which determines the range of motion achievable without injury at a joint or group of joints”(Holt et al., 1996:172). Flexibility can be mechanically measured as static and dynamic flexibility. Static flexi-bility refers to the usual linear or angular measurements of the actual limits of motion in a joint or jointcomplex. Static flexibility measurements have elements of subjectivity because of variations in testers andpatient tolerance of stretch. Dynamic flexibility is the increase in the muscle group resistance to stretch(stiffness) and is a less subjective measure of flexibility (Knudson et al., 2000). Inactivity and immobilizationhave been shown to decrease static range of motion (SROM) and increase muscle group stiffness (Akesonet al., 1987; Heerkens et al., 1986).

Stretching is a common practice in physical conditioning and sports. Stretching exercises must be carefullyprescribed to focus tension on the MTUs and not the ligaments that maintain joint integrity (Knudson,1998). Long-term stretching programs likely increase static range of motion by stimulating the productionof new sarcomeres in muscle fibers (De Deyne, 2001) and neuromuscular factors (Guissard & Duchateau,2006). While much is known about the acute and chronic effects of stretching on static flexibility, less isknow about its effect on dynamic flexibility or muscle-tendon stiffness (see Knudson et al., 2000). One ex-ample of the complications in examining the effects of stretching by measuring muscle stiffness is thethixotropic property of muscle. Thixotropy is the variation in muscle stiffness because of previous mus-cle actions. If an active muscle becomes inactive for a long period of time, like sitting in a car or a long lec-ture, its stiffness will increase. Do your muscles feel tight after a long ride in the car? Enoka (2002) providesa nice review of this phenomenon and uses ketchup to illustrate its cause.A gel like ketchup if allowed tostand tends to “set” (like actin and myosin bound in a motionless muscle), but when shaken tends to changestate and flow more easily. Most all of the increased stiffness in inactive muscles can be eliminated with a lit-tle physical activity or stretching.This does not, however, represent a long-term change in the stiffness of themuscles. Some of the most recent studies suggest that long-term effects of vigorous stretching are decreas-es in muscle viscosity and hysteresis, with no changes in tendon stiffness (Kubo et al., 2001a, 2002). Recentstudies of the in vivo change in length of muscle fibers and tendons using ultrasound and MRI show that thatthe limits of SROM are within the toe region of the muscle and tendon load-deformation curve for the ham-strings and gastrocnemius (Magnusson et al., 2000; Muraoka et al., 2002). Even if consistent stretching did cre-ate long-term decreases in muscle stiffness, it is unclear if this would translate to improved performance orlower risk of injury. More research is needed on the effects of stretching on muscle stiffness.

Interestingly, many studies have shown that the hypothesized performance-enhancing benefits of stretchingprior to activity are incorrect. Stretching in the warm-up prior to activity has been shown to decrease mus-cular performance in a wide variety of tests (Knudson, 1999b; Magnusson & Renstrom, 2006; Shrier, 2004).Muscle activation and muscular strength are significantly decreased for 15 and 60 minutes, respectively, fol-lowing stretching (Fowles et al., 2000a).The dose of stretching that significantly decreases strength may bebetween 20 and 40 seconds (Knudson & Noffal, 2005).The large stresses placed on MTUs in passive stretch-ing create short-term weakening, but these loads have not been shown to increase protein synthesis (Fowleset al, 2000b).Recent biomechanical and epidemiological research has also indicated that stretching during warm-up doesnot decrease the risk of injury (Knudson et al., 2000; Shirier, 1999; Magnusson & Renstrom, 2006). Severallines of evidence now suggest that the best time to program stretching in conditioning programs is duringthe cool-down phase. Recommendations on stretching and flexibility testing have been published(Knudson,1999b) and Knudson et al. (2000). Injury risk may be reduced, however, by generalized warm-up(Fradkin, Gabbe, & Cameron, 2006; Knudson, 2007a).

Flexibility is also strongly related to variations in body position because the passive tension increases in eachMTU, especially in multiarticular MTUs (passive insufficiency).This is why there are strict rules for body po-sitioning in flexibility testing.What muscles of the leg and thigh are unloaded when students try to cheat bybending their knees in a sit-and-reach test? What calf muscle is unloaded in a seated toe-touch stretch whenthe ankle is plantar flexed?

bouts. We will see in the next section thatmuscle mechanical properties also changein response to activity and inactivity.

THREE MECHANICAL CHARAC-TERISTICS OF MUSCLE

Previously we discussed the passive ten-sion in an MTU as it is passively stretched.Now it is time to examine the tensile forcesthe MTU experiences in the wide varietyactions, lengths, and other active conditionsencountered in movement. The force poten-tial of an MTU varies and can be describedby three mechanical characteristics. Thesecharacteristics deal with the variations inmuscle force because of differences in ve-locity, length, and the time relative to acti-vation.

Force–Velocity Relationship

The Force–Velocity Relationship explainshow the force of fully activated musclevaries with velocity. This may be the mostimportant mechanical characteristic sinceall three muscle actions (eccentric, isomet-ric, concentric) are reflected in the graph.

We will see that the force or tension a mus-cle can create is quite different across ac-tions and across the many speeds of move-ment. The discovery and formula describ-ing this fundamental relationship in con-centric conditions is also attributed to A. V.Hill. Hill made careful measurements ofthe velocity of shortening when a prepara-tion of maximally stimulated frog musclewas released from isometric conditions.These studies of isolated preparations ofmuscle are performed in what we term invitro (Latin for “in glass”) conditions.Figure 4.7 illustrates the shape of the com-plete Force–Velocity Relationship of skele-tal muscle. The Force–Velocity curve essen-tially states that the force the muscle cancreate decreases with increasing velocity ofshortening (concentric actions), while theforce the muscle can resist increases withincreasing velocity of lengthening (eccen-tric actions). The force in isometric condi-tions is labeled P0 in Hill's equation. Theright side of the graph corresponds to howthe tension potential of the muscle rapidlydecreases with increases in speed of con-centric shortening. Also note, however, that


Figure 4.7. The in vitro Force–Velocity Relationship of muscle. Muscle force potential rapidly decreases with in-creasing velocity of shortening (concentric action), while the force within the muscle increases with increasing ve-locity of lengthening (eccentric action). The rise in force for eccentric actions is much higher than illustrated.

increasing negative velocities (to the left ofisometric) show how muscle tension risesin faster eccentric muscle actions. In isolat-ed muscle preparations the forces that themuscle can resist in fast eccentric actionscan be almost twice the maximum isomet-ric force (Alexander, 2002). It turns out theextent of damage done to a muscle eccentri-cally overstretched is strongly related to thepeak force during the stretch (Stauber,2004). In athletics they say the sprinter“pulled or strained” his hamstring, but theinjury was the results of very large forces(high mechanical stress) from a too intenseeccentric muscle action.

If the force capability of an in vitro mus-cle preparation varies with velocity, canthis behavior be generalized to a wholeMTU or muscle groups in normal move-ment? Researchers have been quite interest-ed in this question and the answer is astrong, but qualified “yes.” The torque amuscle group can create depends on theprevious action, activation, rate of force de-velopment, and the combination of thecharacteristics of the muscles acting at thatand nearby joints. Despite these complica-tions, the in vivo (in the living animal)torque–angular velocity relationship ofmuscle groups usually matches the shapeof the in vitro curve. These in vivo torque–angular velocity relationships are estab-lished by testing at many angular velocitieson isokinetic and specialized dynamome-ters. These studies tend to show that in re-peated isokinetic testing the peak eccentrictorques are higher than peak isometrictorques, but not to the extent of isolatedmuscle preparations (Holder-Powell &Rutherford, 1999), while concentric torquesdecline with varying slopes with increasingspeed of shortening (De Koning et al., 1985;Gulch, 1994; Pinniger et al., 2000).

This general shape of a muscle's poten-tial maximum tension has many implica-tions for human movement. First, it is notpossible for muscles to create large forces at

high speeds of shortening. Muscles can cre-ate high tensions to initiate motion, but asthe speed of shortening increases their abil-ity to create force (maintain acceleration)decreases. Second, the force potential ofmuscles at small speeds of motion (in themiddle of the graph) depends strongly onisometric muscular strength (Zatsiorsky &Kraemer, 2006). This means that muscularstrength will be a factor in most move-ments, but this influence will vary depend-ing on the speed and direction (moving orbraking) the muscles are used. Third, theinverse relationship between muscle forceand velocity of shortening means you can-not exert high forces at high speeds ofshortening, and this has a direct bearing onmuscular power. In chapter 6 we will studymechanical power and look more closely atthe right mix of force and velocity that cre-ates peak muscular power output. This alsomeans that isometric strength and musclespeed are really two different muscularabilities. Athletes training to maximizethrowing speed will train differently basedon the load and speed of the implements intheir sport. Athletes putting the shot will dohigher weight and low repetition lifting,compared to athletes that throw lighter ob-jects like a javelin, softball, or baseball, whowould train with lower weights and higherspeeds of movement. One of the best booksthat integrates the biomechanics of move-ment and muscle mechanics in strengthand conditioning is by Zatsiorsky &Kraemer (2006).

So there are major implications for hu-man movement because of the functionalrelationship between muscle force and ve-locity. What about training? Does trainingalter the relationship between muscle forceand velocity or does the Force–VelocityRelationship remain fairly stable and deter-mine how you train muscle? It turns outthat we cannot change the nature (shape) ofthe Force–Velocity Relationship with train-ing, but we can shift the graph upward to


improve performance (De Koning et al.,1985; Fitts & Widrick, 1996). Weight train-ing with high loads and few repetitions pri-marily shifts the force–velocity curve upnear isometric conditions (Figure 4.8),while fast lifting of light loads shiftsthe curve up near Vmax, which is the maxi-mum velocity of shortening for a muscle.

Another area where the Force–VelocityRelationship shows dramatic differences inmuscle performance is related to musclefiber types. Skeletal muscle fibers fall on acontinuum between slow twitch (Type I)and fast twitch (Type II). Type I are alsocalled Slow-Oxidative (SO) because of theirhigh oxidative glycolysis capacity (consid-erable mitochrondion, myoglobin, triglyc-erides, and capillary density). Type II fibersare also called Fast-Glycolytic (FG) becauseof their greater anaerobic energy capacity(considerable intramuscular ATP and gly-colytic enzymes). Muscle fibers with inter-mediate levels are usually called FOG (Fast-

Oxidative-Glycolytic) fibers. Muscle fiberstype have been classified in many ways(Scott, Stevens, & Binder-Macleod, 2001),but biomechanics often focuses on thetwitch response and velocity of shorteningcharacteristics of fiber types. This is be-cause the force potential of fast and slowtwitch fibers per given physiological cross-sectional area are about the same. The tim-ing that the muscle fibers create force andspeed of shortening, however, are dramati-cally different. This fact has major implica-tions for high-speed and high-power move-ments.

The easiest way to illustrate these dif-ferences is to look at the twitch response ofdifferent fiber types. If an in vitro musclefiber is stimulated one time, the fiber willrespond with a twitch. The rate of tensiondevelopment and decay of the twitch de-pends on the fiber type of the fiber. Figure4.9 illustrates a schematic of the twitch re-sponses of several fiber types. A fiber at the


Figure 4.8. Training shifts the Force–Velocity curve upward and is specific to the kind of training. Heavy weighttraining primarily shifts the curve upward for isometric and slow concentric actions, while speed training im-proves muscle forces at higher concentric speeds.

slow end of the fiber type continuum grad-ually rises to peak tension in between 60and 120 ms (about a tenth of a second). Afiber at the high end of the continuum (FG)would quickly create a peak tension in 20 to50 ms. This means that the muscle with agreater percentage of FG fibers can create agreater velocity of shortening than a similar(same number of sarcomeres) one with pre-dominantly SO muscle fibers. Muscles withhigher percentages of SO fibers will have aclear advantage in long-duration, en-durance-related events.

Human muscles are a mix of fibertypes. There are no significant differencesin fiber types of muscles across gender, butwithin the body the antigravity muscles(postural muscles that primarily resist thetorque created by gravity) like the soleus,

erector spinae, and abdominals tend tohave a higher percentage of slow fibersthan fast fibers. The fiber type distributionof elite athletes in many sports has beenwell documented. There is also interest inthe trainability and plasticity of fiber types(Fitts & Widrick, 1996; Kraemer, Fleck, &Evans, 1996). Figure 4.10 illustrates theForce–Velocity Relationship in the predom-inantly slow-twitch soleus and predomi-nantly fast-twitch medial gastrocnemiusmuscles in a cat. This fiber distribution andmechanical behavior are likely similar tohumans. If the gastrocnemius were a moresignificant contributor to high-speed move-ments in sport, how might exercise positionand technique be used to emphasize thegastrocnemius over the soleus?


Figure 4.9. The twitch response of fast-twitch (FG) and slow-twitch (SO) muscle fibers. Force output is essential-ly identical for equal cross-sectional areas, but there are dramatic differences in the rise and decay of tension be-tween fiber types that affect the potential speed of movement.


Interdisciplinary Issue: Speed

Running speed in an important ability in manysports.The force–velocity relationship suggeststhat as muscles shorten concentrically fasterthey can create less tension to continue to in-crease velocity.What are the main factors thatdetermine sprinting speed? Do muscle me-chanical properties dominate sprinting per-formance or can technique make major im-provements in to running speed? Several linesof research suggest that elite sprinting abilitymay be more related to muscular and structur-al factors than technique. Near top runningspeed, stride rate appears to be the limitingfactor rather than stride length (Chapman &Caldwell, 1983; Luthanen & Komi, 1978b; Mero,Komi, & Gregor, 1992). In the 100-meter dashrunning speed is clearly correlated with per-centage of fast twitch fibers (Mero, Luthanen,Viitasalo, & Komi, 1981) and the length of mus-cle fascicles (Abe, Kumagai, & Brechue, 2000;Kumagai, Abe, Brechue, Ryushi, Takano, &Mizuno, 2000) in high-level sprinters. Athleteswith longer fascicles are faster. Future researchinto genetic predisposition to fiber dominanceand trainability might be combined with bio-mechanical research to help improve the selec-tion and training of sprinters.

Application: Domains of MuscularStrength

Therapists, athletes, and coaches often refer toa functional characteristic called muscularstrength.While muscular strength is common-ly measured in weight training with one-repeti-tion maxima (1RM is the maximum weight aperson can lift only one time), most researchersdefine muscular strength in isometric condi-tions at a specific joint angle to eliminate themany mechanical factors affecting muscle force(e.g., Atha, 1981; Knuttgen & Kraemer, 1987).Many fitness test batteries include tests forcomponents called muscular strength and muscu-lar endurance. Early physical education researchdemonstrated that muscular strength has sev-eral domains of functional expression. Statisticalanalysis of fitness testing demonstrated thatmuscular strength is expressed as static (iso-metric), dynamic (slow to moderate move-ments), and explosive for fast movement(Jackson & Frankiewicz, 1975; Myers et al.,1993). This corresponds closely to the majorchanges in force capability in the Force–VelocityRelationship. Others experts often include an-other domain of muscular strength related toeccentric actions: stopping strength (Zatsiorsky& Kraemer, 2006). Functional muscular strengthis also complicated by the fact that the force amuscle group can express also depends on theinertia of the resistance. The peak force thatcan be created in a basketball chest pass isnowhere near peak bench press isometricstrength because of the small inertia of the ball.The ball is easily accelerated (because of its lowmass), and the force the muscles can create athigh shortening velocities rapidly declines, sothe peak force that can be applied to the ball ismuch less than with a more massive object. Sothe Force–Velocity property of skeletal muscleand other biomechanical factors is manifestedin several functional “strengths.” Kinesiologyprofessionals need to be aware of how thesevarious “muscular strengths” correspond to themovements of their clients. Professionalsshould use muscular strength terminology cor-rectly to prevent the spread of inaccurate infor-mation and interpret the literature carefully be-cause of the many meanings of the wordstrength.

Figure 4.10. Differences in the Force–Velocity Rela-tionship of the primarily fast-twitch medial gastrocne-mius and primarily slow-twitch soleus of the cat.Reprinted, by permission, from Edgerton, Roy, Gregor,& Rugg, (1986).

Force–Length Relationship

The length of a muscle also affects the abil-ity of the muscle to create tension. TheForce–Length Relationship documentshow muscle tension varies at differentmuscle lengths. The variation in potentialmuscle tension at different muscle lengths,like the Force–Velocity Relationship, alsohas a dramatic effect on how movement iscreated. We will see that the Force–LengthRelationship is just as influential on thetorque a muscle group can make as thegeometry (moment arm) of the musclesand joint (Rassier, MacIntosh, & Herzog,1999).

Remember that the tension a musclecan create has both active and passivesources, so the length–tension graph ofmuscle will have both of these components.Figure 4.11 illustrates the Force–LengthRelationship for a skeletal muscle fiber. Theactive component of the Force–LengthRelationship (dashed line) has a logical as-sociation with the potential numbers of

cross-bridges between the actin and myosinfilaments in the Sliding Filament Theory.Peak muscle force can be generated whenthere are the most cross-bridges. This iscalled resting length (L0) and usually corre-sponds to a point near the middle of therange of motion. Potential active muscletension decreases for shorter or longer mus-cle lengths because fewer cross-bridges areavailable for binding. The passive tensioncomponent (solid line) shows that passivetension increases very slowly near L0 butdramatically increases as the muscle iselongated. Passive muscle tension usuallydoes not contribute to movements in themiddle portion of the range of motion, butdoes contribute to motion when musclesare stretched or in various neuromusculardisorders (Salsich, Brown, & Mueller, 2000).The exact shape of the Force–LengthRelationship slightly varies between mus-cles because of differences in active (fiberarea, angle of pennation) and passive(tendon) tension components (Gareis, Solo-monow, Baratta, Best, & D'Ambrosia, 1992).


Figure 4.11. The Force–Length Relationship of human skeletal muscle. The active component follows an inverted“U” pattern according to the number of potential cross-bridges as muscle length changes. Passive tension increas-es as the muscle is stretched beyond its resting length (L0). The total tension potential of the muscle is the sum ofthe active and passive components of tension.

The active tension component of theForce–Length Relationship has three re-gions (Figure 4.12). The ascending limb rep-resents the decreasing force output of themuscle as it is shortened beyond restinglength. Movements that require a musclegroup to shorten considerably will not beable to create maximal muscle forces. Theplateau region represents the high muscleforce region, typically in the midrange ofthe anatomical range of motion. Move-ments initiated near the plateau region willhave the potential to create maximal muscleforces. The descending limb represents thedecreasing active tension a muscle canmake as it is elongated beyond restinglength. At extremes of the descending limbthe dramatic increases in passive tensionprovide the muscle force to bring astretched muscle back to shorter lengths,even though there are virtually no potentialcross-bridge attachment sites. Biomechani-cal research has begun to demonstrate that

muscles adapt to chronic locomotor move-ment demands and the coordination ofmuscles may be organized around musclessuited to work on the ascending, plateau, ordescending limb of the force–length curve(Maganaris, 2001; Rassier et al., 1999). It isclear that the length of muscles influenceshow the central nervous system coordi-nates their actions (Nichols, 1994).


Figure 4.12. The three regions of the active component of the Length–Tension Relationship. Differences in thework (W = F • d) the muscle can do in the ascending limb (WA) versus the plateau region (WP) are illustrated. Workcan be visualized as the area under a force–displacement graph.

Activity: Force–Length Relationship

Active insufficiency is the decreased ten-sion of a multiarticular muscle when it isshortened across one or more of itsjoints.Vigorously shake the hand of a part-ner. Fully flex your wrist, and try to createa large grip force.What happened to yourstrength? Which limb of the Force–LengthRelationship creates this phenomenon?

The implications for a muscle workingon the ascending limb versus the plateauregion of the force–length curve are dra-matic. The mechanical work that a musclefiber can create for a given range of motioncan be visualized as the area under thegraph because work is force times displace-ment. Note the difference in work (area)created if the muscle fiber works in the as-cending limb instead of near the plateau re-gion (Figure 4.12). These effects also inter-act with the force–velocity relationship todetermine how muscle forces create move-ment throughout the range of motion.These mechanical characteristics also inter-act with the time delay in the rise and fall ofmuscle tension, the force–time relationship.

Force–Time Relationship

Another important mechanical characteris-tic of muscle is related to the temporal de-lay in the development of tension. TheForce–Time Relationship refers to the de-lay in the development of muscle tensionof the whole MTU and can be expressedas the time from the motor action poten-tial (electrical signal of depolarization ofthe fiber that makes of the electromyo-graphic or EMG signal) to the rise or peakin muscle tension.

The time delay that represents theForce–Time Relationship can be split intotwo parts. The first part of the delay is relat-ed to the rise in muscle stimulation some-


Application: Strength Curves

The torque-generating capacity of a muscle primarily depends on its physiological cross-section-al area, moment arm, and muscle length (Murray, Buchanan, & Delp, 2000).The maximum torquethat can be created by a muscle group through the range of motion does not always have a shapethat matches the in vitro force–length relationship of muscle fibers.This is because muscles withdifferent areas, moment arms, and length properties are summed and often overcome some an-tagonistic muscle activity in maximal exertions (Kellis & Baltzopoulos, 1997).There is also someevidence that the number of sarcomeres in muscle fibers may adapt to strength training and in-teract with muscle moment arms to affect were the peak torque occurs in the range of motion(Koh, 1995). “Strength curves” of muscle are often documented by multiple measurements ofthe isometric or isokinetic torque capability of a muscle group throughout the range of motion(Kulig,Andrews, & Hay, 1984).The torque-angle graphs created in isokinetic testing also can beinterpreted as strength curves for muscle groups.The peak torque created by a muscle grouptends to shift later in the range of motion as the speed of rotation increases, and this shift maybe related to the interaction of active and passive sources of tension (Kawakami, Ichinose, Kubo,Ito, Imai, & Fukunaga, 2002). How the shape of these strength curves indicates various muscu-loskeletal pathologies is controversial (Perrin, 1993). Knowledge of the angles where musclegroups create peak torques or where torque output is very low is useful in studying movement.Postures and stances that put muscle groups near their peak torque point in the range of mo-tion maximizes their potential contribution to motion or stability (Zatsiorsky & Kraemer, 2006).In combative sports an opponent put in an extreme joint position may be easily immobilized (ac-tive insufficiency, poor leverage, or pain from the stretched position).Accommodating resistanceexercise machines (Nautilus™ was one of the first) are usually designed to match the averagestrength curve of the muscle group or movement. These machines are designed to stay nearmaximal resistance (match the strength curve) throughout the range of motion (Smith, 1982),but this is a difficult objective because of individual differences (Stone, Plisk, & Collins, 2002).There will be more discussion of strength curves and their application in Chapter 7.

times called active state or excitation dy-namics. In fast and high-force movementsthe neuromuscular system can be trained torapidly increase (down to about 20 ms)muscle stimulation. The second part of thedelay involves the actual build-up of ten-sion that is sometimes called contractiondynamics. Recall that the contraction dy-namics of different fiber types was about 20ms for FG and 120 ms for SO fibers. Whenmany muscle fibers are repeatedly stimu-lated, the fusion of many twitches meansthe rise in tension takes even longer. Thelength of time depends strongly on the cog-nitive effort of the subject, training, kind ofmuscle action, and the activation history ofthe muscle group. Figure 4.13 shows aschematic of rectified electromyography(measure the electrical activation of muscle)and the force of an isometric grip force.Note that peak isometric force took about500 ms. Revisit Figure 3.14 for another ex-ample of the electromechanical delay (de-lay from raw EMG to whole muscle force).Typical delays in peak tension of whole

muscle groups (the Force–Time Relation-ship) can be quite variable. Peak force canbe developed in as little as 100 ms and up toover a second for maximal muscularstrength efforts. The Force–Time Relation-ship is often referred to as the electro-mechanical delay in electromyographic(EMG) studies. This delay is an importantthing to keep in mind when looking atEMG plots and trying to relate the timingof muscle forces to the movement. Recallthat the rise in muscle tension is also affect-ed by the stiffness of the connective tissuecomponents of muscle (passive tensionfrom SEC and PEC), so the size of theelectromechanical delay is affected by theslack or tension in the connective tissue(Muraoka et al., 2004). In chapter 5 we willsee that kinematics provides a precise de-scription of how motion builds to a peakvelocity and where this occurs relative tothe accelerations that make it occur.

This delay in the development of mus-cle tension has implications for the coordi-nation and regulation of movement. It


Figure 4.13. The rectified electromyographic (REMG) signal from the quadriceps and the force of knee extensionin an isometric action. The delay between the activation (REMG) and the build-up of force in the whole muscle isthe electromechanical delay and represents the Force–Time Relationship of the muscle. It takes 250 to 400 ms for peakforce to be achieved after initial activation of the muscle group.

turns out that deactivation of muscle (tim-ing of the decay of muscle force) also affectsthe coordination of movements (Neptune &Kautz, 2001), although this section will lim-it the discussion of the Force–TimeRelationship to a rise in muscle tension.

Kinesiology professionals need toknow about these temporal limitations sothey understand the creation of fast move-ments and can provide instruction or cuesconsistent with what the mover's bodydoes. For example, it is important forcoaches to remember that when they seehigh-speed movement in the body, theforces and torques that created that move-ment preceded the peak speeds of motionthey observed. The coach that providesurging to increase effort late in the move-ment is missing the greater potential for ac-celeration earlier in the movement and isasking the performer to increase effortwhen it will not be able to have an effect.Muscles are often preactivated before toprepare for a forceful event, like the activa-tion of plantar flexors and knee extensorsbefore a person lands from a jump. A delayin the rise of muscle forces is even morecritical in movements that cannot be pre-programmed due to uncertain environmen-tal conditions. Motor learning researchshows that a couple more tenths of a secondare necessary for reaction and processingtime even before any delays for increases inactivation and the electromechanical delay.To make the largest muscle forces at the ini-tiation of an intended movement, the neu-romuscular system must use a carefullytimed movement and muscle activationstrategy. This strategy is called the stretch-shortening cycle and will be discussed inthe following section.

STRETCH-SHORTENINGCYCLE (SSC)

The mechanical characteristics of skeletalmuscle have such a major effect on the force

and speed of muscle actions that the centralnervous system has a preferred muscle ac-tion strategy to maximize performance inmost fast movements. This strategy is mostbeneficial in high-effort events but is alsousually selected in submaximal move-ments. Most normal movements uncon-sciously begin a stretch-shortening cycle(SSC): a countermovement away from theintended direction of motion that is sloweddown (braked) with eccentric muscle action


Application: Rate of Force Development

Biomechanists often measure force or torqueoutput of muscle groups or movements withdynamometers. One variable derived fromthese force–time graphs is the rate of force de-velopment (F/t), which measures how quicklythe force rises.A high rate of force developmentis necessary for fast and high-power move-ments. The vertical ground reaction forces ofthe vertical jump of two athletes are illustratedin Figure 4.14. Note that both athletes createthe same peak vertical ground reactionforce, but athlete A (dashed line) has a higherrate of force development (steeper slope) thanathlete B (solid line). This allows athlete A tocreate a larger vertical impulse and jump higher.The ability to rapidly increase the active stateand consequently muscle force has beendemonstrated to contribute strongly to verticaljump performance (Bobbert & van Zandwijk,1999). Rate of force development is even moreimportant in running jumps, where muscle ac-tions and ground contact times are much short-er (50 to 200 ms) than in a vertical jump orMVC (Figure 4.13). Training the neuromuscularsystem to rapidly recruit motor units is veryimportant in these kinds of movements(Aagaard, 2003). What kinds of muscle fibershelp athletes create a quick rise in muscle force?What kinds of muscle actions allow musclesto create the largest tensions? The next twosections will show how the neuromuscular sys-tem activates muscles and coordinates move-ments to make high rates of muscle force devel-opment possible.

that is immediately followed by concentricaction in the direction of interest. Thisbounce out of an eccentric results in poten-tiation (increase) of force in the followingconcentric action if there is minimal delaybetween the two muscle actions (Elliott,Baxter, & Besier, 1999; Wilson, Elliott, &Wood, 1991). In normal movements mus-cles are also used in shortening-stretch cy-cles where the muscle undergoes concentricshortening followed by eccentric elonga-tion as the muscle torque decreases belowthe resistance torque (Rassier et al., 1999).

Early research on frog muscle byCavagna, Saibene, & Margaria (1965)demonstrated that concentric muscle workwas potentiated (increased) when precededby active stretch (eccentric action). Thisphenomenon is know as the stretch-short-ening cycle or stretch-shorten cycle and hasbeen extensively studied by Paavo Komi(1984, 1986). The use of fiberoptic tendonforce sensors and estimates of MTU lengthhas allowed Komi and his colleagues to cre-

ate approximate in vivo torque–angular ve-locity diagrams (Figure 4.15). The loop inthe initial concentric motion shows thehigher concentric tensions that are createdfollowing the rather less-than-maximal ec-centric tensions. The performance benefit ofSSC coordination over purely concentric ac-tions is usually between 10 and 20% (see“Stretch-Shortening Cycle” activity), butcan be even higher, and the biomechanicalorigin of these functional benefits is stillunclear. Many biomechanical variableshave been examined to study the mecha-nism of the SSC, and the benefits of the SSCare dependent on when these variables arecalculated (Bird & Hudson, 1998) and theresistance moved (Cronin, McNair, &Marshall, 2001b).

The mechanisms of the beneficial ef-fects of SSC coordination is of considerableinterest to biomechanics scholars. There arefour potential sources of the greater muscleforce in the concentric phase of an SSC: con-tractile potentiation, reflex potentiation,


Figure 4.14. Vertical jump ground reaction forces in units of bodyweight (BW) for two athletes. Athlete A (dashedline) has a greater rate of force development compared to athlete B (solid line). The rate of force development isthe slope of the graphs when vertical forces are building above 1BW. Do not interpret the up and down motion ofthe graph as motion of the jumper's body; it represents the sum of the vertical forces the athlete makes againstthe ground.

storage and reutilization of elastic energy,and the time available for force develop-ment (Komi, 1986; van Ingen Schenau,Bobbert, & de Haan, 1997). Contractile po-tentiation of muscle force is one of severalvariations in muscle force potential basedon previous muscles actions. These phe-nomena are called history-dependent be-haviors (see Herzog, Koh, Hasler, &Leonard, 2000; Sale, 2002). Shortening ac-tions tend to depress force output of subse-quent muscle actions, while eccentric ac-tions tend to increase concentric actionsthat immediately follow. Force potentiationof muscle is also dependent on musclelength (Edman et al., 1997).

Another mechanism for the beneficialeffect of an SSC is a greater contributionfrom the myotatic or stretch reflex (see thesection on “Proprioception of MuscleAction and Movement”). Muscle spindlesare proprioceptors of muscle length and areparticularly sensitive to fast stretch. Whenmuscles are rapidly stretched, like in anSSC movement, muscle spindles activate ashort reflex loop that strongly activates themuscle being stretched. Studies of athleteshave shown greater activation of musclesin the concentric phase of an SSC move-ment compared to untrained subjects(Komi & Golhoffer, 1997). The lack of a pre-cise value for the electromechanicaldelay (the Force–Time Relationship) makesit unclear if stretch reflexes contribute togreater muscle forces in the late eccentricphase or the following concentric phase.The contribution of reflexes to the SSC re-mains controversial and is an importantarea of study.

One of the most controversial issues isthe role of elastic energy stored in the ec-centric phase, which can be subsequentlyrecovered in the concentric phase of an SSC.There has been considerable interest in thepotential metabolic energy savings in thereutilization of stored elastic energy in SSCmovements. It may be more accurate to say


Figure 4.15. Schematic of the in-vivo muscle force–ve-locity behavior during an SSC movement, andforce–velocity behavior derived from multiple isoki-netic tests (see Barclay, 1997). Initial concentric short-ening in an SSC creates higher forces than the classicForce–Velocity Curve. Muscle length is not measureddirectly but inferred from joint angle changes, so thetrue behavior of the muscle in human SSC motions isnot known.

Activity: Stretch-Shortening Cycle

The benefits of stretch-shortening cycle muscleactions are most apparent in vigorous, full-effortmovements.To see the size of the benefit for per-formance, execute several overarm throws fordistance on a flat, smooth field. Measure the dis-tance of your maximal-effort throw with yourfeet still and body facing the direction of yourthrow. Have someone help you determine abouthow far your trunk and arm backswing was in thenormal throw. Measure the distance of a primari-ly concentric action beginning from a static posi-tion that matches your reversal trunk and armposition in the normal throw. Calculate the ben-efit of the SSC (prestretch augmentation) in thethrow as (Normal – Concentric)/Concentric.Compare your results with those of others, thelab activity, and research on vertical jumping(Walshe, Wilson, & Murphy, 1996; Kubo et al.,1999). The benefit of the SSC to other fastermovements is likely to be even higher than in ver-tical jumping (Komi & Gollhofer, 1997).What fac-tors might affect amount of prestretch augmen-tation? What might be the prestretch augmenta-tion in other movements with different loads?

elastic mechanisms in the SSC are prevent-ing energy loss or maintaining muscle effi-ciency (Ettema, 2001), rather than an ener-gy-saving mechanism. Animal studies (e.g.,wallabies and kangaroo rats) have beenused to look at the extremes of evolutionaryadaptation in muscletendon units related toSSC movement economy (Biewener, 1998;Biewener & Roberts, 2000; Griffiths, 1989;1991). A special issue of the Journal of Ap-plied Biomechanics was devoted to the role ofstored elastic energy in the human verticaljump (Gregor, 1997). Recent in vivo studiesof the human gastrocnemius muscle in SSCmovements has shown that the complianttendon allows the muscle fibers to act innear isometric conditions at joint reversaland while the whole muscle shortens to al-low elastic recoil of the tendinous struc-tures to do more positive work (Kubo,Kanehisa, Takeshita, Kawakami, Fukashiro,& Fukunaga, 2000b; Kurokawa, Fukunaga,& Fukashiro, 2001). The interaction of ten-don and muscle must be documented tofully understand the benefits of the SSC ac-tion of muscles (Finni et al., 2000).

Another mechanism for the beneficialeffect of SSC coordination is related to thetiming of force development. Recall that therate of force development and theForce–Time Relationship have dramatic ef-fect on high-speed and high-power move-ments. The idea is that if the concentricmovement can begin with near-maximalforce and the slack taken out of the elasticelements of the MTU, the initial accelera-tion and eventual velocity of the movementwill be maximized. While this is logical, theinteraction of other biomechanical factors(Force–Length Relationship, architecture,and leverage) makes it difficult to examinethis hypothesis. Interested students shouldsee papers on this issue in the vertical jump(Bobbert, Gerritsen, Litjens, & van Soest,1996; Bobbert & van Zandwijk, 1999) andsprint starts (Kraan, van Veen, Snijders, &Storm, 2001).

The most influential mechanism for thebeneficial effect of an SSC will likely de-pend on the movement. Some events likethe foot strike in sprinting or running jump(100 to 200 ms) require high rates of forcedevelopment that are not possible from restdue to the Force–Time Relationship. Thesehigh-speed events require a well-trainedSSC technique and likely have a differentmix of the four factors than a standing ver-tical jump.

Plyometric (plyo=more metric=length)training will likely increase the athlete'sability to tolerate higher eccentric muscleforces and increase the potentiation of ini-tial concentric forces (Komi, 1986). Plyo-metrics are most beneficial for athletes inhigh-speed and power activities. There hasbeen considerable research on the biome-chanics of lower-body drop jumping plyo-metrics (Bobbert, 1990). Early studiesshowed that jumpers tend to spontaneous-ly adopt one of two techniques (Bobbert,Makay, Schinkelshoek, Huijing, & vanIngen Schenau, 1986) in drop jumping exer-cises. Recent research has focused on tech-nique adaptations due to the compliance ofthe landing surface (Sanders & Allen, 1993),the effect of landing position (Kovacs et al.,1999), and what might be the optimal dropheight (Lees & Fahmi, 1994). Less researchhas been conducted on the biomechanics ofupper body plyometrics (Newton, Krae-mer, Hakkinen, Humphries, & Murphy,1996; Knudson, 2001c). Loads for plyomet-ric exercises are controversial, with loadsranging between 30 and 70% of isometricmuscular strength because maximum pow-er output varies with technique and themovement (Cronin, McNair, & Marshall,2001a; Izquierdo, Ibanez, Gorostiaga,Gaurrues, Zuniga, Anton, Larrion, &Hakkinen, 1999; Kaneko, Fuchimoto, Toji,& Suei, 1983; Newton, Murphy, Hum-phries, Wilson, Kraemer, & Hakkinen, 1997;Wilson, Newton, Murphy, & Humphries,1993).


Plyometrics are not usually recom-mended for untrained subjects. Eventhough eccentric muscle actions are normal,intense unaccustomed eccentric activity isclearly associated with muscle damage.Eccentric-induced muscle fiber damage hasbeen extensively studied and appears to berelated to excessive strain in sarcomeres(see the review by Lieber & Friden, 1999)rather than the high forces of eccentric ac-tions. Kinesiology professionals shouldcarefully monitor plyometric techniqueand exercise intensity to minimize the riskof injury.

FORCE–TIME PRINCIPLE

The Force–Time Principle for applying bio-mechanics is not the same as theForce–Time Relationship of muscle me-chanics. The Force–Time Principle statesthat the time available for force applicationis as important as the size of the forces usedto create or modify movement. So theForce–Time Principle is concerned with thetemporal strategy of force application inmovements, while the Force–Time Rela-tionship (electromechanical delay) states afact that the tension build-up of muscletakes time. The electromechanical delay isclearly related to how a person selects theappropriate timing of force application. TheForce–Time Principle will be illustrated inusing forces to slow down an external ob-ject, and to project or strike an object.

Movers can apply forces in the oppositedirection of the motion of an object to grad-ually slow down the object. Movementslike catching a ball or landing from a jump(Figure 4.16) employ primarily eccentricmuscle actions to gradually slow down amass over some period of time. Positioningthe body to intercept the object early allowsthe mover to maximize the time the objectcan be slowed down. How does a gymnast

maximize the time of force application tocushion the landing from a dismount froma high apparatus? Near complete extensionof the lower extremities at touchdown onthe mat allows near maximal joint range ofmotion to flex the joints and more time tobring the body to a stop.

The primary biomechanical advantageof this longer time of force application issafety, because the peak force experiencedby the body (and consequently the stress intissues) will be lower than during a shortapplication of force. Moving the body andreaching with the extremities to maximizethe time of catching also has strategic ad-vantages in many sports. A team handballplayer intercepting the ball early not onlyhas a higher chance of a successful catch,but they may prevent an opponent from in-tercepting. The distance and time the ball isin the air before contacting the catcher'shands is decreased with good arm exten-sion, so there is less chance of an opponentintercepting the pass.

Imagine you are a track coach whoseobservations of a discus thrower indicatethey are rushing their motion across thering. The Force–Motion Principle and theforce–velocity relationship make you thinkthat slowing the increase in speed on theturns and motion across the circle might al-low for longer throws. There is likely a lim-it to the benefit of increasing the time to ap-ply because maximizing discus speed in anappropriate angle at release is the objectiveof the event. Are there timing data for elitediscus throwers available to help with thisathlete, or is there a little art in the applica-tion of this principle? Are you aware of oth-er sports or activities where coaches focuson a controlled build-up in speed or un-rushed rhythm?

So there are sometimes limits to thebenefit of increasing the time of force appli-cation. In movements with high demandson timing accuracy (baseball batting or atennis forehand), the athlete should not


maximize the time of force application be-cause extra speed is of lower importancethan temporal accuracy. If a tennis playerpreferred a large loop backswing wherethey used a large amount of time and theforce of gravity to create racket head speed,the player will be vulnerable to fast and un-predictable strokes from an opponent. Thewise opponent would mix up shot place-ments, spin, and increase time pressure tomake it difficult for the player to get theirlong stroke in.

Suppose a patient rehabilitating fromsurgery is having difficulty using even the

smallest weights in the clinic. How could atherapist use the Force–Time Principle toprovide a therapeutic muscular overload?If bodyweight or assistive devices wereavailable, could the therapist have the pa-tient progressively increase the time theyisometrically hold various positions? Whilethis approach would tend to benefit muscu-lar endurance more so than muscularstrength, these two variables are relatedand tend to improve the other. Increasingthe time of muscle activity in isometric ac-tions or by modifying the cadence ofdynamic exercises is a common training


Figure 4.16. The extension of the limbs before contact and increasing flexion in landing increases the time thatforces can be applied to slow down the body. In chapter 6 we will see that this decreases the peak force on the bodyand decreases the risk of injury.

device used in rehabilitation and strengthtraining. Timing is an important aspectof the application of force in all humanmovement.

In studying the kinetics of humanmovement (chapters 6 and 7), we will seeseveral examples of how the human bodycreates forces over time. There will bemany examples where temporal and otherbiomechanical factors make it a poor strat-egy to increase the time to apply force. In

sprinting, each foot contact has to remainshort (about 100 ms), so increasing rate offorce development (Force–Motion Prin-ciple) is more appropriate than increasingthe time of force application. It is importantto realize that applying a force over a longtime period can be a useful principle to ap-ply, but it must be weighed with the otherbiomechanical principles, the environment,and subject characteristics that interact withthe purpose of the movement.

NEUROMUSCULAR CONTROL

The mechanical response of muscles alsostrongly depends on how the muscles areactivated. The neuromuscular control ofmovement is an active area of study wherebiomechanical research methods have beenparticularly useful. This section will sum-marize the important structures and theirfunctions in the activation of muscles toregulate muscle forces and movement.

The Functional Unit of Control:Motor Units

The coordination and regulation of move-ment is of considerable interest to manyscholars. At the structural end of the neuro-muscular control process are the functionalunits of the control of muscles: motor units.A motor unit is one motor neuron and allthe muscle fibers it innervates. A musclemay have from a few to several hundredmotor units. The activation of a motor axonresults in stimulation of all the fibers of thatmotor unit and the resulting twitch. Allfibers of a motor unit have this synchro-nized, “all-or-nothing” response. Pioneer-ing work in the neurophysiology of muscleactivation was done in the early 20th centu-ry by Sherrington, Arian, and Denny-Brown (Burke, 1986).


Application: Force–Time and Range-of-Motion Principle Interaction

Human movements are quite complex, andseveral biomechanical principles often apply.This is a challenge for the kinesiology profes-sional, who must determine how the task,performer characteristics, and biomechanicalprinciples interact. In the sport of weight lift-ing, coaches know that the initial pull on thebar in snatch and clean-and-jerk lifts shouldnot be maximal until the bar reaches aboutknee height. This appears counter to theForce–Time principle, where maximizing ini-tial force over the time of the lift seems to beadvantageous. It turns out that there areranges of motion (postural) and muscle me-chanical issues that are more important thana rigid application of the Force–TimePrinciple. The whole-body muscular strengthcurve for this lift is maximal near knee level,so a fast bar speed at the strongest body po-sition compromises the lift because of the de-crease in muscle forces in increasing speed ofconcentric shortening (Garhammer, 1989;Zatsiorsky, 1995). In other words, there is aForce–Motion advantage of a nearly-maximalstart when the bar reaches knee level thattends to outweigh maximal effort at the startof the movement. Olympic lifts require agreat deal of practice and skill.The combina-tion of speed and force, as well as the motorskills involved in Olympic lifting, makes thesewhole-body movements popular conditioningexercises for high power sports (Garhammer,1989).

Regulation of Muscle Force

If the muscle fibers of a motor unit twitch inunison, how does a whole muscle generatea smooth increase in tension? The preciseregulation of muscle tension results fromtwo processes: recruitment of different mo-tor units and their firing rate.

Recruitment is the activation of differ-ent motor units within a muscle. Physio-logical research has determined three im-portant properties of recruitment of motorunits. First, motor units tend to be organ-ized in pools or task groups (Burke, 1986).Second, motor units tend to be recruited inan asynchronous fashion. Different motorunits are stimulated at slightly differenttimes, staggering the twitches to helpsmooth out the rise in tension. There is evi-dence that some motor unit synchroniza-tion develops to increase rate of force devel-opment (Semmler, 2002), but too much syn-chronous recruitment results in pulses oftension/tremor that is associated with dis-ease (Parkinson's) or extreme fatigue (finalrepetition of an exhaustive set of weightlifting). The recruitment of motor units islikely more complex than these generaltrends since serial and transverse connec-tions between parallel architecture musclesallows active fibers to modify the tensionand length of nearby fibers (Sheard, 2000).

The third organizational principle of re-cruitment has been called orderly recruit-ment or the size principle (Denny-Brown &Pennybacker, 1938; Henneman, Somjen, &Carpenter, 1965). It turns out that motorunits tend to have specialized innervationand homogeneous fiber types, so motorunits take on the characteristics of a partic-ular fiber type. A small motor unit consistsof a motor axon with limited myelinationand primarily SO muscle fibers, while alarge motor unit has a large motor axon(considerable myelination) and primarilyFG fibers. The recruitment of a large motorunit by the brain results in the quickest

message and build-up in tension, while re-cruitment of a small motor unit has a slow-er nerve conduction velocity and a gradualtension build-up (Figure 4.17).

In essence, the size principle says thatmotor units are recruited progressivelyfrom small (slow-twitch) to large (fast-twitch). A gradual increase in muscle forcewould result from recruitment of SO domi-nant motor units followed by FOG and FGdominant units, and motor units would bederecruited in reverse order if the force is togradually decline. This holds true for mostmovements, but there is the ability to in-crease firing rate of large motor units with-in the size principle to move quickly or rap-idly build up forces (Bawa, 2002; Burke,1986). Have you ever picked up a light ob-ject (empty suitcase) when you expected aheavy one? If so, you likely activated manypools of large and small motor units imme-diately and nearly threw the object.Athletes in events requiring high rates offorce development (jumping, throwing)will need to train their ability to overridethe size principle and activate many motorunits rapidly. There are also many otherfactors that complicate the interpretationthat the size principle is an invariant in mo-tor control (Enoka, 2002). One example isthat recruitment tends to be patterned forspecific movements (Desmedt & Godaux,1977; Sale, 1987), so the hamstring musclesmay not be recruited the same in a jump,squat, or knee flexion exercise. Activationof muscles also varies across the kinds ofmuscle actions (Enoka, 1996; Gandevia,1999; Gielen, 1999) and can be mediated byfatigue and sensory feedback (Enoka, 2002).

Firing rate or rate coding is the repeatedstimulation of a particular motor unit overtime. To create the muscle forces for normalmovements, the frequency (Hz) that motorunits are usually rate coded is between 10and 30 Hz, while FG motor units have afaster relaxation time and can be rate codedbetween 30 and 60 Hz (Sale, 1992). The re-



Figure 4.17. Schematic of the differences in the size of motor units. Typical twitch response, size of the motornerve, and typical recruitment are illustrated.

Interdisciplinary Issue:The Control of Movement

With hundreds of muscles, each with hundreds of motor units that must be repeatedly stim-ulated, to coordinate in a whole-body movement, can the brain centrally control all thosemessages? If the brain could send all those messages in a preprogrammed fashion, could italso monitor and evaluate efferent sensory and proprioceptive information and adjust themovement? Early motor learning research and theory focused on the brain's central controlof movement or a motor program. More recent research is based on a Bernstein or dynam-ical systems perspective (Feldman, Levin, Mitnitski, & Archambault, 1998; Schmidt & Wrisberg,2000), where more general control strategies interact with sensory feedback. Since kineticvariables (torques, forces, EMG) can be measured or calculated using biomechanics, manymotor control scholars are interested in looking at these variables to uncover clues as tohow movement is coordinated and regulated. Some biomechanists are interested in the con-trol of movement, so here is an ideal area for interdisciplinary research.

peated stimulation of a motor unit increas-es the twitch force above the level of a sin-gle twitch (up to 10 times) because the ten-sion in the fibers begins at a higher level,before the decay or relaxation in tension.Since recruitment tends to be asynchronousand firing rates vary with motor unit size,the twitches of the motor units in a wholemuscle combine and fill in variations, re-sulting in smooth changes in tension. Whenmuscle is artificially stimulated for researchor training purposes to elicit maximal force,the frequency used is usually higher than60 Hz to make sure that motor unit twitch-es fuse into a tetanus. A tetanus is the sum-mation of individual twitches into a smoothincrease in muscle tension.

Both recruitment and firing rate have adramatic influence on the range of muscleforces that can be created. How recruitmentand firing rate interact to increase muscleforces is quite complex, but it appears thatrecruitment dominates for forces up to 50%of maximum with increasing importance offiring rate (Enoka, 2002). The combined ef-fect of recruitment and firing rate of motorunits is reflected in the size, density, andcomplexity of the eletromyographic (EMG)signal. Special indwelling EMG electrodetechniques are used to study the recruit-ment of individual motor units (Basmajian& DeLuca, 1985).

Recall that in chapter 3 we learned howEMG research has shown that at the wholemuscle level muscles are activated to incomplex synergies to achieve movementor stabilization tasks. Muscles are activatedin short bursts that coordinate with otherforces (external and segmental interactions)to create human movement. Figure 4.18shows the lower extremity muscle activa-tion in several pedal strokes in cycling.Compare the pattern of activation inFigures 4.13 and 4.18. Physical medicineprofessionals often take advantage of thisflexibility of the neuromuscular system bytraining muscle actions that compensate for


Application: NeuromuscularTraining

Unfortunately, athletes are often stereo-typed as dumb jocks with gifted physicalabilities. How much of movement abilitydo physical characteristics like muscularstrength, speed, and coordination con-tribute to performance compared to neu-romuscular abilities (a good motor brain)?Think about the ability your favorite athletewould have if he/she had a stroke that af-fected part of their motor cortex. In train-ing and conditioning there are several areasof research where there is evidence thatthe effects of training on muscle activationby the central nervous system is underrat-ed. First, it is well known that the majorityof the initial gains in strength training (firstmonth) are related to the neural driverather than hypertrophy (see Sale 1992).Second, it is known that both normal andinjured subjects are not usually able toachieve true maximum muscle force in amaximal voluntary contraction. This iscalled muscle inhibition and is studiedusing an electrical stimulation methodcalled twitch interpolation technique(Brondino, Suter, Lee, & Herzog, 2002).Another area of neuromuscular researchrelates to the inability to express bilateralmuscular strength (both arms or legs) equalto the sum of the unilateral strength ofeach extremity.This phenomenon has beencalled the bilateral deficit but the decre-ments (3–20%) are not always observed(Jakobi & Cafarelli, 1998). Interest in thebiomechanics of the vertical jump has madethis movement a good model for examininga potential bilateral deficit (Challis, 1998).How might a professional try to differenti-ate true differences in muscular strengthbetween sides of the body and a bilateraldeficit? If there truly is a bilateral deficitthat limits the neuromuscular activation oftwo extremities, how should you train forbilateral movements (bilaterally, stronger orweaker limb)?

physical limitations from disease or injury.Motor learning scholars are interested inEMG and the activation of muscles as cluesto neuromuscular strategies in learningmovements. While there has not been ex-tensive research in this area, it appears thatchanges in EMG with practice/training de-pend on the nature of the task (Gabriel &Boucher, 2000). As people learn submaxi-mal movements, the duration of EMGbursts decrease, there are decreases in ex-traneous and coactivation of muscles, and areduction in EMG magnitude as the bodylearns to use other forces (inertial and grav-itational) to efficiently create the movement

(Englehorn, 1983; Moore & Marteniuk,1986; Newell, Kugler, van Emmerick, &McDonald, 1989). Maximal-effort move-ments are believed to be more reliant onchanges in the magnitude and rise time ofactivation, than the duration of muscle acti-vation (Gottlieb, Corcos, & Agarwal, 1989).In maximal high-speed movements, themagnitude and rate of increase in activationtends to increase (Corcos, Jaric, Agarwal, &Gottlieb, 1993; Darling & Cooke, 1987;Gabriel & Boucher, 2000) with practice. Theactivation and cooperative actions of mus-cles to create skilled human movement arevery complex phenomena.


Figure 4.18. Raw EMG of leg muscles in cycling. The position of top dead center (vertical pedal position: T) is in-dicated by the line. Reprinted from Laplaud et al., Journal of Electromyography and Kinesiology © (2006), withpermission from Elsevier.

Proprioception of Muscle Actionand Movement

Considerable information about the bodyand its environment are used in the regula-tion of many movements. While personsuse all their senses to gather informationabout the status or effectiveness of theirmovements, there are musculoskeletal re-ceptors that provide information to thebrain to help produce movement. These re-ceptors of information about the motionand force in muscles and joints are calledproprioceptors. While we usually do notconsciously attend to this information, thisinformation and the various reflexes theyinitiate are important in the organization ofmovement. A reflex is an involuntary re-sponse initiated by some sensory stimulus.Reflexes are only initiated if the sensorystimulus is above some threshold.

There are many proprioceptive recep-tors that monitor aspects of movement.Information about joint position is provid-ed by four kinds of receptors. The vestibu-lar system of the inner ear provides infor-mation about the head's orientation withrespect to gravity. This section will summa-rize the important MTU proprioceptorsthat provide information on muscle length(muscle spindles) and force (Golgi tendonorgans). Human movement performancerelies on an integration of all sensory or-gans, and training can be quite effective inutilizing or overriding various sensory orreflex responses. A dancer spinning in thetransverse plane prevents dizziness (frommotion in inner ear fluid) by spotting—ro-tating the neck opposite to the spin to keepthe eyes fixed on a point followed by aquick rotation with the spin so as to findthat point again. Athletes in “muscularstrength” sports not only train their muscletissue to shift the Force–Velocity Rela-tionship upward, they train their centralnervous system to activate more motor

units and override the inhibitory effect ofGolgi tendon organs.

When muscle is activated, the tensionthat is developed is sensed by Golgi tendonorgans. Golgi tendon organs are located atthe musculotendinous junction and havean inhibitory effect on the creation of ten-sion in the muscle. Golgi tendon organsconnect to the motor neurons of that mus-cle and can relax a muscle to protect it fromexcessive loading. The intensity of this au-togenic inhibition varies, and its functionalsignificance in movement is controversial(Chalmers, 2002). If an active muscle wereforcibly stretched by an external force, theGolgi tendon organs would likely relax thatmuscle to decrease the tension and protectthe muscle. Much of high speed and highmuscular strength performance is trainingthe central nervous system to override thissafety feature of the neuromuscular system.The rare occurrence of a parent lifting partof an automobile off a child is an extremeexample of overriding Golgi tendon organinhibition from the emotion and adrena-line. The action of Golgi tendon organs isalso obvious when muscles suddenly stopcreating tension. Good examples are thecollapse of a person's arm in a close wristwrestling match (fatigue causes the personto lose the ability to override inhibition) orthe buckling of a leg during the great load-ing of the take-off leg in running jumps.

Muscle spindles are sensory receptorslocated between muscle fibers that sensethe length and speed of lengthening orshortening. Muscle spindles are sensitive tostretch and send excitatory messages to ac-tivate the muscle and protect it fromstretch-related injury. Muscle spindles aresensitive to slow stretching of muscle, butprovide the largest response to rapidstretches. The rapid activation of a quicklystretched muscle (100–200 ms) from musclespindles is due to a short reflex arc. Musclespindle activity is responsible for this myo-


tatic reflex or stretch reflex. Use of a smallrubber reflex hammer by physicians allowsthem to check the stretch reflex responsesof patients. The large numbers of spindlesand their innervation allows them to be sen-sitive and reset throughout the range of mo-tion. Recall that a stretch reflex is one possi-ble mechanism for the benefit of an SSC.Stretch reflexes may contribute to the eccen-tric braking action of muscles in follow-throughs. In performing stretching exercis-es, the rate of stretch should be minimizedto prevent activation of muscle spindles.

The other important neuromuscular ef-fect of muscle spindles is inhibition of theantagonist (opposing muscle action) mus-cle when the muscle of interest is shorten-ing. This phenomenon is call reciprocal in-hibition. Relaxation of the opposing mus-cle of a shortening muscle contributes to ef-ficient movement. In lifting a drink to yourmouth the initial shortening of the bicepsinhibits triceps activity that would makethe biceps work harder than necessary.Reciprocal inhibition is often overridden bythe central nervous system when coactiva-tion of muscles on both sides of a joint isneeded to push or move in a specific direc-tion. Reciprocal inhibition also plays a rolein several stretching techniques designed to

utilize neuromuscular responses to facili-tate stretching. The contract–relax–ago-nist–contract technique of proprioceptiveneuromuscular facilitation (PNF) is de-signed to use reciprocal inhibition to relaxthe muscle being stretched by contractingthe opposite muscle group (Hutton, 1993;Knudson, 1998). For example, in stretchingthe hamstrings, the stretcher activates thehip flexors to help relax the hip extensorsbeing stretched. The intricacies of proprio-ceptors in neuromuscular control (Enoka,2002; Taylor & Prochazka, 1981) are rele-vant to all movement professionals, but areof special interest to those who deal withdisorders of the neuromuscular system(e.g., neurologists, physical therapists).

SUMMARY

Forces applied to the musculoskeletal sys-tem create loads in these tissues. Loads arenamed based on their direction and line ofaction relative to the structure. Several me-chanical variables are used to document themechanical effect of these loads on thebody. How hard forces act on tissue is me-chanical stress, while tissue deformation ismeasured by strain. Simultaneous meas-urement of force applied to a tissue and itsdeformation allow biomechanists to deter-mine the stiffness and mechanical strengthof biological specimens. Musculoskeletaltissues are viscoelastic. This means thattheir deformation depends on the rate ofloading and they lose some energy (hys-teresis) when returning to normal shape.Bones are strongest in compression, whileligaments and tendon are strongest in ten-sion. Three major mechanical characteris-tics of muscle that affect the tension skeletalmuscles can create are the force–velocity,force–length, and force–time relationships.An important neuromuscular strategy usedto maximize the initial muscle forces in


Interdisciplinary Issue:Muscle Inhibition and Disinhibition

The neuromuscular aspects of training and de-training are fertile areas for the cooperation ofscholars interested in human movement. Re-habilitation (physical therapists, athletic train-ers, etc.) and strength and conditioning profes-sionals, as well as neurophysiologists, and bio-mechanists all might be involved in understand-ing the inhibition of muscle activation followingan injury. They might also collaborate on re-search questions if the neuromuscular changesin strength development are similar in strengthredevelopment following injury and disuse.

most movements is the rapid reversal of acountermovement with an eccentric muscleaction into a concentric action. This strategyis called the stretch-shortening cycle. Thecreation of muscular force is controlled byrecruitment of motor units and modulatingtheir firing rate. Several musculotendonproprioceptors provide length and tensioninformation to the central nervous systemto help regulate muscle actions. TheForce–Time Principle is the natural applica-tion of the mechanical characteristics ofmuscle. The timing of force application is asimportant as the size of the forces the bodycan create. In most movement, increasingthe time of force application can enhancesafety, but kinesiology professionals mustbe aware of how this principle interactswith other biomechanical principles. Theapplication of biomechanical principles isnot easy, because they interact with eachother and also with factors related to thetask, individual differences, or the move-ment environment.

REVIEW QUESTIONS

1. What are the major kinds of mechan-ical loads experienced by muscle, tendon,and bone?

2. What are the mechanical variablesthat can be determined from a load-defor-mation curve, and what do they tell usabout the response of a material to loading?

3. Compare and contrast the mechani-cal strength of muscle, tendon, ligamentsand bone. How does this correspond to theincidence of various musculoskeletal in-juries?

4. How does the passive behavior of themuscletendon unit affect the prescription ofstretching exercises?

5. What are the functional implicationsof the Force–Velocity Relationship of skele-tal muscle for strength training?

6. Use the Force–Length Relationship todescribe how the active and passive com-ponents of muscle tension vary in the rangeof motion.

7. Compare and contrast the Force–Time Relationship of muscle with theForce–Time Principle of biomechanics.

8. When might increasing the time offorce application not benefit the develop-ment of movement speed and why?

9. How does the brain control muscleforce and how is muscle fiber type related?

10. What is the stretch-shortening cycleand in what kinds of movements is it mostimportant?

11. What are the two major propriocep-tors in muscle that monitor length andforce?

12. How can range of motion in amovement be defined?

13. Explain how range of motion affectsthe speed, accuracy and force potential ofmovement. Give an example of when theRange of Motion Principle is mediated byother mechanical factors.

14. What biomechanical properties helpcontribute to the beneficial effect of contin-uous passive movement therapy (i.e., theslow, assisted motion of an injured limb)following surgery?

15. Write a complete description of astretching or conditioning exercise. Identifythe likely muscle actions and forces con-tributing to the movement.

KEY TERMS

bendingcreepcompressiondegrees of freedomelectromechanical delayenergy (mechanical)firing rate(rate coding)force–length relationship


force–time relationship(see electromechanical delay)

force–velocity relationshiphysteresisisokineticloadmotor unitmyotatic reflexreciprocal inhibitionrecruitmentshearstrainstrength (mechanical)stressstress fracturestress relaxationstretch-shortening cycletetanusthixotropytorsionviscoelasticWolff's LawYoung's modulus

SUGGESTED READING

Alexander, R. M. (1992). The human machine.New York: Columbia University Press.

Biewener, A. A., & Roberts, T. J. (2000). Muscleand tendon contributions to force, work, andelastic energy savings: a comparative perspec-tive. Exercise and Sport Sciences Reviews, 28,99–107.

Enoka, R. (2002). The neuromechanical basis ofhuman movement (3rd ed.). Champaign, IL:Human Kinetics.

De Luca, C. J. (1997). The use of surface elec-tromyography in biomechanics. Journal of Ap-plied Biomechanics, 13, 135–163.

Fung, Y. C. (1981). Biomechanics: Mechanicalproperties of living tissues. New York: Springer-Verlag.

Guissard, N., & Duchateau, J. (2006). Neuralaspects of muscle stretching. Exercise and SportSciences Reviews, 34, 154–158.

Gulch, R. W. (1994). Force–velocity relations inhuman skeletal muscle. International Journal ofSports Medicine, 15, S2–S10.

Kawakami, Y., & Fukunaga, T. (2006). New in-sights into in vivo human skeletal muscle func-tion. Exercise and Sport Sciences Reviews, 34,16–21.

Komi, P. V. (Ed.). (1992). Strength and power insport. London: Blackwell Scientific Publica-tions.

Latash, M. L., & Zatsiorsky, V. M. (Eds.) (2001).Classics in movement science. Champaign, IL:Human Kinetics.

Lieber, R. L., & Bodine-Fowler, S. C. (1993).Skeletal muscle mechanics: Implications for re-habilitation. Physical Therapy, 73, 844–856.

Moritani, T., & Yoshitake, Y. (1998). The use ofelectromyography in applied physiology. Jour-nal of Electromyography and Kinesiology, 8, 363–381.

Meyers, D. C., Gebhardt, D. L., Crump, C. E.,& Fleishman, E. A. (1993). The dimensionsof human physical performance: factor analy-sis of strength, stamina, flexibility, and bodycomposition measures. Human Performance, 6,309–344.

Nordin, M., & Frankel, V. (2001). Basic biome-chanics of the musculoskeletal system (3rd ed.).Baltimore: Williams & Wilkins.

Panjabi, M. M., & White, A. A. (2001).Biomechanics in the musculoskeletal system. NewYork: Churchill Livingstone.

Patel, T. J., & Lieber, R. L. (1997). Force trans-mission in skeletal muscle: From actomyosin toexternal tendons. Exercise and Sport SciencesReviews, 25, 321–364.

Rassier, D. E., MacIntosh, B. R., & Herzog, W.(1999). Length dependence of active force pro-


duction in skeletal muscle. Journal of AppliedPhysiology, 86, 1445–1457.

Scott, W., Stevens, J., & Binder-Macleod, S. A.(2001). Human skeletal muscle fiber type clas-sifications. Physical Therapy, 81, 1810–1816.

Vogel, S. (2001). Prime mover: a natural history ofmuscle. New York: W.W. Norton & Co.

Whiting, W. C., & Zernicke, R. F. (1998).Biomechanics of musculoskeletal injury. Cham-paign, IL: Human Kinetics.

Zatsiorksy, V. M., & Kraemer, W. J. (2006).Science and practice of strength training, 2d ed.Champaign, IL: Human Kinetics.

Zernicke, R.F., & Schneider, K. (1993).Biomechanics and developmental neuromotorcontrol. Child Development, 64, 982-1004.


WEB LINKS

Electromyography (EMG) papers by Carlo DeLuca.http://www.delsys.com/KnowledgeCenter/Tutorials.html

MSRC—Musculoskeletal Research Center at the University of Pittsburgh focuses on the mechanical response of tissues to forces.

http://www.pitt.edu/~msrc/

ISEK Standards—International Society for Electrophysiological Kinesiology standards for reporting EMG research.

http://http://isek-online.org/standards.html

Muscle Physiology Online—UC San Diego website with a comprehensive review of physiological and biomechanical aspects of muscle. See the macroscopic structure and muscle–joint interactions.

http://muscle.ucsd.edu/index.html

Orthopaedic Information— American Academy of Orthopaedic Surgeons website forpatient information.

http://orthoinfo.aaos.org/

Visible Human Project—National Institutes of Health human body imaging project.http://www.nlm.nih.gov/research/visible/visible_human.html

PARTIIIMECHANICAL BASES

Mechanics is the branch of phy-sics that measures the motion ofobjects and explains the causes ofthat motion. The images herepresent illustrations of the kine-matic and kinetic branches of bio-mechanics. Measurement of thethree-dimensional motion of agolfer provides a precise kinemat-ic description of the golf swing.The angular velocities of key bodysegments are plotted in the graph.The representation of the orienta-tion of the key segments of the legand the resultant force applied bythe foot to the pedal of an exercisebike represents the kinetics, or theforces that cause human move-ment. A knowledge of the me-chanics of exercise movements al-lows kinesiology professionals tounderstand those movements, de-velop specific training exercises,and change movement techniqueto improve performance. Thechapters in part III introduce youto three key areas of this parentdiscipline of biomechanics: kine-matics, kinetics, and fluid me-chanics. The related lab activitiesexplore qualitative and quantita-tive analyses of key mechanicalvariables important in under-standing human movement.

Golf illustration provided courtesyof Skill Technologies Inc., Phoenix,AZ—www.skilltechnologies.com.

105

Kinematics is the accurate description ofmotion and is essential to understandingthe biomechanics of human motion. Kine-matics can range from anatomical descrip-tions of joint rotations to precise mathemat-ical measurements of musculoskeletal mo-tions. Recall from chapter 2 that kinematicsis subdivided according to the kinds ofmeasurements used, either linear or angu-lar. Whatever the form of measurement,biomechanical studies of the kinematics ofskilled performers provide valuable infor-mation on desirable movement technique.Biomechanics has a long history of kine-matic measurements of human motion(Cappozzo, Marchetti, & Tosi, 1990). Accu-rate kinematic measurements are some-times used for the calculation of more com-plex, kinetic variables. This chapter will in-troduce key kinematic variables in docu-menting both linear and angular humanmotions. The principles of biomechanicsthat apply kinematics to improving humanmovement are Optimal Projection and theCoordination Continuum.

LINEAR MOTION

Motion is change in position with respect tosome frame of reference. In mathematicalterms, linear motion is simple to define: fi-nal position minus initial position. The sim-plest linear motion variable is a scalarcalled distance (l). The use of the symbol lmay be easy to remember if you associate itwith the length an object travels irrespec-

tive of direction. Typical units of distanceare meters and feet. Imagine an outdoor ad-venturer leaves base camp and climbs for 4hours through rough terrain along the pathillustrated in Figure 5.1. If her final positiontraced a 1.3-km climb measured relative tothe base camp (0 km) with a pedometer, thedistance she climbed was 1.3 km (final po-sition – initial position). Note that 1.3 km(kilometers) is equal to 1300 meters. Theodometer in your car works in a similarfashion, counting the revolutions (angularmotion) of the tires to generate a measure-ment of the distance (linear variable) thecar travels. Because distance is a scalar,your odometer does not tell you in what di-rection you are driving on the one-waystreet!

The corresponding vector quantity todistance is displacement (d). Linear dis-placements are usually defined relative toright-angle directions, which are convenientfor the purpose of the analysis. For mosttwo-dimensional (2D) analyses of humanmovements, like in Figure 5.1, the directionsused are horizontal and vertical, so displace-ments are calculated as final position minusinitial position in that particular direction.The usual convention is that motions to theright on the x-axis and upward along the y-axis are positive, with motion in the oppositedirections negative. Since displacement is avector quantity, if motion upward and to theright is defined as positive, motion down-ward and motion to the left is a negative dis-placement. Recall that the sign of a numberin mechanics refers to direction.

CHAPTER 5

Linear and AngularKinematics

107

Assuming Figure 5.1 is drawn to thescale shown, it looks like the climber had apositive 0.8 km of horizontal displacementand 0.7 km of vertical displacement. Thiseyeballing of the horizontal and verticalcomponents of the hike will be fairly accu-rate because displacement is a vector.Vectors can be conveniently represented bycombinations of right-angle components,like the horizontal and vertical displace-ments in this example. If our adventurerwere stranded in a blizzard and a helicop-ter had to lower a rescuer from a height of0.71 km above base camp, what would bethe rescuer's vertical displacement to theclimber? The vertical displacement of therescuer would be –0.01 km or 100 meters(final vertical position minus initial verticalposition or 0.7 km – 0.71 km).

Biomechanists most often use measuresof displacement rather than distance be-cause they carry directional informationthat is crucial to calculation of otherkinematic and kinetic variables. There area couple of subtleties to these examples.First, the analysis is a simple 2D model oftruly 3D reality. Second, the human body ismodeled as a point mass. In other words,we know nothing about the orientation ofthe body or body segment motions; we justconfine the analysis to the whole body massacting at one point in space. Finally, anabsolute frame of reference was used, whenwe are interested in the displacement rela-tive to a moving object—like the helicopter,a relative frame of reference can be used.

In other biomechanical studies of hu-man motion the models and frames of ref-


Figure 5.1. An outdoor adventurer climbs from base camp to a camp following the illustrated path. The distancethe climber covers is 1.3 km. Her displacement is 0.8 km horizontally and 0.7 km vertically.

erence can get quite complicated. Theanalysis might not be focused on whole-body movement but how much a muscle isshortening between two attachments. Athree-dimensional (3D) analysis of thesmall accessory gliding motions of the kneejoint motion would likely measure alonganatomically relevant axes like proximal-distal, medio-lateral, and antero-posterior.Three-dimensional kinematic measure-ments in biomechanics require considerablenumbers of markers, spatial calibration,and mathematical complexity for comple-tion. Degrees of freedom represent thekinematic complexity of a biomechanicalmodel. The degrees of freedom (dof) corre-spond to the number of kinematic measure-ments needed to completely describe theposition of an object. A 2D point mass mod-el has only 2 dof, so the motion of the objectcan be described with an x (horizontal) anda y (vertical) coordinate.

The 3D motion of a body segment has 6dof, because there are three linear coordi-nates (x, y, z) and three angles (to define theorientation of the segment) that must bespecified. For example, physical therapylikes to describe the 6 dof for the lower legat the knee joint using using the termsarthrokinematics (three anatomical rota-tions) and osteokinematics (three smallgliding or linear motions between the twojoint surfaces). The mathematical complexi-ty of 3D kinematics is much greater thanthe 2D kinematics illustrated in this text.Good sources for a more detailed descrip-tion of kinematics in biomechanics areavailable (Allard, Stokes, & Blanchi, 1995;Zatsiorsky, 1998). The field of biomechanicsis striving to develop standards for report-ing joint kinematics so that data can be ex-changed and easily applied in various pro-fessional settings (Wu & Cavanagh, 1995).

The concept of frame of reference is, inessence, where you are measuring or ob-serving the motion from. Reference framesin biomechanics are either absolute or rela-

tive. An absolute or global frame of refer-ence is essentially motionless, like the ap-parent horizontal and vertical motion weexperience relative to the earth and its grav-itational field (as in Figure 5.1). A relativeframe of reference is measuring from apoint that is also free to move, like the mo-tion of the foot relative to the hip or theplant foot relative to the soccer ball. There isno one frame of reference that is best, be-cause the biomechanical description that ismost relevant depends on the purpose ofthe analysis.

This point of motion being relative toyour frame of reference is important forseveral reasons. First, the appearance andamount of motion depends on where themotion is observed or measured from. Youcould always answer a question about adistance as some arbitrary number from an“unknown point of reference,” but the ac-curacy of that answer may be good for onlypartial credit. Second, the many ways todescribe the motion is much like the differ-ent anatomical terms that are sometimesused for the identical motion. Finally, this isa metaphor for an intellectually mature ki-nesiology professional who knows there isnot one single way of seeing or measuringhuman motion because your frame of refer-ence affects what you see. The next sectionwill examine higher-order kinematic vari-ables that are associated with the rates ofchange of an object's motion. It will be im-portant to understand that these new vari-ables are also dependent on the model andframe of reference used for their calcula-tion.

Speed and VelocitySpeed is how fast an object is moving with-out regard to direction. Speed is a scalarquantity like distance, and most peoplehave an accurate intuitive understanding ofspeed. Speed (s) is defined as the rate ofchange of distance (s = l/t), so typical unitsare m/s, ft/s, km/hr, or miles/hr. It is very

CHAPTER 5: LINEAR AND ANGULAR KINEMATICS 109

important to note that our algebraic short-hand for speed (l/t), and other kinematicvariables to come, means “the change in thenumerator divided by the change in the de-nominator.” This means that the calculatedspeed is an average value for the time inter-val used for the calculation. If you went jog-ging across town (5 miles) and arrived atthe turn-around point in 30 minutes, youraverage speed would be (5 miles / 0.5hours), or an average speed of 10 miles perhour. You likely had intervals where youran faster or slower than 10 mph, so we willsee how representative or accurate the kine-matic calculation is depends on the size oftime interval and the accuracy of your lin-ear measurements.

Since biomechanical studies have usedboth the English and metric systems ofmeasurements, students need to be able toconvert speeds from one system to the oth-er. Speeds reported in m/s can be convert-ed to speeds that make sense to Americandrivers (mph) by essentially doubling them(mph = m/s • 2.23). Speeds in ft/s can beconverted to m/s by multiplying by 0.30,and km/hour can be converted to m/s bymultiplying by 0.278. Other conversion fac-

tors can be found in Appendix B. Table 5.1lists some typical speeds in sports and oth-er human movements that have been re-ported in the biomechanics literature.Examine Table 5.1 to get a feel for some ofthe typical peak speeds of human move-ment activities.

Be sure to remember that speed is alsorelative to frame of reference. The motion of


Table 5.1TYPICAL PEAK SPEEDS IN HUMAN MOVEMENT

Speedm/s mph

Bar in a bench press 0.25 0.6

Muscle shortening 0.5 1.1

Walking 1.1–1.8 2.5–4.0

Vertical jump 2.3 5.1

Free throw 7.0 15.7

Sprinting 12.0 26.8

Tennis forehand 20.0 44.6

Batting 31.3 70.0

Soccer kick 35.0 78.0

Baseball pitch 45.1 101

Tennis serve 62.6 140

Golf drive 66.0 148

Application: Speed

One of the most important athletic abilities inmany sports is speed. Coaches often quip that“luck follows speed” because a fast athlete canarrive in a crucial situation before their oppo-nent. Coaches that often have a good under-standing of speed are in cross-country andtrack.The careful timing of various intervals ofa race, commonly referred to as pace, can beeasily converted average speeds over that in-terval. Pace (time to run a specific distance) canbe a good kinematic variable to know, but itsvalue depends on the duration of the interval,how the athlete's speed changes over that in-terval, and the accuracy of the timing. How ac-curate do you think stopwatch measures oftime and, consequently, speed are in track?What would a two-tenths-of-a-second errormean in walking (200 s), jogging (100 s), orsprinting (30 s) a lap on a 220 m track? Averagespeeds for these events are 1.1, 2.2, and 7.3m/s, with potential errors of 0.1, 0.2, and 0.7%.Less than 1%! That sounds good, but whatabout shorter events like a 100-m dash or thehang time of a punt in football? American foot-ball has long used the 40-yard dash as a meas-ure of speed, ability, and potential for athletesdespite little proof of its value (see Maisel,1998). If you measured time by freezing andcounting frames of video (30 Hz), how muchmore accurate would a 40-meter dash timingbe? If the current world record for 100 m is9.79 seconds and elite runners cover 40 m(43.7 yards) out of the starting blocks in about4.7 seconds, should you believe media guidesthat say that a certain freshman recruit atBiomechanical State University ran the forty(40-yard dash) in 4.3 seconds?

the runner in Figure 5.2 can correctly be de-scribed as 8 meters per second (m/s), 1m/s, or –1.5 m/s. Runner A is moving 8m/s relative to the starting line, 1 m/sfaster than runner B, and 1.5 m/s slowerthan runner C. All are correct kinematic de-scriptions of the speed of runner A.

Velocity is the vector corresponding tospeed. The vector nature of velocity makesit more complicated than speed, so manypeople incorrectly use the words inter-changeably and have incorrect notionsabout velocity. Velocity is essentially thespeed of an object, in a particular direction.Velocity is the rate of change of displace-ment (V = d/t), so its units are the same asspeed, and are usually qualified by a direc-tional adjective (i.e., horizontal, vertical, re-sultant). Note that when the adjective “an-gular” is not used, the term velocity refers tolinear velocity. If you hear a coach say apitcher has “good velocity,” the coach is notusing biomechanical terminology correctly.A good question to ask in this situation is:“That's interesting. When and in what di-rection was the pitch velocity so good?”

The phrase “rate of change” is very im-portant because velocity defines howquickly position is changing in the specifieddirection (displacement). Most students

might recognize this phrase as the sameone used to describe the derivative or theslope of a graph (like the hand dynamome-ter example in Figure 2.4).

Remember to think about velocity as aspeed, but in a particular direction. A sim-ple example of the velocity of humanmovement is illustrated by the path (dottedline in Figure 5.3) of a physical educationstudent in a horizontal plane as he changesexercise stations in a circuit-training pro-gram. The directions used in this analysisare a fixed reference frame that is relevantto young students: the equipment axis andwater axis.

The student's movement from his ini-tial position (I) to the final position (F) canbe vectorially represented by displace-ments along the equipment axis (dE) andalong the water axis (dW). Note that the def-inition of these axes is arbitrary since thestudent must combine displacements inboth directions to arrive at the basketballsor a drink. The net displacements for thisstudent's movement are positive, becausethe final position measurements are largerthan the initial positions. Let's assume thatdE = 8 m and dW = 2 m and that the time ittook this student to change stations was 10seconds. The average velocity along the


Figure 5.2. The speed of runner A depends on the frame of reference of the measurement. Runner A can bedescribed as moving at 8 m/s relative to the track or –1.5 m/s relative to runner C.

water axis would be VW = dW/t = 2/10 =0.2 m/s. Note that the motion of most inter-est to the student is the negative displace-ment (–dW), which permits a quick trip tothe water fountain. The average velocityalong the equipment axis would be 0.8 m/s(VE = dL/t = 8/10). Right-angle trigonome-try can then be used to calculate the magni-tude and direction of the resultant displace-ment (dR) and then the average velocity ofthe student. We will use right-angletrigonometry in chapter 6 to analyze the ef-fect of force vectors. By the way, if yourright-angle trigonometry is a little rusty,check out appendix D for a refresher.

Calculations of speed and velocity us-ing algebra are average velocities over thetime interval used. It is important to realizethat the smaller the time interval the greaterthe potential accuracy of kinematic calcula-

tions. In the previous example, for instance,smaller time intervals of measurementwould have detected the negative velocity(to get a drink) and positive velocity of thestudent in the water direction. Biome-chanics research often uses high-speed filmor video imaging (Gruen, 1997) to makekinematic measurements over very smalltime intervals (200 or thousands of picturesper second). The use of calculus allows forkinematic calculations (v = dd/dt) to bemade to instantaneous values for any pointin time of interest. If kinematic calculationsare based over a too large time interval, youmay not be getting information much betterthan the time or pace of a whole race, oryou may even get the unusual result of zerovelocity because the race finished where itstarted.


Figure 5.3. The horizontal plane path (dashed line) of a physical education student changing practice stations. Thelinear displacements can be measured along a water fountain axis and equipment axis.

Graphs of kinematic variables versustime are extremely useful in showing a pat-tern within the data. Because human move-ment occurs across time, biokinematic vari-ables like displacement, velocity, and accel-eration are usually plotted versus time, al-though there are other graphs that are ofvalue. Figure 5.4 illustrates the horizontaldisplacement and velocity graphs for anelite male sprinter in a 100-m dash. Graphsof the speed over a longer race preciselydocument how the athlete runs the race.Notice that the athlete first approaches topspeed at about the 40- to 50-meter mark.You can compare your velocity profile toFigure 5.4 and to those of other sprinters inLab Activity 5.

Acceleration

The second derivative with respect to time,or the rate of change of velocity, is accelera-tion. Acceleration is how quickly velocity ischanging. Remember that velocity changeswhen speed or direction change. This vec-

tor nature of velocity and accelerationmeans that it is important to think of accel-eration as an unbalanced force in a particu-lar direction. The acceleration of an objectcan speed it up, slow it down, or change itsdirection. It is incorrect to assume that “ac-celeration” means an object is speeding up.The use of the term “deceleration” shouldbe avoided because it implies that the objectis slowing down and does not take into ac-count changes in direction.

Let's look at an example that illustrateswhy it is not good to assume the directionof motion when studying acceleration.Imagine a person is swimming laps, as il-lustrated in Figure 5.5. Motion to the rightis designated positive, and the swimmerhas a relatively constant velocity (zero hor-izontal acceleration) in the middle of thepool and as she approaches the wall. As herhand touches the wall there is a negativeacceleration that first slows her down andthen speeds her up in the negative direc-tion to begin swimming again. Thinking ofthe acceleration at the wall as a push in thenegative direction is correct throughout the


Figure 5.4. The displacement–time (dashed curve) and velocity–time (solid curve) graphs for the 100-m dash ofan elite male sprinter.

turn. As the swimmer touches the otherwall there is a positive acceleration that de-creases her negative velocity, and if shekeeps pushing (hasn't had enough exercise)will increase her velocity in the positive di-rection back into the pool.

The algebraic definition of acceleration(a) is V/t, so typical units of accelerationare m/s2 and ft/s2. Another convenientway to express acceleration is in units ofgravitational acceleration (g's). When youjump off a box you experience (in flight)one g of acceleration, which is about –9.81m/s/s or –32.2 ft/s/s. This means that, inthe absence of significant air resistance,your vertical velocity will change 9.81 m/severy second in the negative direction.Note that this means you slow down 9.81m/s every second on the way up and speedup 9.81 m/s every second on the waydown. G's are used for large accelerationevents like a big change of direction on aroller coaster (4 g's), the shockwaves in thelower leg following heel strike in running

(5 g's), a tennis shot (50 g's), or head acceler-ation in a football tackle (40–200 g's). Whena person is put under sustained (severalseconds instead of an instant, like the previ-ous examples) high-level acceleration likein jet fighters (5–9 g's), pilots must a wearpressure suit and perform whole-body iso-metric muscle actions to prevent blackingout from the blood shifting in their body.

Acceleration due to gravity always actsin the same direction (toward the center ofthe earth) and may cause speeding up orslowing down depending on the directionof motion. Remember to think of accelera-tion as a push in a direction or a tendency tochange velocity, not as speed or velocity.The vertical acceleration of a ball at peakflight in the toss of a tennis serve is 1 g, notzero. The vertical velocity may be instanta-neously zero, but the constant pull of gravi-ty is what prevents it from staying up there.

Let's see how big the horizontal acceler-ation of a sprinter is in getting out of theblocks. This is an easy example because the


Figure 5.5. The motion and accelerations of swimmers as they change direction in lap swimming. If motion to theright is designated positive, the swimmer experiences a negative acceleration as they make the turn at the poolwall. The negative acceleration first slows positive velocity, and then begins to build negative velocity to startswimming in the negative direction. It is important to associate signs and accelerations with directions.

rules require that the sprinter have an ini-tial horizontal velocity of zero. If videomeasurements of the sprinter showed thatthey passed the 10-m point at 1.9 secondswith a horizontal velocity of 7 m/s, whatwould be the runner's acceleration? Thesprinter's change in velocity was 7 m/s (7 –0), so the sprinter's acceleration was: a =V/t = 7/1.9 = 3.7 m/s/s. If the sprintercould maintain this acceleration for threeseconds, how fast would he be running?

Close examination of the displacement,velocity, and acceleration graphs of an ob-ject's motion is an excellent exercise in qual-itative understanding of linear kinematics.Examine the pattern of horizontal accelera-tion in the 100-m sprint mentioned earlier(see Figure 5.4). Note that there are essen-tially three phases of acceleration in thisrace that roughly correspond to the slope ofthe velocity graph. There is a positive accel-eration phase, a phase of near zero acceler-ation, and a negative acceleration phase.Most sprinters struggle to prevent runningspeed from declining at the end of a race.Elite female sprinters have similar velocitygraphs in 100-m races. What physiologicalfactors might account for the inability ofpeople to maintain peak speed in sprinting?

Note that the largest accelerations(largest rates of change of velocity) do notoccur at the largest or peak velocities. Peakvelocity must occur when acceleration iszero. Coaches often refer to quickness as theability to react and move fast over short dis-tances, while speed is the ability to covermoderate distances in a very short time.Based on the velocity graph in Figure 5.4,how might you design running tests to dif-ferentiate speed and quickness?

Acceleration is the kinematic (motiondescription) variable that is closest to a ki-netic variable (explanation of motion).Kinesiology professionals need to remem-ber that the pushes (forces) that create ac-celerations precede the peak speeds theyeventually create. This delay in the devel-

opment of motion is beyond the Fore–TimePrinciple mentioned earlier. Coaches ob-serving movement cannot see acceleration,but they can perceive changes in speed ordirection that can be interpreted as acceler-ation. Just remember that by the time thecoach perceives the acceleration the muscu-lar and body actions which created thoseforces occurred just before the motionchanges you are able to see.

Uniformly Accelerated Motion

In rare instances the forces acting on an ob-ject are constant and therefore create a con-stant acceleration in the direction of the re-sultant force. The best example of this spe-cial condition is the force of earth's gravityacting on projectiles. A projectile is an ob-ject launched into the air that has no self-propelled propelling force capability(Figure 5.6). Many human projectile move-ments have vertical velocities that are suffi-ciently small so that the effects of air resist-ance in the vertical direction can be ignored(see chapter 8). Without fluid forces in thevertical direction, projectile motion is uni-formly accelerated by one force, the force ofgravity. There are exceptions, of course(e.g., skydiver, badminton shuttle), but forthe majority of human projectiles we cantake advantage of the special conditions ofvertical motion to simplify kinematic de-scription of the motion. The Italian GalileoGalilei is often credited with discoveringthe nearly constant nature of gravitationalacceleration using some of the first accurateof measurements of objects falling androlling down inclines. This section willbriefly summarize these mathematical de-scriptions, but will emphasize several im-portant facts about this kind of motion, andhow this can help determine optimal anglesof projection in sports.

When an object is thrown or kickedwithout significant air resistance in the ver-


tical direction, the path or trajectory will besome form of a parabola. The uniform na-ture of the vertical force of gravity creates alinear change in vertical velocity and a sec-ond-order change in vertical displacement.The constant force of gravity also assuresthat the time it takes to reach peak verticaldisplacement (where vertical velocity isequal to zero) will be equal to the time ittakes for the object to fall to the same heightthat it was released from. The magnitude ofthe vertical velocity when the object fallsback to the same position of release will bethe same as the velocity of release. A golfball tossed vertically at shoulder height at10 m/s (to kill time while waiting to playthrough) will be caught at the same shoul-der level at a vertical velocity of –10 m/s.The velocity is negative because the motionis opposite of the toss, but is the same mag-nitude as the velocity of release. Thinkabout the 1 g of acceleration acting on this

golf ball and these facts about uniformly ac-celerated motion to estimate how many sec-onds the ball will be in flight.

This uniformly changing vertical mo-tion of a projectile can be determined at anygiven instant in time using three formulasand the kinematic variables of displace-ment, velocity, acceleration, and time. Myphysics classmates and I memorized theseby calling them VAT, SAT, and VAS. Thevarious kinematic variables are obvious, ex-cept for “S,” which is another commonsymbol for displacement. The final verticalvelocity of a projectile can be uniquely de-termined if you know the initial velocity(Vi) and the time of flight of interest (VAT:Vf

2 = Vi + at). Vertical displacement is alsouniquely determined by initial velocity andtime of flight (SAT: d = Vit + 0.5at2). Finally,final velocity can be determined from initialvelocity and a known displacement (VAS:Vf

2 = Vi2 + 2ad).


Figure 5.6. Softballs (left) and soccer balls (right) are projectiles because they are not self-propelled when thrownor kicked.

Let's consider a quick example of usingthese facts before we examine the implica-tions for the best angles of projecting ob-jects. Great jumpers in the NationalBasketball Association like Michael Jordanor David Thompson are credited withstanding vertical jumps about twice as high(1.02 m or 40 inches) as typical collegemales. This outstanding jumping ability isnot an exaggeration (Krug & LeVeau, 1999).Given that the vertical velocity is zero at thepeak of the jump and the jump height, wecan calculate the takeoff velocity of our elitejumper by applying VAS. Solving for Vi inthe equation:

Vf2 = Vi

2 + 2ad

0 = Vi2 + 2(–9.81)(1.002)

Vi = 4.47 m/s or 9.99 mph

We select the velocity to be positive whentaking the square root because the initialvelocity is opposite to gravity, which acts inthe negative direction. If we wanted to cal-culate his hang time, we could calculate thetime of the fall with SAT and double it be-cause the time up and time down are equal:

d = Vit + 0.5at2

–1.02 = 0 + 0.5(–9.81)t2

t = 0.456 s

So the total fight time is 0.912 seconds.If you know what your vertical jump is,you can repeat this process and compareyour takeoff velocity and hang time to thatof elite jumpers. The power of these empir-ical relationships is that you can use themathematics as models for simulations ofprojectiles. If you substitute in reasonablevalues for two variables, you get good pre-dictions of kinematics for any instant intime. If you wanted to know when a partic-

ular height was reached, what two equa-tions could you use? Could you calculatehow much higher you could jump if you in-creased your takeoff velocity by 10%?

So we can see that uniformly accelerat-ed motion equations can be quite useful inmodeling the vertical kinematics of projec-tiles. The final important point about uni-formly accelerated motion, which rein-forces the directional nature of vectors, isthat, once the object is released, the verticalcomponent of a projectile's velocity is inde-pendent of its horizontal velocity. The ex-treme example given in many physicsbooks is that a bullet dropped the same in-stant another is fired horizontally wouldstrike level ground at the same time. Givenconstant gravitational conditions, theheight of release and initial vertical veloci-ty uniquely determine the time of flight ofthe projectile. The range or horizontal dis-tance the object will travel depends on thistime of flight and the horizontal velocity.Athletes may increase the distance they canthrow by increasing the height of release(buying time against gravity), increasingvertical velocity, and horizontal velocity.The optimal combination of these dependson the biomechanics of the movement, notjust the kinematics or trajectory of uniform-ly accelerated motion. The next section willsummarize a few general rules that comefrom the integration of biomechanical mod-els and kinematic studies of projectile activ-ities. These rules are the basis for the Opti-mal Projection Principle of biomechanics.

OPTIMAL PROJECTIONPRINCIPLE

For most sports and human movements in-volving projectiles, there is a range of an-gles that results in best performance. TheOptimal Projection Principle refers to theangle(s) that an object is projected toachieve a particular goal. This section will


outline some general rules for optimal pro-jections that can be easily applied by coach-es and teachers. These optimal angles are“rules of thumb” that are consistent withthe biomechanical research on projectiles.Finding true optimal angles of projectionrequires integration of descriptive studiesof athletes at all ability levels (e.g., Bartlett,Muller, Lindinger, Brunner, & Morriss,1996), the laws of physics (like uniformlyaccelerated motion and the effects of air re-sistance; see chapter 8), and modeling stud-ies that incorporate the biomechanical ef-fects of various release parameters.Determining an exact optimal angle of pro-jection for the unique characteristics of aparticular athlete and in a particular envi-ronment has been documented using acombination of experimental data andmodeling (Hubbard, de Mestre, & Scott,2001). There will be some general trends orrules for teaching and coaching projectileevents where biomechanical research hasshown that certain factors dominate the re-sponse of the situation and favor certain re-lease angles.

In most instances, a two-dimensionalpoint-mass model of a projectile is used todescribe the compromise between theheight of release and the vertical and hori-zontal components of release velocity(Figure 5.7). If a ball was kicked and thenlanded at the same height, and the air re-sistance was negligible, the optimal angleof projection for producing maximum hor-izontal displacement would be 45º. Forty-five degrees above the horizontal is the per-fect mix of horizontal and vertical velocityto maximize horizontal displacement.Angles above 45º create shorter ranges be-cause the extra flight time from larger verti-cal velocity cannot overcome the loss inhorizontal velocity. Angles smaller than 45ºcause loss of flight time (lower vertical ve-locity) that cannot be overcome by the larg-er horizontal velocity. Try the activity be-low to explore optimal angles of projection.

Note how the optimal angle of projectionchanges from 45º when the height of releaseis above and below the target.


Figure 5.7. The three variables that determine the re-lease parameters of a projectile in two-dimensions:height of release, and the horizontal and vertical veloc-ities of release.

Activity:Angles of Projection

Use a garden hose to water the grass andtry various angles of projection of the wa-ter.The air resistance on the water shouldbe small if you do not try to project thewater too far. Experiment and find the an-gle that maximizes the distance the wateris thrown. First see if the optimal angle isabout 45º, when the water falls back tothe height that it comes out of the hose.What happens to the optimal angle dur-ing long-distance sprinkling as the heightof release increases?

Before we can look at generalizationsabout how these factors interact to applythe Optimal Projection Principle, the vari-ous goals of projections must be analyzed.The mechanical objectives of projectiles aredisplacement, speed, and a combination ofdisplacement and speed. The goal of anarcher is accuracy in displacing an arrow tothe target. The basketball shooter in Figure5.7 strives for the right mix of ball speedand displacement to score. A soccer goaliepunting the ball out of trouble in his end ofthe field focuses on ball speed rather thankicking the ball to a particular location.

When projectile displacement or accu-racy is the most important factor, the rangeof optimal angles of projection is small. Intennis, for example, Brody (1987) hasshown that the vertical angle of projection(angular “window” for a serve going in)depends on many factors but is usually lessthan 4º. The goal of a tennis serve is theright combination of displacement and ballspeed, but traditionally the sport and itsstatistics have emphasized the importanceof consistency (accuracy) so as to keep theopponent guessing. In a tennis serve theheight of projection above the target, thenet barrier, the spin on the ball, the objec-tive of serving deep into the service box,and other factors favor angles of projectionat or above the horizontal (Elliott, 1983).Elite servers can hit high-speed serves 3ºbelow the horizontal, but the optimal serv-ing angle for the majority of players is be-tween 0 and 15º above the horizontal(Elliott, 1983; Owens & Lee, 1969).

This leads us to our first generalizationof the Optimal Projection Principle. In mostthrowing or striking events, when a mix of max-imum horizontal speed and displacement are ofinterest, the optimal angle of projection tends tobe below 45º. The higher point of release anddramatic effect of air resistance on mostsport balls makes lower angles of releasemore effective. Coaches observing softballor baseball players throwing should look

for initial angles of release between 28 and40º above the horizontal (Dowell, 1978).Coaches should be able to detect the initialangle of a throw by comparing the initialflight of the ball with a visual estimate of45º angle (Figure 5.8). Note that there is alarger range of optimal or desirable anglesthat must accommodate differences in theperformer and the situation. Increasing theheight of release (a tall player) will tend toshift the optimal angle downward in therange of angles, while higher speeds of re-lease (gifted players) will allow higher an-gles in the range to be effectively used.What do you think would happen to theoptimal angles of release of a javelin giventhe height of release and speed of approachdifferences of an L5-disabled athlete com-pared to an able-bodied athlete?

There are a few exceptions to this gen-eralization, which usually occur due to thespecial environmental or biomechanicalconditions of an event. In long jumping, forexample, the short duration of takeoff onthe board limits the development of verti-cal velocity, so that takeoff angles are usual-ly between 18 and 23º (Hay, Miller, & Can-terna, 1986; Linthorne et al., 2005). In thestanding long jump, jumpers prefer slight-ly higher takeoff angles with relativelysmall decreases in performance (Wakai &Linthorne, 2005). We will see in chapter 8that the effect of air resistance can quicklybecome dominant on the optimal releaseparameters for many activities. In footballplace-kicking, the lower-than-45º general-ization applies (optimal angles are usuallybetween 25 and 35º), but the efficient waythe ball can be punted and the tactical im-portance of time during a punt make theoptimal angle of release about 50º. With thewind at the punter's back he might kickabove 50º, while using a flatter kick againsta wind. The backspin put on various golfshots is another example of variations inthe angle of release because of the desirableeffects of spin on fluid forces and the


bounce of the ball. Most long-distanceclubs have low pitches, which agrees withour principle of a low angle of release, buta golfer might choose a club with more loftin situations where he wants higher trajec-tory and spin rate to keep a ball on thegreen.

The next generalization relates to pro-jectiles with the goal of upward displace-ment from the height of release. The optimalangle of projection for tasks emphasizing dis-placement or a mix of vertical displacement andspeed tends to be above 45º. Examples of thesemovements are the high jump and basket-ball shooting. Most basketball players (notthe giants of the NBA) release a jump shotbelow the position of the basket.Considerable research has shown that theoptimal angle of projection for basketball

shots is between 49 and 55º (see Knudson,1993). This angle generally corresponds tothe arc where the minimum speed may beput on the ball to reach the goal, which isconsistent with a high-accuracy task.Ironically, a common error of beginningshooters is to use a very flat trajectory thatrequires greater ball speed and may noteven permit an angle of entry so that theball can pass cleanly through the hoop!Coaches that can identify appropriate shottrajectories can help players improve morequickly (Figure 5.9). The optimal angles ofrelease in basketball are clearly not “high-arc” shots, but are slightly greater than 45ºand match the typical shooting conditionsin recreational basketball.

The optimal angle of projection princi-ple involves several generalizations about


Figure 5.8. Coaches can visually estimate the initial path of thrown balls to check for optimal projection. The ini-tial path of the ball can be estimated relative to an imaginary 45° angle. When throwing for distance, many smallchildren select very high angles of release that do not maximize the distance of the throw.

desirable initial angles of projection. Thesegeneral rules are likely to be effective formost performers. Care must be taken in ap-plying these principles in special popula-tions. The biomechanical characteristics ofelite (international caliber) athletes orwheelchair athletes are likely to affect theoptimal angle of projection. Kinesiologyprofessionals should be aware that biome-chanical and environmental factors interactto affect the optimal angle of projection. Forexample, a stronger athlete might use anangle of release slightly lower than expect-ed but which is close to optimal for her. Herextra strength allows her to release the im-plement at a higher point without losingprojectile speed so that she is able to use a

slightly lower angle of release. Profes-sionals coaching projectile sports must keepup on the biomechanical research related tooptimal conditions for their athletes.

ANGULAR MOTION

Angular kinematics is the description ofangular motion. Angular kinematics is par-ticularly appropriate for the study of hu-man movement because the motion of mosthuman joints can be described using one,two, or three rotations. Angular kinematicsshould also be easy for biomechanics stu-dents because for every linear kinematicvariable there is a corresponding angularkinematic variable. It will even be easy todistinguish angular from linear kinematicsbecause the adjective “angular” or a Greekletter symbol is used instead of the Arabicletters used for linear kinematics.

Angular displacement (��: theta) is thevector quantity representing the change inangular position of an object. Angular dis-placements are measured in degrees, radi-ans (dimensionless unit equal to 57.3º), andrevolutions (360º). The usual convention tokeep directions straight and be consistentwith our 2D linear kinematic calculations isto consider counterclockwise rotations aspositive. Angular displacement measuredwith a goniometer is one way to measurestatic flexibility. As in linear kinematics,the frames of reference for these angularmeasurements are different. Some tests de-fine complete joint extension as 0º whileother test refer to that position as 180º. Fora review of several physical therapy staticflexibility tests, see Norkin & White (1995).

In analyzing the curl-up exerciseshown in Figure 5.10, the angle betweenthe thoracic spine and the floor is oftenused. This exercise is usually limited to thefirst 30 to 40º above the horizontal to limitthe involvement of the hip flexors(Knudson, 1999a). The angular displace-ment of the thoracic spine in the eccen-


Figure 5.9. The optimal projection angles for most bas-ketball jump shots are between 49 and 55° above thehorizontal (hatched). These initial trajectories repre-sent the right mix of low ball speed and a good angleof entry into the hoop. Novice shooters (N) oftenchoose a low angle of release. Skilled shooters (S) real-ly do not shoot with high arcs, but with initial trajecto-ries that are in the optimal range and tailored to theconditions of the particular shot.

tric phase would be –38º (final angle minusinitial angle: 0 – 38 = –38º). This trunk angleis often called an absolute angle because itis measured relative to an “unmoving”earth frame of reference. Relative anglesare defined between two segments that canboth move. Examples of relative angles inbiomechanics are joint angles. The knee an-gle (��K) in Figure 5.10 is a relative angle thatwould tell if the person is changing the po-sitioning of their legs in the exercise.

Angular Velocity

Angular velocity (��: omega) is the rate ofchange of angular position and is usuallyexpressed in degrees per second or radiansper second. The formula for angular veloci-ty is �� = ��/t, and calculations would be thesame as for a linear velocity, except the dis-placements are angular measurements.Angular velocities are vectors are drawn bythe right-hand rule, where the flexed fin-gers of your right hand represent the rota-tion of interest, and the extended thumbwould be along the axis of rotation andwould indicate the direction of the angular

velocity vector. This book does not give de-tailed examples of this technique, but willemploy a curved arrow just to illustrate an-gular velocities and torques (Figure 5.11).


Figure 5.10. The angular kinematics of a curl-up exercise can be measured as the angle between the horizontal anda thoracic spine segment. This is an example of an absolute angle because it defines the angle of an object relativeto external space. The knee joint angle (�K) is a relative angle because both the leg and thigh can move.

Figure 5.11. The average angular velocity of the firsthalf of a knee extension exercise can be calculated fromthe change in angular displacement divided by thechange in time.

The angular velocities of joints are par-ticularly relevant in biomechanics, becausethey represent the angular speed of ana-tomical motions. If relative angles are calcu-lated between anatomical segments, theangular velocities calculated can representthe speed of flexion/extension and otheranatomical rotations. Biomechanical re-search often indirectly calculates joint an-gles from the linear coordinates (measure-ments) derived from film or video images,or directly from electrogoniometers at-tached to subjects in motion. It is also use-ful for kinesiology professionals to beknowledgeable about the typical angularvelocities of joint movements. This allowsprofessionals to understand the similaritybetween skills and determine appropriatetraining exercises. Table 5.2 lists typicalpeak joint angular speeds for a variety ofhuman movements.

Let's calculate the angular velocity of atypical knee extension exercise and com-pare it to the peak angular velocity in thetable. Figure 5.11 illustrates the exercise andthe data for the example. The subject ex-tends a knee, taking their leg from a verticalorientation to the middle of the range ofmotion. If we measure the angle of the low-er leg from the vertical, the exerciser hasmoved their leg 40º in a 0.5-second periodof time. The average knee extension angu-lar velocity can be calculated as follows: ��K= ��/t = 40/0.5 = 80 deg/s. The angular ve-locity is positive because the rotation iscounterclockwise. So the exercise averages80º per second of knee extension velocityover the half-second time interval, but theinstantaneous angular velocity at the posi-tion shown in the figure is likely larger thanthat. The peak knee extension angular ve-locity in this exercise likely occurs in themidrange of the movement, and the kneeextension velocity must then slow to zeroat the end of the range of motion. This illus-trates some limitations of free-weight exer-cises. There is a range of angular velocities(which have an affect on the linearForce–Velocity Relationship of the mus-cles), and there must be a decrease in theangular velocity of the movement at theend of the range of motion. This negativeacceleration (if the direction of motion ispositive) protects the joints and ligaments,but is not specific to many events wherepeak speed is achieved near the release ofan object and other movements can gradu-ally slow the body in the follow-through.

Angular Acceleration

The rate of change of angular velocity is an-gular acceleration (�� = ��/t). Angular accel-eration is symbolized by the Greek letter al-pha (��). The typical units of angular accel-eration are deg/s/s and radians/s/s. Likelinear acceleration, it is best to think about


Table 5.2TYPICAL PEAK ANGULAR SPEEDS IN HUMAN

MOVEMENT

Speeddeg/s rad/s

Knee extension:sit-to-stand 150 2.6

Trunk extension:vertical jump 170 3.0

Elbow flexion:arm curl 200 3.5

Knee extension:vertical jump 800 14.0

Ankle extension:vertical jump 860 15.0

Wrist flexion:baseball pitching 1000 17.5

Radio/ulnar pronation:tennis serve 1400 24.4

Knee extension:soccer kick 2000 34.9

Shoulder flexion:softball pitch 5000 87.3

Shoulder internalrotation: pitching 7400 129.1

angular acceleration as an unbalanced ro-tary effect. An angular acceleration of –200rad/s/s means that there is an unbalancedclockwise effect tending to rotate the objectbeing studied. The angular acceleration ofan isokinetic dynamometer in the middleof the range of motion should be zero be-cause the machine is designed to match orbalance the torque created by the person, so

the arm of the machine should be rotatingat a constant angular velocity.

Angular kinematics graphs are particu-larly useful for providing precise descrip-tions of how joint movements occurred.Figure 5.12 illustrates the angular displace-ment and angular velocity of a simple el-bow extension and flexion movement in thesagittal plane. Imagine that the data repre-


Interdisciplinary Issue: Specificity

One of the most significant principles discovered by early kinesiology research is the principle ofspecificity. Specificity applies to the various components of fitness, training response, and motorskills. Motor learning research suggests that there is specificity of motor skills, but there is poten-tial transfer of ability between similar skills. In strength and conditioning the principle of specificitystates that the exercises prescribed should be specific, as close as possible to the movement thatis to be improved. Biomechanics research that measures the angular kinematics of various sportsand activities can be used to assess the similarity and potential specificity of training exercises.Given the peak angular velocities in Table 5.2, how specific are most weight training or isokineticexercise movements that are limited to 500º per second or slower? The peak speed of joint rota-tions is just one kinematic aspect of movement specificity. Could the peek speeds of joint rotationin different skills occur in different parts of the range of motion? What other control, learning, psy-chological, or other factors affect the specificity of an exercise for a particular movement?

Interdisciplinary Issue: Isokinetic Dynamometers

Isokinetic (iso = constant or uniform, kinetic = motion) dynamometers were developed by J.Perrine in the 1960s. His Cybex machine could be set at different angular velocities and would ac-commodate the resistance to the torque applied by a subject to prevent angular acceleration beyondthe set speed. Since that time, isokinetic testing of virtually every muscle group has become a wide-ly accepted measure of muscular strength in clinical and research settings. Isokinetic dynamometershave been influential in documenting the balance of strength between opposing muscle groups(Grace, 1985).There is a journal (Isokinetics and Exercise Science) and several books (e.g., Brown, 2000;Perrin, 1993) that focus on the many uses of isokinetic testing. Isokinetic machines, however, are nottruly isokinetic throughout the range of motion, because there has to be an acceleration to the setspeed at the beginning of a movement that often results in a torque overshoot as the machine neg-atively accelerates the limb (Winter,Wells, & Orr, 1981) as well as another negative acceleration atthe end of the range of motion.The effects of inertia (Iossifidou & Baltzopoulos, 2000), shifting of thelimb in the seat/restraints (Arampatzis et al., 2004), and muscular co-contraction (Kellis &Baltzopoulos, 1998) are other recent issues being investigated that affect the validity of isokinetictesting. It is important to note that the muscle group is not truly shortening or lengthening in an iso-kinetic fashion. Muscle fascicle-shortening velocity is not constant (Ichinose, Kawakami, Ito, Kanehisa,& Fukunaga, 2000) in isokinetic dynamometry even when the arm of the machine is rotating at a con-stant angular velocity.This is because linear motion of points on rotating segments do not directlycorrespond to angular motion in isokinetic (Hinson, Smith, & Funk, 1979) or other joint motions.


Figure 5.12. The angular displacement and angular velocity of a simple elbow extension/flexion movement tograb a book. See the text for an explanation of the increasing complexity of the higher-order kinematic variables.

sented a student tired of studying exercisephysiology, who reached forward to grab arefreshing, 48-ounce Fundamentals ofBiomechanics text. Note as we look at thekinematic information in these graphs thatthe complexity of a very simple movementgrows as we look at the higher-order deriv-atives (velocity).

The elbow angular displacement datashow an elbow extended (positive angulardisplacement) from about a 37º to about an146º elbow angle to grasp the book. The ex-tension movement took about 0.6 seconds,but flexion with the book occurred moreslowly. Since the elbow angle is defined onthe anterior aspect of a subject's arm, largernumbers mean elbow extension. The corre-sponding angular velocity–time graph rep-resents the speed of extension (positive ��)or the speed of flexion (negative ��). The el-bow extension angular velocity peaks atabout 300 deg/s (0.27 sec) and graduallyslows. The velocity of elbow flexion in-creases and decreases more gradually thanthe elbow extension.

The elbow angular acceleration wouldbe the slope of the angular velocity graph.Think of the elbow angular acceleration asan unbalanced push toward extension orflexion. Examine the angular velocitygraph and note the general phases of accel-eration. When are there general upward ordownward trends or changes in the angu-lar velocity graph? Movements like this of-ten have three major phases. The extensionmovement was initiated by a phase of pos-itive acceleration, indicated by an increas-ing angular velocity. The second phase is anegative acceleration (downward move-ment of the angular velocity graph) thatfirst slows elbow extension and then initi-ates elbow flexion. The third phase is asmall positive angular acceleration thatslows elbow flexion as the book nears theperson's head. These three phases of angu-lar acceleration correspond to typical mus-cle activation in this movement. This move-

ment would usually be created by a tri-phasic pattern of bursts from the elbow ex-tensors, flexors, and extensors. Accelera-tions (linear and angular) are the kinematicvariables closest to the causes (kinetics) ofthe motion, and are more complex thanlower-order kinematic variables like angu-lar displacements.

Figure 5.13 plots the ankle angle, angu-lar velocity, plantar flexor torque, andREMG for the gastrocnemius muscle in aconcentric-only and an SSC hop. Noticehow only the SSC has a negative angularvelocity (describing essentially the speed ofthe eccentric stretch of the calf muscles) andthe dramatic difference in the pattern andsize of the plantar flexor torque created.

Angular and linear kinematics give sci-entists important tools to describe and un-derstand exactly how movement occur.Remember to treat the linear and angularmeasurements separately: like the old say-ing goes, “don't mix apples and oranges.” Agood example is your CD player. As the CDspins, a point near the edge travels a largerdistance compared to a point near the cen-ter. How can two points make the same rev-olutions per minute and travel at differentspeeds? Easy, if you notice the last sentencemixes or compares angular and linear kine-matic variables. In linear kinetics we willlook at the trigonometric functions that al-low linear measurements to be mapped toangular.

Biomechanists usually calculate angu-lar kinematic variables from linear coordi-nates of body segments with trigonometry.There is another simple formula that con-verts linear to angular kinematics in specialconditions. It is useful to illustrate why thebody tends to extend segments prior to re-lease events. The linear velocity of a pointon a rotating object, relative to its axis of rota-tion, can be calculated as the product of itsangular velocity and the distance from theaxis to the point (called the radius): V =�� • r. The special condition for using this


formula is to use angular velocity in radi-ans/second. Using a dimensionless unitlike rad/s, you can multiply a radius meas-ured in meters and get a linear velocity inmeters/second.

The most important point is to noticethat the angular velocity and the radius areequally important in creating linear veloci-

ty. To hit a golf ball harder you can eitheruse a longer club or rotate the club faster.We will see in chapter 7 that angular kinet-ic analysis can help us decide which ofthese two options is best for a particular sit-uation. In most throwing events the arm isextended late in the throw to increase thelinear velocity of a projectile. Angular ki-


Figure 5.13. Ankle angle, angular velocity, torque, and rectified EMG in a concentric-only (PFJ: plantar flexionjump) and SSC hop exercise (RJ: rebound jump). Figure reprinted permission of Sugisaki et al. (2005).

netics is necessary to understand why thisextension or increase in the radius of seg-ments is delayed to just before release.

COORDINATION CONTINUUMPRINCIPLE

Many kinesiology professionals are inter-ested in the coordination of movement.Coordination is commonly defined as thesequence and timing of body actions usedin a movement. Unfortunately there is nouniversally agreed-upon definition or wayto study coordination in the kinesiology lit-erature. A wide variety of approaches hasbeen proposed to describe the coordinationof movement. Some approaches focus onthe kinematics of the joint or segmental ac-tions (Hudson, 1986; Kreighbaum &Bartels, 1996), while others are based on thejoint forces and torques (kinetics) that cre-ate the movement (Chapman & Sanderson,1990; Prilutsky, 2000; Putnam, 1991, 1993;Roberts, 1991; Zajac, 1991). This sectionpresents the Coordination ContinuumPrinciple, which is adapted from two kine-matic approaches to defining coordination(Hudson, 1986; Kreighbaum & Bartels,1996), because teachers and coaches mostoften modify the spatial and temporal as-pects of movement. While teaching cuesthat focus on muscular effort may be usedoccasionally, much of the and coaching ofmovement remains in the positioning andmotions of the body.

Kinematic coordination of movementscan be pictured as a continuum rangingfrom simultaneous body actions to sequen-tial actions. The Coordination ContinuumPrinciple suggests that movements requir-ing the generation of high forces tend to uti-lize simultaneous segmental movements,while lower-force and high-speed move-ments are more effective with more sequen-tial movement coordination. A person lift-ing a heavy box simultaneously extends the

hips, knees, and ankles (Figure 5.14). Inoverarm throwing, people usually use amore sequential action of the whole kine-matic chain, beginning with the legs, fol-lowed by trunk and arm motions.

Because coordination falls on a contin-uum and the speed and forces of movementvary widely, it is not always easy to deter-mine what coordination pattern is best. Invertical jumping, resistance is moderateand the objective is to maximize height oftakeoff and vertical velocity. While a verti-cal jump looks like a simultaneous move-ment, biomechanical studies show that thekinematics and kinetics of different jump-ers have simultaneous and sequential char-acteristics (Aragon-Vargas & Gross, 1997a;Bobbert & van Ingen Schenau, 1988; Hud-son, 1986). Kinesiology professionals needto remember that coordination is not an ei-ther/or situation in many activities. Untilthere is more research determining themost effective technique, there will be quite


Figure 5.14. Coordination to move a heavy load usu-ally involves simultaneous joint motions like in thissquat lift.

a bit of art to the coaching of movementsnot at the extremes of the continuum.

The motor development of high-speedthrowing and striking skills tends to beginwith restricted degrees of freedom and si-multaneous actions. Children throwing,striking, or kicking tend to make initial at-tempts with simultaneous actions of only afew joints. Skill develops with the use ofmore segments and greater sequential ac-tion. In high-speed throwing, for example,the sequential or “differential” rotation ofthe pelvis and upper trunk is a late-devel-oping milestone of high-skill throwing(Roberton & Halverson, 1984). It is criticalthat physical educators know the proper se-quential actions in these low-force andhigh-speed movements. Kinematic studieshelp identify these patterns of motion inmovement skills. Unfortunately, the youthof biomechanics means that kinematic doc-umentation of coordination in the wide va-riety of human movements is not complete.Early biomechanics research techniquesemphasized elite male performers, leavinglittle information on gender, special popu-lations, lower skill levels, or age.

Suppose a junior high volleyball coachis working with a tall athlete on spiking.The potential attacker lacks a strong over-arm pattern and cannot get much speed onthe ball (Figure 5.15). The kinematics of thepreparatory action lacks intensity, stretch,and timing. At impact the player's elbowand upper arm are well forward of hershoulder. The coach suspects that her over-arm throwing pattern is still immature andmust be developed before skilled spiking ispossible. This coach has integrated biome-chanical and motor development informa-tion to determine the best course of actionto help this player improve. The lack of ballspeed (kinematics), and muscle stretch-shortening cycles within a sequential coor-dination are biomechanical factors missingin this athlete. The forward elbow positionat impact is a motor development indicator

of an immature trunk and arm action with-in an overarm pattern. How coaches workon this problem may vary, but one goodstrategy would be to simplify the move-ment and work on throwing the volleyball.Sequential rotation of the trunk, arm, fore-arm, and wrist is the focus of training.

Strength and conditioning profession-als closely monitor training technique, be-cause body position and motion in exercis-es dramatically affect muscular actions andrisk of injury. In strength training, resistanc-es are near maximal, so coordination inmost exercises tends to be simultaneous.Imagine someone performing a squat exer-cise with a heavy weight. Is the safest tech-nique to simultaneously flex the hips andknees in the eccentric phase and then si-multaneously extend in the concentricphase? If the resistance is lighter (body-


Figure 5.15. Poor sequential coordination in throwingand striking results in slow segment speeds at impactthat can be visually identified by slow ball speeds, lackof eccentric loading of distal segments, or limitedmovement in the follow-through (like this volleyballspike).

weight), like in standing up out of a chair,after a person leans forward to put their up-per bodyweight over their feet, do the ma-jor joints of the body simultaneously act tostand? In the next chapter we will examinevariations in conditioning for high-powerand high-speed movements that are differ-ent than high-force (strength) movements.Do you think high-power movements willalso have simultaneous coordination, orwill the coordination shift a little toward se-quential? Why?

SUMMARY

A key branch of biomechanics is kinemat-ics, the precise description or measurementof human motion. Human motion is meas-ured relative to some frame of referenceand is usually expressed in linear (meters,feet) or angular (radians, degrees) units.Angular kinematics are particularly appro-priate in biomechanics because these can beeasily adapted to document joint rotations.There are many kinematic variables thatcan be used to document the human mo-tion. Simple kinematic variables are scalars,while others are vector quantities that takeinto account the direction of motion. Thetime derivatives (rates of change) of posi-tion measurements are velocity and accel-eration. The Optimal Projection Principlestates that sporting events involving pro-jectiles have a range of desirable initial an-gles of projection appropriate for most per-formers. The kinematic timing of segmentmotions falls on a Coordination Continuumfrom simultaneous to sequential move-ment. High-force movements use more si-multaneous joint rotations while high-speed movements use more sequential jointrotations.

REVIEW QUESTIONS

1. What is a frame of reference and whyis it important in kinematic measurements?

2. Compare and contrast the scalar andvector linear kinematic variables.

3. Explain the difference between calcu-lation of average and instantaneous veloci-ties, and how does the length of the time in-terval used affect the accuracy of a velocitycalculation?

4. Use the velocity graph in Figure 5.4to calculate the average acceleration of thesprinter in the first and the last 10-m inter-vals.

5. A patient lifts a dumbbell 1.2 m in 1.5s and lowers it back to the original positionin 2.0 s. Calculate the average vertical ve-locity of the concentric and eccentric phas-es of the lift.

6. Explain why linear and angular ac-celerations should be thought of as pushesin a particular direction rather than speed-ing up or slowing down.

7. Why are angular kinematics particu-larly well suited for the analysis of humanmovement?

8. From the anatomical position a per-son abducts their shoulder to 30º above thehorizontal. What is the angular displace-ment of this movement with the usual di-rectional (sign) convention?

9. A soccer player attempting to stealthe ball from an opponent was extendingher knee at 50 deg/s when her foot struckthe opponent's shin pads. If the player'sknee was stopped (0 deg/s) within 0.2 sec-onds, what angular acceleration did theknee experience?

10. A golfer drops a ball to replace a lostball. If the ball had an initial vertical veloc-ity of 0 m/s and had a vertical velocity be-fore impact of –15.7 m/s exactly 1.6 secondslater, what was the vertical acceleration ofthe ball?


11. A softball coach is concerned thather team is not throwing at less than 70%speed in warm-up drills. How could she es-timate or measure the speeds of the warm-up throws to make sure her players are notthrowing too hard?

12. A biomechanist uses video imagesto measure the position of a box in thesagittal plane relative to a worker's toesduring lifting. Which coordinate (x or y)usually corresponds to the height of the boxand the horizontal position of the box rela-tive to the foot?

13. Use the formula for calculating lin-ear velocity from angular velocity (V =�� • r) to calculate the velocity of a golf clubrelative to the player's hands (axis of rota-tion). Assume the radius is 1.5 m and theangular velocity of the club was 2000deg/s. Hint: remember to use the correctunits.

14. Give an example of a fixed and a rel-ative frame of reference for defining jointangular kinematics. Which frame of refer-ence is better for defining anatomical rota-tions versus rotations in space?

15. What is the vertical acceleration of avolleyball at the peak of its flight after theball is tossed upward in a jump serve?

KEY TERMS

absolute angle

acceleration

coordination continuum

degrees of freedom

displacement

distance

goniometer

isokinetic

point mass

relative angle

speed

static flexibility

trajectory

velocity

SUGGESTED READING

Cappozzo, A., Marchetti, M., & Tosi, V. (Eds.)(1990). Biolocomotion: A century of research usingmoving pictures. Rome: Promograph.

Hudson, J. L. (1986). Coordination of segmentsin the vertical jump. Medicine and Science inSports and Exercise, 18, 242–251.

Kreighbaum, E., & Barthels, K. M. (1996).Biomechanics: A qualitative approach to studyinghuman movement. Boston: Allyn & Bacon.

Lafortune, M. A., & Hennig, E. M. (1991). Con-tribution of angular motion and gravity to tib-ial acceleration. Medicine and Science in Sportsand Exercise, 23, 360–363.

Mero, A., Komi, P. V., & Gregor, R. J. (1992).Biomechanics of sprint running: A review.Sports Medicine, 13, 376–392.

Plagenhoef, S. (1971). Patterns of human motion:A cinematographic analysis. Englewood Cliffs,NJ: Prentice-Hall.

Zatsiorsky, V. M. (1998). Kinematics of humanmotion. Champaign, IL: Human Kinetics.



WEB LINKS

Projectiles—page on the path of the center of gravity of a skater by Debra King andothers from Montana State University.

http://btc.montana.edu/olympics/physbio/default.htm

Free kinematic analysis software by Bob Schleihauf at San Francisco State.http://www.kavideo.sfsu.edu/

Human Movement Analysis software by Tom Duck of York University.http://www.hma-tech.com/

Kinematics of Vectors and Projectiles—Tutorials on vectors and projectiles from ThePhysics Classroom.

http://www.physicsclassroom.com/mmedia/vectors/vectorsTOC.html

Kinematics of Gait—Introduction to kinematic variables, their use in the analysis ofhuman walking, and some of the determinants of gait. Teach-in feature of theClinical Gait Analysis website.

http://guardian.curtin.edu.au/cga/teach-in/kinematics.html

In the previous chapter we learned thatkinematics or descriptions of motion couldbe used to provide information for improv-ing human movement. This chapter willsummarize the important laws of kineticsthat show how forces overcome inertia andhow other forces create human motion.Studying the causes of linear motion isthe branch of mechanics known as linearkinetics. Identifying the causes of mo-tion may be the most useful kind of me-chanical information for determining whatpotential changes could be used to improvehuman movement. The biomechanicalprinciples that will be discussed in thischapter are Inertia, Force–Time, andSegmental Interaction.

LAWS OF KINETICS

Linear kinetics provides precise ways todocument the causes of the linear motion ofall objects. The specific laws and mechani-cal variables a biomechanist will choose touse in analyzing the causes of linear motionoften depends on the nature of the move-ment. When instantaneous effects are of in-terest, Newton's Laws of Motion are mostrelevant. When studying movements overintervals of time is of interest, theImpulse–Momentum Relationship is usual-ly used. The third approach to studying thecauses of motion focuses on the distancecovered in the movement and uses theWork–Energy Relationship. This chaptersummarizes these concepts in the context of

human movement. Most importantly, wewill see how these laws can be applied tohuman motion in the biomechanical princi-ples of Force–Motion, Force–Time, andCoordination Continuum Principles.

NEWTON'S LAWS OF MOTION

Arguably, some of the most important dis-coveries of mechanics are the three laws ofmotion developed by the Englishman, SirIsaac Newton. Newton is famous for manyinfluential scientific discoveries, includingdevelopments in calculus, the Law ofUniversal Gravitation, and the Laws ofMotion. The importance of his laws cannotbe overemphasized in our context, for theyare the keys to understanding how humanmovement occurs. The publication of theselaws in his 1686 book De Philosophiae Natu-ralis Principia Mathematica marked one ofthe rare occasions of scientific break-through. Thousands of years of dominanceof the incorrect mechanical views of theGreek philosopher Aristotle were over-turned forever.

Newton's First Law andFirst Impressions

Newton's first law is called the Law ofInertia because it outlines a key property ofmatter related to motion. Newton statedthat all objects have the inherent propertyto resist a change in their state of motion.

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133

His first law is usually stated somethinglike this: objects tend to stay at rest or inuniform motion unless acted upon by anunbalanced force. A player sitting and“warming the bench” has just as much iner-tia as a teammate of equal mass running ata constant velocity on the court. It is vitallyimportant that kinesiology professionalsrecognize the effect inertia and Newton'sfirst law have on movement technique. Thelinear measure of inertia (Figure 6.1) ismass and has units of kg in the SI systemand slugs in the English system. This sec-tion is an initial introduction to the fascinat-ing world of kinetics, and will demonstratehow our first impressions of how thingswork from casual observation are often in-correct.

Understanding kinetics, like Newton'sfirst law, is both simple and difficult: sim-ple because there are only a few physicallaws that govern all human movement, andthese laws can be easily understood anddemonstrated using simple algebra, withonly a few variables. The study of biome-chanics can be difficult, however, becausethe laws of mechanics are often counterin-tuitive for most people. This is because theobservations of everyday life often lead toincorrect assumptions about the nature ofthe world and motion. Many children andadults have incorrect notions about inertia,

and this view of the true nature of motionhas its own “cognitive inertia,” which ishard to displace. The natural state of objectsin motion is to slow down, right? Wrong!The natural state of motion is to continuewhatever it is doing! Newton's first lawshows that objects tend to resist changes inmotion, and that things only seem to natu-rally slow down because forces like frictionand air or water resistance that tend to slowan object's motion. Most objects around usappear at rest, so isn't there something nat-ural about being apparently motionless?The answer is yes, if the object is initially atrest! The same object in linear motion hasthe same natural or inertial tendency tokeep moving. In short, the mass (and conse-quently its linear inertia) of an object is thesame whether it is motionless or moving.

We also live in a world where mostpeople take atmospheric pressure for grant-ed. They are aware that high winds can cre-ate very large forces, but would not believethat in still air there can be hundreds ofpounds of force on both sides of a housewindow (or a person) due to the pressure ofthe atmosphere all around us. The true na-ture of mechanics in our world often be-comes more apparent under extreme condi-tions. The pressure of the sea of air we livein becomes real when a home explodesor implodes from a passing tornado, or a


Figure 6.1. All objects have the inherent property of inertia, the resistance to a change in the state of motion. Themeasure of linear motion inertia is mass. A medicine ball has the same resistance to acceleration (5 kg of mass) inall conditions of motion, assuming it does not travel near the speed of light.

fast-moving weather system brings achange in pressure that makes a person'sinjured knee ache. People interested in scu-ba diving need to be knowledgeable aboutpressure differences and the timing of thesechanges when they dive.

So casual observation can often lead toincorrect assumptions about the laws ofmechanics. We equate forces with objects incontact or a collision between two objects.Yet we live our lives exercising our musclesagainst the consistent force of gravity, aforce that acts at quite a distance whetherwe are touching the ground or not. We alsotend to equate the velocity (speed and di-rection) of an object with the force thatmade it. In this chapter we will see that theforces that act on an object do not have to beacting in the direction of the resultant mo-tion of the object (Figure 6.2). It is theskilled person that creates muscle forces toprecisely combine with external forces tobalance a bike or throw the ball in the cor-rect direction.

Casual visual observation also hasmany examples of perceptual illusionsabout the physical realities of our world.Our brains work with our eyes to give us amental image of physical objects in theworld, so that most people routinely mis-take this constructed mental image for theactual object. The color of objects is also anillusion based on the wavelengths of lightthat are reflected from an object's surface.So what about touch? The solidity of objectsis also a perceptual illusion because the vastmajority of the volume in atoms is “empty”space. The forces we feel when we touchthings are the magnetic forces of electronson the two surfaces repelling each other,while the material strength of an object webend is related to its physical structure andchemical bonding. We also have a distortedperception of time and the present. We relyon light waves bouncing off objects and to-ward our eyes. This time delay is not aproblem at all, unless we want to observe

very high-speed or distant objects like inastronomy. There are many other examplesof our molding or construction of the na-ture of reality, but the important point isthat there is a long history of careful scien-tific measurements which demonstrate thatcertain laws of mechanics represent the truenature of object and their motion. Theselaws provide a simple structure that shouldbe used for understanding and modifyingmotion, rather than erroneous perceptionsabout the nature of things. Newton's firstlaw is the basis for the Inertia Principle inapplying biomechanics.

CHAPTER 6: LINEAR KINETICS 135

Figure 6.2. Force and motion do not always act in thesame direction. This free-body diagram of the forcesand resultant force (FR) on a basketball before releaseillustrates how a skilled player applies a force to an ob-ject (Fh) that combines with the force of gravity (Fg) tocreate the desired effect. The motion of the ball will bein the direction of FR.

Newton's Second Law

Newton's second law is arguably the mostimportant law of motion because it showshow the forces that create motion (kinetics)are linked to the motion (kinematics). Thesecond law is called the Law of Momen-tum or Law of Acceleration, depending onhow the mathematics is written. The mostcommon approach is the famous F = ma.This is the law of acceleration, which de-scribes motion (acceleration) for any instantin time. The formula correctly written is �F= m • a, and states that the acceleration anobject experiences is proportional to the re-sultant force, is in the same direction, and isinversely proportional to the mass. Thelarger the unbalanced force in a particular

direction, the greater the acceleration of theobject in that direction. With increasingmass, the inertia of the object will decreasethe acceleration if the force doesn't change.

Let's look at an example using skatersin the push-off and glide phases during iceskating (Figure 6.3). If the skaters have amass of 59 kg and the horizontal forces areknown, we can calculate the acceleration ofthe skater. During push-off the net horizon-tal force is +200 N because air resistance isnegligible, so the skater's horizontal accel-eration is: �F = m • a, 200 = 59a, so a = 3.4m/s/s. The skater has a positive accelera-tion and would tend to speed up 3.4 m/severy second if she could maintain herpush-off force this much over the air resist-ance. In the glide phase, the friction force isnow a resistance rather than a propulsiveforce. During glide the skater's accelerationis –0.08 m/s/s because: �F = m • a, –5 = 59a,so a = –0.08 m/s/s.

The kinesiology professional can quali-tatively break down movements withNewton's second law. Large changes in thespeed or direction (acceleration) of a personmeans that large forces must have been ap-plied. If an athletic contest hinges on theagility of an athlete in a crucial play, thecoach should select the lightest and quick-est player. An athlete with a small mass iseasier to accelerate than an athlete with alarger mass, provided they can create suffi-cient forces relative to body mass. If asmaller player is being overpowered by alarger opponent, the coach can substitutea larger more massive player to defendagainst this opponent. Note that increasingforce or decreasing mass are both importantin creating acceleration and movement.

Newton's second law plays a criticalrole in quantitative biomechanics. Biome-chanists wanting to study the net forcesthat create human motion take accelerationand body segment mass measurements andapply F = ma. This working backward fromkinematics to the resultant kinetics is called


Interdisciplinary Issue:Body Composition

A considerable body of kinesiology re-search has focused on the percentage offat and lean mass in the human body.There are metabolic, mechanical, and psy-chological effects of the amount and loca-tion of fat mass. In sports performance,fat mass can be both an advantage (in-creased inertia for a football lineman orsumo wrestler) and a disadvantage.Increasing lean body mass usually benefitsperformance, although greater massmeans increasing inertia, which could de-crease agility and quickness.When coach-es are asked by athletes “How muchshould I weigh?” they should answer care-fully, focusing the athlete's attention firston healthy body composition. Then thecoach can discuss with the athlete the po-tential risks and benefits of changes inbody composition. How changes in anathlete's inertia affect their sport per-formance should not be evaluated with-out regard to broader health issues.

inverse dynamics. Other scientists buildcomplex computer models of biomechani-cal systems and use direct dynamics, essen-tially calculating the motion from the“what-if” kinetics and body configurationsthey input.

Newton's Third Law

Newton's third law of motion is called theLaw of Reaction, because it is most oftentranslated as: for every action there is anequal and opposite reaction. For every forceexerted, there is an equal and opposite forcebeing exerted. If a patient exerts a sidewaysforce of +150 N on an elastic cord, there hasto be –150-N reaction force of the cord onthe patient's hand (Figure 6.4). The key in-sight that people often miss is that a force isreally a mutual interaction between twobodies. It may seem strange that if youpush horizontally against a wall, the wall issimultaneously pushing back toward you,but it is. This is not to say that a force on afree-body diagram should be representedby two vectors, but a person must under-stand that the effect of a force is not just on

one object. A free body diagram is one ob-ject or mechanical system and the forcesacting on it, so the double vectors inFigures 6.4 and 6.5 can sometimes be con-fusing because they are illustrating bothobjects and are not true free body dia-grams. If someone ever did not seem to kissyou back, you can always take some com-fort in the fact that at least in mechanicalterms they did.

An important implication of the law ofreaction is how reaction forces can changethe direction of motion opposite to our ap-plied force when we exert our force on ob-jects with higher force or inertia (Figure6.5a). During push-off in running the ath-lete exerts downward and backward pushwith the foot, which creates a ground reac-tion force to propel the body upward andforward. The extreme mass of the earth eas-ily overcomes our inertia, and the groundreaction force accelerates our body in theopposite direction of force applied to theground. Another example would be eccen-tric muscle actions where we use our mus-cles as brakes, pushing in the opposite di-rection to another force. The force exerted


Figure 6.3. Friction forces acting on ice skaters during push-off and gliding. Newton' Second Law of Motion ap-plied in the horizontal direction (see text) will determine the horizontal acceleration of the skater.


Figure 6.4. Newton's third law states that all forces have an equal and opposite reaction forces on the other object,like in this elastic exercise. The –150-N (FA) force created by the person on the elastic cord coincides with a 150-Nreaction force (FB) exerted on the person by the cord.

Figure 6.5. A major consequence of Newton's third law is that the forces we exert on an object with larger inertiaoften create motion in the direction opposite of those forces. In running, the downward backward push of the footon the ground (FA) late in the stance (a) creates a ground reaction force which acts forward and upward, propellingthe runner through the air. A defensive player trying to make a tackle (FT) from a poor position (b) may experiencereaction forces (FR) that create eccentric muscle actions and injurious loads.

by the tackler in Figure 6.5b ends up beingan eccentric muscle action as the inertia andground reaction forces created by the run-ner are too great. Remember that when wepush or pull, this force is exerted on someother object and the object pushes or pullsback on us too!

There are several kinds of force-meas-uring devices used in biomechanics tostudy how forces modify movement. Twoimportant devices are the force platform(or force plates) and pressure sensor arrays.A force plate is a rigid platform that meas-ures the forces and torques in all three di-mensions applied to the surface of the plat-form (Schieb, 1987). Force plates are oftenmounted in a floor to measure the groundreaction forces that are equal and oppositeto the forces people make against theground (see Figure 6.5). Since the 1980s,miniaturization of sensors has allowed forrapid development of arrays of small-forcesensors that allow measurement of the dis-tribution of forces (and pressure becausethe area of the sensor is known) on a body.Several commercial shoe insoles with thesesensors are available for studying the pres-sure distribution under a person's foot (seeMcPoil, Cornwall, & Yamada, 1995). Thereare many other force-measuring devices(e.g., load cell, strain gauge, isokinetic dy-namometer) that help biomechanics schol-ars study the kinetics of movement.

INERTIA PRINCIPLE

Newton's first law of motion, or the Lawof Inertia, describes the resistance of all ob-jects to a change in their state of linear mo-tion. In linear motion, the measure of iner-tia is an object's mass. Application ofNewton's first law in biomechanics istermed the Inertia Principle. This sectionwill discuss how teachers, coaches, andtherapists adjust movement inertia to ac-commodate the task. Our focus will be on

the linear inertia (mass) of movement, sothe inertial resistance to rotation will besummarized in chapter 7.

The first example of application of theinertia principle is to reduce mass in orderto increase the ability to rapidly accelerate.Obvious examples of this principle in trackare the racing flats/shoes used in competi-tion versus the heavier shoes used in train-ing. The heavier shoes used in training pro-vide protection for the foot and a small in-ertial overload. When race day arrives, thesmaller mass of the shoes makes the ath-lete's feet feel light and quick. We will see inchapter 7 that this very small change inmass, because of its position, makes a muchlarger difference in resistance to rotation(angular inertia). Let's add a little psychol-ogy and conditioning to the application oflowering inertia. Warm-up for many sportsinvolves a gradual increase in intensity ofmovements, often with larger inertia. Inbaseball or golf, warm-up swings are oftentaken with extra weights, which when tak-en off make the “stick” feel very light andfast (Figure 6.6).

In movements where stability is de-sired over mobility, the Inertia Principlesuggests that mass should be increased.Linemen in football and centers in basket-ball have tasks that benefit more from in-creasing muscle mass to increase inertia,than from decreasing inertia to benefitquickness. Adding mass to a golf club ortennis racket will make for faster andlonger shots if the implement can be swungwith the same velocity at impact. If an exer-cise machine tends to slide around in theweight room, a short-term solution mightbe to store some extra weights on the baseor legs of the machine. If these new weightsare not a safety risk (in terms of height orpotential for tripping people), the increasedinertia of the station would likely make themachine safer.

Another advantage of increased inertiais that the added mass can be used to mod-


ify the motion of another body segment.The preparatory leg drives and weightshifts in many sporting activities have sev-eral benefits for performance, one beingputting more body mass in motion towarda particular target. The forward motion of agood percentage of body mass can be trans-ferred to the smaller body segments justprior to impact or release. We will be look-ing at this transfer of energy later on in thischapter when we consider the SegmentalInteraction Principle. The defensive movesof martial artists are often designed to takeadvantage of the inertia of an attacker. Anopponent striking from the left has inertiathat can be directed by a block to throw tothe right.

An area where modifications in inertiaare very important is strength and condi-tioning. Selecting masses and weights for

training and rehabilitation is a complicatedissue. Biomechanically, it is very importantbecause the inertia of an external object hasa major influence on amount of muscularforce and how those forces can be applied(Zatsiorsky & Kraemer, 2006). Baseballpitchers often train by throwing heavier orlighter than regulation baseballs (see, e.g.,Escamilla, Speer, Fleisig, Barrentine, &Andrews, 2000). Think about the amount offorce that can be applied in a bench pressexercise versus a basketball chest pass. Thevery low inertia of the basketball allows itto accelerate quickly, so the peak force thatcan be applied to the basketball is muchlower than what can be applied to a barbell.The most appropriate load, movement, andmovement speed in conditioning for a par-ticular human movement is often difficultto define. The principle of specificity says


Figure 6.6. Mass added to sporting implements in warm-up swings makes the inertia of the regular implement(when the mass is removed) feel very light and quick. Do you think this common sporting ritual of manipulatinginertia is beneficial? If so, is the effect more biomechanical or psychological?

the movement, speed, and load should besimilar to the actual activity; therefore, theoverload should only come from moderatechanges in these variables so as to not ad-versely affect skill.

Suppose a high school track coach hasshot put athletes in the weight room throw-ing medicine balls. As you discuss the pro-gram with the coach you find that they areusing loads (inertia) substantially lowerthan the shot in order to enhance the speedof upper extremity extension. How mightyou apply the principle of inertia in this sit-uation? Are the athletes fully using theirlower extremities in a similar motion toshot putting? Can the athletes build uplarge enough forces before acceleration ofthe medicine ball, or will the force–velocityrelationship limit muscle forces? Howmuch lower is the mass of the medicine ballthan that of the shot? All these questions, aswell as technique, athlete reaction, and ac-tual performance, can help you decide iftraining is appropriate. The biomechanicalresearch on power output in multi-segmentmovements suggests that training loadsshould be higher than the 30 to 40% of 1RMseen in individual muscles and musclegroups (see the following section on musclepower; Cronin et al., 2001a,b; and Funato,Matsuo, & Fukunaga, 1996). Selecting theinertia for weight training has come a longway from “do three sets of 10 reps at 80% ofyour maximum.”

MUSCLE ANGLE OF PULL:QUALITATIVE AND

QUANTITATIVE ANALYSISOF VECTORS

Before moving on to the next kinetic ap-proach to studying the causes of move-ment, it is a good time to review the specialmathematics required to handle vectorquantities like force and acceleration. The

linear kinetics of a biomechanical issuecalled muscle angle of pull will be explored inthis section. While a qualitative under-standing of adding force vectors is enoughfor most kinesiology professionals, quanti-fying forces provides a deeper level of ex-planation and understanding of the causesof human movement. We will see that thelinear kinetics of the pull of a muscle oftenchanges dramatically because of changes inits geometry when joints are rotated.

Qualitative Vector Analysis ofMuscle Angle of Pull

While the attachments of a muscle do notchange, the angle of the muscle's pull onbones changes with changes in joint angle.The angle of pull is critical to the linear andangular effects of that force. Recall that aforce can be broken into parts or compo-nents. These pulls of a muscle's force in twodimensions are conveniently resolved intolongitudinal and rotational components.This local or relative frame of referencehelps us study how muscle forces affect thebody, but do not tell us about the orienta-tion of the body to the world like absoluteframes of reference do. Figure 6.7 illustratestypical angles of pull and these compo-nents for the biceps muscle at two points inthe range of motion. The linear kinetic ef-fects of the biceps on the forearm can be il-lustrated with arrows that represent forcevectors.

The component acting along the longi-tudinal axis of the forearm (FL) does notcreate joint rotation, but provides a loadthat stabilizes or destabilizes the elbowjoint. The component acting at right anglesto the forearm is often called the rotarycomponent (FR) because it creates a torquethat contributes to potential rotation.Remember that vectors are drawn to scaleto show their magnitude with an arrow-head to represent their direction. Note that


in the extended position, the rotary compo-nent is similar to the stabilizing compo-nent. In the more flexed position illustrat-ed, the rotary component is larger than thesmaller stabilizing component. In both po-sitions illustrated, the biceps muscle tendsto flex the elbow, but the ability to do so(the rotary component) varies widely.

This visual or qualitative understand-ing of vectors is quite useful in studyinghuman movement. When a muscle pulls ata 45º angle, the two right-angle compo-nents are equal. A smaller angle of pull fa-vors the longitudinal component, while therotary component benefits from larger an-gles of pull. Somewhere in the midrange ofthe arm curl exercise the biceps has an an-gle of pull of 90º, so all the bicep's force canbe used to rotate the elbow and there is nolongitudinal component.

Vectors can also be qualitatively addedtogether. The rules to remember are that the

forces must be drawn accurately (size anddirection), and they then can be added to-gether in tip-to-tail fashion. This graphicalmethod is often called drawing a parallelo-gram of force (Figure 6.8). If the vastus later-alis and vastus medialis muscle forces onthe right patella are added together, we getthe resultant of these two muscle forces.The resultant force from these two musclescan be determined by drawing the twomuscle forces from the tip of one to the tailof the other, being sure to maintain correctlength and direction. Since these diagramscan look like parallelograms, they are calleda parallelogram of force. Remember thatthere are many other muscles, ligaments,and joint forces not shown that affect kneefunction. It has been hypothesized that animbalance of greater lateral forces in thequadriceps may contribute to patello-femoral pain syndrome (Callaghan &Oldham, 1996). Does the resultant force (FR)


Figure 6.7. Typical angles of pull of the biceps brachii muscle in an arm curl. The angular positions of the shoul-der and elbow affect the angle of pull of the muscle, which determines the size of the components of the muscleforce. Muscle forces (F) are usually resolved along the longitudinal axis of the distal segment (FL) and at right an-gles to the distal segment to show the component that causes joint rotation (FR).

in Figure 6.8 appear to be directed lateral tothe longitudinal axis of the femur?

Quantitative Vector Analysis ofMuscle Angle of Pull

Quantitative or mathematical analysis pro-vides precise answers to vector resolution(in essence subtraction to find components)or vector composition. Right-angle trigo-nometry provides the perfect tool for thisprocess. A review of the major trigonomet-ric relationships (sine, cosine, tangent) isprovided in Appendix D. Suppose an ath-lete is training the isometric stabilizationability of their abdominals with leg raises ina Roman chair exercise station. Figure 6.9aillustrates a typical orientation and magni-tude of the major hip flexors (the iliopsoas

group) that hold their legs elevated. Themagnitude of the weight of the legs and thehip flexor forces provide a large resistancefor the abdominal muscles to stabilize. Thisexercise is not usually appropriate for un-trained persons.

If an iliopsoas resultant muscle force of400 N acts at a 55º angle to the femur, whatare the rotary (FR) and longitudinal (FL)components of this force? To solve thisproblem, the rotating component is movedtip to tail to form a right triangle (Figure6.9b). In this triangle, right-angle trigonom-etry says that the length of the adjacent sideto the 55º angle (FL) is equal to the resultantforce times cos 55º. So the stabilizing com-ponent of the iliopsoas force is: FL = 400(cos55º) = 229 N, which would tend to com-press the hip joint along the longitudinalaxis of the femur. Likewise, the rotary com-ponent of this force is the side opposite the55º angle, so this side is equal to the result-ant force times sin 55º. The component ofthe 400-N iliopsoas force that would tendto rotate the hip joint, or in this exampleisometrically hold the legs horizontally, is:FR = 400 sin 55º = 327 N upward. It is oftena good idea to check calculations with aqualitative assessment of the free body dia-gram. Does the rotary component looklarger than the longitudinal component? Ifthese components are the same at 45º, doesit make sense that a higher angle would in-crease the vertical component and decreasethe component of force in the horizontal di-rection?

When the angle of pull (��) or push of aforce can be expressed relative to a horizon-tal axis (2D analysis like above), the hori-zontal component is equal to the resultanttimes the cosine of the angle ��. The verticalcomponent is equal to the resultant timesthe sine of the angle ��. Consequently, howthe angle of force application affects thesize of the components is equal to the shapeof a sine or cosine wave. A qualitative un-derstanding of these functions helps one


Figure 6.8. Any vectors acting on the same object, likethe vastus medialis (FVM) and vastus lateralis (FVL) ofthe right knee, can be added together to find a result-ant (FR). This graphical method of adding vectors iscalled a parallelogram of forces.

understand where the largest changes oc-cur and what angles of force application arebest. Let's look at a horizontal componentof a force in two dimensions. This is analo-gous to our iliopsoas example, or how anyforce applied to an object will favor the hor-izontal over the vertical component. A co-sine function is not a linear function likeour spring example in chapter 2. Figure 6.10plots the size of the cosine function as a per-centage of the resultant for angles of pullfrom 0 to 90º.

A 0º (horizontal) angle of pull has novertical component, so all the force is in thehorizontal direction. Note that, as the angleof pull begins to rise (0 to 30º), the cosine orhorizontal component drops very slowly,so most of the resultant force is directedhorizontally. Now the cosine function be-gins to change more rapidly, and from 30 to60º the horizontal component has droppedfrom 87 to 50% the size of the resultantforce. For angles of pull greater than 60º, thecosine drops off very fast, so there is a dra-


Figure 6.9. Right-angle trigonometry is used to find the components of a vector like the iliopsoas muscle force il-lustrated. Notice the muscle force is resolved into components along the longitudinal axis of the femur and at rightangles to the femur. The right angle component is the force that creates rotation (FR).

matic decrease in the horizontal componentof the force, with the horizontal componentbecoming 0 when the force is acting at 90º(vertical). We will see that the sine and co-sine relationships are useful in angular ki-netics as well. These curves allow for calcu-lation of several variables related to angularkinetics from linear measurements. Right-angle trigonometry is also quite useful instudying the forces between two objects incontact, or precise kinematic calculations.

CONTACT FORCES

The linear kinetics of the interaction of twoobjects in contact is also analyzed by resolv-

ing the forces into right-angle components.These components use a local frame of ref-erence like the two-dimensional muscle an-gle of pull above, because using horizontaland vertical components are not alwaysconvenient (Figure 6.11). The forces be-tween two objects in contact are resolvedinto the normal reaction and friction. Thenormal reaction is the force at right anglesto the surfaces in contact, while friction isthe force acting in parallel to the surfaces.Friction is the force resisting the sliding ofthe surfaces past each other.

When the two surfaces are dry, theforce of friction (F) is equal to the product ofthe coefficient of friction (�) and the normalreaction (FN), or F = � • FN. The coefficient


Figure 6.10. Graph of the cosine of angle �� between 0 and 90° (measured from the right horizontal) shows the per-centage effectiveness of a force (F) in the horizontal direction (FH). This horizontal component is equal to F cos(��),and angle �� determines the tradeoff between the size of the horizontal and vertical components. Note that the hor-izontal component stays large (high percentage of the resultant) for the first 30° but then rapidly decreases. Thesine and cosine curves are the important nonlinear mathematical functions that map linear biomechanical vari-ables to angular.

of friction depends on the texture and na-ture of the two surfaces, and is determinedby experimental testing. There are coeffi-cients of static (non-moving) friction (�S)and kinetic (sliding) friction (�K). The coef-ficients of kinetic friction are typically 25%smaller than the maximum static friction. Itis easier to keep an object sliding over a sur-face than to stop it and start the object slid-ing again. Conversely, if you want frictionto stop motion, preventing sliding (likewith anti-lock auto brakes) is a good strate-gy. Figure 6.12 illustrates the friction forcebetween an athletic shoe and a force plat-form as a horizontal force is increased.Please note that the friction grows in a lin-ear fashion until the limiting friction isreached (�S • FN), at which point the shoebegins to slide across the force platform. Ifthe weight on the shoe created a normal re-action of 300 N, what would you estimatethe �S of this rubber/metal interface?

Typical coefficients of friction in humanmovement vary widely. Athletic shoes havecoefficients of static friction that range from0.4 to over 1.0 depending on the shoe andsport surface. In tennis, for example, thelinear and angular coefficients of frictionrange from 0.4 to over 2.0, with shoes re-sponding differently to various courts


Figure 6.11. Forces of contact between objects are usu-ally resolved into the right-angle components of nor-mal reaction (FN) and friction.

Figure 6.12. The change in friction force between an athletic shoe and a force platform as a horizontal force is ap-plied to the shoe. The ratio of the friction force (FH) on this graph to the normal force between the shoe and forceplatform determine the coefficient of friction for these two surfaces.

(Nigg, Luthi, & Bahlsen, 1989). Epidemio-logical studies have shown that playing onlower-friction courts (clay) had a lower riskof injury (Nigg et al., 1989). Many teamsthat play on artificial turf use flat shoesrather than spikes because they believe thelower friction decreases the risk of severeinjury. The sliding friction between ice anda speed skating blade has been measured,demonstrating coefficients of kinetic fric-tion around 0.005 (van Ingen Schenau, DeBoer, & De Groot, 1989).

IMPULSE–MOMENTUMRELATIONSHIP

Human movement occurs over time, somany biomechanical analyses are based onmovement-relevant time intervals. For ex-ample, walking has a standardized gait cy-cle (Whittle, 2001), and many sport move-ments are broken up into phases (usually,preparatory, action, and follow-through).The mechanical variables that are oftenused in these kinds of analyses are impulse(J) and momentum (p). These two variablesare related to each other in the original lan-guage of Newton's second law: the changein momentum of an object is equal to theimpulse of the resultant force in that direc-tion. The impulse–momentum relationshipis Newton's Second law written over a timeinterval, rather than the instantaneous (F =ma) version.

Impulse is the effect of force acting overtime. Impulse (J) is calculated as the prod-uct of force and time (J = F • t), so the typi-cal units are N•s and lb•s. Impulse can bevisualized as the area under a force–timegraph. The vertical ground reaction forceduring a foot strike in running can be meas-ured using a force platform, and the areaunder the graph (integral with respect totime) represents the vertical impulse(Figure 6.13). A person can increase the mo-tion of an object by applying a greater im-

pulse, and both the size of the force and du-ration of force application are equally im-portant. Impulse is the mechanical variablediscussed in the following section on the“Force–Time Principle.” In movement, themomentum a person can generate, or dissi-pate in another object, is dependent on howmuch force can be applied and the amountof time the force is applied.

Newton realized that the mass of anobject affects its response to changes inmotion. Momentum is the vector quantitythat Newton said describes the quantityof motion of an object. Momentum (p) iscalculated as the product of mass and ve-locity (p = m • v). The SI unit for momen-tum is kg•m/s. Who would you rather acci-dentally run into in a soccer game at a 5-m/s closing velocity: a 70- or 90-kg oppo-nent? We will return to this question andmathematically apply the impulse–mo-mentum relationship later on in this chap-ter once we learn about a similar kineticvariable called kinetic energy.

The association between impulse(force exerted over time) and change inmomentum (quantity of motion) is quite


Figure 6.13. The vertical impulse (JV) of the verticalground reaction force for a footstrike in running is thearea under the force–time graph.

useful in gaining a deeper understandingof many sports. For example, many impactscreate very large forces because the timeinterval of many elastic collisions is soshort. For a golf ball to change from zeromomentum to a very considerable momen-tum over the 0.0005 seconds of impact withthe club requires a peak force on the golfball of about 10,000 N, or greater than 2200pounds (Daish, 1972). In a high-speed soc-cer kick, the ball is actually on the foot forabout 0.016 seconds, so that peak forces

on the foot are above 230 pounds (Tol, Slim,van Soest, & van Dijk, 2002; Tsaousidis &Zatsiorsky, 1996). Fortunately, for manycatching activities in sport an athlete canspread out the force applied to the ball overlonger periods of time. The Impulse–Mo-mentum Relationship is the mechanical lawthat underlies the Force–Time Principle in-troduced earlier in chapters 2 and 4. Let'srevisit the application of the Force–TimePrinciple with our better understanding oflinear kinetics.


Interdisciplinary Issue:Acute and Overuse Injuries

A very important area of research by many kinesiology and sports medicine scholars is related tomusculoskeletal injuries. Injuries can be subclassified into acute injuries or overuse injuries.Acuteinjuries are single traumatic events, like a sprained ankle or breaking a bone in a fall from a horse.In an acute injury the forces create tissue loads that exceed the ultimate strength of the biologi-cal tissues and cause severe physical disruption. Overuse injuries develop over time (thus, chron-ic) from a repetitive motion, loading, inadequate rest, or a combination of the three. Injuries fromrepetitive vocational movements or work-related musculoskeletal disorders (WMSDs) are exam-ples of chronic injuries (Barr & Barbe, 2002). Stress fractures and anterior tibial stress syndrome(shin splits) are classic examples of overuse injuries associated with running. Runners who over-train, run on very hard surfaces, and are susceptible can gradually develop these conditions. If over-use injuries are untreated, they can develop into more serious disorders and injuries. For exam-ple, muscle overuse can sometimes cause inflammation of tendons (tendinitis), but if the conditionis left untreated degenerative changes begin to occur in the tissue that are called tendinoses (Khan,Cook, Taunton, & Bonar, 2000). Severe overuse of the wrist extensors during one-handed back-hands irritates the common extensor tendon attaching at the lateral epicondyle, often resulting in“tennis elbow.”

The etiology (origin) of overuse injuries is a complex phenomenon that requires interdiscipli-nary research.The peak force or acceleration (shock) of movements is often studied in activitiesat risk of acute injury. It is less clear if peak forces or total impulse are more related to the devel-opment of overuse injuries. Figure 6.14 illustrates the typical vertical ground reaction forces meas-ured with a force platform in running, step aerobics, and walking. Note that the vertical forces arenormalized to units of bodyweight. Notice that step aerobics has peak forces near 1.8 BW becauseof the longer time of force application and the lower intensity of movement.Typical vertical groundreaction forces in step aerobics look very much like the forces in walking (peak forces of 1.2 BWand lower in double support) but tend to be a bit larger because of the greater vertical motion.The peak forces in running typically are about 3 BW because of the short amount of time the footis on the ground. Do you think the vertical impulses of running and step aerobics are similar?Landing from large heights and the speed involved in gymnastics are very close to injury-produc-ing loads. Note the high peak force and rate of force development (slope of the F–t curve) in therunning ground reaction force. Gymnastic coaches should limit the number of landings during prac-tice and utilize thick mats or landing pits filled with foam rubber to reduce the risk of injury intraining because the rate of loading and peak forces are much higher (8 BW) than running.

FORCE-TIME PRINCIPLE

The applied manifestation of Newton'sSecond Law of Motion as the Impulse–Momentum Relationship is the Force–TimePrinciple. If a person can apply force over alonger period of time (large impulse), theywill be able to achieve a greater speed(change in momentum) than if they usedsimilar forces in a shorter time interval.Unfortunately, in many human movementsthere is not an unlimited amount of time toapply forces, and there are several musclemechanical characteristics that complicateapplication of this principle. Recall fromchapter 4 that maximizing the time forceapplication is not always the best strategyfor applying the Force–Time Principle. Themovement of interest, muscle characteris-tics, and the mechanical strengths of tissues

all affect optimal application of forces tocreate motion.

There are a few movements that do al-low movers to maximize the time of forceapplication to safely slow down an object.In landing from a jump, the legs are extend-ed at contact with the ground, so there isnear maximal joint range of motion to flexthe joints and absorb impact forces. A soft-ball infielder is taught to lean forward andextend her glove hand to field a groundball so that she can absorb the force of theball over a longer time interval. Figure 6.15illustrates two people catching balls: whichathlete is using a technique that is correctlyapplying the Force–Time Principle? Youngchildren often catch by trapping the objectagainst the body and even turn their headsin fear. Even professional football players(6.15, below) occasionally rely on their


Figure 6.14. Typical vertical ground reaction forces (in units of bodyweight) for running (solid), walking (dashed),and step aerobic exercise (dotted).

talent or sense of self-preservation morethan coaching and use a similar catchingtechnique. For how much time can forcesbe applied to slow the balls in these cases?The momentum of the ball in these situa-tions is often so great that the force betweenthe person's body and the ball builds up sofast that the ball bounces out of their grasp.If these people extended their arms andhands to the ball, the time the force is ap-plied to slow down the ball could be morethan ten times longer. Not only does this in-crease the chance of catching the ball, but itdecreases the peak force and potential dis-comfort involved in catching.

Athletes taught to reach for the groundand “give” with ankle, hip, and knee flex-ion dramatically increase the time of forceapplication in landing and decrease thepeak ground reaction forces. Exactly howthe muscles are positioned and pre-tensedprior to landing affects which musclegroups are used to cushion landing (DeVita& Skelly, 1992; Kovacs et al., 1999; Zhang,Bates, & Dufek, 2000). How to teach this im-portant skill has not been as well re-searched. The sound of an impact often tellsan athlete about the severity of a collision,so this has been used as a teaching point incatching and landing. It has also beenshown that focusing attention on decreas-ing the sound of landing is an effectivestrategy to decrease peak forces duringlanding (McNair, Prapavessis, & Callender,2000). Increasing the “give” of the cushion-ing limbs increases the time of force appli-


Figure 6.15. Catching the ball close to the body (theAmerican football example) is a poor application ofthe Force–Time Principle because there is minimaltime or range of motion to slow down the ball. Thesoftball catcher has increased the time and range ofmotion that can be used to slow down the ball.

cation and decreases the tone and intensityof the sound created by the collision.

In some movements there are other bio-mechanical factors involved in the activitythat limit the amount of time that force canbe applied. In these activities, increasingtime of force application would decreaseperformance, so the only way to increasethe impulse is to rapidly create force duringthe limited time available. A good exampleof this is long jumping. Recall that in thekinematics chapter we learned that longjumpers have low takeoff angles (approxi-mately 20º). The takeoff foot is usually onthe board for only 100 ms, so there is littletime to create vertical velocity. Skilled longjumpers train their neuromuscular systemto strongly activate the leg muscles prior tofoot strike. This allows the jumper to rapid-ly increase ground reaction forces so theycan generate vertical velocity without los-ing too much horizontal velocity. Similartemporal limitations are at work in runningor throwing. In many sports where playersmust throw the ball quickly to score or pre-vent an opponent scoring, the player maymake a quicker throw than they would dur-ing maximal effort without time restric-tions. A quick delivery may not use maxi-mal throwing speed or the extra time it

takes to create that speed, but it meets theobjective of that situation. Kinesiology pro-fessionals need to instruct movers as towhen using more time of force applicationwill result in safer and more effective move-ment, and when the use of longer force ap-plication is not the best movement strategy.

WORK–ENERGYRELATIONSHIP

The final approach to studying the kineticsof motion involves laws from a branch ofphysics dealing with the concepts of workand energy. Since much of the energy in thehuman body, machines, and on the earthare in the form of heat, these laws are usedin thermodynamics to study the flow ofheat energy. Biomechanists are interestedin how mechanical energies are used to cre-ate movement.

Mechanical Energy

In mechanics, energy is the capacity to dowork. In the movement of everyday ob-jects, energy can be viewed as the mover ofstuff (matter), even though at the atomiclevel matter and energy are more closely re-lated. Energy is measured in Joules (J) andis a scalar quantity. One Joule of energyequals 0.74 ft·lbs. Energy is a scalar becauseit represents an ability to do work that canbe transferred in any direction. Energy cantake many forms (for example, heat, chem-ical, nuclear, motion, or position). There arethree mechanical energies that are due toan object's motion or position.

The energies of motion are linear andangular kinetic energy. Linear or transla-tional kinetic energy can be calculated us-ing the following formula: KET = ½mv2.There are several important features of thisformula. First, note that squaring velocitymakes the energy of motion primarily de-pendent on the velocity of the object. The


Activity: Impulse–MomentumRelationship

Fill a few small balloons with water toroughly softball size.Throw the water bal-loon vertically and catch it.Throw the bal-loon several times trying to maximize thevertical height thrown. Imagine that thewater balloon represents your bodyfalling and the catching motions representyour leg actions in landing.What catchingtechnique points modify the force andtime of force application to the balloon tocreate a vertical impulse to reduce themomentum of the balloon to zero?

energy of motion varies with the square ofthe velocity, so doubling velocity increasesthe kinetic energy by a factor of 4 (22).Squaring velocity also eliminates the effectof the sign (+ or –) or vector nature of veloc-ity. Angular or rotational kinetic energy canbe calculated with a similar formula: KER =½I�2. We will learn more about angular ki-netics in chapter 7.

The mathematics of kinetic energy(½mv2) looks surprisingly similar to mo-mentum (mv). However, there are majordifferences in these two quantities. First,momentum is a vector quantity describingthe quantity of motion in a particular direc-tion. Second, kinetic energy is a scalar thatdescribes how much work an object in mo-tion could perform. The variable momen-tum is used to document the current stateof motion, while kinetic energy describesthe potential for future interactions. Let'sconsider a numerical example from Ameri-can football. Imagine you are a small (80-kg) halfback spinning off a tackle with oneyard to go for a touchdown. Who wouldyou rather run into just before the goal line:a quickly moving defensive back or a verylarge lineman not moving as fast? Figure6.16 illustrates the differences between ki-netic energy and momentum in an inelasticcollision.

Applying the impulse–momentum re-lationship is interesting because this willtell us about the state of motion or whethera touchdown will be scored. Notice thatboth defenders (small and big) have thesame amount of momentum (–560kg•m/s), but because the big defender hasgreater mass you will not fly backwards asfast as in the collision with the defensiveback. The impulse–momentum relationshipshows that you do not score either way(negative velocity after impact: V2), but thedefensive back collision looks very dramat-ic because you reverse directions with afaster negative velocity. The work–energyrelationship tells us that the total mechani-

cal energy of the collision will be equal tothe work the defender can do on you. Someof this energy is transferred into sound andheat, but most of it will be transferred intodeformation of your pads and body! Notethat the sum of the energies of the two ath-letes and the strong dependence of kineticenergy on velocity results in nearly twice(2240 versus 1280 J) as much energy in thecollision with the defensive back. In short,the defensive back hurts the most because itis a very high-energy collision, potentiallyadding injury to the insult of not scoring.

There are two types of mechanical ener-gy that objects have because of their posi-tion or shape. One is gravitational potentialenergy and the other is strain energy.Gravitational potential energy is the ener-gy of the mass of an object by virtue of itsposition relative to the surface of the earth.Potential energy can be easily calculatedwith the formula: PE = mgh. Potential ener-gy depends on the mass of the object, theacceleration due to gravity, and the heightof the object. Raising an object with a massof 35 kg a meter above the ground stores343 J of energy in it (PE = 35 • 9.81 • 1 = 343).If this object were to be released, the poten-tial energy would gradually be convertedto kinetic energy as gravity accelerated theobject toward the earth. This simple exam-ple of transfer of mechanical energies is anexample of one of the most important lawsof physics: the Law of Conservation ofEnergy.

The Law of Conservation of Energystates that energy cannot be created or de-stroyed; it is just transferred from one formto another. The kinetic energy of a tossedball will be converted to potential energy orpossibly strain energy when it collides withanother object. A tumbler taking off from amat has kinetic energy in the vertical direc-tion that is converted into potential energyon the way up, and back into kinetic energyon the way down. A bowler who increasesthe potential energy of the ball during the


approach can convert this energy to kineticenergy prior to release (Figure 6.17). In asimilar manner, in golf or tennis a forwardswing can convert the potential energyfrom preparatory movement into kineticenergy. A major application area of conser-vation of energy is the study of heat or ther-modynamics.

The First Law of Thermodynamics isthe law of conservation of energy. This is

the good news: when energy is added intoa machine, we get an equal amount of oth-er forms of energy out. Unlike theseexamples, examination of the next mechan-ical energy (strain energy) will illustrate thebad news of the Second Law of Thermo-dynamics: that it is impossible to createa machine that converts all input energyinto some useful output energy. In otherwords, man-made devices will always lose


Figure 6.16. Comparison of the kinetic energy (scalar) and momentum (vector) in a football collision. If you werethe running back, you would not score a touchdown against either defender, but the work done on your bodywould be greater in colliding with the smaller defender because of their greater kinetic energy.

energy in some non-useful form and neverachieve 100% efficiency. This is similar tothe energy losses (hysteresis) in strain ener-gy stored in deformed biological tissuesstudied in chapter 4.

Strain energy is the energy stored inan object when an external force deformsthat object. Strain energy can be viewedas a form of potential energy. A polevaulter stores strain energy in the polewhen loading the pole by planting it in thebox. Much of the kinetic energy stored inthe vaulter's body during the run up is con-verted into strain energy and back into ki-netic energy in the vertical direction.Unfortunately, again, not all the strain ener-gy stored in objects is recovered as usefulenergy. Often large percentages of energyare converted to other kinds of energy thatare not effective in terms of producingmovement. Some strain energy stored inmany objects is essentially lost because it is

converted into sound waves or heat. Somemachines employ heat production to dowork, but in human movement heat is abyproduct of many energy transformationsthat must be dissipated. Heat is often evenmore costly than the mechanical energy inhuman movement because the cardiovas-cular system must expend more chemicalenergy to dissipate the heat created by vig-orous movement.

The mechanical properties of an objectdetermine how much of any strain energyis recovered in restitution as useful work.Recall that many biomechanical tissues areviscoelastic and that the variable hysteresis(area between the loading and unloadingforce-displacement curves) determines theamount of energy lost to unproductive en-ergies like heat. The elasticity of a materialis defined as its stiffness. In many sports in-volving elastic collisions, a simpler variablecan be used to get an estimate of the elastic-


Figure 6.17. Raising a bowling ball in the approach stores more potential energy in the ball than the kinetic ener-gy from the approach. The potential energy of the ball can be converted to kinetic energy in the downswing.

ity or energy losses of an object relative toanother object. This variable is called the co-efficient of restitution (COR and e arecommon abbreviations). The coefficient ofrestitution is a dimensionless number usu-ally ranging from 0 (perfectly plastic colli-sion: mud on your mother's kitchen floor)to near 1 (very elastic pairs of materials).The coefficient of restitution cannot beequal to or greater than 1 because of the sec-ond law of thermodynamics. High coeffi-cients of restitution represent elastic colli-sions with little wasted energy, while lowercoefficients of restitution do not recoveruseful work from the strain energy storedin an object.

The coefficient of restitution can be cal-culated as the relative velocity of separationdivided by the relative velocity of approachof the two objects during a collision (Hatze,1993). The most common use of the coeffi-cient of restitution is in defining the relativeelasticities of balls used in sports. Mostsports have strict rules governing the di-mensions, size, and specifications, includ-ing the ball and playing surfaces. Officialsin basketball or tennis drop balls from astandard height and expect the ball to re-bound to within a small specified range al-lowed by the rules. In these uniformly ac-celerated flight and impact conditionswhere the ground essentially doesn't move,e can be calculated with this formula: e =(bounce/drop)1/2. If a tennis ball weredropped from a 1-meter height and it re-bounded to 58 cm from a concrete surface,the coefficient of restitution would be(58/100)1/2 = 0.76. Dropping the same ten-nis ball on a short pile carpet might result ina 45-cm rebound, for an e = 0.67. The coeffi-cient of restitution for a sport ball varies de-pending on the nature of the other object orsurface it interacts with (Cross, 2000), thevelocity of the collision, and other factorslike temperature. Squash players know thatit takes a few rallies to warm up the balland increase its coefficient of restitution.

Also, putting softballs in a refrigerator willtake some of the slugging percentage out ofa strong hitting team.

Most research on the COR of sport ballshas focused on the elasticity of a ball in thevertical direction, although there is a CORin the horizontal direction that affects fric-tion and the change in horizontal ball veloc-ity for oblique impacts (Cross, 2002). Thehorizontal COR strongly affects the spincreated on the ball following impact. This isa complicated phenomenon because ballsdeform and can slide or rotate on a surfaceduring impact. How spin, in general, affectsthe bounce of sport balls will be briefly dis-cussed in the section on the spin principlein chapter 8.

Mechanical Work

All along we have been defining mechani-cal energies as the ability to do mechanicalwork. Now we must define work and un-derstand that this mechanical variable isnot exactly the same as most people's com-mon perception of work as some kind of ef-fort. The mechanical work done on an ob-ject is defined as the product of the forceand displacement in the direction of theforce (W = F • d). Joules are the units ofwork: one joule of work is equal to one Nm.In the English system, the units of work areusually written as foot-pounds (ft•lb) toavoid confusion with the angular kineticvariable torque, whose unit is the lb•ft. Apatient performing rowing exercises(Figure 6.18) performs positive work (W =70 • 0.5 = +35 Nm or Joules) on the weight.In essence, energy flows from the patient tothe weights (increasing their potential ener-gy) in the concentric phase of the exercise.In the eccentric phase of the exercise thework is negative, meaning that potentialenergy is being transferred from the load tothe patient's body. Note that the algebraicformula assumes the force applied to the


load is constant over the duration of themovement. Calculus is necessary to calcu-late the work of the true time-varyingforces applied to weights in exercises. Thisexample also assumes that the energy loss-es in the pulleys are negligible as theychange the direction of the force created bythe patient.

Note that mechanical work can only bedone on an object when it is moved relativeto the line of action of the force. A morecomplete algebraic definition of mechani-cal work in the horizontal (x) direction thattakes into account the component of mo-tion in the direction of the force on an objectwould be W = (F cos �) • dx. For example, aperson pulling a load horizontally on a dol-ly given the data in Figure 6.19 would do435 Nm or Joules of work. Only the hori-zontal component of the force times the dis-placement of object determines the workdone. Note also that the angle of pull in thisexample is like the muscle angle of pull an-alyzed earlier. The smaller the angle of pull,the greater the horizontal component of theforce that does work to move the load.

The vertical component of pull doesnot do any mechanical work, although itmay decrease the weight of the dolly orload and, thereby decrease the rolling fric-tion to be overcome. What is the best angleto pull in this situation depends on manyfactors. Factoring in rolling friction and thestrength (force) ability in various pullingpostures might indicate that a higher angleof pull that doesn't maximize the horizontalforce component may be “biomechanical-ly” effective for this person. The inertia ofthe load, the friction under the person'sfeet, and the biomechanical factors ofpulling from different postures all interactto determine the optimal angle for pullingan object. In fact, in some closed kinematicchain movements (like cycling) the optimaldirection of force application does not al-ways maximize the effectiveness or thecomponent of force in the direction of mo-tion (Doorenbosch et al., 1997).

Mechanical work does not directly cor-respond to people's sense of muscular ef-fort. Isometric actions, while taking consid-erable effort, do not perform mechanical


Figure 6.18. The mechanical work done on a weight in this rowing exercise is the product of the force and thedisplacement.

work. This dependence on the object’s dis-placement of mechanical work makes thework–energy relationship useful in biome-chanical studies where the motion of anobject may be of more interest than tempo-ral factors.

This brings us to the Work–EnergyRelationship, which states that the me-chanical work done on an object is equal tothe change in mechanical energy of that ob-ject. Biomechanical studies have used thework–energy relationship to study the ki-netics of movements. One approach calcu-lates the changes in mechanical energies ofthe segments to calculate work, while theother calculates mechanical power and in-tegrates these data with respect to time tocalculate work. The next section will dis-cuss the concept of mechanical power.

Mechanical Power

Mechanical power is an important kineticvariable for analyzing many human move-ments because it incorporates time. Poweris defined as the rate of doing work, so me-chanical power is the time derivative of me-chanical work or work divided by time (P =W/t). Note that a capital “P” is used be-cause lower-case “p” is the symbol for mo-

mentum. Typical units of power are Watts(one J/s) and horsepower. One horsepoweris equal to 746 W. Maximal mechanicalpower is achieved by the right combinationof force and velocity that maximizes themechanical work done on an object. This isclear from the other formula for calculatingpower: P = F • v. Prove to yourself that thetwo equations for power are the same bysubstituting the formula for work W anddo some rearranging that will allow you tosubstitute v for its mechanical definition.

If the concentric lift illustrated inFigure 6.18 was performed within 1.5 sec-onds, we could calculate the average pow-er flow to the weights. The positive workdone on the weights was equal to 35 J, so P= W/t = 35/1.5 = 23.3 W. Recall that thesealgebraic definitions of work and powercalculate a mean value over a time intervalfor constant forces. The peak instantaneouspower flow to the weight in Figure 6.18would be higher than the average powercalculated over the whole concentric phaseof the lift. The Force–Motion Principlewould say that the patient increased thevertical force on the resistance to more thanthe weight of the stack to positively acceler-ate it and would reduce this force to belowthe weight of the stack to gradually stop the


Figure 6.19. Mechanical work is calculated as displacement of the object in the direction of the force. This calcu-lation is accurate if the 80-N force is constant during horizontal displacement of the dolly. If you were pulling thisdolly, what angle of pull would you use?

weight at the end of the concentric phase.Instantaneous power flow to the weightsalso follows a complex pattern based on acombination of the force applied and themotion of the object.

What movements do you think requiregreater peak mechanical power deliveredto a barbell: the lifts in the sport of Olympicweight lifting or power lifting? Don't let thenames fool you. Since power is the rate ofdoing work, the movements with the great-est mechanical power must have highforces and high movement speeds. Olym-pic lifting has mechanical power outputsmuch higher than power lifting, and powerlifting is clearly a misnomer given the truedefinition of power. The dead lift, squat,and bench press in power lifting are high-strength movements with large loads butvery slow velocities. The faster movementsof Olympic lifting, along with smallerweights, clearly create a greater power flowto the bar than power lifting. Peak powerflows to the bar in power lifting are be-tween 370 and 900 W (0.5–1.2 hp), while thepeak power flow to a bar in Olympic lifts isoften as great as 4000 W or 5.4 hp (see Gar-hammer, 1989). Olympic lifts are often usedto train for “explosive” movements, andOlympic weight lifters can create signifi-cantly more whole-body mechanical powerthan other athletes (McBride, Triplett-McBride, Davie, & Newton, 1999).

Many people have been interested inthe peak mechanical power output ofwhole-body and multi-segment move-ments. It is believed that higher power out-put is critical for quick, primarily anaerobicmovements. In the coaching and kinesiolo-gy literature these movements have beendescribed as “explosive.” This terminologymay communicate the point of high rates offorce development and high levels of bothspeed and force, but a literal interpretationof this jargon is not too appealing!Remember that the mechanical power out-put calculated for a human movement will

strongly depend on the model (point mass,linked segment, etc.) used and the time in-terval used in the calculation. The averageor instantaneous power flows within thebody and from the body to external objectsare quite different. In addition, other bio-mechanical factors affect how much me-chanical power is developed during move-ments.

The development of maximal poweroutput in human movement depends onthe direction of the movement, the numberof segments used, and the inertia of the ob-ject. If we're talking about a simple move-ment with a large resistance, the right mixof force and velocity may be close to 30 to45% of maximal isometric strength becauseof the Force–Velocity Relationship (Izqui-erdo et al., 1999; Kaneko et al., 1983; Wilsonet al., 1993). Figure 6.20 shows the in vitroconcentric power output of skeletal musclederived from the product of force and ve-locity in the Force–Velocity Relationship. Inmovements requiring multi-joint move-ments, specialized dynamometer measure-ments indicate that the best resistances forpeak power production and training arelikely to be higher than the 30–45% and dif-fer between the upper and lower extremi-


Figure 6.20. The in vitro mechanical power outputof skeletal muscle. Note that peak power in concentricactions does not occur at either the extremes of force orvelocity.

ties (Funato et al., 1996, 2000; Newton et al.,1996). The best conditioning for “explo-sive” movements may be the use of moder-ate resistances (just less than strength levelsthat are usually >70% 1RM), which aremoved as quickly as possible. Oftentimesthese exercises use special equipment likethe Plyometric Power System, which al-lows for the resistance to be thrown(Wilson et al., 1993). The disadvantage ofhigh-speed exercise is that it focuses train-ing on the early concentric phase, leavingmuch of the range of motion submaximallytrained. Even slow, heavy weight trainingexercises have large submaximal percent-ages (24–52%) of range of motion due tonegative acceleration of the bar at the endof the concentric phase (Elliott, Wilson, &Kerr, 1989).

There are several field tests to estimateshort-term explosive leg power, but theutility and accuracy of these tests are con-troversial. The Margaria test (Margaria,Aghemo, & Rovelli, 1966) estimatespower from running up stairs, and various


Interdisciplinary Issue: Efficiency

One area of great potential for interdiscipli-nary cooperation is in determining the effi-ciency of movement.This efficiency of humanmovement is conceptually different from theclassical definition of efficiency in physics.Physics defines efficiency as the mechanicalwork output divided by the mechanical workinput in a system, a calculation that helps en-gineers evaluate machines and engines. Forendurance sports like distance running, ad-justing a formula to find the ratio of mechan-ical energy created to metabolic cost appearsto be an attractive way to study human move-ment (van Ingen Schenau & Cavanagh, 1999).Progress in this area has been hampered bythe wide variability of individual performanceand confusion about the various factors thatcontribute to this movement efficiency(Cavanagh & Kram, 1985). Cavanagh andKram argued that the efficiency of running,for example, could be viewed as the sum ofseveral efficiencies (e.g., biochemical, biome-chanical, physiological, psychomotor) and oth-er factors. Examples of the complexity of thisarea are the difficulty in defining baselinemetabolic energy expenditure and calculatingthe true mechanical work because morework is done than is measured by ergome-ters. For instance, in cycle ergometry the me-chanical work used to move the limbs is notmeasured. Biomechanists are also strugglingto deal with the zero-work paradox in move-ments where there no net mechanical workis done, like in cyclic activities, co-contractingmuscles, or forces applied to the pedal in anineffective direction. Figure 6.21 illustratesthe typical forces applied to a bicycle pedal at90º (from vertical).The normal component ofthe pedal force does mechanical work in ro-tating the pedal (FN), while the other compo-nent does no work that is transferred to thebike's flywheel.Movement efficiency is an areawhere cooperative and interdisciplinary re-search may be of interest to many scientistsand may be an effective tool for improvinghuman movement.

Figure 6.21. Only some of the force applied to a bicy-cle pedal creates work and mechanical power. Notehow the angle of the pedal illustrated means that asmall component of FT actually resists the normal force(FN) creating rotation.

vertical jump equations (see Johnson &Bahamonde, 1996; Sayers, Harackiewicz,Harman, Frykman, & Rosenstein, 1999)have been proposed that are based on theoriginal Sargent (1921) vertical jump test.Companies now sell mats that estimate theheight and power of a vertical jump (fromtime and projectile equations). Althoughmechanical power output in such jumps ishigh, these tests and devices are limited be-cause the resistance is limited to body mass,the many factors that affect jump height,and the assumptions used in the calcula-tion. There has been a long history of criti-cism of the assumptions and logic of usingvertical jump height to estimate muscularpower (Adamson & Whitney, 1971; Barlow,1971; Winter, 2005). Instantaneous meas-urements of power from force platforms orkinematic analysis are more accurate butare expensive and time-consuming. Futurestudies will help determine the role of me-chanical power in various movements,how to train for these movements, andwhat field tests help coaches monitor ath-letes.

SEGMENTAL INTERACTIONPRINCIPLE

Human movement can be performed in awide variety of ways because of the manykinematic degrees of freedom our linkedsegments provide. In chapter 5 we saw that

coordination of these kinematic chainsranges along a continuum from simultane-ous to sequential. Kinetics provides severalways in which to examine the potentialcauses of these coordination patterns. Thetwo expressions of Newton's second lawand the work–energy relationship havebeen employed in the study of the coordi-nation of movement. This section proposesa Principle of Segmental Interaction thatcan be used to understand the origins ofmovement so that professionals can modifymovement to improve performance and re-duce risk of injury.

The Segmental Interaction Principlesays that forces acting between the seg-ments of a body can transfer energy be-tween segments. The biomechanics litera-ture has referred to this phenomenon inseveral ways (Putnam, 1993). The contribu-tion of body segments to movement hasbeen called coordination of temporal im-pulses (Hochmuth & Marhold, 1978), thekinetic link principle (Kreighbaum & Bar-thels, 1996), summation of speed (Bunn,1972), summation or continuity of jointtorques (Norman, 1975), the sequential orproximal-to-distal sequencing of move-ment (Marshall & Elliott, 2000), and thetransfer of energy or transfer of momentum(Lees & Barton, 1996; Miller, 1980). Themany names for this phenomenon and thethree ways to document kinetics are a goodindication of the difficulty of the problem


Application: Strength vs. Power

The force–velocity relationship and domains of strength discussed in chapter 4, as well as this chapter's discussionof mechanical power should make it clear that muscular strength and power are not the same thing. Like the pre-vious discussion on power lifting, the common use of the term power is often inappropriate. Muscular strength isthe expression of maximal tension in isometric or slow velocities of shortening.We have seen that peak power isthe right combination of force and velocity that maximizes mechanical work. In cycling, the gears are adjusted tofind this peak power point. If cadence (pedal cycles and, consequently, muscle velocity of shortening) is too high,muscular forces are low and peak power is not achieved. Similarly, power output can be submaximal if cadence istoo slow and muscle forces high.The right mix of force and velocity seems to be between 30 and 70% of maxi-mal isometric force and depends on the movement. Kinesiology professionals need to keep up with the growingresearch on the biomechanics of conditioning and sport movements. Future research will help refine our under-standing of the nature of specific movements and the most appropriate exercise resistances and training programs.

and the controversial nature of the causesof human motion.

Currently it is not possible to have de-finitive answers on the linear and angularkinetic causes for various coordinationstrategies. This text has chosen to empha-size the forces transferred between seg-ments as the primary kinetic mechanismfor coordination of movement. Most elec-tromyographic (EMG) research has shownthat in sequential movements muscles areactivated in short bursts that are timed totake advantage of the forces and geometrybetween adjacent segments (Feldman et al.,1998; Roberts, 1991). This coordination ofmuscular kinetics to take advantage of“passive dynamics” or “motion-depend-ent” forces (gravitational, inertial forces)has been observed in the swing limb duringwalking (Mena, Mansour, & Simon, 1981),running (Phillips, Roberts, & Huang, 1983),kicking (Roberts, 1991), throwing (Feltner,1989; Hirashima, Kadota, Sakurai, Kudo, &Ohtsuki, 2002), and limb motions towardtargets (Galloway & Koshland, 2002) andlimb adjustments to unexpected obstacles(Eng, Winter, & Patla, 1997).

Some biomechanists have theorizedthat the segmental interaction that drivesthe sequential strategy is a transfer of ener-gy from the proximal segment to the distalsegment. This theory originated from ob-servations of the close association betweenthe negative acceleration of the proximalsegment (see the activity on SegmentalInteraction below) with the positive accel-eration of the distal segment (Plagenhoef,1971; Roberts, 1991). This mechanism is log-ically appealing because the energy of largemuscle groups can be transferred distallyand is consistent with the large forces andaccelerations of small segments late in base-ball pitching (Feltner & Dapena, 1986;Fleisig, Andrews, Dillman, & Escamilla,1995; Roberts, 1991). Figure 6.22 illustratesa schematic of throwing where the negativeangular acceleration of the arm (��A) creates

a backward elbow joint force (FE) that accel-erates the forearm (��FA). This view of theSegment Interaction Principle states thatslowing the larger proximal segment willtransfer energy to the distal segment. Itis clear that this movement strategy is high-ly effective in creating high-speed move-ments of distal segments, but the exactmechanism of the segmental interactionprinciple is not clear.

When you get down to this level of ki-netics, you often end up with a chicken-or-egg dilemma. In other words, whichforce/torque was created first and which isthe reaction force/torque (Newton's thirdlaw)? There are some scholars who havederived equations that support the proxi-mal-to-distal transfer of energy (Hong,Cheung, & Roberts, 2000; Roberts, 1991),while others show that the acceleration of


Figure 6.22. Simple sagittal plane model of throwingillustrates the Segmental Interaction Principle. Jointforces (FE) from a slowing proximal segment create asegmental interaction to angularly accelerate the moredistal segments (��FA).

the distal segment causes slowing of theproximal segment (Putnam, 1991, 1993;Nunome et al., 2002, 2006; Sorensen et al.,1996). Whatever the underlying mechanismor direction of transfer, fast human move-ments utilize a sequential (proximal-to-dis-tal) coordination that relies on the transferof forces/energy between segments. We aretruly fortunate to have so many musclesand degrees of freedom to create a wide va-riety and speeds of motion.

A good example of the controversy re-lated to the Segmental Interaction Principleis the role of the hand and wrists in the golfswing. Skilled golf shots can be accuratelymodeled as a two-segment (arm and club)system with motion occurring in a diagonalplane. Golf pros call this the swing plane.Some pros say the golfer should activelydrive the club with wrist action, while oth-ers teach a relaxed or more passive wrist re-lease. A recent simulation study found thatcorrectly timed wrist torques could in-crease club head speed by 9% (Sprigings &Neal, 2000), but the small percentage andtiming of these active contributions sug-gests that proximal joint forces are the pri-mary accelerator of the club. Jorgensen(1994) has provided simple qualitativedemonstrations and convincing kineticdata that support the more relaxed use ofwrist action and explain how weight shiftscan be timed to accelerate the golf club.

It is clear that forces are transferred be-tween segments to contribute to the motionof the kinematic chain (Zajac & Gordon,1989). The exact nature of that segmentalinteraction remains elusive, so kinesiologyprofessionals can expect performers to havea variety (sequential to simultaneous) ofcombinations of joint motion. It would beunwise to speculate too much on the mus-cular origins of that transfer. This view isconsistent with the EMG and biomechani-cal modeling research reviewed in chapter3. So how can kinesiology professionalsprescribe conditioning exercises and learn-ing progressions so as to maximize the seg-mental interaction effect? Currently, thereare few answers, but we can make a fewtentative generalizations about condition-ing and learning motor skills.

Physical conditioning for any humanmovement should clearly follow the train-ing principle of specificity. Biomechanically,this means that the muscular actions andmovements should emulate the movementas much as possible. Since the exact kineticmechanism of segmental interaction is notclear, kinesiology professionals shouldselect exercises that train all the musclesinvolved in a movement. In soccer kicking,it is not clear whether it is the activity of thequadriceps or hip flexors that predomi-nantly contribute to acceleration of the low-er leg. Selecting exercises that train both


Activity: Segmental Interaction

Segmental interaction or the transfer of energy from a proximal to a distal segment can beeasily simulated using a two-segment model. Suspend a rigid stick (ruler, yardstick, racket) be-tween the tips of your index finger and thumb. Using your hand/forearm as the proximal seg-ment and the stick as the distal segment, simulate a kick.You can make the stick extend or kickwithout any extensor muscles by using intersegmental reaction forces.Accelerate your arm inthe direction of the kick (positive).When you reach peak speed, rapidly slow (negatively ac-celerate) your arm and observe the positive acceleration of the stick. Positive acceleration ofyour arm creates an inertial lag in the stick, while negative acceleration of your arm creates abackward force at the joint, which creates a torque that positively accelerates the stick.

muscles is clearly indicated. More recenttrends in rehabilitation and conditioninghave focused on training with “functional”movements that emulate the movement,

rather than isolating specific musclegroups. The resistance, body motion,speed, and balance aspects of “functional”exercises may be more specific forms oftraining; unfortunately, there has been lim-ited research on this topic.

Learning the sequential coordination ofa large kinematic chain is a most difficulttask. Unfortunately, there have been rela-tively few studies on changes in joint kinet-ics accompanied by learning. Assumingthat the energy was transferred distally ina sequential movement (like our immaturevolleyball spike in the previous chapter), itwould not be desirable to practice the skillin parts because there would be no energyto learn to transfer. Recent studies have re-inforced the idea that sequential skillsshould be learned in whole at submaximalspeed, rather than in disconnected parts(see Sorensen, Zacho, Simonsen, Dyhre-Poulsen, & Klausen, 2000). Most modelingand EMG studies of the vertical jump havealso shown the interaction of muscle acti-vation and coordination (Bobbert & vanZandwijk, 1999; Bobbert & van Soest, 1994;van Zandwijk, Bobbert, Munneke, & Pas,2000), while some other studies haveshown that strength parameters do not af-fect coordination (Tomioka, Owings, &Grabiner, 2001). Improvements in comput-ers, software, and biomechanical modelsmay allow more extensive studies of thechanges in kinetics as skills are learned.Currently, application of the SegmentalInteraction Principle involves correctionsin body positioning and timing. Practiceshould focus on complete repetitions of thewhole skill performed at submaximalspeeds. Improvement should occur withmany practice repetitions, while graduallyincreasing speed. This perspective is consis-tent with more recent motor learning inter-est in a dynamical systems theory under-standing of coordination, rather than cen-tralized motor program (Schmidt & Wris-berg, 2000).


Interdisciplinary Issue:Kinematic Chain

A kinematic chain is an engineeringterm that refers to a series of linkedrigid bodies.The concept of kinematicchains was developed to simplify themathematics of the kinematics andkinetics of linked mechanical systems.A classic biomechanics textbook(Steindler, 1955) adapted this termi-nology to refer to the linked segmentsof the human body as a “kinetic chain”and to classify movements as primari-ly “open” or “closed” kinetic chains.Aclosed kinetic chain is a movementwhere the motion of the distal seg-ment is restrained by “considerableexternal resistance.” Over the years,the rehabilitation and conditioningprofessions have adopted this termi-nology, referring to open kinetic chainexercises (knee extension) and closedkinetic chain exercises (leg press orsquat). Considerable research has fo-cused on the forces and muscle activa-tion involved in various exercises clas-sified as open or closed kinetic chains.This research has shown both similar-ities and differences in muscular func-tion between similar open and closedkinetic chain movements. There are,however, problems in uniquely defin-ing a closed chain or what constitutes“considerable resistance.” The vaguenature of the classification of many ex-ercises has prompted calls to avoidthis terminology (Blackard et al., 1999;di Fabio, 1999; Dillman et al., 1994).

SUMMARY

Linear kinetics is the study of the causes oflinear motion. There are several laws of me-chanics that can be applied to a study of thecauses of linear motion: Newton's laws, theimpulse–momentum relationship, and thework–energy relationship. The most com-mon approach involves Newton's Laws ofMotion, called the laws of Inertia, Momen-

tum/Acceleration, and Reaction. Inertia is thetendency of all objects to resist changes intheir state of motion. The Inertia Principlesuggests that reducing mass will make ob-jects easier to accelerate, while increasingmass will make objects more stable andharder to accelerate. Applying the InertiaPrinciple might also mean using more massin activities where there is time to overcomethe inertia, so that it can be used later in the


Application:Arm Swing Transfer of Energy

Many movements incorporate an arm swing that is believed to contribute to performance.How much does arm swing contribute to vertical jump performance? Several studies haveshown that the height of a jump increases by about 10% with compared to those without armswing (see Feltner, Fraschetti, & Crisp, 1999).There are several possible mechanisms involvingmultiple transfers of energy or momentum between the arms and body (Lees et al., 2004).Logically, vigorous positive (upward) acceleration of the arms creates a downward reactionforce on the body that increases the vertical ground reaction force. It has also been hypothe-sized that this downward force creates a pre-loading effect on the lower extremities that lim-its the speed of knee extension, allowing greater quadriceps forces because of theForce–Velocity Relationship.A detailed kinetic study (Feltner et al., 1999) found that augment-ing knee torques early in a jump with arm swings combined with slowing of trunk extensionlate in the jump may be the mechanisms involved in a good arm swing during a vertical jump.Late in the jump, the arms are negatively accelerated, creating a downward force at the shoul-der that slows trunk extension and shortening of the hip extensors.While the arms do notweigh a lot, the vigor of these movements does create large forces, which can be easily seenby performing this arm swing pattern standing on a force platform.

What segmental interactions create and transfer this energy? This answer is less clear anddepends on the model and kinetic variable used during analysis.The muscular and segmentalcontributions to a vertical jump have been analyzed using force platforms (Luthanen & Komi,1978a,b), computer modeling (Bobbert & van Soest, 1994; Pandy, Zajac, Sim, & Levine, 1990),joint mechanical power calculations (Fukashiro & Komi, 1987; Hubley & Wells, 1983; Nagano,Ishige, & Fukashiro, 1998), angular momentum (Lees & Barton, 1996), and net joint torque con-tributions to vertical motion (Feltner et al., 1999, 2004; Hay,Vaughan, & Woodworth, 1981).While the jumping technique may look quite similar, there is considerable between-subjectvariation in the kinetics of the vertical jump (Hubley & Wells, 1983).The problems involved inpartitioning contributions include defining energy transfer, energy transfer of biarticular mus-cles, muscle co-activation, and bilateral differences between limbs.While there is much yet tolearn, it appears that the hip extensors contribute the most energy, closely followed by theknee extensors, with smaller contributions by the ankle plantar flexors. Conditioning for ver-tical jumping should utilize a variety of jumps and jump-like exercises. If specific muscle groupsare going to be isolated for extra training, the hip and knee extensors appear to be the groupswith the greatest contribution to the movement.

movement. When two objects are in con-tact, the forces of interaction between thebodies are resolved into right-angle direc-tions: normal reaction and friction. The Im-

pulse–Momentum Relationship says thatthe change in momentum of an object isequal to the impulse of the resultant forcesacting on the object. This is Newton's sec-ond law when applied over a time interval.The real-world application of this relation-ship is the Force–Time Principle. Energy isthe capacity to do mechanical work; me-chanical energies include strain, potential,and kinetic energy. The Work–Energy Rela-tionship says that mechanical work equalsthe change in mechanical energy. Mechani-cal power is the rate of doing work, and canalso be calculated by the product of forceand velocity. The Segmental InteractionPrinciple says that energy can be trans-ferred between segments. While the exactnature of these transfers has been difficultto determine, both simultaneous and se-quentially coordinated movements takeadvantage of the energy transferredthrough the linked segment system of thebody.

REVIEW QUESTIONS

1. Which has more inertia, a 6-kg bowl-ing ball sitting on the floor or one rollingdown the lane? Why?

2. What are the two ways to expressNewton's second law?

3. When might it be advantageous for aperson to increase the inertia used in amovement?

4. Do smaller or larger muscle angles ofpull on a distal segment tend to create morejoint rotation? Why?

5. What are strategies to increase the fric-tion between a subject's feet and the floor?

6. What two things can be changed toincrease the impulse applied to an object?What kinds of human movement favor oneover the other?

7. If the force from the tibia on the fe-mur illustrated below was 1000 N acting at30º to the femur, what are the longitudinal


Interdisciplinary Issue:Power in Vertical Jumping

One of the contentious uses of theword “power” occurs in the strengthand conditioning literature, specificallyas it relates to the use of the verticaljump as a measure of lower extremitymuscular function. Soon after theSargent (1921) jump test that waspublished, many authors have tried touse the standing vertical jump as ameasure of the external power or“explosive” anaerobic power.There isa correlation between measures ofexternal power flow to a force plat-form and jump height, so many regres-sion equations can be used to esti-mate average or peak power fromjump height and body mass. Despiteeloquent arguments, Newton’sSecond law, and experiments showingnet impulse is really the mechanicalvariable that determines jump height(Adamson & Whitney, 1971; Barlow,1971;Winter, 2005), the coaching andconditioning literature continues touse the terms “muscular” or “musclepower” in misleading ways related tovertical jump tests. Students can helpthe field progress by correct use ofterminology and contributing to inter-disciplinary research in this area.When measurement, biomechanics,strength and conditioning, and exer-cise physiology scholars collaborateand consistently use terminology, realprogress can be made in understand-ing muscular performance.

(causing knee compression) and normal(knee shear) components of this force?Hint: move one component to form a righttriangle and solve.

8. Give human movement examples ofthe three mechanical energies.

9. Compare and contrast muscularstrength and muscular power.

10. How is momentum different fromkinetic energy?

11. A rock climber weighing 800 N hasfallen and is about to be belayed (caughtwith a safety rope) by a 1500-N verticalforce. Ignoring the weight of the rope andsafety harness, what is the vertical acceler-ation of the climber? Hint: remember tosum forces with correct signs (related to di-rection).

12. Draw a free-body diagram of aproximal segment of the body showing allforces from adjacent segments. Draw a freebody diagram of an adjacent segment usingNewton's third law to determine the sizeand direction at the joint.

13. What are the potential kineticmechanisms that make a sequential motionof segments in high-speed movements theoptimal coordination?

14. Do the angles of pull (relative to thebody) of free weights change during an ex-ercises? Why?

15. An Olympic lifter exerts a 4000-Nupward (vertical) force to a 30-kg barbell.What direction will the bar tend to move,and what is its vertical acceleration?

KEY TERMS

conservation of energy (Law ofConservation of Energy)

degrees of freedomdirect dynamicsenergyforce platformforce–time principlefrictionimpulseimpulse–momentum relationshipinverse dynamicskinetic energyLaw of AccelerationLaw of InertiaLaw of Reactionmomentumnormal reactionpotential energypower (mechanical)strain energywork (mechanical)work–energy relationship

SUGGESTED READING

Abernethy, P., Wilson, G., & Logan, P. (1995).Strength and power assessment: Issues, contro-versies and challenges. Sports Medicine, 19,401–417.

Cavanagh, P. R., & LaFortune, M. A. (1980).Ground reaction forces in distance running.Journal of Biomechanics, 15, 397–406.

Dowling, J. J., & Vamos, L. (1993). Identifica-tion of kinetic and temporal factors related tovertical jump performance. Journal of AppliedBiomechanics, 9, 95–110.


Jorgensen, T. P. (1994). The physics of golf. NewYork: American Institute of Physics.

Lees, A., & Barton, G. (1996). The interpretationof relative momentum data to assess the contri-bution of the free limbs to the generation ofvertical velocity in sports activities. Journal ofSports Sciences, 14, 503–511.

McPoil, T. G., Cornwall, M. W., & Yamada, W.(1995). A comparison of two in-shoe plantarpressure measurement systems. The LowerExtremity, 2, 95–103.

Schieb, D. A. (1987, January). The biomechan-ics piezoelectric force plate. Soma, 35–40.

Zatsiorsky, V. M. (2002). Kinetics of human mo-tion. Champaign, IL: Human Kinetics.

Zajac, F. E. (2002). Understanding muscle co-ordination of the human leg with dynamicalsimulations. Journal of Biomechanics, 35,1011–1018.

Zajac, F. E., & Gordon, M. E. (1989). Deter-mining muscle's force and action in multi-artic-ular movement. Exercise and Sport SciencesReviews, 17, 187–230.


WEB LINKS

Linear Kinetics—Page on the kinetics of winter olympic sports by Debra King andcolleagues from Montana State University.

http://btc.montana.edu/olympics/physbio/physics/dyn01.html

Ankle power flow tutorial from the Clinical Gait Analysis website.http://guardian.curtin.edu.au:16080/cga/teach-in/plantarflexors/

Kinetics Concepts—See the Newton’s Laws, momentum, and work and energy tuto-rials from the The Physics Classroom.

http://www.physicsclassroom.com/mmedia/index.html

Angular kinetics explains the causes of ro-tary motion and employs many variablessimilar to the ones discussed in the previ-ous chapter on linear kinetics. In fact,Newton's laws have angular analogues thatexplain how torques create rotation. Thenet torque acting on an object creates an an-gular acceleration inversely proportional tothe angular inertia called the moment of in-ertia. Angular kinetics is quite useful be-cause it explains the causes of joint rota-tions and provides a quantitative way todetermine the center of gravity of the hu-man body. The application of angular kinet-ics is illustrated with the principles ofInertia and Balance.

TORQUE

The rotating effect of a force is called atorque or moment of force. Recall that amoment of force or torque is a vector quan-tity, and the usual two-dimensional con-vention is that counterclockwise rotationsare positive. Torque is calculated as theproduct of force (F) and the moment arm.The moment arm or leverage is the perpen-dicular displacement (d⊥) from the line ofaction of the force and the axis of rotation(Figure 7.1). The biceps femoris pictured inFigure 7.1 has moment arms that create hipextension and knee flexion torques. An im-portant point is that the moment arm is al-ways the shortest displacement betweenthe force line of action and axis of rotation.This text will use the term torque synony-

mously with moment of force, even thoughthere is a more specific mechanics-of-mate-rials meaning for torque.

CHAPTER 7

Angular Kinetics

169

Figure 7.1. The moment arms (d⊥) for the bicepsfemoris muscle. A moment arm is the right-angle dis-tance from the line of action of the force to the axis ofrotation.

In algebraic terms, the formula fortorque is T = F • d⊥, so that typical units oftorque are N•m and lb•ft. Like angular kine-matics, the usual convention is to call coun-terclockwise (ccw) torques positive andclockwise ones negative. Note that the sizeof the force and the moment arm are equal-ly important in determining the size of thetorque created. This has important implica-tions for maximizing performance in manyactivities. A person wanting to create moretorque can increase the applied force or in-crease their effective moment arm. In-creasing the moment arm is often easierand faster than months of conditioning!Figure 7.2 illustrates two positions where atherapist can provide resistance with ahand dynamometer to manually test theisometric strength of the elbow extensors.By positioning their arm more distal (posi-tion 2), the therapist increases the momentarm and decreases the force they must cre-ate to balance the torque created by the pa-tient and gravity (Tp).


Figure 7.2. Increasing the moment arm for the thera-pist's (position 2) manual resistance makes it easier toperform a manual muscle test that balances the exten-sor torque created by the patient (Tp).

Activity:Torque and Levers

Take a desk ruler (�12-inch) and bal-ance it on a sturdy small cylinder likea highlighter. Place a dime at the 11-inch position and note the behaviorof the ruler.Tap the 1-inch position onthe ruler with your index finger andnote the motion of the dime. Whichtorque was larger: the torque createdby the dime or your finger? Why? Tapthe ruler with the same effort on dif-ferent positions on the ruler with thedime at 11 inches and note the mo-tion of the dime. Modify the position(axis of rotation) of the highlighter tomaximize the moment arm for thedime and note how much force yourfinger must exert to balance the leverin a horizontal position. How muchmotion in the dime can you create ifyou tap the ruler? In these activitiesyou have built a simple machine calleda lever.A lever is a nearly rigid objectrotated about an axis. Levers can bebuilt to magnify speed or force. Mosthuman body segment levers magnifyspeed because the moment arm forthe effort is less than the momentarm for the resistance being moved.Abiceps brachii must make a large forceto make a torque larger than thetorque created by a dumbbell, but asmall amount of shortening of themuscle creates greater rotation andspeed at the hand. Early biomechani-cal research was interested in usinganatomical leverage principles for atheory of high-speed movements, butthis turned out to be a dead endbecause of the discovery of sequentialcoordination of these movements(Roberts, 1991).

Let's look at another example of apply-ing forces in an optimal direction to maxi-mize torque output. A biomechanics stu-dent takes a break from her studies to bringa niece to the playground. Let's calculatethe torque the student creates on the merry-go-round by the force F1 illustrated inFigure 7.3. Thirty pounds of force times themoment arm of 4 feet is equal to 120 lb•ft oftorque. This torque can be considered posi-tive because it acts counterclockwise. If onthe second spin the student pushes with thesame magnitude of force (F2) in a differentdirection, the torque and angular motioncreated would be smaller because of thesmaller moment arm (dB). Use the conver-sion factor in Appendix B to see how manyN•m are equal to 120 lb•ft of torque.

Good examples of torque measure-ments in exercise science are the jointtorques measured by isokinetic dyna-mometers. The typical maximum isometrictorques of several muscle groups for malesare listed in Table 7.1. These torques shouldgive you a good idea of some “ballpark”maximal values for many major joints. Peak

torques from inverse dynamics in sportingmovements can be larger than those seenin isokinetic testing because of antagonistactivity in isokinetics testing, segment in-teraction in dynamic movements, thestretch-shortening cycle, and eccentricmuscle actions. Most isokinetic norms arenormalized to bodyweight (e.g., lb•ft/lb)and categorized by gender and age. Recall

CHAPTER 7:ANGULAR KINETICS 171

Figure 7.3. Calculating the torque created by a person pushing on a merry-go-round involves multiplying theforce times its moment arm. This torque can be converted to other units of torque with conversion factors(Appendix B).

TABLE 7.1

Typical Isometric Joint Torques Measuredby Isokinetic Dynamometers

Peak torquesN•m lb•ft

Trunk extension 258 190Trunk flexion 177 130Knee extension 204 150Knee flexion 109 80Hip extension 150 204Ankle plantar flexion 74 102Elbow flexion 20 44.6Wrist flexion 8 11Wrist extension 4 5

that the shape of the torque-angle graphsfrom isokinetic testing reflects the integra-tion of many muscle mechanical variables.The angle of the joints affects the torquethat the muscle group is capable of produc-

ing because of variations in moment arm,muscle angle of pull, and the force–lengthrelationship of the muscle. There are sever-al shapes of torque-angle diagrams, butthey most often look like an inverted “U”because of the combined effect of changesin muscle moment arm and force–length re-lationship (Figure 7.4).

Torque is a good variable to use for ex-pressing muscular strength because it is notdependent on the point of application offorce on the limb. The torque an isokineticmachine (T) measures will be the same foreither of the two resistance pad locations il-lustrated in Figure 7.5 if the subject's effortis the same. Sliding the pad toward the sub-ject's knee will decrease the moment armfor the force applied by the subject, increas-ing the force on the leg (F2) at that point tocreate the same torque. Using torque in-stead of force created by the subject allowsfor easier comparison of measurements be-tween different dynamometers.


Figure 7.4. Joint torque–angle diagrams represent thestrength curves of muscle groups. The shapes of jointsvary based primarily upon the combined effect ofchanges in muscle length properties and muscle mo-ment arms. Reprinted by permission from Zatsiorsky(1995).

Figure 7.5. Isokinetic dynamometers usually measuretorque because torque does not vary with variation inpad placement. Positioning the pad distally decreasesthe force the leg applies to the pad for a given torquebecause the moment arm for the leg is larger.

SUMMING TORQUES

The state of an object's rotation depends onthe balance of torques created by the forcesacting on the object. Remember that sum-ming or adding torques acting on an objectmust take into account the vector nature oftorques. All the muscles of a muscle groupsum together to create a joint torque in aparticular direction. These muscle grouptorques must also be summed with torquesfrom antagonist muscles, ligaments, andexternal forces to determine the net torque

at a joint. Figure 7.6 illustrates the forces ofthe anterior deltoid and long head of the bi-ceps in flexing the shoulder in the sagittalplane. If ccw torques are positive, thetorques created by these muscles would bepositive. The net torque of these two mus-cles is the sum of their individual torques,or 6.3 N•m (60 • 0.06 + 90 • 0.03 = 6.3 N•m).If the weight of this person's arm multi-plied by its moment arm created a gravita-tional torque of –16 N•m, what is the nettorque acting at the shoulder? Assumingthere are no other shoulder flexors or exten-


Application: Muscle-Balance and Strength Curves

Recall that testing with an isokinetic dynamometer documents the strength curves (jointtorque–angle graphs) of muscle groups. Normative torques from isokinetic testing also pro-vide valuable information on the ratio of strength between opposing muscle groups. Many dy-namometers have computerized reports that list test data normalized to bodyweight and ex-pressed as a ratio of the peak torque of opposing muscle groups. For example, peak torquescreated by the hip flexors tend to be 60 to 75% of peak hip extensor torques (Perrin, 1993).Another common strength ratio of interest is the ratio of the quadriceps to the hamstrings.This ratio depends on the speed and muscle action tested, but peak concentric hamstringtorque is typically between 40 and 50% of peak concentric quadriceps torque (Perrin, 1993),which is close to the physiological cross-sectional area difference between these musclegroups. Greater emphasis has more recently been placed on more functional ratios (seeAagaard, Simonsen, Magnusson, Larsson, & Dyhre-Poulsen, 1998), like hamstring eccentric toquadriceps concentric strength (Hecc:Qcon), because hamstrings are often injured (“pulled” incommon parlance) when they slow the vigorous knee extension and hip flexion before footstrike in sprinting. In conditioning and rehabilitation, opposing muscle group strength ratios areoften referred to as muscle balance. Isokinetic (see Perrin, 1993) and hand dynamometer (seePhillips, Lo, & Mastaglia, 2000) testing are the usual clinical measures of strength, while strengthand conditioning professionals usually use one-repetition maxima (1RM) for various lifts.Theseforms of strength testing to evaluate muscle balance are believed to provide importantsources of information on the training status, performance, and potential for injury of athletes.In rehabilitation and conditioning settings, isokinetic and other forms of strength testing areuseful in monitoring progress during recovery.Athletes are cleared to return to practice whenmeasurements return to some criterion/standard, a percentage of pre-injury levels, or a per-centage of the uninvolved side of their body. It is important for kinesiology professionals toremember that the strength (torque capability) of a muscle group is strongly dependent onmany factors: testing equipment, protocol, and body position, among others, affect the resultsof strength testing (Schlumberger et al., 2006). If standards in testing are being used to qualifypeople for jobs or athletic participation, there needs to be clear evidence correlating the cri-terion test and standard with safe job performance.

sors active to make forces, we can sum thegravitational torque (–16 N•m) and the netmuscle torque (6.3 N•m) to find the result-ant torque of –9.7 N•m. This means thatthere is a resultant turning effect actingat the shoulder that is an extension torque,where the shoulder flexors are acting ec-centrically to lower the arm. Torques can besummed about any axis, but be sure tomultiply the force by the moment arm andthen assign the correct sign to represent thedirection of rotation before they aresummed.

Recall the isometric joint torques re-ported in Table 7.1. Peak joint torques dur-ing vigorous movement calculated from in-verse dynamics are often larger than thosemeasured on isokinetic dynamometers(Veloso & Abrantes, 2000). There are sever-al reasons for this phenomenon, includingtransfer of energy from biarticular muscles,differences in muscle action, and coactiva-tion. Coactivation of antagonist muscles is agood example of summing opposingtorques. EMG research has shown that iso-kinetic joint torques underestimate net ago-nist muscle torque because of coactivation

of antagonist muscles (Aagaard, Simonsen,Andersen, Magnusson, Bojsen-Moller, &Dyhre-Poulsen, 2000: Kellis & Baltzopou-los, 1997, 1998).

ANGULAR INERTIA (MOMENTOF INERTIA)

A moment of force or torque is the mechanicaleffect that creates rotation, but what is theresistance to angular motion? In linear ki-netics we learned that mass was the me-chanical measure of inertia. In angular ki-netics, inertia is measured by the momentof inertia, a term pretty easy to rememberbecause it uses the terms inertia and momentfrom moment of force. Like the mass (linearinertia), moment of inertia is the resistanceto angular acceleration. While an object'smass is constant, the object has an infinitenumber of moments of inertia! This is be-cause the object can be rotated about an in-finite number of axes. We will see that rotat-ing the human body is even more interest-ing because the links allow the configura-tion of the body to change along with theaxes of rotation.


Figure 7.6. The shoulder flexion torques of anterior deltoid and long head of the biceps can be summed to obtainthe resultant flexion torque acting to oppose the gravitational torque from the weight of the arm.

The symbol for the moment of inertiais I. Subscripts are often used to denote theaxis of rotation associated with a momentof inertia. The smallest moment of inertia ofan object in a particular plane of motion isabout its center of gravity (I0). Biomechani-cal studies also use moments of inertiaabout the proximal (IP) and distal (ID) endsof body segments. The formula for a rigid-body moment of inertia about an axis (A) isIA = �mr2. To determine the moment of in-ertia of a ski in the transverse plane aboutan anatomically longitudinal axis (Figure7.7), the ski is cut into eight small masses(m) of know radial distances (r) from theaxis. The sum of the product of these mass-es and the squared radius is the moment ofinertia of the ski about that axis. Note thatthe SI units of moment of inertia are kg•m2.

The formula for moment of inertiashows that an object's resistance to rotationdepends more on distribution of mass (r2)

than mass (m). This large increase in mo-ment of inertia from changes in location ofmass relative to the axis of rotation (be-cause r is squared) is very important in hu-man movement. Modifications in the mo-


Figure 7.7. The moment of inertia of a ski about a specific axis can be calculated by summing the products of themasses of small elements (m) and the square of the distance from the axis (r).

Activity: Moment of Inertia

Take a long object like a baseball bat, tennisracket, or golf club and hold it in one hand.Slowly swing the object back and forth in ahorizontal plane to eliminate gravitationaltorque from the plane of motion.Try to sensehow difficult it is to initiate or reverse the ob-ject's rotation. You are trying to subjectivelyevaluate the moment of inertia of the object.Grab the object in several locations and notehow the moment of inertia changes.Add massto the object (e.g., put a small book in the rack-et cover) at several locations. Does the mo-ment of inertia of the object seem to be morerelated to mass or the location of the mass?

ment of inertia of body segments can helpor hinder movement, and the moment ofinertia of implements or tools can dramati-cally affect their effectiveness.

Most all persons go through adoles-cence with some short-term clumsiness.Much of this phenomenon is related to mo-tor control problems from large changes inlimb moment of inertia. Imagine the bal-ance and motor control problems from amajor shift in leg moment of inertia if ayoung person grows two shoe sizes and 4inches in a 3-month period. How muchlarger is the moment of inertia of thisteenager's leg about the hip in the sagittalplane if this growth (dimension and mass)was about 8%? Would the increase in themoment of inertia of the leg be 8% or larg-er? Why?

When we want to rotate our bodies wecan skillfully manipulate the moment of in-

ertia by changing the configuration of ourbody segments relative to the axis of rota-tion. Bending the joints of the upper andlower extremities brings segmental massesclose to an axis of rotation, dramatically de-creasing the limb's moment of inertia. Thisbending allows for easier angular accelera-tion and motion. For example, the faster aperson runs the greater the knee flexion inthe swing limb, which makes the leg easy torotate and to get into position for anotherfootstrike. Diving and skilled gymnastictumbling both rely on decreasing the mo-ment of inertia of the human body to allowfor more rotations, or increasing the lengthof the body to slow rotation down. Figure7.8 shows the dramatic differences in themoment of inertia for a human body in thesagittal plane for different body segmentconfigurations relative to the axis of rota-tion.


Figure 7.8. The movement of body segments relative to the axis of rotation makes for large variations in the mo-ment of inertia of the body. Typical sagittal plane moments of inertia and axes of rotation for a typical athlete areillustrated for long jump (a,b) and high bar (c) body positions.

Variations in the moment of inertia ofexternal objects or tools are also very im-portant to performance. Imagine you aredesigning a new unicycle wheel. You de-sign two prototypes with the same mass,but with different distributions of mass.Which wheel design (see Figure 7.9) do youthink would help a cyclist maintain bal-ance: wheel A or wheel B? Think about themovement of the wheel when a person bal-ances on a unicycle. Does agility (low iner-tia) or consistency of rotation (high inertia)benefit the cyclist? If, on the other hand,you are developing an exercise bike thatwould provide slow and smooth changes inresistance, which wheel would you use? Aheavy ski boot and ski dramatically affectthe moments of inertia of your legs aboutthe hip joint. Which joint axis do you thinkis most affected?

The moment of inertia of many sportimplements (golf clubs and tennis rackets)is commonly called the “swing weight.” Alonger implement can have a similar swing

weight to a shorter implement by keepingmass proximal and making sure the addedlength has low mass. It is important to real-ize that the three-dimensional nature ofsports equipment means that there are mo-ments of inertia about the three principal ordimensional axes of the equipment. Tennisplayers often add lead tape to their racketsso as to increase shot speed and racket sta-bility. Tape is often added to the perimeterof the frame for stability (by increasing thepolar moment of inertia) against off-centerimpacts in the lateral directions. Weight atthe top of the frame would not affectthis lateral stability, but would increase themoments of inertia for swinging the racketforward and upward. The large radius ofthis mass (from his grip to the tip of theracket), however, would make the racketmore difficult to swing. Recent base-ball/softball bat designs allow for varia-tions in where bat mass is located, makingfor wide variation in the moment of inertiafor a swing. It turns out that an individual


Figure 7.9. The distribution of mass most strongly affects moment of inertia, so wheel A with mass close to theaxle would have much less resistance to rotation than wheel B. Wheel A would make it easier for a cyclist to makequick adjustments of the wheel back and forth to balance a unicycle.

batting style affects optimal bat mass(Bahill & Freitas, 1995) and moment of iner-tia (Watts & Bahill, 2000) for a particularbatter.

You can now see that the principle ofinertia can be extended to angular motionof biomechanical systems. This applicationof the concepts related to moment of inertiaare a bit more complex than mass in linearkinetics. For example, a person putting onsnowshoes will experience a dramatic in-crease (larger than the small mass of theshoes implies) in the moment of inertia ofthe leg about the hip in the sagittal planebecause of the long radius for this extramass. A tennis player adding lead tape tothe head of their racket will more quicklymodify the angular inertia of the racketthan its linear inertia. Angular inertia ismost strongly related to the distribution ofmass, so an effective strategy to decreasethis inertia is to bring segment masses closeto the axis of rotation. Coaches can getplayers to “compact” their extremities orbody to make it easier to initiate rotation.

NEWTON'S ANGULARANALOGUES

Newton's laws of motion also apply to an-gular motion, so each may be rephrased us-ing angular variables. The angular ana-logue of Newton's third law says that forevery torque there is an equal and oppositetorque. The angular acceleration of an ob-ject is proportional to the resultant torque,is in the same direction, and is inverselyproportional to the moment of inertia. Thisis the angular expression of Newton's sec-ond law. Likewise, Newton's first lawdemonstrates that objects tend to stay intheir state of angular motion unless actedupon by an unbalanced torque. Biomecha-nists often use rigid body models of the hu-man body and apply Newton's laws to cal-culate the net forces and torques acting onbody segments.

This working backward from videomeasurements of acceleration (second de-rivatives) using both the linear and angularversions of Newton's second law is calledinverse dynamics. Such analyses to under-stand the resultant forces and torques thatcreate movement were first done using la-borious hand calculations and graphing(Bressler & Frankel, 1950; Elftman, 1939),but they are now done with the assistanceof powerful computers and mathematicalcomputation programs. The resultant or netjoint torques calculated by inverse dynam-ics do not account for co-contraction ofmuscle groups and represent the sum ofmany muscles, ligaments, joint contact, andother anatomical forces (Winter, 1990).

Despite the imperfect nature of thesenet torques (see Hatze, 2000; Winter 1990),inverse dynamics provides good estimatesof the net motor control signals to createhuman movement (Winter & Eng, 1995),and can detect changes with fatigue(Apriantono et al., 2006) or practice/learn-ing (Schneider et al., 1989; Yoshida,Cauraugh, & Chow, 2004). Figure 7.10 illus-


Figure 7.10. The net joint hip (thick line) and knee(thin line) joint torques in a soccer kick calculated frominverse dynamics. The backswing (BS), range of deep-est knee flexion (DKF), forward swing (FS), and im-pact (IMP) are illustrated. Adapted with permissionfrom Zernicke and Roberts (1976).

trates the net joint torques at the hip andknee in a soccer toe kick. These torques aresimilar to the torques recently reported in athree-dimensional study of soccer kicks(Nunome et al., 2002). The kick is initiatedby a large hip flexor torque that rapidly de-creases before impact with the soccer ball.The knee extensor torque follows the hipflexor torque and also decreases to nearzero at impact. This near-zero knee exten-sor torque could be expected because thefoot would be near peak speed at impact,with the body protecting the knee from hy-perextension. If the movement were a punt,there would usually be another rise andpeak in hip flexor torque following the de-cline in knee torque (Putnam, 1983). It ispretty clear from this planar (2D) exampleof inverse dynamics that the hip flexormusculature may make a larger contribu-tion to kicking than the knee extensors. It isnot as easy to calculate or interpret 3D ki-netics since a large joint torque might havea very small resistance arm and not make alarge contribution to a desired motion, or atorque might be critical to positioning asegment for another torque to be able to ac-celerate the segment (Sprigings et al., 1994;Bahamonde, 2000).

The resultant joint torques calculated ininverse dynamics are often multiplied bythe joint angular velocity to derive net jointpowers. When the product of a net jointtorque and joint angular velocity are posi-tive (in the same direction), the muscle ac-tion is hypothesized to be primarily con-centric and generating positive work.Negative joint powers are hypothesized torepresent eccentric actions of musclegroups slowing down an adjacent segment.These joint powers can be integrated withrespect to time to calculate the net workdone at joints. Other studies first calculatedmechanical energies (kinetic and potentialenergies), and summed them to estimatework and eventually calculate power.Unfortunately, these summing of mechani-

cal energy analyses do not agree well withdirect calculation of joint power fromtorques because of difficulties in modelingthe transfer of mechanical energies betweenexternal forces and body segments(Aleshinsky, 1986a,b; Wells, 1988) and coac-tivation of muscles (Neptune & van denBogert, 1998).

EQUILIBRIUM

An important concept that grows out ofNewton's first and second laws is equilibri-um. Mechanical equilibrium occurs whenthe forces and torques acting on an objectsum to zero. Newton's second law accountsfor both linear and angular conditions ofstatic equilibrium (�F = 0, �T = 0), wherean object is motionless or moving at a con-stant velocity. Dynamic equilibrium isused to refer to the kinetics of acceleratedbodies using Newton's second law (�F = m• a, �T = I • ��). In a sense, dynamic equilib-rium fits the definition of equilibrium ifyou rearrange the equations (i.e., �F – m • a= 0). The m • a term in the previous equa-tion is often referred to as the inertial force.This inertial force is not a real force and cancause confusion in understanding the ki-netics of motion.

This text will focus on static equilibri-um examples because of their simplicityand because summation of forces andtorques is identical to dynamic equilibrium.Biomechanics studies often use static orquasi-static analyses (and thus employ stat-ic equilibrium equations and avoid difficul-ties in calculating accurate accelerations) inorder to study slow movements with smallaccelerations. The occupational lifting stan-dards set by the National Institute forOccupational Safety and Health (NIOSH)were based in large part on static biome-chanical models and analyses of lifting.Static equilibrium will also be used in thefollowing section to calculate the center ofgravity of the human body.


Equilibrium and angular kinetics arethe mechanical tools most often used in thestudy of balance. We will see in the nexttwo sections that the center of gravity of thehuman body can be calculated by summingmoments in a static equilibrium form, andthese kinds of data are useful in examiningthe state of mobility and stability of thebody. This control of stability and ability tomove is commonly called balance. What me-chanics tells us about balance is summa-rized in the Principle of Balance.

CENTER OF GRAVITY

A natural application of angular kineticsand anthropometrics is the determinationof the center of gravity of the body. Thecenter of gravity is the location in space

where the weight (gravitational force) of anobject can be considered to act. The centerof small rigid objects (pencil, pen, bat) canbe easily found by trying to balance the ob-ject on your finger. The point where the ob-ject balances is in fact the center of gravity,which is the theoretical point in spacewhere you could replace the weight of thewhole object with one downward force.There is no requirement for this location tobe in a high-mass area, or even within or onthe object itself. Think about where the cen-ter of gravity of a basketball would be.

The center of gravity of the humanbody can move around, because joints al-low the masses of body segments to move.In the anatomical position, the typical loca-tion of a body's center of gravity in thesagittal plane is at a point equivalent to 57


Interdisciplinary Issue:The Spine and Low-Back Pain

One of the most common complaints is low-back pain.The medical literature would say thatthe etiology (origin) of these problems is most often idiopatic (of unknown origin).The diag-nostic accuracy of advanced imaging techniques like magnetic resonance imaging (MRI) for iden-tifying spinal abnormalities (e.g., disk herniation) that correlate with function and symptoms oflow-back pain is poor (Beattie & Meyers, 1998).The causes of low-back pain are complicatedand elusive. Biomechanics can contribute clues that may help solve this mystery. Mechanically,the spine is like a stack of blocks separated by small cushions (McGill, 2001). Stability of thespine is primarily a function of the ligaments and muscles, which act like the guy wires that sta-bilize a tower or the mast of a boat.These muscles are short and long and often must simulta-neously stabilize and move the spine.Total spine motion is a summation of the small motions ateach intervertebral level (Ashton-Miller & Schultz, 1988). Biomechanical studies of animal andcadaver spines usually examine loading and rotation between two spinal levels in what is calleda motion segment. Individuals even exhibit different strategies for rotation of motion segmentsin simple trunk flexion movements (Gatton & Pearcy, 1999; Nussbaum & Chaffin, 1997), so thatneuromuscular control likely plays an important role in injury and rehabilitation (Ebenbichler,Oddsson, Kollmitzer, & Erim, 2001). Occasionally a subject is unfortunate and gets injured in abiomechanical study. Cholewicki and McGill (1992) reported x-ray measurements of the “buck-ling” of a single spinal segment that occurred during a heavy deadlift. Biomechanics research us-ing computer models and EMG are trying to understand how muscles and loads affect the spine,and the nature of this motion segment buckling (Preuss & Fung, 2005).This information mustbe combined with occupational, epidemiological, neurologic, and rehabilitative research to un-derstand the development and treatment of low-back pain.

and 55% of the height for males and fe-males, respectively (Hay & Reid, 1982). Canyou name some structural and weight dis-tribution differences between the gendersthat account for this general difference?Knowing where the force of gravity acts invarious postures of the human body allowsbiomechanists to study the kinetics and sta-bility of these body positions.

There are two main methods used tocalculate the center of gravity of the humanbody, and both methods employ the equa-tions of static equilibrium. One lab method,which requires a person to hold a certainbody position, is called the reaction changeor reaction board method. The other methodused in research is called the segmentalmethod. The segmental method uses an-thropometric data and mathematicallybreaks up the body into segments to calcu-late the center of gravity.

The reaction board method requires arigid board with special feet and a scale(2D) or scales (3D) to measure the groundreaction force under the feet of the board.

The “feet” of a reaction board are knife-likeedges or small points similar to the point ofa nail. A 2D reaction board, a free-body di-agram, and static equilibrium equations tocalculate the center of gravity in the sagittalplane are illustrated in Figure 7.11. Notethat the weight force of the board itself isnot included. This force can be easily addedto the computation, but an efficient bio-mechanist zeros the scale with the board inplace to exclude extra terms from the calcu-lations. The subject in Figure 7.11 weighs185 pounds, the distance between the edgesis 7 feet, and the scale reading is 72.7pounds. With only three forces acting onthis system and everything known but thelocation of the center of gravity, it is rathersimple to apply the static equilibrium equa-tion for torque and solve for the center ofgravity (d⊥). Note how the sign of thetorque created by the subject's body is neg-ative according to convention, so a negatived⊥ (to the left) of the reaction board edgefits this standard, and horizontal displace-ment to the left is negative. In this case, the


Figure 7.11. Application of static equilibrium and a reaction board to calculate whole body center of gravity.Summing torques about the reaction board edge at the feet and solving for the moment arm (d⊥) for gravity locatesthe center of gravity.

subject's center of gravity is 2.75 feet upfrom the edge of the reaction board. If thesubject were 5.8 feet in height, his center ofgravity in this position would be 47% of hisor her height.

In the segmental method, the body ismathematically broken up into segments.The weight of each segment is then estimat-ed from mean anthropometric data. For ex-ample, according to Plagenhoef, Evans, &Abdelnour (1983), the weight of the fore-arm and hand is 2.52 and 2.07% for a manand a woman, respectively. Mean anthro-

pometric data are also used to locate thesegmental centers of gravity (percentagesof segment length) from either the proximalor distal point of the segment. Figure 7.12depicts calculation of the center of gravityof a high jumper clearing the bar using athree-segment biomechanical model. Thissimple model (head+arms+trunk, thighs,legs+feet) illustrates the segmental methodof calculating the center of gravity of alinked biomechanical system. Points on thefeet, knee, hip, and shoulder are locatedand combined with anthropometric data to


Figure 7.12. Calculating the horizontal position of the whole body center of gravity of a high jumper using thesegmental method and a three-segment model of the body. Most sport biomechanical models use more segments,but the principle for calculating the center of gravity is the same.

calculate the positions of the centers ofgravity of the various segments of the mod-el. Most biomechanical studies use rigid-body models with more segments to moreaccurately calculate the whole-body centerof gravity and other biomechanical vari-ables. If a biomechanist were studying ahigh jump with high-speed video (120 Hz),a center of gravity calculation much likethis would be made for every image (videosnapshot) of the movement.

The segmental method is also based onstatic equilibrium. The size and location(moment arm) of the segmental forces areused to calculate and sum the torques creat-ed by each segment. If this body posture inthe snapshot were to be balanced by atorque in the opposite direction (product ofthe whole bodyweight acting in the oppo-site direction times the center of gravity lo-cation: 182 • d⊥), the total torque would bezero. By applying the law of statics andsumming torques about the origin of ourframe of reference, we calculate that theperson's bodyweight acts 8.9 inches fromthe origin. These distances are small be-cause the numbers represent measurementson an image. In a 2D biomechanical analy-sis, the image-size measurements are scaledto real-life size by careful set-up proceduresand imaging a control object of known di-mensions.

Finding the height of the center of grav-ity is identical, except that the y coordinatesof the segmental centers of gravity are usedas the moment arms. Students can thenimagine the segment weight forces actingto the left, and the height of the center ofgravity is the y coordinate that, multipliedby the whole bodyweight acting to theright, would cancel out the segmentaltorques toward the left. Based on the sub-ject's body position and the weights of thethree segments, guess the height in cen-timeters of the center of gravity. Did thecenter of gravity pass over the bar? Finishthe calculation in Figure 7.12 to check your

guess. The segmental method can be ap-plied using any number of segments, and inall three dimensions during 3D kinematicanalysis. There are errors associated withthe segmental method, and more complexcalculations are done in situations whereerrors (e.g., trunk flexion/extension, ab-dominal obesity) are likely (Kingma,Toussaint, Commissaris, Hoozemans, &Ober, 1995).

PRINCIPLE OF BALANCE

We have seen than angular kinetics pro-vides mathematical tools for understandingrotation, center of gravity, and rotationalequilibrium. The movement concept of bal-ance is closely related to these angular ki-netic variables. Balance is a person's abilityto control their body position relative tosome base of support (Figure 7.13). Thisability is needed in both static equilibriumconditions (e.g., handstand on a balancebeam) and during dynamic movement(e.g., shifting the center of gravity from the


Activity: Center of Gravity and Moment of Inertia

Take a 12-inch ruler and balance it onyour finger to locate the center of gravi-ty. Lightly pinch the ruler between yourindex finger and thumb at the 1-inchpoint, and allow the ruler to hang vertical-ly below your hand. Swing the ruler in avertical plane and sense the resistance ofthe ruler to rotation. Tape a quarter tovarious positions on the ruler and notehow the center of gravity shifts and howthe resistance to rotation changes.Whichchanges more: center of gravity or mo-ment of inertia? Why? What factors makeit difficult to sense changes in ruler mo-ment of inertia?

rear foot to the forward foot). Balance canbe enhanced by improving body segmentpositioning or posture. These adjustmentsshould be based on mechanical principles.There are also many sensory organs andcognitive processes involved in the controlof movement (balance), but this section fo-cuses on the mechanical or technique fac-tors affecting balance and outlines applica-tion of the Principle of Balance.

Before we apply this principle to sever-al human movements, it is important to ex-amine the mechanical paradox of stabilityand mobility. It turns out that optimal pos-ture depends on the right mix of stabilityand mobility for the movement of interest.This is not always an easy task, because sta-bility and mobility are inversely related.Highly stable postures allow a person to re-sist changes in position, while the initiationof movement (mobility) is facilitated by theadoption of a less stable posture. The

skilled mover learns to control the positionof their body for the right mix of stabilityand mobility for a task.

The biomechanical factors that can bechanged to modify stability/mobility arethe base of support, and the position andmotion of the center of gravity relative tothe base of support. The base of support isthe two-dimensional area formed by thesupporting segments or areas of the body(Figure 7.14). A large base of support pro-vides greater stability because there isgreater area over which to keep the body-weight. Much of the difficulty in manygymnastic balancing skills (e.g., handstandor scale) comes from the small base of sup-port on which to center bodyweight.

The posture of the body in stance orduring motion determines the position ofthe center of gravity relative to the base ofsupport. Since gravity is the major externalforce our body moves against, the horizon-


Figure 7.13. Balance is the degree of control a personhas over their body. Balance is expressed in static(track start) and dynamic conditions (basketball play-er boxing out an opponent). Track image used withpermission from Getty Images.

tal and vertical positions of the center ofgravity relative to the base of support arecrucial in determining the stability/mobili-ty of that posture. The horizontal distancefrom the edge of the base of support to thecenter of gravity (line of action of gravity)determines how far the weight must beshifted to destabilize a person (Figure7.15a). If the line of gravity falls outside thebase of support, the gravitational torquetends to tip the body over the edge of thebase of support. The vertical distance orheight of the center of gravity affects thegeometric stability of the body. When theposition of the center of gravity is higher, itis easier to move beyond the base of sup-port than in postures with a lower centerof gravity. Positioning the line of gravityoutside the base of support can facilitate therotation of the body by the force of gravity(Figure 7.15b).

Biomechanical studies of balance oftendocument the motion of the two importantforces of interest, body weight and the reac-

tion force under the base of support. Videomeasurements using the segmental methodmeasure the motion of the center of gravityover the base of support. Imagine wherethe center of gravity would be and how itwould move in the base of supports illus-trated in Figure 7.14. Force platforms allowthe measurement of the misnomer centerof pressure, the location of the resultant re-action force relative to the base of support.In quiet standing, the center of gravitysways around near the center of the base ofsupport, while the center of pressure moveseven faster to push the weight force back tothe center of the base of support. The totalmovement and velocities of these two vari-ables are potent measures of a person's bal-ance.

Recall that the inertia (mass and mo-ment of inertia), and other external forceslike friction between the base and support-ing surface all affect the equilibrium of anobject. There are also biomechanical factors(muscle mechanics, muscle moment arms,


Figure 7.14. The base of support is the two-dimensional area within all supporting or suspending points of thebiomechanical system.

angles of pull, and so on) that affect theforces and torques a person can create to re-sist forces that would tend to disrupt theirbalance. The general base of support andbody posture technique guidelines in manysports and exercises must be based on inte-gration of the biological and mechanicalbases of movement. For example, manysports use the “shoulder width apart” cuefor the width of stances because this baseof support is a good compromise betweenstability and mobility. Wider bases of sup-port would increase potential stability butput the limbs in a poor position to createtorques and expend energy, creating oppos-ing friction forces to maintain the base ofsupport.

The Principle of Balance is based on themechanical tradeoff between stability andmobility. The Principle of Balance is similarto the Coordination Continuum becausethe support technique can be envisioned asa continuum between high stability andhigh mobility. The most appropriate tech-nique for controlling your body depends on

where the goal of the movement falls on thestability–mobility continuum. Coaches,therapists, and teachers can easily improvethe ease of maintaining stability or initiat-ing movement (mobility) in many move-ments by modifying the base of supportand the positions of the segments of thebody. It is important to note that good me-chanical posture is not always required forgood balance. High levels of skill and mus-cular properties allow some people to haveexcellent balance in adverse situations. Askater gliding on one skate and a basketballplayer caroming off defenders and stillmaking a lay-up are examples of good bal-ance in less than ideal conditions.

Imagine that a physical therapist ishelping a patient recover from hip joint re-placement surgery. The patient has re-gained enough strength to stand for shortlengths of time, but must overcome somediscomfort and instability when transition-ing to walking. The patient can walk safelybetween parallel bars in the clinic, so thetherapist has the patient use a cane. This ef-


Figure 7.15. The position of the line of gravity relative to the limits of the base of support determines how far theweight must be shifted for gravity to tend to topple the body (a) or the size of the gravitational torque helps cre-ate desired rotation (b).

fectively increases the base of support, be-cause the therapist thinks increasing stabil-ity (and safety) is more important. If wecombine angular kinetics with the Principleof Balance, it is possible to determine onwhat side of the body the cane should beheld. If the cane were held on the same (af-fected) side, the base of support would belarger, but there would be little reduction inthe pain of the hip implant because thegravitational torque of the upper bodyabout the stance hip would not be reduced.If the patient held the cane in the hand onthe opposite (unaffected) side, the base ofsupport would also be larger, and the armcould now support the weight of the upperbody, which would reduce the need for hipabductor activity by the recovering hip.Diagram the increase in area of the base ofsupport from a single-leg stance in walkingto a single-leg stance with a cane in eachhand. Estimate the percentage increase inbase of support area using the cane in eachhand.

Classic examples of postures thatwould maximize mobility are the startingpositions during a (track or swimming)race where the direction of motion isknown. The track athlete in Figure 7.16 haselongated his stance in the direction of hisstart, and in the “set” position moves hiscenter of gravity near the edge of his baseof support. The blocks are not extended toofar backwards because this interacts withthe athlete's ability to shift weight forwardand generate forces against the ground. Fora summary of the research on the effect ofvarious start postures on sprint time, seeHay (1993). Hay also provides a good sum-mary of early research on basic footworkand movement technique factors in manysports.

In many sports, athletes must take ondefensive roles that require quick move-ment in many directions. The Principle ofBalance suggests that postures that fostermobility over stability have smaller basesof support, with the center of gravity of the


Figure 7.16. The starting position of a sprinter in the blocks shifts the line of gravity toward the front of the stanceand the intended direction of motion. This stance favors mobility forward over stability.

body not too close to the base of support.When athletes have to be ready to move inall directions, most coaches recommend aslightly staggered (one foot slightly for-ward) stance with feet about shoulderwidth apart. Compare the stance and pos-ture of the volleyball and basketball playersin Figure 7.17. Compare the size of the baseof support and estimate the location of thecenter of gravity in both body positions.What posture differences are apparent, andare these related to the predominant motionrequired in that sport? Bases of supportneed only be enlarged in directions wherestability is needed or the direction of mo-tion is known.

There are movement exceptions tostrict application of the Principle of Balancebecause of high skill levels or the interac-tion of other biomechanical factors. In well-learned skills like walking, balance is easilymaintained without conscious attentionover a very narrow base of support.Gymnasts can maintain balance on verysmall bases of support as the result of con-siderable skill and training. A platform div-


Figure 7.17. Comparison of the ready positions of a basketball player and a volleyball player. How are the me-chanical features of their stance adapted to the movement they are preparing for?

Interdisciplinary Issue:Gender Differences

It is generally considered that the lowercenter of gravity in women gives thembetter balance than men.What is the bio-mechanical significance of the structuraland physiological differences betweenmen and women? While there is substan-tial research on the physiological differ-ences between the genders, there is lesscomparative research on the biomechan-ical differences. Motor control and er-gonomic studies have observed signifi-cant differences in joint angles duringreaching (Thomas, Corcos, & Hasan,1998) and lifting (Lindbeck & Kjellberg,2000). Greater interest in gender differ-ences seems to focus on issues related torisk of injury, for example, to like the an-terior collateral ligament (ACL)(Charlton, St. John, Ciccotti, Harrison, &Schweitzer, 2002; Malinzak, Colby,Kirkendall,Yu, & Garrett, 2001).

er doing a handstand prior to a dive keepstheir base of support smaller than oneshoulder width because extra side-to-sidestability is not needed and the greatershoulder muscle activity that would be re-quired if the arms were not directly under-neath the body. Another example might bethe jump shot in basketball. Many coachesencourage shooters to “square up” or facethe basket with the body when shooting.Ironically, the stance most basketball play-ers spontaneously adopt is staggered, withthe shooting side foot slightly forward. Thisadded base of support in the forward–back-ward direction allows the player to transi-tion from pre-shot motion to the primarilyvertical motion of the jump. It has also beenhypothesized that this stagger in the stanceand trunk (not squaring up) helps the play-er keep the shooting arm aligned with theeyes and basket, facilitating side-to-side ac-curacy (Knudson, 1993).

Balance is a key component of mostmotor skills. While there are many factorsthat affect the ability to control body mobil-ity and stability, biomechanics focuses on

the base of support and position of the cen-ter of gravity. Mechanically, stability andmobility are inversely related. Coaches canapply the Principle of Balance to select thebase of support and postures that will pro-vide just the right mix of stability/mobilityfor a particular movement. Angular kinet-ics is the ideal quantitative tool for calculat-ing center of gravity, and for examining thetorques created by gravity that the neuro-muscular system must balance.

SUMMARY

The key mechanical variable in under-standing the causes of rotary motion is themoment of force or torque. The size of thetorque that would rotate an object is equalto the force times its moment arm. The mo-ment of inertia is a variable expressing theangular inertia of an object about a specificaxis of rotation. The moment of inertia most


Application: Inverse Dynamicsof Walking

The ground reaction forces measured byforce platforms in walking are used inclinical biomechanics labs to calculate netforces and torques in joints (inverse dy-namics). For the sagittal and frontal planesillustrated (Figure 7.18), can you see howthe typical ground reaction force createsa knee flexor and adductor torques instance? Can you draw the moment armsrelative to the knee joint axis for theseforces? The stance limb activates musclesto create a net knee extensor torque tosupport body weight in the sagittal plane(A), and a knee abductor torque to stabi-lize the knee in the frontal plane (B). Figure 7.18. Typical ground reaction force vectors

in the stance phase of walking in the sagittalplane (A) and frontal plane (B). What torques dothese forces make about the knee joint axes?

strongly depends on the distribution ofmass relative to the axis of rotation of inter-est. When all the torques acting on an objectsum to zero, the object is said to be in staticequilibrium. The equations of static equilib-rium are often used to calculate the centerof gravity of objects. Biomechanics most of-ten uses the reaction change and segmentalmethods to calculate the center of gravity ofthe human body. Balance is the ability of aperson to control their body position rela-tive to some base of support. The BalancePrinciple deals with the mechanical factorsthat affect balance, and the tradeoff be-tween stability and mobility in variousbody postures.

REVIEW QUESTIONS

1. What are the two most important pa-rameters that determine the size of a torqueor moment of force?

2. What is the inertial resistance to an-gular acceleration object about an axis, andwhat factors affect its size?

3. Give examples of how the humanbody can position itself to increase or de-crease its inertial resistance to rotation.

4. Calculate the shoulder flexion torquerequired to hold an 80-lb barbell just aboveyour chest in a bench press. The horizontaldistance from your shoulder axis to the bar-bell is 0.9 feet.

5. Restate Newton's three laws of mo-tion in angular kinetic terms.

6. Explain how static equilibrium canbe used to calculate the center of gravity ofthe human body.

7. Draw or trace a few freeze-frameimages of the human body in several posi-tions from sport or other human move-ments. Estimate the location of the centerof gravity.

8. A mischievous little brother runsahead of his sister and through a revolving

door at a hotel. The little brother pushes inthe opposite direction of his sister trying toexit. If the brother pushes with a maximumhorizontal force of 40 pounds acting at aright angle and 1.5 feet from the axis of therevolving door, how much force will thesister need to create acting at 2.0 feet fromthe axis of rotation to spoil his fun?

9. What mechanical factors can be usedto maximize stability? What does this do toa person's mobility?

10. What movement factors can a kine-siology professional qualitatively judgethat show a person's balance in dynamicmovements?

11. Say the force F2 applied by the stu-dent in Figure 7.3 acted 55º in from the tan-gent to the merry-go-round. Calculate thetorque created by the student.

12. Draw a free-body diagram of a per-son standing on a reaction board (hint: thesystem is the body plus the board).Estimate the length of the board and thehorizontal distance to the person's center ofgravity. Calculate the reaction force on theboard if you were the person on it.

13. If the rotary component of abrachialis force is 70 N and the muscle at-taches 0.4 m from the axis of rotation, whatis the flexor torque created by the muscle?What other information do you need in or-der to calculate the resultant force createdby the brachialis?

KEY TERMS

Balance Principlecenter of gravityinertial forcemoment armmoment or moment of forcemoment of inertiareaction changesegmental methodstatic equilibriumtorque


SUGGESTED READING

Brown, L. E. (Ed.) (2000). Isokinetics in humanperformance. Champaign, IL: Human Kinetics.

Chaffin, B. D., Andersson, G. B. J., & Martin,B. J. (1999). Occupational biomechanics (3rd ed.).New York: Wiley.

Huxham, F. E., Goldie, P. A., & Patla, A. E.(2001). Theoretical considerations in balanceassessment. Australian Journal of Physiotherapy,47, 89–100.

Mann, R. V. (1981). A kinetic analysis of sprint-ing. Medicine and Science in Sports and Exercise,13, 325–328.

McGill, S. M., & Norman, R. W. (1985).Dynamically and statically determined lowback moments during lifting. Journal ofBiomechanics, 18, 877–886.

Murray, M. P., Seireg, A., & Scholz, R. C. (1967).Center of gravity, center of pressure, and sup-

portive forces during human activities. Journalof Applied Physiology, 23, 831–838.

Winter, D. A. (1984). Kinematic and kinetic pat-terns of human gait: Variability and compen-sating effects. Human Movement Science, 3,51–76.

Winter, D. A. (1995). Human balance and pos-ture control during standing and walking. Gaitand Posture, 3, 193–214.

Winters, J. M., & Woo, S. L.-Y. (Eds.) (1990).Multiple muscle systems. New York: Springer.

Zatsiorsky, V. M. (2002). Kinetics of human mo-tion. Champaign, IL: Human Kinetics.

Zernicke, R. F., & Roberts, E. M. (1976). Humanlower extremity kinetic relationships duringsystematic variations in resultant limb velocity.In P. V. Komi (Ed.), Biomechanics V–B (pp. 41-50). Baltimore: University Park Press.


WEB LINKS

Torque tutorial—part of the physics tutorials at University of Guelph.http://eta.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html

Support moment—torques in leg joints in walking are examined in this teach-in exercisefrom the Clinical Gait Analysis website.

http://guardian.curtin.edu.au:16080/cga/teach-in/support/

Center of mass and center of pressure from the Clinical Gait Analysis website.http://guardian.curtin.edu.au:16080/cga/teach-in/grv/

External forces that have a major effecton most human movements are relatedto immersion in or flow of fluids pasta body. This chapter reviews the mechani-cal effect of moving through air and water,the two most common fluids encounteredin human movement. Fluid forces usuallyresult in considerable resistance to high-ve-locity movements through fluids, so manysport techniques and pieces of equipmentare designed to minimize fluid resistance.Fluid forces, however, can also be used tocreate movement, like in the skillful appli-cation of spin to projectiles. This chapterconcludes with application of this use offluid forces in the Principle of Spin.

FLUIDS

You may have studied the various states ofmatter in physics or noticed that many sub-stances are not easily classified as totallysolid or liquid. Mechanically, fluids are de-fined as substances that flow or continuouslydeform when acted upon by shear forces. Athorough review of all the nuances of fluidmechanics is not possible, so key conceptsrelated to the supporting force of immer-sion in fluids and the forces that arise frommoving through fluids will be reviewed.Several references are cited to guide stu-dents interested in digging deeper into thenuances of fluid mechanics.

FLUID FORCES

For the purposes of this chapter, the majorfluid forces that affect human motion are

classified according to an object's positionor velocity within a fluid. When an object isplaced in a fluid there is a resultant upwardforce or supporting fluid force called buoy-ancy. The fluid force related to how the flu-id flows past the object is resolved intoright-angle components called lift anddrag. In most movement, people have con-siderable control over factors that affectthese forces. Let's see how these fluid forcesaffect human movement.

BuoyancyThe vertical, supporting force of a fluid iscalled buoyancy. When an inanimate objectis put in a fluid (like water), the vector sumof gravity and the buoyant force deter-mines whether or not the object will float(Figure 8.1). The Archimedes Principlestates that the size of the buoyant force isequal to the weight of the fluid displacedby the object. Folklore says that the famous

CHAPTER 8

Fluid Mechanics

193

Figure 8.1. The resultant vector of gravity (W) andbuoyancy (FB) will determine if an inanimate objectfloats. This golf ball will sink to the bottom of the wa-ter hazard.

Greek physicist/mathematician realizedthis important principle when noticing wa-ter level changes while taking a bath.

A sailboat floats at a level where theweight of the boat and contents are equal insize to the weight of the volume of waterdisplaced. Flotation devices used for waterexercise and safety increase the buoyancyof a person in two ways: having a lowerdensity (mass/volume) than water andhaving a hollow construction. These flota-tion devices displace water that weighsmore than the device, increasing the buoy-ancy of the person.

In a gravitational field the mass of a flu-id is attracted in a particular direction. Theweight of water is typically 9800 N per cu-bic meter, but this figure gradually increas-es for water at greater depths. The deeper ascuba diver descends, the greater the fluidpressure around them (because of thegreater mass of water essentially “on top”of them). This increased pressure in a par-ticular volume of fluid means that the vol-ume of water weighs more than a similarvolume of water at the surface, so the buoy-ant force on objects tends to slightly in-crease as depth increases. A similar phe-nomenon occurs as we descend from amountain, where the fluid pressure of theatmosphere on us increases. The buoyantforce on the human body from the “sea” ofatmospheric gases also depends on ourdepth (opposite of elevation), but is usuallya fraction of a pound and can be ignored invertical kinetic calculations of humanmovement.

The density of the human body is veryclose to that of water, largely due to thehigh water content of all tissue. Lean tissue(muscle and bone) have densities greaterthan water, while body fat tends to be lessdense than water. The buoyant force on aswimmer varies with changes in body com-position and when the person inhales or ex-hales. Taking a deep breath expands thechest, which increases the volume of the

body and increases the buoyant force. Ifyou have ever taught a swimming class youknow that people typically fall into threegroups based on their somotype and bodycomposition: floaters, conditional floaters,and sinkers. The majority of your swimclass can easily float when holding theirbreath (conditional floaters). There will be afew folks who easily float (floaters) or can-not float (sinkers) without some form ofpropulsion or flotation device.

The buoyant force in water acts up-ward at the center of buoyancy. The centerof buoyancy is essentially the centroid ofthe volume of water displaced by an object.In the human body, the trunk makes upmost of the volume, so the center of buoy-ancy is located 1–2 cm superior (McLean &Hinrichs, 2000a) to the center of gravity(Figure 8.2). Since so much body volume isin the upper trunk, moving the rest of thebody makes smaller changes in the centerof buoyancy than in the center of gravity.Note that the weight force and buoyantforce create a force couple that will tend torotate the swimmer's legs down until the


Activity

The next time you are at a pool, see if youcan detect an increase in buoyant forcewith increasing depth. Hold a large sportball (water polo, soccer, football) in onehand and gradually submerge it. Note thedownward vertical force you exert to bal-ance the buoyant force of the ball as it de-scends. Also note the horizontal forcesyou must exert to keep your hand forcesbalanced with the buoyant force and grav-ity! Another simple activity is to mark thewater line on a floating ping pong ball.Tape dimes to the ball and find the maxi-mum buoyant force of a ping pong ball.Does a forcibly submerged ball have po-tential energy?

weight and buoyant force are nearly colin-ear. Swimmers still scared of the water havegreat difficulty floating on their back be-cause they tend to pike and lift thehead/upper trunk out of the water. The re-sulting loss of buoyant force (from less wa-ter displacement) tends to dip the swim-mer's head deeper into the water. If you arehaving difficulty getting a swimmer to re-lax and do a back float, how can you shifttheir limbs to shift the center of gravity andmaintain a large buoyant force?

We have seen that objects in a fluid ex-perience a supporting force related to theposition of the object in the fluid and thedensity of the object. The next section willdeal with the interaction forces between anobject and the fluid when there is relativemotion between the two. These fluid mo-tion forces can be quite large. The fluidforces between the air and your body arenearly identical if you are falling at 120km/hr while skydiving in a specific bodyposition or if you are apparently still on topof a column of 120 km/hr airflow in a sim-ulator. In both these situations the dragforces on the body are equal to your bodyweight. In the first case the body is fallingthrough essentially still air while in the sec-ond case the body is essentially stationarywith air flowing over it.

Drag

The fluid force resisting motion between anobject and a fluid is called drag. Drag actsin the same direction (parallel) as the rela-tive flow of the fluid past an object and inthe opposite direction of the object's motionin the fluid. Drag forces act on the fisher-man (creek) and the fly (air) due to the rel-ative motion of the fluid past the objects(see Figure 8.3). If there are no propulsiveforces acting on the object, like a projectile(see chapter 5, p. 113), the drag force tendsto slow down the motion of the projectilethrough the fluid. Since the drag force actsparallel to the relative flow of the fluid, it ismuch like the contact force of friction stud-ied in chapter 6.

Research has shown that the size of thedrag force (FD) that must be overcome in afluid can be calculated using the followingformula: FD = ½CD � AP V2. The coefficientof drag (CD) is a dimensionless numbermuch like the coefficient of friction or resti-tution. We will see later that CD depends onmany object and fluid flow factors. Drag

CHAPTER 8: FLUID MECHANICS 195

Figure 8.2. The center of buoyancy of the human bodyis superior to the center of gravity because of the largevolume of the upper body.

Application: Hydrotherapy

Therapeutic exercises in water utilize its buoyant forceto unload the lower extremity.The amount of unload-ing of the body can be easily manipulated by the extentof submersion.This exercise modality differs from sus-pension systems that unload the body by pulleys liftingup the trunk because of other fluid forces.The flow ofwater also creates lift and drag forces that have beenshown to create differences in muscle activation inexercise (Poyhonen, Kryolainen, Keskien, Hautala,Savolainen, & Malkia, 2001).Therapy pools that createcurrents for exercise likely exaggerate the neuromus-cular differences between these movements and dryland movement.

also depends on fluid density (�) and theprojected frontal area (AP) in the path of thefluid flow. The most important factor af-fecting drag is the relative velocity (V2) ofthe fluid past the object.

Like the velocity term in kinetic energy,the force of drag varies with the square ofthe relative fluid velocity. This means that,all other things being equal, a cyclist thatdoubles and then triples his pace increasesdrag by 4 and 9 times compared to his ini-tial speed! This explains why running fasteror into a strong breeze feels much more dif-ficult. The importance of the adjective “rel-ative” can be easily appreciated by notingthat it is easier to run with a strong breezebehind you. The dramatic effect of drag onsprint performance has forced the Inter-national Amateur Athletic Federation to notratify sprint records if the wind assisting arunner exceeds 2.0 m/s. World records arealways a controversial issue, but currentweighting of records in many events does

not take into account the effect of altitude(Mureika, 2000) or latitude (Mizera &Horvath, 2002). Remember that relative ve-locity means that we are talking about a lo-cal kinematic frame of reference—in otherwords, the speed and direction of fluid flowrelative to the object of interest. These dragforces increase with the square of velocityand often dramatically affect performance.

The Drag force on an object has severalsources: surface drag, pressure drag, and wavedrag. Understanding these drag forces isimportant for minimizing these resistancesin many sports and activities.

Surface drag can be thought of as a flu-id friction force, much like solid frictionforce studied in chapter 6. Surface drag isalso commonly called friction drag or skinfriction drag. It results from the frictionalforce between fluid molecules moving pastthe surface of an object and the frictionalforce between the various layers of the flu-id. Viscosity is the internal resistance of a


Figure 8.3. The fluid force of drag (FD) acts in a direction opposing the relative flow of fluid past the object.

fluid to flow. Air has a lower viscosity thanwater, which has a lower viscosity thanmaple syrup.

Suppose a surfer is floating on theirboard waiting for the right wave (Figure8.4). The fluid flow below the apparentlystationary surfboard creates surface dragfrom the flow of the ocean under the board.Water molecules immediately adjacent tothe board are slowed by shear forces be-tween them and the molecules of the board.So the fluid close to the board moves slow-er than the ocean water farther from theboard. In fact, there is a region of water lay-ers close to the board that moves moreslowly because of viscous (fluid friction)forces between the fluid particles. This re-gion of fluid affected by surface drag andviscosity near an object is called the bound-ary layer. Layers of fluid more distant fromthe object that are not affected by dragforces with the object represent the freestream velocity. Have you ever started driv-ing your car and notice a small insect on thehood or windshield wipers? I am willing towager that most of you noticed the consid-erable speed you had to drive to disrupt theboundary layer the insect stood in before itwas swept away! We will see that this rela-tive or free stream velocity is one of themost important factors affecting the dragand lift forces between objects and fluids.

Performers cannot change the viscosityof the fluid they move in, but they can mod-ify the roughness of their body or equip-ment to decrease surface drag. Surfboardsand skis are waxed, a swimmer may shavebody hair, or very smooth body suits maybe worn to decrease surface drag. Somesuits actually introduce texture on portionsof the fabric to modify both lift and dragforces (Benjanuvatra, Dawson, Blanksby, &Elliott, 2002). While it is important to mini-mize surface drag, the largest fluid resist-ance in many sports tends to be from pres-sure drag.

The second kind of drag force thatdominates the fluid resistance in manysports is pressure drag. Pressure drag is theresistance force to fluid flow that is createdby a pressure differential when the fluidflows around a submerged object. A simpli-fied illustration of this phenomenon is pre-sented in Figure 8.5. The collision of the ob-ject and molecules of fluid creates a highpressure on the front of the object, while alower-pressure region or wake is formedbehind the object. The region of higherpressure “upstream” creates a resultantforce backward on the object. We will seethat the mechanics of this pressure differen-tial is a bit more complicated and related tomany factors. Fortunately, many of thesefactors can be modified to reduce the fluid


Figure 8.4. The water nearest a surfboard forms a boundary layer that flows more slowly (VB) past the board thanthe free stream velocity (VFS) because of friction with the board and fluid friction.

resistance to many human movements.Some human movements may also usedrag as a propulsive force.

To understand the variations in pres-sure drag, one must differentiate two dif-ferent kinds of fluid flow in the boundarylayer: laminar and turbulent. The air flowpast a tennis ball can be highlighted bysmoke introduced into a wind tunnel, de-picted in Figure 8.6, which shows both pre-dominantly laminar and turbulent flow.Laminar flow typically occurs in low-veloc-ity conditions with streamlined objectswhere the fluid particles can flow relativelyundisturbed in parallel layers. Turbulentflow occurs when fluid molecules bounceoff the object and each other, mixing inchaotic fashion.

The kind of fluid flow over an objectalso affects pressure drag. At low velocitiesthe boundary layer is laminar and cannot

flow very far around a non-rotating spherebefore peeling away from the surface(Figure 8.7a), creating a large form drag. At


Figure 8.5. Form drag forces (FD) result from a vacuum pressure formed in the pocket formed behind a submergedobject (a). Decreasing the pressure in this wake is how contouring the rear profile of an object (streamlining)decreases form drag (b).

Figure 8.6. The air flow past a tennis ball shows bothlaminar (L) and turbulent (T) fluid motion. The top-spin on the ball deflects the air flow creating anotherfluid force called lift. Photo courtesy of NASA AmesResearch Center Fluid Mechanics Laboratory andCislunar Aerospace, Inc.

higher velocities, the boundary layer flowis turbulent and more resistant to the pres-sure gradient as it flows around the object.This results in a later point of separation(Figure 8.7b) and lower pressure drag thanlaminar flow. In most objects there is not adistinct transition from laminar to turbu-lent flow, but a critical or transition regionwhere flow is unstable can be either lami-nar or turbulent. This transition region isimportant in the flight of spherical balls be-cause the coefficient of drag can drop dra-matically, creating a “drag crisis.” Increas-ing the roughness of the ball (scuffing abaseball or putting dimples on a golf ball)can decrease the velocity where these lowerdrag forces occur. Scientists interested influid mechanics use a dimensionless ratio(the Reynolds number: Re) to combine theeffects of object geometry on fluid flow.This chapter will not go into detail onReynolds numbers, but interested studentscan see Mehta (1985) or Mehta and Pallis(2001a,b) for more information on Reynoldsnumbers related to sports balls.

Much of the variation in the flight char-acteristics of many sport balls is related todifferences in drag and lift forces that aredirectly related to variations in fluid flow inthe transition region of Reynolds numbers.This provides a great opportunity for skill

and coaching to modify the flight character-istics of many shots or throws in sports.Many of these important effects are coun-terintuitive. For example, slightly increas-ing the roughness of a sphere (golf or base-ball) might decrease drag by promoting amore turbulent boundary layer, while in-creasing the lift forces generated. Anotherexample is the nature of the felt on tennisballs. The felt has a major influence on thedrag coefficient (Mehta & Pallis, 2001a), soprofessional tennis players when servingselect balls in part based on the amount offelt fluff and wear. In the next section wewill study how surface roughness of rotat-ing balls can also be used to increase thefluid force of lift.

The two major techniques employed todecrease pressure drag in human move-ment are (a) decreasing the frontal area and(b) streamlining. The smaller the frontalarea, the less the fluid must be acceleratedto flow around the object. Extending thedownstream lines of an object also decreas-es pressure drag by delaying separationand decreasing the turbulent wake behindthe object. Swimming strokes often strike abalance between maintaining a streamlinedbody position and a one that maximizespropulsion. The high speeds and large sur-face areas in cycling make streamlined


Figure 8.7. Spheres like sport balls create different fluid flows and drag force depending on many factors.Primarily laminar flow (a) can result in large pressure drag because of early separation of the boundary layer fora large wake, while turbulent flow (b) will often delay boundary separation and decrease pressure drag.

equipment and body positions critical(Figure 8.8).

The third kind of drag is wave drag. Atthe surface of a fluid it is possible thatdisturbances will create waves within thefluid that resist the motion of an object witharea projecting at this surface. Wave dragcan constitute a major resistance in swim-ming (Rushall, Sprigings, Holt, & Cappaert,1994). Triathletes swimming in the openwater must overcome wave drag from boththe wind and from their fellow competitors.Swimmers in enclosed pools are less affect-ed by wave drag than those swimming inthe open water because of lane makers andgutters designed to dampen waves. Smallvariations in lane placement, however, may

affect the wave drag experienced by aswimmer.

Lift

The fluid force acting at right angles to theflow of fluid is called lift (Figure 8.9). Justlike contact forces are resolved into right-angle components (friction and normal re-action), fluid forces are resolved into theright-angle forces of drag and lift. Since liftacts at right angles to the flow of the fluid,the direction of the lift force in space variesand depends on the shape, velocity, and ro-tation of the object. It is unwise to assumethat the lift always acts upward. For exam-ple, the wings on race cars are designed to


Application: Drafting

Sports with very high relative velocities offluid flow are strongly affected by drag. Onestrategy used to minimize drag forces inthese sports (cycling, car racing) is drafting.Drafting means following closely behind an-other competitor, essentially following intheir wake. The athlete in front will usemore energy against greater pressure drag,while the drafting athlete experiences lessfluid resistance and can use less energywhile they draft.The strategy of the draft-ing athlete is often to outsprint the leadernear the end of the race. In many team rac-ing sports it is the teammate who expendsthe extra energy to be in the front early inthe race who makes it possible for otherteam members to finish in a higher final po-sition. Drafting even has advantages insome lower-velocity events like swimming(Chatard & Wilson, 2003). An athlete run-ning about 1 m behind another runner candecrease air resistance, decreasing themetabolic cost of running by about 7%(Pugh, 1971).

Figure 8.8. High-speed sports like cycling (or sking)use streamlining to decrease speed losses due to dragforces. Image used with permission from Getty Images.

create a downward lift force to stabilize thecar and keep it in contact with the ground.

The size of the lift force can also bemodeled with a coefficient of lift (CL) and afamiliar equation: FL = ½CL � AP V2. Justlike drag, lift varies with the square of therelative velocity (V2) of fluid. Earlier wecharacterized drag as primarily a fluidresistance. Lift tends to be a fluid force andis often used for propulsion. One of the ear-

ly leaders in swimming research, “Doc”Counsilman at Indiana University, usedhigh-speed films of skilled swimmers tomeasure the complex patterns of arm andleg motions and was instrumental indemonstrating the importance of lift as apropulsive force in swimming (Counsil-man, 1971). Whether lift or drag is the pri-mary propulsive force used in swimming isa controversial issue (Sanders, 1998), andother theories like vortices (Arellano, 1999)and axial fluid flow (Toussaint et al., 2002)are currently being examined. The impor-tant thing for swim coaches to realize is thatprecise arm and leg movements are re-quired to use the hands and feet effectively,and that skilled swimmers learn to use bothlift and drag forces for propulsion.

Synchronized swimming and competi-tive swimming tend to use small “sculling”hand movements to create lift forces forpropulsion. A skilled swimmer preciselyadjusts the pitch of their hands to maxi-mize the down-the-pool resultant of the liftand drag forces (Figure 8.10). This is muchlike the high-tech propellers in modern air-


Figure 8.9. The fluid force acting at right angles to therelative flow of fluid is called lift. Lift acts in all direc-tions, not just upward.

Figure 8.10. The inward sweep skill of a freestyle swimmer's hand may be selected to maximize the down-the-poolresultant of the lift and drag acting on the hand (a). This angle of attack (�A) is critical to the lift and drag created (b).

craft that change the pitch of a blade basedon flying conditions. The complexity of flu-id flow over the human body has made itdifficult to resolve the controversy overwhich fluid forces are most influential inpropulsion. Another example of controver-sy and potential research is to understandwhy elite swimmers usually keep their fin-gers slightly spread. It is unknown if thisimproves performance from increased sur-face area for the hand, or that the flowthrough the fingers acts like a slotted air-plane wing in modifying the lift created atlower speeds of fluid flow. Coaches shouldbase their instruction on the kinematics ofelite swimmers and allow scholars to sortout whether lift, drag, or a vortex (swirlingeddies) modifying the flow of fluid is theprimary propulsive mechanism for specificswimming strokes.

There are two common ways of ex-plaining the cause of lift: Newton's Lawsand Bernoulli's Principle. Figure 8.11 showsa side view of the air flow past a discus inflight. The lift force can be understood us-ing Newton's second and third laws. Theair molecules striking the undersurface ofthe discus are accelerated or deflected offits surface. Since the fluid is accelerated inthe direction indicated, there must havebeen a resultant force (FA) acting in that di-rection on the fluid. The reaction force (FR)acting on the discus creates the lift and dragforces on the discus.

The other explanation for lift forcesis based on pressure differences in fluidswith different velocities discovered bythe Swiss mathematician Daniel Bernoulli.Bernoulli's Principle states that the pres-sure in a fluid is inversely proportional tothe velocity of the fluid. In other words, thefaster the fluid flow, the lower the pressurethe fluid will exert. In many textbooks thishas been used to explain how lift forces arecreated on airplane wings. Airplane wingsare designed to create lift forces from air-flow over the wing (Figure 8.12). Fluid mol-


Activity

After trying the ball-submersion experi-ment, try out this little activity usingfreestyle swimming technique. Comparethe number of arm pulls it takes to crossthe pool using two extremes in arm pulltechnique. First, try an arm pull with aprimarily paddling motion, straightdownward under your shoulder. Thenext arm pull should be more like thetraditional freestyle technique, scullingthe hand/arm in a narrow “S” pattern(frontal plane view) down the body.Thepaddle stroke would use primarily dragfor propulsion, while the sculling motionwould combine lift and drag for propul-sion.Attempt to match the speed/tempoof the pulls and employ a flotation assist(like a pull buoy), and no flutter kick fora true comparison. Which fluid forceseems to be most effective in pullingyour body through the water with thefewest strokes?

Figure 8.11. The kinetics of the lift and drag forces canbe explained by Newton's laws and the interaction ofthe fluid and the object. The air molecules (·) deflectingoff the bottom of the discus creates the lift (FL) anddrag (FD) acting on the discus.

ecules passing over the top of the wing cov-er a greater distance than molecules pass-ing under the wing in the same amount oftime and, therefore, have a greater averagespeed than the airflow under the wing. Thelower pressure above the wing relativeto below the wing creates a lift force to-ward the top of the wing. Unfortunately,this simplistic explanation is not technicallycorrect. Rather, it's an oversimplification ofa complex phenomenon (visit the NASABernoulli vs. Newton webpage, about thecompeting theories about lift forces in flu-ids at http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html). Bernoulli'sequation only accounts for force changesdue to fluid pressure (no work, heat, or fric-tion) or a frictionless (inviscid) flow. This isnot the case in most fluid dynamics situa-tions (airplane wings or hands in the pool).Unfortunately, Bernoulli's Principle has

also been overgeneralized to lift forces onsport balls.

The Magnus Effect

Lift forces can also be created by the spinimparted to spherical balls. These lift forcesarise because of pressure differences andfluid deflection resulting from ball spin.This phenomenon of lift force in spinningballs is called the Magnus Effect, after Ger-man engineer Gustav Magnus, though itmay have been discovered a century earlier(Watts & Bahill, 2000). Sport balls hit orthrown with topspin have trajectories thatcurve more downward than balls with min-imal spin or backspin. This greater down-ward break comes from the vertical result-ant force from gravity and the primarilydownward lift force from the Magnus Effect.


Figure 8.12. The lift force (FL) acting on a discus or airplane wing can be explained using Bernoulli's Principle. Thegreater distance (and faster speed of fluid flow) over the top of the wing (lT) compared to the distance under thebottom (lB) creates a pressure differential. The high pressure below and lower pressure above the wing lifts the air-plane.

Activity: Bernoulli's Principle

An easy way to demonstrate Bernoulli's Principle is to use a small (5 � 10 cm) piece of reg-ular weight paper to simulate an airplane wing. If you hold the sides of the narrow end of thepaper and softly blow air over the top of the sagging paper, the decrease in pressure abovethe paper (higher pressure below) will lift the paper.

Recall that it was noted that Bernoulli'sPrinciple is often overgeneralized to ex-plain the lift force from the Magnus Effect.This oversimplification of a complex phe-nomenon essentially begins by noting thata rotating sphere affects motion in theboundary layer of air (Figure 8.13) becauseof the very small irregularities in the sur-face of the ball and the viscosity of the fluidmolecules. Fluid flow past the ball isslowed where the boundary layer rotationopposes the flow, but the free stream fluidflow will be faster when moving in thesame direction as the boundary layer. Forthe tennis ball with topspin illustrated inFigure 8.13, Bernoulli's Principle would saythat there is greater pressure above the ballthan below it, creating a resultant down-ward lift force. As direct and appealing asthis explanation is, it is incorrect becauseBernoulli's Principle does not apply to the

kinds of fluid flow past sport balls since thefluid flow has viscous properties that createa separation of the boundary layer (Figure8.6). Bernoulli's Principle may only apply topressure differences away from or outsidethe boundary layer of a spinning ball.

A better explanation of the lift force isbased on how ball spin creates a deflectionof the fluid, as evidenced by the shifted sep-aration point of the boundary layer. At thespin rates that occur in sports, the bound-ary layers cannot stick to the ball all theway around because of an adverse pressuregradient behind the ball. Note how the top-spin on the ball in Figure 8.6 creates earlierseparation of the boundary layer on the topof the ball, which results in upward deflec-tion of the wake behind the ball (Mehta &Pallis, 2001a). The backward motion of theboundary layer on the bottom of the ball in-creases the momentum of the boundary


Figure 8.13. The lift forces created on spinning spheres is called the Magnus Effect. An overly simplified applica-tion of Bernoulli's Principle is often incorrectly used to explain the cause of this fluid force. Spin on the tennis balldrags the boundary layer of fluid in the direction of the spin. Fluid flow past the ball is slowed where the bound-ary layer opposes the free stream flow, increasing the fluid pressure. The topspin on this ball (like the ball in figure8.6) creates a downward lift force that combines with gravity to make a steep downward curve in the trajectory.

layer, allowing it to separate later (down-stream), while the boundary layer separatessooner on top of the ball. This asymmetricseparation of the boundary layer results inan upward deflection on the wake. An up-ward force on the fluid means that an equaland opposite downward lift (Newton'sthird law) is acting on the ball.

The lift force created by the MagnusEffect is apparent in the curved trajectory ofmany sport balls. Golf balls are hit withbackspin to create lift forces in flight that re-sist gravity and alter the trajectory of shots.Golf balls given sidespin create lift forcesthat curve a ball's flight more in the hori-zontal plane. Figure 8.14 renders a schemat-ic of flight for various golf shots created us-ing different sidespins. A tennis player im-

parting sidespin to a ball also creates a lat-eral lift force that makes the ball curve inflight. The flat trajectory of a fastball pitchin baseball results from an upward compo-nent of lift force that decreases the effect ofgravity. Lift forces on sport balls are vecto-rially added to other forces like drag andweight to determine the resultant forces onthe ball. The interaction of these forces cre-ates the trajectory or flight path of the ball.The lift forces in a fastball are not largerthan the weight of the baseball, so playerperceptions of fastballs “rising” is an illu-sion based on their expectation that the ballwill drop more before it crosses the plate.Fastballs don't rise; they just drop less thansimilar pitches with minimal backspin ortopspin.


Figure 8.14. Horizontal plane trajectories of various golf shots and the ball spin (curved arrows) creating thesecurves with Magnus forces.

Much of the skill of baseball pitchingrelies on a pitcher's ability to vary the speedand spin of pitches. A curveball is pitchedwith an element of topspin that has a liftcomponent in the same direction as gravity,so there is greater downward break as theball nears the plate. The steepness of thisbreak has resulted in hitters saying that agood curveball looks like it “drops off thetable.” Looking at the curveball in baseball(much like topspin shots in other sports,like volleyball and tennis) will provide anice review of the kinetics of lift forces.

Figure 8.15 shows a three-dimensionalreconstruction of a major league curveballfrom two perspectives. The curveball has agradual break that looks much steeper fromthe relatively poor vantage point of the hit-ter. Why does so much of the ball's breakoccur late in the trajectory when the hitter isswinging the bat and cannot change theirswing? The major factors are the changingdirection of the Magnus force in space andthe slowing of the ball from drag.

Recall that the Magnus force acts per-pendicular to the flow of fluid past the ball.This means that the Magnus force for acurveball primarily acts downward, add-ing to the drop created by gravity, but thehorizontal component of the lift forcechanges. As the direction of the pitchchanges, so does the fluid flow and lift force(Figure 8.16). As the ball breaks downward,the Magnus force has a backward compo-

nent that slows the ball even more. This ex-tra slowing and extra downward force con-tribute to the increasing “break” in thepitch late in its trajectory. Novice golferscan experience the same surprise if theyconsistently have trouble with “hooking”or “slicing” their drives. A “hooked” drivemight initially look quite straight when themoderate sideward force is hard to detectdue to the great initial speed of the ball.Unfortunately, as they watch their “nice”drive later in its trajectory, the ball seems tobegin curving sideways late in flight.Diagram a transverse plane view of a“hooked” shot in golf. Draw the lift forceacting on the ball and note its change in di-rection as the direction of the ball changes.

The coefficient of lift (CL) in spinningballs tends to be less sensitive to variationsin Reynolds numbers than drag, so the sizeof the Magnus force depends mostly onspin and ball roughness (Alaways et al.,2001). Athletes can create more break onballs by increasing spin or increasing thesurface roughness of the ball. In baseball,pitches can be thrown with four seams per-pendicular to the throw, which increases CLtwo to three times more than a two-seamrotation (Alaways et al., 2001).

Interesting exceptions to the dominanteffect of lift forces on the flight of manysport balls are projections with minimalball spin. A baseball “knuckleball” and avolleyball “floater” serve are examples of


Activity: Lift and Angle of Attack

When driving on an uncrowded road, roll down a window and put your hand out just into theflow of the air rushing past. Drive at a constant speed to standardize air speed and experi-ment with various hand shapes and angles of attack to the air.Think about the sport balls/ob-jects your hand can simulate and note the drag you (and the simulated object) experience atthat relative velocity of air flow. How much does the drag increase as you increase the frontalarea of your hand? Can you make the lift force act downward? Find the angle of attack thatseems to have the most lift and the least drag (maximum lift/drag ratio). See if your classmateshave observed similar results.


Figure 8.15. Trajectory of the same curveball thrown by a major league player from two perspectives. Note the ma-jority of the downward break occurs late in the trajectory, creating the illusion (to the hitter) of the ball “droppingoff the table.” Adapted from Allman (1984).

techniques where the ball is projected withvirtually no spin. The erratic trajectory andbreak of these balls are due to unpre-dictable variations in air flow past the ball.As the ball gradually rotates, air flow canbe diverted by a seam or valve stem, mak-ing the ball take several small and unpre-dictable “breaks” during its trajectory. Sospin, and the lack of it, on a sport ball has amajor effect on trajectory.

PRINCIPLE OF SPIN

It is clear that fluid forces affect the motionof objects through a fluid. Lift is a key fluidforce that can be modified by impartingspin on a projectile. The Principle of Spinis related to using the spin on a projectile toobtain an advantageous trajectory orbounce. Kinesiology professionals can usethe principle of spin to understand the mostsuccessful techniques in many activities.The upward lift force created by backspinin a golf shot increases the distance of adrive (Figure 8.17a), while the backspin ona basketball jump shot is primarily used tokeep the ball close to the hoop when im-pacting the rim or backboard (Figure 8.17b).The bottom of a basketball with backspin ismoving faster than the center of the ball be-

cause the ball is rotating. This increases thefriction force between the ball and the rim,decreasing the horizontal velocity of theball, which makes the ball bounce higher. Inapplying the spin principle, professionalsshould weigh the trajectory and bounce ef-fects of spin changes.

Applying spin to projectiles by throw-ing or striking have a key element in com-mon that can be used to teach clients. Thebody or implement applies force to the balloff-center, creating a torque that producesspin on the projectile. The principles oftorque production can be applied to the cre-ation of spin, in that a larger force or a larg-er moment arm will increase the torque andspin produced. Coaching athletes to projector hit balls with minimal spin to create er-ratic trajectories requires that the object bein contact with a force in line with the ball'scenter of gravity. In volleyball, for example,the athlete is taught to strike through thecenter of the ball with minimal wrist snap.The flat impact through the ball's center ofgravity and minimal torque from wrist ro-tation ensures that the ball will have mini-mal spin.

Unfortunately, the linear speed of theprojectile is inversely proportional to thespin created. In other words, the more spinproduced in the throw or hit comes at a cost


Figure 8.16. The late “break” of a curveball can be explained by the changing direction of the Magnus force (FL)on the ball and gravity (W). The downward deflection of the ball accelerates because the lift forces not only actdownward with gravity, but backward (toward the pitcher). Slowing of the ball allows for more downward break.

of lower ball speed. In tennis the lateralbreak of a ball with slice (sidespin) will nottravel as fast as a flat serve (minimal spin)hit with the same effort. Much of the art ofteaching and coaching is being able to eval-uate a person's performance, diagnosingthe factors related to spin and speed pro-duction that are appropriate for a specificsituation.

There is one more advantage of impart-ing spin to a projectile that is not related tofluid or contact forces on a surface. Thisthird advantage of projectile spin is relatedto Newton's laws and conservation of an-gular momentum. Any object in angularmotion without external-acting torques(like a projectile) will conserve angular mo-mentum. This inertia in a rotating objectcan be used to keep the projectile in a cer-tain orientation. A pass in American foot-ball does not create significant lift force, butthe spin stabilizes the flight of the ball in astreamlined position. Divers and gymnasts

(human body projectiles) can overcomethis inertia and move body parts relative toan axis of rotation with internal muscleforces. In these situations athlete can trans-fer angular momentum from one axis to an-other (e.g., add a twist in the middle ofsomersaults) by asymmetric motions ofbody parts. Coaches of these sports need tobe familiar with this interesting applicationof the spin principle (see Yeadon, 1991,1997).

Knowing what advantage of spin in aparticular situation is important and how tomechanically create it are critical, butthis knowledge must be integrated withknowledge from other kinesiology disci-plines. A physical educator could ask a jun-ior high student to “use an eccentric force”or “increase the effective moment arm” andmay be mechanically correct, but a goodteacher selects an appropriate cue that com-municates the essential correction withoutusing such technical language. Think about


Figure 8.17. The principle of spin is used on a golf ball to create lift forces (FL) that affect ball trajectory, while spinon a basketball is primarily used to modify ball rebound to increase the chance of a made basket.

what would be good cues for hitting a sportball to create topspin, backspin, right or leftsidespin. Deciding whether cues about theball (target) or body action (technique) aremost relevant depends on the situation.This is another example of how a biome-chanical principle must be integrated in aninterdisciplinary fashion with other kinesi-ology disciplines (e.g., motor development,motor learning, psychology).

SUMMARYFluid forces from air and water have a sig-nificant effect on human movement. Themain fluid forces are buoyancy, lift, anddrag. Buoyancy is the supporting or float-ing force that a fluid exerts on an object asit is submerged in the fluid. The size of thebuoyant force can be determined byArchimedes Principle. The fluid force thatacts in the same direction as the relativeflow of fluid is drag, while the fluid forceacting at right angles to the flow is lift. Thesize of the lift and drag forces depends onmany factors, but they vary with the squareof the relative velocity of the fluid. Liftforces can be created on spinning sphericalballs through the Magnus Effect. Kinesiolo-gy professionals can apply the Spin Princi-ple to help performers create spin on pro-jectiles like sport balls. Imparting morespin to a projectile usually comes at the ex-pense of a loss in some linear velocity, butthe lift force can be used to gain an advan-tage from an altered flight or bounce rela-tive to a no-spin projection.

KEY TERMS

Archimedes PrincipleBernoulli's principleboundary layerbuoyancycenter of buoyancydragliftMagnus Effectspin principle

REVIEW QUESTIONS

1. What are the major fluid forces andin what directions do they act?

2. What factors affect the fluid resist-ance acting on projectiles? What factor ismost influential in creating fluid forces?

3. Compare and contrast the motion ofthe center of gravity and center of buoyan-cy with various body segment movements.

4. Explain why streamlining decreasesfluid resistance.

5. How do fluid forces affect the opti-mal projection angles proposed earlier inchapter 5?

6. Why do golf balls have dimples?7. Draw or trace a person and estimate

their center of buoyancy. Trace the persontwo more times with various exercise andswimming flotation devices and re-esti-mate the likely center of buoyancy.

8. How is the density of water related towhether an object will float in water?

9. Explain why topspin serves in vol-leyball curve downward?

10. What are the benefits of impartingspin to round balls in sports?

11. How are the spin and the “break” ofa ball in flight related?

12. Draw a free-body diagram of a golfball in flight and explain how the resultantforces on the ball affect its flight.

13. Why do swimmers and cyclistsshave their body, but a baseball pitchers il-legally roughen the surface of the ball?

14. What forces increase and decreasewhen exercising in water?

SUGGESTED READING

Adair, R. (1990). The physics of baseball. NewYork: Harper & Row.

Alaways, L. W., Mish, S. P., & Hubbard, M.(2001). Identification of release conditions andaerodynamic forces in pitched-baseball trajec-tories. Journal of Applied Biomechanics, 17, 63–76.


Arellano, R. (1999). Vortices and propulsion. InR. Sanders & J. Linsten (Eds.), SWIMMING:Applied proceedings of the xvii international sym-posium on biomechanics in sports (Vol. 1, p.53–66). Perth, WA: Edith Cowan University.

Berger, M. A. M., de Groot, G., & Hollander,A. P. (1995). Hydrodynamic drag and lift forceon human hand/arm models. Journal ofBiomechanics, 28, 125–133.

Counsilman, J. E. (1971). The application ofBernoulli's Principle to human propulsion inwater. In L. Lewillie and J. Clarys (Eds.), Firstinternational symposium on biomechanics of swim-ming (pp.59–71). Brussels: Université Libre deBruxelles.

McLean, S. P., & Hinrichs, R. N. (2000a).Influence of arm position and lung volume onthe center of buoyancy of competitive swim-mers. Research Quarterly for Exercise and Sport,71, 182–189.

McLean, S. P., & Hinrichs, R. N. (2000b). Buo-yancy, gender, and swimming performance.Journal of Applied Biomechanics, 16, 248–263.

Mehta, R. D., & Pallis, J. M. (2001b). Sports ballaerodynamics: Effects of velocity, spin and sur-face roughness. In F. H. Froes, & S. J. Haake(Eds.), Materials and science in sports (pp.185–197). Warrendale, PA: The Minerals,Metals and Materials Society [TMS].

Mureika, J. R. (2000). The legality of wind andaltitude assisted performances in the sprints.New Studies in Athletics, 15(3/4), 53–58.

Olds, T. (2001). Modelling of human locomo-tion: Applications to cycling. Sports Medicine,31, 497–509.

Toussaint, H. M., van den Berg, C., & Beek,W. J. (2002). “Pumped-up propulsion” duringfront crawl swimming. Medicine and Science inSports and Exercise, 34, 314–319.

Watts, R. G., & Bahill, A. T. (2000). Keep your eyeon the ball: The science and folklore of baseball (2nded.). New York: W.H. Freeman.

Yeadon, M. R. (1997). The biomechanics of hu-man flight. American Journal of Sports Medicine,25, 575–580.


WEB LINKS

Aerodynamics—NASA educational pages on fluid mechanics.http://www.grc.nasa.gov/WWW/K-12/airplane/short.html

Aerodynamics in Tennis—NASA/Cislunar Aerospace project to promote science educa-tion through sport science.

http://wings.avkids.com/Tennis/Book/index.html

Cycling Aerodynamics—cycling page by Smits and Royce of Princeton University.http://www.princeton.edu/~asmits/Bicycle_web/bicycle_aero.html

Cycling Aerodynamics and power calculation page.http://www.exploratorium.edu/cycling/aerodynamics1.html

Bernoulli vs. Newton—NASA webpage on the competing theories for lift forces in fluids.http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html

ISBS Coaching Information Service—select swimming link.http://coachesinfo.com/

PARTIVAPPLICATIONS OF BIOMECHANICS

IN QUALITATIVE ANALYSIS

The personal trainer depicted here is usingthe principles of biomechanics to qualita-tively analyze the exercise technique of hisclient. Biomechanical principles must beintegrated with other kinesiology sciencesin the qualitative analysis of human move-ment. The chapters in part IV provideguided examples of applying biomechan-ics in qualitative analysis for several kinesi-ology professions: physical education,coaching, strength and conditioning, andsports medicine. A variety of guided exam-ples and questions for discussion are pre-sented. The lab activities related to part IVprovide students with opportunities tointegrate biomechanical principles withother subdisciplines of kinesiology in thequalitative analysis of human movement.A sample table with the principles of bio-mechanics for qualitative analysis can befound in Appendix E.

213

Physical educators teach a wide variety ofhuman movements, and biomechanics pro-vides a rationale critical for evaluating tech-nique and prescribing intervention to helpyoung people improve. Biomechanics alsoallows physical educators to identify exer-cises and physical activities that contributeto the physical development of variousmuscle groups and fitness components.This chapter illustrates how biomechanicalknowledge and the nine principles of bio-mechanics can be integrated with othersport sciences in qualitative analysis of hu-man movement. Five skills commonlytaught in physical education are discussed,and the various tasks of qualitative analysis(Knudson & Morrison, 2002) are empha-sized in the examples. Real movement per-formances and typical teaching cues areused to show how biomechanics is appliedto real-world physical education. Qualita-tive analysis is a critical evaluative anddiagnostic skill that can be employed forimprovement of movement in physical ed-ucation.

QUALITATIVE ANALYSIS OFKICKING TECHNIQUE

The primary task of a professional physicaleducator may be the qualitative analysis ofmovement technique to facilitate learningof motor skills. Biomechanics is the primarysport science focusing on movement tech-nique, so it is logical that physical educa-tors should use the principles of biome-

chanics in helping students move safelyand effectively. Biomechanics providesknowledge relevant to all four tasks ofqualitative analysis (Figure 2.9).

Imagine that you are an elementaryphysical educator planning a lesson onkicking as a lead-up to soccer, so you are in-volved in the preparatory task of qualita-tive analysis. In preparing to teach andqualitatively analyze kicking, you list thecritical features and teaching points of themovement (Table 9.1). As students practicethis skill, you are planning to evaluate thesecritical features and diagnose student per-formance using biomechanical principles.Which biomechanical principles seem mostrelevant to the critical features of high-speed place-kicking?

Five of the critical features presented inTable 9.1 are strongly related to several ofthe biomechanical principles. The opposi-tion and coordination involved in high-

CHAPTER 9

Applying Biomechanics inPhysical Education

215

Table 9.1CRITICAL FEATURES AND TEACHING CUES

FOR FAST PLACE KICKING

Critical Possible teachingfeature /intervention cues

Visual focus Head down and focus on the ball

Opposition Turn your hip to the ball

Foot plant Plant your foot next to the ball

Coordination Swing your hip and leg

Impact position Kick the center of the ball

Follow-through Follow-through toward the target

speed kicking are all strongly influenced bythe principles of range of motion, coordina-tion, and segmental interaction. In addi-tion, the force–motion, force–time, and op-timal projection principles are important inkicking as well. The teacher might plan tokeep the principles of inertia, spin, and bal-ance in the back of their mind, so they willnot be a focus of observation. These threeprinciples are not likely to play a significantrole in the kicking executed by most pri-mary school children.

A child making a full-effort kick to-ward a goal is observed to consistentlyhave a technique like that illustrated inFigure 9.1. Remember that good qualitativeanalysis requires the analyst to observeseveral performances so that clear trends ofstrengths and weaknesses can be identi-fied, rather than jumping to conclusions oridentifying unimportant “errors” (Knudson& Morrison, 2002). What critical featuresare strongly and weakly performed? These

judgments are part of the evaluationprocess within the evaluation/diagnosistask of qualitative analysis.

The child illustrated in Figure 9.1 isclearly at a low developmental level ofkicking. The teacher could praise the stu-dent's focus on the ball, strong approach,and balance during the kick. The list of bio-mechanical weaknesses is long at this be-ginning stage of learning. The biomechani-cal principles that are weakly incorporatedinto the kick are force–motion, optimal pro-jection, inertia, range of motion, coordina-tion, and segmental interaction. The stu-dent applies a suboptimal force to the ballbecause they plant the support foot well be-hind the ball, and impact the ball with theirtoe rather than the proximal instep (top ofthe shoelaces). Low-trajectory shots are de-sirable, but this kick, rolling along theground, will slow the ball down as it rolls,making it easier for opponents to intercept.Finally, the student needs considerable


Figure 9.1. The technique of a young person making a high-speed soccer kick. The time between images is 0.08 s.

practice to increase the range of motion ofthe kick and to refine a well-timed sequen-tial coordination that transfers energythrough segmental interactions. Highlyskilled kickers will approach the ball at anangle to increase the contralateral hip rangeof motion that can be sequentially com-bined with the hip and knee motions of thekicking leg. Which of these weaknesses doyou think is most important to kicking suc-cess? One effective intervention strategywould be to provide a cue to plant their footnext to the ball. This is a simple correctionthat might be related to other weaknessesand might motivate the student with initialsuccess and improvement.

Toward the end of the lesson you noticeanother child consistently kicking as in thesequence illustrated in Figure 9.2. Whatbiomechanical principles are strongly orweakly performed in Figure 9.2?

The student depicted in Figure 9.2 ismore skilled than the student from the pre-

vious example. Note the more vigorous ap-proach to the ball. The intensity (inertia) ofthis approach is apparent in the length ofthe hurdle to the plant leg and the trunklean used to maintain balance. It is hard tojudge from the figure, but the ball is kickedat the desirable low trajectory. Some educa-tors might conclude that all the biomechan-ical principles were well applied in thiskick. The only two principles that might beslightly improved are range of motion andcoordination. If the student were to ap-proach the ball from a more oblique angle,the rotation of the pelvis on the left hipcould be increased (range of motion) andcombined (sequential coordination) withthe good coordination of the kicking hipand knee.

Which of these small improvements,range of motion or coordination, do youthink could be easily changed by this stu-dent in practice? Improvement in whatprinciple would increase performance the

CHAPTER 9:APPLYING BIOMECHANICS IN PHYSICAL EDUCATION 217

Figure 9.2. The technique of another soccer player kicking for maximum speed. Time between images is 0.08 s.

most? These are the issues that are impor-tant for a physical educator to examine inthe diagnosis and intervention stages ofqualitative analysis. The teacher might re-view some recent research and review pa-pers on kicking (Barfield, 1998; Davids,Lees, & Burwitz, 2000; Dorge, Bull Ander-sen, Sorensen, & Simonsen, 2002). The fol-lowing examples of qualitative analysiswill illustrate the use of the biomechanicalprinciples in these more difficult phases ofqualitative analysis.

QUALITATIVE ANALYSISOF BATTING

Imagine you are a physical educator work-ing on batting with young boys and girls.Most primary school children receive someexperience intercepting and striking objectsfrom elementary physical education. Thedifficulty of the skill dramatically increaseswhen these young people move from bat-ting slow-moving or stationary (batting tee)objects, to balls thrown with greater speedand spin. Use the technique points and cuesin Table 9.2 to analyze the batting techniqueof the student illustrated in Figure 9.3.Assume the technique illustrated is repre-sentative of most batting attempts off a bat-ting tee by this child. What biomechanical

principles seem to be well applied by thischild, and what principles are poorly ap-plied? More importantly, prioritize theweaknesses in an order that you thinkwould result in the best batting perform-ance if the weaknesses were improved.

Most all of the biomechanical princi-ples are relevant to batting performance.The student in Figure 9.3 strongly incorpo-rates many biomechanical principles intobatting. His strengths include balance, iner-tia, and coordination. He strides into theswing and gets the bat in line with the ball.The force–motion principle could be im-proved since the bat does not squarely col-lide with the ball (note the tipping battingtee). The principles of force–time and rangeof motion may be the major weaknessesthat could be improved. The student exag-gerates the stride and uses an abbreviatedfollow-through. The physical educatormust diagnose the situation and decide ifinstruction should be focused on the largerthan normal range of motion and time inthe stride or on the less than expectedtime/range of motion in the follow-through. Weighing the importance of theseprinciples so as to lead to potential im-provement is very difficult. Remember, wenoted that this student would soon be ap-plying this skill in the more dynamic condi-tion of impacting a moving ball.

Since the student has good balance,their long stride (which increases range ofmotion and time of force application) couldgenerate more speed without adversely af-fecting accuracy. This is typical for a youngperson with limited upper body strengthtrying to clobber a ball off a batting tee.Maintaining a long (time and distance)stride in hitting pitched balls, however, isgenerally a bad tradeoff. Accuracy in con-tacting the ball becomes more important indynamic hitting conditions.

It may even be possible to maintain asimilar bat speed with a shorter stride if thestudent improves his follow-through. An


Table 9.2CRITICAL FEATURES AND TEACHING

CUES FOR BATTING

Critical Possible teaching/feature intervention cues

Visual focus Head down and focus on the ball

Opposition Sideward stance

Readiness Bat up and elbow back

Weight shift Short stride toward the pitch

Coordination Throw your hands through the ball

Follow-through Follow-through around your body

abbreviated follow-through means that thehitter is slowing down the bat before im-pact. Skilled striking involves generatingpeak velocity at impact, delaying negativeaccelerations until that point (Knudson &Bahamonde, 2001). The force–time andrange-of-motion principles also imply thata short follow-through may increase therisk of injury since the peak forces slowingthe movement must be larger. Since the fol-low-through is an important strategy forminimizing the risk of injury in manymovements, the physical educator shouldrate this intervention ahead of adjusting thepreparatory (stride) range of motion. Oncethe student gets comfortable swingingthrough the ball, they may have more batspeed at impact, and might be more willingto reduce their stride and weight shift whenhitting pitched balls. More recent researchon baseball batting has focused on differ-

ences in various bats (Greenwald, Penna, &Crisco, 2001) and hitting from both sides ofthe plate (McLean and Reeder, 2000). Thenext section provides an example of diag-nosis using biomechanical principles inbasketball shooting.

QUALITATIVE ANALYSIS OF THEBASKETBALL FREE THROW

The previous qualitative analysis examplesinvolved movements that must be matchedto unpredictable environmental conditions.Motor learning classifies these movementsas open skills, while skills with very stableconditions are called closed skills. Whenphysical educators teach and analyzeclosed motor skills, they can be confidentthat performance is more strongly depend-ent on stereotypical technique rather than a


Figure 9.3. A physical education student batting a ball from a tee. Time between images is 0.1 seconds.

variety of effective techniques. The stan-dardized conditions of the free throw inbasketball mean that the stereotypical tech-niques of a set shot would be optimal. Table9.3 lists the key technique points and inter-vention cues that describe good free throwshooting technique.

Suppose an elementary school studentis working on her free throw using modi-fied equipment. Using a smaller ball andlower basket is critical to teaching goodshooting technique with young children.At this age, they typically cannot employgood shooting technique using a regularball and a 10-foot-high basket because oftheir lack of strength. Suppose that obser-vations of the free throw attempts of ayoung child shows technique consistentwith that illustrated in Figure 9.4. Identifythe biomechanical principles that arestrengths and weaknesses. Then diagnosethe situation to determine what biomechan-ical principle should be the focus of any in-tervention.

The principles she can be compliment-ed on are her good balance, simultaneouscoordination, and spin on the ball. It is dif-ficult to see in Figure 9.4, but this child usedonly one hand and one leg to shoot becauseshe stepped into the shot. Weaknesses inher shooting technique are the limited useof range of motion and the force–time prin-ciples since she is not easily generating theball speed needed for the shot. Anotherweakness is in the principle of optimal tra-jectory. Biomechanical research on shootinghas shown that the optimal angles of pro-jection for most set and jump shots are be-tween 49 and 55º above the horizontal(Knudson, 1993). Young basketball playersoften select “flat” shooting trajectories,which actually require greater ball speedand often have angles of entry that do notallow the ball to pass cleanly through thehoop. This weighing of potential benefits ofworking on range of motion or initial shottrajectory is the essential diagnostic deci-

sion in this case. There are several biome-chanical reasons why it is likely more bene-ficial to work on shot trajectory than in-creasing range of motion. First, using thedesirable trajectory increases the angle ofentry and the probability of a made shot.Second, this slightly higher trajectory re-quires less ball speed than a very flat one.Third, the young player is likely to increaseher strength while the desirable trajectorywill remain the same. The interaction ofbiomechanics and performer characteristicssuggests to the teacher that subsequentpractice should focus on a slightly highershot trajectory.

EXERCISE/ACTIVITYPRESCRIPTION

Another important content area ofphysical education is fitness. Physical edu-cators planning to increase student physicalfitness must employ biomechanical knowl-edge to determine the most effective exer-cises for various parts of the body and fit-ness components. Like strength and condi-tioning professionals, physical educatorsqualitatively analyze exercise technique tobe sure that students are safely trainingtheir bodies.


Table 9.3CRITICAL FEATURES AND TEACHING

CUES FOR THE FREE THROW


Staggered stance Shooting side foot forward

Shooting plane Align your arm with the basket

Height of release Release high above your head

Coordination Extend your whole body

Angle of release Shoot with high arc

Ball rotation Flip your wrist

During the first week of your highschool weight-training unit, you noticemany students performing their curl-up ex-ercises like the student depicted in Figure9.5. You want to immediately provide somegroup feedback to help many students withthis exercise technique and reinforce someof the technique points you made earlier.Make a list of the critical features or tech-nique points that are important in the curl-up exercise. What biomechanical principlesare most related to the objectives of doingcurl-ups for health-related fitness (muscu-lar endurance)? Which of the biomechani-cal principle(s) seem to be weakly appliedin the concentric phase of the curl-up forthe student shown in Figure 9.5?

The purpose of curl-up exercises is tofocus a conditioning stimulus on the ab-dominal muscles by limiting the contribu-tion of hip flexors and other muscles. The

biomechanical principles that are importantin this objective are Force–Motion, Range ofMotion, Inertia, and Force–Time. The iner-tia of the body provides the resistance forthe exercise, and the range of motion for theexercise should focus the stress (force–mo-tion) on the abdominal muscles. The repeti-tions should be slow and controlled (Force–Time) for safety and to promote training formuscular endurance.

The student in Figure 9.5 has severalweaknesses in his curl-up technique. Heuses too much range of motion, performingmore of a sit-up (hip flexion) than a trunkcurl. In a curl-up exercise, the abdominalmuscles should raise the shoulders to abouta 30 to 40º angle with the hip (Knudson,1996), just lifting the shoulder blades off theground. Hip flexion is required if the shoul-ders are to be raised further. The studentalso decreases the resistance or inertia by


Figure 9.4. An elementary student shooting a free throw at an 8-foot-high hoop. Time between images is 0.07 s.

keeping the weight of the arms close to thetransverse axis of rotation for trunk flexion.The third weakness is in stabilizing his feetwith the weight bench. This affects both theForce–Motion Principle and the Principle ofInertia. By stabilizing the feet with thebench, the performer has essentially unlim-ited inertia for the lower extremities. Thisallows hip flexor activation to contribute totrunk flexion through the kinematic chainof the lower extremity, so the Force–MotionPrinciple is not applied well for the trainingobjective of isolating the abdominal mus-cles. Performing the curl-up without footstabilization would require greater abdom-inal activation and stabilization to lift thetrunk without hip flexors. The time infor-mation in the caption for Figure 9.5 sug-gests that the student was applying theForce–Time Principle well; in other words,he did not perform the exercise too fast.

The best intervention in this situation isto provide group intervention, remindingall students to perform curl-ups withoutlower-extremity stabilization. This exercisemay feel more difficult, but the teacher canuse this opportunity to reinforce the idea

that the students are training and teachingtheir abdominal muscles an importanttrunk-stabilizing task. Focusing on usingmore abdominal muscles for a longer time(Force–Time Principle) better simulates thenearly isometric actions of the muscles instabilizing the trunk and pelvis. There is alarge body of physical therapy literature fo-cused on training specific abdominal mus-cles so as to stabilize the trunk (McGill,1998; Vezina & Hubley-Kozey, 2000). Theteacher could then provide some individu-alized intervention for the student. Onegood strategy would be to compliment (re-inforce) the good exercise cadence, butchallenge the student to place his hands ontop of his head and keep the arms back toincrease the resistance for the exercise.

QUALITATIVE ANALYSISOF CATCHING

Imagine that you are a junior high schoolphysical educator teaching a basketballunit. You have been ingenious in getting thestudents to realize the rewards of moving


Figure 9.5. Concentric phase technique of a curl-up for a high school student. Time between images is 0.17 s.

without the ball and passing rather thandribbling. There is one small problem thatmany of the students have poor catchingskills. You previously taught students thecritical features of catching (Table 9.4) usinga variety of cues. In watching a passingdrill, you notice a student receiving passessimilar to what is illustrated in Figure 9.6.What biomechanical principles are well orpoorly incorporated in catching the basket-ball? Diagnose the situation and prioritizethe importance of the biomechanical princi-ples in successful catching for this playerand think about what the best interventionwould be.

The player has good balance and usessimultaneous coordination in receiving theball. The Force–Motion Principle was wellapplied by predicting the location of theball, intercepting the ball with the hands,and applying the force through the centerof gravity of the ball. The two principles

that could be improved are Range ofMotion and Force–Time. Since you are agood physical educator, you also note thenon-biomechanical factors relevant in thissituation: the player appears to visually fo-cus on the ball, is motivated, and is tryingher best.


Table 9.4CRITICAL FEATURES AND TEACHING CUES

FOR TWO-HANDED CATCHING


Readiness Athletic stance

Visual focus Watch the ball

Intercept Move and reach towards the ball

Hand position Thumbs in or thumbs out

Absorption Give with your hands and arms

Figure 9.6. A junior high school basketball player catching a pass. Time between images is 0.1 seconds.

Diagnosis of this situation is not as dif-ficult as many qualitative analyses becausethe two weaknesses demonstrated in thisexample are closely related. Increasing therange of motion in receiving the ball willgenerally increase the time of force applica-tion. You must decide if the player's catch-ing and basketball performance would im-prove most if her attention were focused onreaching more to intercept the ball or em-phasizing how the arms bring the ball in.Both biomechanical principles are impor-tant. Can you really say one is more impor-tant than the other? The player wouldclearly improve if she stepped and reachedmore to intercept the ball earlier and pro-vide more body range of motion to slowthe ball down. Increasing range of motionalso has a secondary benefit by reducingthe risk of a pass being intercepted. Howthe hand forces opposing ball motion, how-ever, has the most influence on whether aball is caught or bounces out of a player'sgrasp. This is a case where some profes-sionals might disagree on the most appro-priate intervention. In class, you only havea few seconds and you provide a cue to astudent to focus on “giving” with herhands and arms as she receives the ball.You say, “See if you can give with yourhands and arms as you catch the ball. Bringthat ball in so you barely hear a sound.”

SUMMARY

The principles of biomechanics provide amethod for physical educators to qualita-tively analyze human movement. Severalsport and exercise situations commonlyfaced by physical educators were dis-cussed. The physical educators in the exam-ples employed cue words or phrases tocommunicate the essence of the biomechan-ical principles to their students. Physicaleducators should also integrate the biome-

chanical principles with their experience,as well as knowledge from other subdisci-plines of kinesiology to provide an interdis-ciplinary approach to qualitative analysis(Knudson & Morrison, 2002).

DISCUSSION QUESTIONS

1. What biomechanical principles aremore important in kicking versus trappinga soccer ball?

2. What are the typical teaching pointsor cues for baseball/softball batting? Whatbiomechanical principles are relevant inthese teaching points?

3. How is the application of biomechan-ical principles different in the free throwversus the jump shot?

4. Which biomechanical principles arerelevant to the pushup exercise? How doeschanging hand position from a wide base ofsupport to a narrow base of support modi-fy the importance of these principles?

5. What biomechanical principles aremost relevant to catching a softball?Catching a medicine ball?

6. What are typical teaching points injumping to rebound a basketball? Whatpoints are most important based on theprinciples of biomechanics?

7. What biomechanical principles areimportant in throwing a pass in Americanfootball?

SUGGESTED READING

Adrian, M. J., & Cooper, J. M. (1995).Biomechanics of human movement (2nd ed.).Madison, WI: Brown & Benchmark.

Hay, J. G. (1993). The biomechanics of sports tech-niques (4th. ed.). Englewood Cliffs, NJ:Prentice-Hall.


Knudson, D. (1991). The tennis topspin fore-hand drive: Technique changes and critical ele-ments. Strategies, 5(1), 19–22.

Knudson, D. (1993). Biomechanics of the bas-ketball jump shot: Six key teaching points.JOPERD, 64(2), 67–73.

Knudson, D., & Morrison, C. (1996). An inte-grated qualitative analysis of overarm throw-ing. JOPERD, 67(6), 31–36.



WEB LINKS

AAHPERD—American Alliance for Health, Physical Education, Recreation, andDance is the first professional HPERD organization in the United States. TheNational Association for Sport and Physical Education (NASPE) should be selected from the list of associations on this site.

http://www.aahperd.org/

Coaching Information Service.http://coachesinfo.com/

PE Links 4U—website for sharing physical education teaching ideas.http://www.pelinks4u.org/

PE Central—website for sharing physical education teaching ideas.http://www.pecentral.com/

Coaching athletics also involves teachingmotor skills to a wide variety of perform-ers. Traditionally, careers in coaching havefocused on working with the physicallygifted in interscholastic athletics; however,there are many other levels of coaching:from parents who volunteer to coachtheir child's team, to the coach of a nationalteam, and to a coach for an individual pro-fessional athlete. All of these coaching posi-tions benefit from application of biome-chanics in coaching decisions. Coaches usebiomechanics to analyze technique, deter-mine appropriate conditioning, and treatinjuries (Elliott & Bartlett, 2006; Knudson,2007b). Biomechanical knowledge is alsoimportant to coaches when coordinating ef-forts with sports medicine professionals.

QUALITATIVE ANALYSIS OFTHROWING TECHNIQUE

Imagine you are a youth softball coachscouting the throwing ability of potentialplayers. You set the players up in the out-field to see how well they can throw the ballto home plate. The technique points foroverarm throwing and the cues one wouldcommonly use are listed in Table 10.1. Oneyoung person trying out for the team showsa throwing technique like that depicted inFigure 10.1. What are the strengths orweaknesses of their performance in termsof biomechanical principles? Are theseweaknesses you are confident can be over-come this season if they become part ofyour team?

The athlete in Figure 10.1 has a very imma-ture throwing pattern, so he has weakness-es in several biomechanical principles. Infact, the straight arm sling this player useslikely places great stress on the throwingshoulder. The principle most in need of im-provement is Range of Motion, whichcould improve with a more vigorous ap-proach and a longer stride with the oppo-site leg. The Inertia of the throwing armshould be reduced in the propulsion phaseby flexing the elbow to about 90º. Thethrower does rotate their trunk away fromand then into the throw, but SequentialCoordination that maximizes SegmentalInteraction will require considerable prac-tice. Like many young players, this personthrows with a high initial trajectory, violat-ing the Optimal Projection principle. The

CHAPTER 10

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Table 10.1TECHNIQUE POINTS AND CUES

FOR OVERARM THROWING

Technique Possible teachingpoints /intervention cues

Approach/stride Step with the opposite foot toward the target

Opposition & Turn your side to the targetcoordination

Arm position Align your arm with your shoulders

Shoulder internal Range of motionrotation

Angle of release Throw the ball low and flat

Relaxation Be loose and relaxed

Applying Biomechanicsin Coaching

optimal throwing angles for maximum dis-tance with baseballs and softballs are about30º (Dowell, 1978).

Some of these weaknesses can be cor-rected quickly, but some will likely takemore than a full season. The athlete shouldbe able to improve his approach, arm ac-tion, and angle of projection. Fine-tuningcoordination of his throw will likely takelonger than a few months. The biomechan-ics of coordination in overarm throwingis quite complex (Atwater, 1979; Feltner &Dapena, 1986; Fleisig et al., 1999). Consis-tent practice over a long period of time willgradually build the sequential rotation thatoptimizes segmental interactions to create askilled overarm throw. To see if he listensand can easily change aspects of his throw-ing technique, ask him to step vigorouslywith his opposite foot and to throw the ball“lower.” It is possible that a youth softballcoach might select this player for his team

based on other factors. Biomechanical tech-nique in one skill may not be as importantas motivational factors or the philosophyemployed to help all players develop.

QUALITATIVE ANALYSIS OFDRIBBLING TECHNIQUE

Put yourself in the role of a youth soccercoach. After working on several dribblingdrills, you begin a more game-like drillwhere one player consistently performs asin the illustration in Figure 10.2. Use thetechnique points and biomechanical princi-ples in Table 10.2 to help guide your obser-vation and qualitative analysis of Figure10.2. What biomechanical principles arestrengths or weaknesses in this perform-ance? Diagnose the performance and de-cide what would be a good intervention tohelp this player improve.


Figure 10.1. A softball player throwing with maximum effort to home plate from the outfield.

This young player shows good balancein this performance since he does not fallwhen stumbling over the ball. He has poorcontrol of the ball, which likely contributedto him stepping on the ball. Despite a small

stumble, he uses his trail leg to recover theball. The player needs to adjust their appli-cation of the Force–Motion and Range-of-Motion principles to improve their drib-bling. Providing a cue that improves one ofthese principles will likely also improve theangle of release or the Optimal Projection ofthe ball. Let's diagnose this situation by pri-oritizing these three weaknesses to providethe best intervention to help this player.

Since this is a young player, you plan topraise his effort and a strong point beforefocusing attention on technique adjust-ments. Good intervention would be topraise his attention to the ball and recoveryfrom the stumble. It is too early in this play-er's development to focus intervention onkeeping his visual attention on the field.The best intervention may be a cue to “pushthe ball softly and keep it close to yourbody.” This cue combines the Force–MotionPrinciple and the Range-of-Motion princi-

CHAPTER 10:APPLYING BIOMECHANICS IN COACHING 229

Figure 10.2. A soccer player dribbling during a scrimmage.


FOR SOCCER DRIBBLING


Close to body Keep the ball close to you

Kinesthetic aware- Feel the ball on your footness/control

Awareness of Head up and watch the fieldsituation

Arch of foot Push the ball with the archof the foot

Angle of release Keep the ball close tothe ground

ples and focuses the player's attention oncorrect technique. More specific cues on ef-fort or range of motion can follow if futureobservations of his dribbling yield similarresults. Note that a young player is not cog-nitively ready for complex technique orstrategic instruction. The biomechanicalcomplexity of dribbling a soccer ball in thedynamic environment of a game must beappreciated by the coach, but not imposedon a young player too soon.

QUALITATIVE ANALYSISOF CONDITIONING

Junior high and high school coaches oftenare primarily responsible for developingconditioning programs for their athletes.Coaches must carefully monitor the exer-cise technique of their athletes to maximizeconditioning effects and reduce risk of in-jury. Suppose you are a junior high basket-ball coach who has his players performpassing drills with a small medicine ball.The technique points and biomechanicalprinciples you are interested in are listed inTable 10.3. One of your players shows thetechnique depicted in Figure 10.3. Whatbiomechanical principles are strengths or

weaknesses of their performance, and diag-nose the situation to set up intervention.

The weaknesses in this player's exercisetechnique are related to stride, arm action,and angle of release. The relevant biome-chanical principles for these techniquepoints are Inertia, Range of Motion, Coordi-nation, and Optimal Projection. While a va-riety of passing techniques are used in bas-ketball, the one-handed flip with littleweight shift that this player used is not themost desirable technique for high-speedpassing. It is hard to judge from the timinginformation in the figure caption, so we willassume that the athlete used good effortand speed in executing the pass. Motiva-tion clearly affects performance, so the


Figure 10.3. A junior high school basketball player throwing a medicine ball. Time between images is 0.12 s.


FOR BASKETBALL PASSING


Stride Step toward the target

Speed Pass quickly

Arm action Extend arms and thumbs down

Angle of release Horizontal trajectory

weaknesses in some athlete's exercise tech-nique are more related to effort than to neu-romuscular errors. The pass will likely havepoor speed to the target since only the rightarm contributes to the horizontal speed ofthe pass.

The coach must next diagnose theseweaknesses and decide on the best inter-vention to help this player improve. A goodcoach would likely focus the player's atten-tion on the correct arm action using botharms (Coordination). The primary reasonfor this diagnosis is safety, because the useof one arm and trunk twist to propel aheavy object may not be safe loads for poor-ly trained adolescents. There is also less re-search on upper body plyometrics thanthere has been on lower body plyometricexercises (Newton et al., 1997), so whatloads and movements are safe is not clear.Cues given for this technique point mayalso correct the angle of release, increase thespeed of the pass, and enhance control ofthe ball. You decide to work on the stridelater for safety reasons. Focusing interven-tion on the stride does not increase ballspeed or decrease the distance (and there-fore time) of the pass as much as good coor-dination with both arms would.

RECRUITMENT

As the golf coach for a university, you havemany parents sending you videotapes oftheir children for potential scholarship con-sideration. These “daddy” videos can be anuisance, but you qualitatively analyze theswings of the golfers on them for potentialplayers you might have missed. This infor-mation combined with the player's per-formance in high school and tournamentswill help you decide what athletes shouldbe offered scholarships. The techniquepoints and biomechanical principles of thefull golf swing you use to analyze swingsare presented in Table 10.4. For the player

illustrated in Figure 10.4, evaluate thestrengths and weaknesses of their down-swing. We will now focus on how the rele-vant biomechanical principles would helpyou diagnose the weaknesses of this playerand her potential as a golfer on your team.

This player has an excellent full swingand control of the club. It is difficult to tellfrom this perspective, but it is likely thisplayer keeps the club in a stable swingplane. The swing has an appropriate rangeof motion since the backswing terminateswith the club virtually horizontal. The play-er has a good weight shift, hip and trunktwist, and a firm forward leg late in theswing. The follow-through is fine. The twotechnique points that are difficult to judgefrom the video (and from the figure) arethe Coordination of the swing and the qual-ity of the impact and shot trajectory (Op-timal Projection). In short, this particularplayer has several strengths that suggestshe has an excellent golf swing. A good golfcoach would be aware of the massiveamount of research on the golf swing (Neal& Wilson, 1985; Sprigings & Neal, 2000;Williams & Sih, 2002). There are no obvious



FOR THE GOLF SWING


Weight shift Push with rear, then the front foot

Swing plane Swing forward and back onsame plane

Backswing Slow and club not past horizontal

Tempo/coor-dination Delayed release of the club

Impact/shottrajectory Divot in front of ball

Follow-through Long slow finish

warning signs, but a complete diagnosis ofthis golf swing is difficult to obtain from asingle video.

It is possible that the tape was edited toshow only the best swings for many shots.To fully diagnose this golf swing, you clear-ly need to know about impact and shot tra-jectory relative to the intended target. Thesound of the impact might suggest that theball is well hit; only observation of the ball'sflight relative to the intended target willprovide clues as to the player's potentialand the many subtleties that set high-levelgolfers apart. A nearly perfect golf swingthat strikes the ball with the club face an-gled away from the target or off-center canproduce very poor golf shots. A good golfcoach using video for qualitative analysiswould get views from several vantagepoints and gather information on the flight

of the ball. This distance and direction in-formation can be written or in recordedform on the audio track of the video. Onlyan integrated qualitative analysis of allthese factors over many strokes would al-low the coach to correctly judge this play-er's potential.

Note how a diagnosis of possiblestrengths and weaknesses is severely limit-ed when all we have is a single view of agolf swing. Remember that the biomechan-ical principles related to the golf swing alsomust be integrated with other kinesiologydisciplines. This player might have a flaw-less swing in practice that turns rough andunpredictable under psychological pres-sure. If this player's tournament results aregood, the coach might invest time talking totheir high school coach and plan a trip tosee them in action.


Figure 10.4. The long iron swing of a prospective golf recruit.

QUALITATIVE ANALYSISOF CATCHING

As a volunteer youth football coach you areworking with your receivers on catchingpasses. Many young players pick up badhabits from playing neighborhood pick-upfootball games or watching the pros get bywith talent rather than optimal technique.The technique points and cues you typical-ly use are listed in Table 10.5. Notice howthe critical features are more advanced andspecialized than the catching techniquepoints in chapter 9 (e.g., Table 9.4). Whichbiomechanical principles are strengths andweaknesses in the catching illustrated inFigure 10.5? How would you diagnosis thissituation and intervene?

The player in Figure 10.5 made a suc-cessful running catch, but the illustrationdoes not show enough of the movement sothat we can tell whether the player protect-

ed the ball by tucking it into their body. Theillustrated view makes it difficult to tell ifthe player extended his arms (Range ofMotion) to intercept the ball and providedtime (Force–Time) to absorb the kinetic en-ergy of the ball. Not only is reaching for theball important in being able to increase the


Figure 10.5. A football player making a catch in practice.

Table 10.5TECHNIQUE POINTS AND CUES FOR

CATCHING A FOOTBALL PASS

Technique Possible teaching/points intervention cues

Visual focus Watch the ball, look for the seams

Intercept Move and reach towards the ball

Hand position Thumbs in or thumbs out

Absorption Give with your hands and arms

Protection Give and tuck the ball away

time of force application in order to slowthe ball, but visual information on thearms/hands may also help intercept projec-tiles (van Donkelaar & Lee, 1994). Evalu-ation of this performance does not clearlyidentify any weaknesses in application ofbiomechanical principles.

A good intervention strategy would beto praise the player's effort and visual focuson the ball. Reinforcement of importanttechnique points and motivation are goodintervention goals while the coach waits tosee if subsequent trials demonstrate no ma-jor weaknesses. How might the coach in-crease the difficulty of the catching drill tosee if poor technique develops? Catching ina game situation involves many more envi-ronmental distractions. A knowledge of re-search concerning technique errors (Wil-liams & McCririe, 1988) and environmentalconstraints (Savelsbergh & Whiting, 1988)in catching is clearly relevant for coachingfootball. What would be a better perspec-tive for the coach to observe if the player isreally reaching away from the body to in-tercept the ball?

SUMMARY

Coaches employ the principles of biome-chanics to qualitatively analyze the move-ments of their athletes. This chapter ex-plored the use of biomechanical principlesin coaching softball, soccer, golf, football,and conditioning for basketball. Like phys-ical educators, coaches often use cue wordsor phrases to communicate intervention toplayers. Coaches must integrate biome-chanical principles with experience andother kinesiology subdisciplines (Knudson& Morrison, 2002). For example, coachesmost often need to take into account condi-tioning (exercise physiology) and motiva-tional issues (sports psychology) whendealing with athletes.


1. Are certain biomechanical principlesmore important to the advanced athlete?Which and why?

2. Athletics coaches often have the op-portunity of working closely with a smallernumber of performers over a greater lengthof time than other kinesiology profession-als. Does this concern for long-term per-formance increase or decrease the impor-tance of biomechanical principles?

3. Have coaching organizations ade-quately promoted continuing education insport sciences like biomechanics?

4. Which biomechanical principles arerelevant to athlete quickness? Can biome-chanics be used to coach an athlete to bequicker? If so, how does this improvementcompare to improvement from condition-ing?

5. Are biomechanical principles rele-vant to talent identification?

6. While the “daddy” videos discussedabove might give the coach a general indi-cation of the swings of players, what im-portant aspects of golf competition may notshow up on these videos? What importantbiomechanical issues might be difficult todetermine from inadequate camera views?

7. Prioritize the following factors basedon their importance in coaching beginning,intermediate, and advanced athletes for aspecific sport: biomechanics, maturation,physiology, psychology.

SUGGESTED READING

Brancazio, P. (1984). Sport science: Physical lawsand optimum performance. New York: Simon &Schuster.

Brody, H. (1987). Tennis science for tennis players.Philadelphia: University of PennsylvaniaPress.


Dyson, G. (1986). Mechanics of athletics (8th ed.).New York: Holmes & Meier.

Ecker, T. (1996). Basic track and field biomechanics(2nd ed.). Los Altos, CA: Tafnews Press.

Elliott, B. C., & Mester, J. (Eds.) (1998). Trainingin sport: Applying sport science. New York: JohnWiley & Sons.

Farrally, M. R., & Cochran, A. J. (Eds.) (1999).Science and golf, III. Champaign, IL: HumanKinetics.

Hay, J. G. (2000). The biomechanics of sport tech-niques, Englewood Cliffs, NJ: Prentice-Hall.


Knudson, D. (2001, July). Improving stroketechnique using biomechanical principles.Coaching and Sport Science Review, pp. 11–13.


Zatsiorsky, V. (Ed.) (2000). Biomechanics in sport:Performance enhancement and injury prevention.London: Blackwell Science.


WEB LINKS

ASEP—American Sport Education Program, which provides resources for developing coaching skills.

http://www.asep.com/

CAC—Coaching Association of Canada, which provides coaching development resources.

http://www.coach.ca/

CIS—ISBS Coaching Information Service, which provides articles applying biomechanics for coaches.

http://coachesinfo.com/

The Coaching and the Australian Sports Commission.http://www.ausport.gov.au/coach/index.asp

The Sport Journal—A coaching journal published the US Sports Academy.www.thesportjournal.org

Strength and conditioning is a profession inwhich a great deal of biomechanical re-search has been conducted recently. TheNational Strength and Conditioning Asso-ciation (NSCA) is the leading professionalstrength and conditioning association in theworld, and their journals—Strength andConditioning Journal and Journal of Strengthand Conditioning Research—have been re-ceptive to articles on the biomechanics ofexercise. Traditionally, strength and condi-tioning careers were limited to coaching thephysically gifted in intercollegiate athletics.However, more and more opportunities ex-ist for personal training with a wide varietyof clients in the private sector.

Strength coaches and personal trainersare responsible for prescribing exercisesthat benefit their clients. On the surface thismay seem a simple task, but in reality it isquite complicated. Exercises must be select-ed and exercise technique monitored. Exer-cises must be relevant, and the intensitymust be sufficient for a training responsebut not too great as to cause overtraining ora high risk of injury. Biomechanics helpsstrength and conditioning professionals toassess these risk:benefit ratios, determinethe most appropriate (sport-specific) exer-cises, and evaluate technique during train-ing. As in teaching and coaching, biome-chanical knowledge is important for thestrength and conditioning professional sothey can coordinate their efforts with sportsmedicine professionals.

QUALITATIVE ANALYSIS OFSQUAT TECHNIQUE

One of the most common and importantexercises in athletic conditioning is the par-allel squat. The squat is a functional exer-cise used for a wide variety of sports andother fitness objectives. The squat is usual-ly performed as a free-weight exercise,making movement technique critical tooverloading the target muscle groups andminimizing the risk of injury. Exacting tech-nique in free-weight exercises is necessarybecause small variations allow other mus-cles to contribute to the lift, diminishingoverload of the muscles or movements ofinterest. What are the main techniquepoints of the squat often emphasized bystrength and conditioning experts? Whichbiomechanical principles are most stronglyrelated to those technique points?

Table 11.1 presents some of the typicaltechnique points and cues for the parallel orfront squat. Evaluate the strengths andweaknesses in the biomechanical principlesrelated to the eccentric phase of the squat il-lustrated in Figure 11.1. Again, assume thelifter has performed a couple of repetitionsthis way and you are confident you canidentify stable strengths and weaknesses inapplication of the principles.

The lifter depicted in Figure 11.1 hasvery good squat technique, so there are vir-tually no weaknesses in application of bio-mechanical principles. His stance width

CHAPTER 11

Applying Biomechanics inStrength and Conditioning

237

is appropriate, and there is no indicationof difficulties in terms of control of thebody or the bar (Balance). The images sug-gest that the motion was smooth, with si-multaneous coordination. The timing infor-mation in the caption indicates the squatwas slow, maximizing the time the muscleswere stressed (Force–Time Principle). Thislifter also keeps his spine straight with nor-mal lordosis, so the spinal loads are prima-rily compression and are evenly appliedacross the disks. This more axial loading be-

tween the spinal segments is safest for thespine. Recent research has shown thatspinal flexion reduces the extensor musclecomponent of force resisting anterior shearin the spine (McGill, Hughson, & Parks,2000), making it more difficult for the mus-cles to stabilize the spine. Strength and con-ditioning coaches would also need to be fa-miliar with research on the effect of weightbelts in squats and other heavy lifting exer-cises.

Our lifter completed this exercise withthe appropriate full Range of Motion, whilenot hyperflexing the knee. There is goodtrunk lean, which distributes the load onboth the hip and knee extensors. Theamount of trunk lean (hip flexion) ina squat is the primary factor in determiningthe distribution of joint moments that con-tribute to the exercise (Escamilla, 2001;Hay, Andrews, Vaughan, & Ueya, 1983; Mc-Laughlin, Lardner, & Dillman, 1978). Themore upright posture in the front squat de-creases the hip and lumbar extensortorques, while increasing the knee extensortorques required in the exercise.


Figure 11.1. The eccentric phase of a person doing a squat. Time between images is 0.2 seconds.

Table 11.1TECHNIQUE POINTS AND CUES FOR THE SQUAT

Technique Possible inter-points vention cues

Stance Athletic position

Extended/neural spine Slight arch

Slow, smooth movement Slow and smooth

Keep thighs above Thighs parallel to horizontal the ground

A large part of the strength and condi-tioning professional's job is motivating andmonitoring athletes. The coach needs tolook for clues to the athlete's effort or achange in their ability to continue training.Some of these judgments involve applica-tion of biomechanical principles. How anathlete's Balance changes over a practice orseveral sets of an exercise could give astrength coach clues about fatigue. Sincethe figure and introduction give no clues tothis aspect of performance, the best inter-vention in this situation is to praise thegood technique of the athlete and possiblyprovide encouragement to motivate them.

Strength and conditioning profession-als also must integrate sport-specific train-ing with other practice and competition.The next example will focus on the sport-specificity of a plyometric training exercise.

QUALITATIVE ANALYSISOF DROP JUMPS

Plyometrics are common exercises for im-proving speed and muscular power move-ments in athletes. Plyometric exercises useweights, medicine balls, and falls to exag-gerate stretch-shortening-cycle muscle ac-tions. Considerable research has focused ondrop jumps as a lower-body plyometric ex-ercise for improving jumping ability(Bobbert, 1990). Recent research has shownthat drop jump exercise programs can in-crease bone density in children (Fuchs,Bauer, & Snow, 2001). Qualitative analysisof drop jumps is important in reducing therisk of injury in these exercises and moni-toring technique that has been observed tovary between subjects (Bobbert et al., 1986).Qualitative analysis is also important be-cause drop jumping and resistance trainingcan affect the technique used in variousjumping movements (Hunter & Marshall,2002). Table 11.2 presents important tech-nique points and cues for drop jumps.

What are the strengths and weaknesses inthe drop jump performance illustrated inFigure 11.2?

The athlete doing the drop jump illus-trated in Figure 11.2 has several good tech-nique points, and possibly one weakness.The strong points of her technique are goodlower-extremity positioning before touch-down, moderate countermovement, and anearly vertical takeoff. This indicates goodBalance during the exercise. It is difficult toevaluate the speed or quickness of the per-formance from the drawings with no tempo-ral information in the caption. This athletedid have a short eccentric phase with aquick reversal into the concentric phase.Occasionally subjects will have a longer ec-centric phase that minimizes the stretch-shortening-cycle effect of drop jumps(Bobbert et al., 1986). The Force–Time Prin-ciple applied to plyometric exercises ex-plains why large forces and high rates offorce development are created over the shorttime of force application in plyometrics.

The obvious weakness is not using herarms in the exercise. Most athletes shouldstrive to utilize an arm swing with coordi-nation similar to jumping or the specificevent for which they are training. If thearms are accelerated downward as the ath-lete lands, this will decrease eccentric load-ing of the lower extremities. For jump-spe-cific training, cue the athletes to swing theirarms downward in the drop so the arms are

CHAPTER 11:APPLYING BIOMECHANICS IN STRENGTH AND CONDITIONING 239

Table 11.2TECHNIQUE POINTS AND CUES FOR DROP JUMPS

Technique Possible inter-points vention cues

Landing position Toe-heel landing

Rapid rebound Quick bounce

Minimize counter-movement Range of motion

Arm integration Arms down and up

swinging behind them during the loadingphase, increasing the intensity of eccentricloading of the lower extremities. The vigor-ous forward and upward swing of the armsfrom this position increases the verticalground-reaction force through segmentalinteraction (Feltner et al., 1999). The cue“arms down and up” could be used to re-mind an athlete of the technique points sheshould be focusing on in the following rep-etitions. A key conditioning principle is thatthe exercises selected for training shouldclosely match the training objectives ormovement that is to be improved. Thismatching of the exercise conditions to per-formance conditions is the conditioningprinciple of specificity. Exercise specificitywill also be examined in the next example.

EXERCISE SPECIFICITY

In the past, exercise specificity was oftenbased on a functional anatomical analysis

(chapter 3) of the movement of interest.Exercises were selected that supposedlytrained the muscles hypothesized to con-tribute to the movement. We saw in chap-ters 3 and 4 that biomechanics research hasdemonstrated that this approach to identi-fying muscle actions often results in incor-rect assumptions. This makes biomechani-cal research on exercise critical to thestrength and conditioning field. Thestrength and conditioning professional canalso subjectively compare the principles ofbiomechanics in the exercise and the move-ment of interest to examine the potentialspecificity of training.

Suppose you are a strength and condi-tioning coach working with the track andfield coach at your university to develop atraining program for javelin throwers. Yousearch SportDiscus for biomechanical re-search on the javelin throw and the condi-tioning literature related to overarm throw-ing patterns. What biomechanical princi-


Figure 11.2. An athlete doing a drop jump exercise.

ples are most relevant to helping you qual-itatively analyze the javelin throw? Thetechnique of a javelin throwing drill is illus-trated in Figure 11.3. These principleswould then be useful for examining poten-tial exercises that would provide specificityfor javelin throwers. Let's see how the prin-ciples of biomechanics can help you decidewhich exercise to emphasize more in theconditioning program: the bench press orpullovers. We will be limiting our discus-sion to technique specificity.

The principles most relevant to thejavelin throw are Optimal Projection, In-ertia, Range of Motion, Force–Motion,Force–Time, Segmental Interaction, and Co-ordination Continuum. Athletes throw thejavelin by generating linear momentum(using Inertia) with an approach that istransferred up the body in a sequential

overarm throwing pattern. These principlescan be used in the qualitative analysis of thethrowing performances of the athletes bycoaches, while the strength and condition-ing professional is interested in training toimprove performance and prevent injury.The fast approach (Range of Motion) andfoul line rules make the event very hard onthe support limb, which must stop andtransfer the forward momentum to thetrunk (Morriss, Bartlett, & Navarro, 2001).This Segmental Interaction using energyfrom the whole body focuses large forces(Force–Motion) in the upper extremity. Thesize and weight of the javelin also con-tribute to the high stresses on the shoulderand elbow joints. While some elastic cordexercises could be designed to train the ath-lete to push in the direction of the throw(Optimal Projection), this section will focus


Figure 11.3. Typical technique for the javelin throw drill.

on the specificity of two exercises: thebench press and pullovers. Space does notpermit a discussion of other specificity is-sues, like eccentric training for the plantfoot or training for trunk stability.

For specificity of training, the exercisesprescribed should match these principlesand focus on muscles that contribute(Force–Motion) to the joint motions (Rangeof Motion), and those which might helpstabilize the body to prevent injury. Whilemuch of the energy to throw a javelin istransferred up the trunk and upper arm, amajor contributor to shoulder horizontaladduction in overarm patterns is likely tobe the pectoralis major of the throwingarm. The question then becomes: which ex-ercises most closely match Range of Motionand Coordination in the javelin throw?Matching the speed of movement and de-termining appropriate resistances are alsospecificity issues that biomechanics wouldhelp inform.

Biomechanical research on the javelincan then help select the exercise and cus-tomize it to match pectoralis major functionduring the event. EMG and kinetic studiescan be used to document the temporal loca-tion and size of muscular demands.Kinematic research help identify the shoul-der range and speed of shoulder motion inthe javelin throw. A good strength and con-ditioning coach would review this researchon the javelin throw with the track coach(Bartlett & Best, 1988; Bartlett et al., 1996).

If the bench press and pullover exercisetechniques remain in their traditional(supine) body position and joint ranges ofmotion, the bench press may provide themost activity-specific training for thejavelin throw. The bench press typically hasthe shoulder in 90º of abduction, matchingits position in the javelin throw. The benchpress could be performed (assuming ade-quate spotting and safety equipment) witha fast speed to mimic the SSC of the javelinthrow. This would also mimic the muscle

actions and rate of force development(Force–Time). Even greater sport specificitymay be achieved by using plyometricbench presses with medicine balls. The ply-ometric power system (Wilson et al., 1993) isa specialized piece of equipment thatwould also allow for dynamic bench pressthrows.

Pullovers often have greater shoulderabduction that is unlike the range of motionin the event. Pullovers also have a range ofmotion that requires greater scapular up-ward rotation and shoulder extension,which tends to compress the supraspinatusbelow the acromion process of the scapula.Athletes in repetitive overarm sports oftensuffer from this impingement syndrome, sopullovers may be a less safe training exer-cise than the bench press.

The other training goal that is also re-lated to movement specificity is preventionof injury. What muscles appear to playmore isometric roles in stabilizing the low-er extremity, the shoulder, and elbow?What research aside from javelin studiescould be used to prescribe exercises thatstabilize vulnerable joints? What musclesare likely to have eccentric actions to “puton the brakes” after release? What exercisesor movements are best for training to re-duce the risk of injury? Why might trainingthe latissimus dorsi potentially contributeto the performance and injury preventiongoals of training for the javelin throw?

INJURY RISK

Imagine you are a strength coach at a juniorcollege. You closely watch many of theyoung men in your preseason conditioningprogram because they have had little seri-ous weight training in their high schools,and others may be pushing themselves toohard to meet team strength standards toqualify for competition. Suppose you see aplayer performing the bench press using


the technique illustrated in Figure 11.4.What are the strengths and weaknesses ofperformance? How would you diagnosisthis performance and what interventionwould you use?

The biomechanical principles relevantto the bench press are Balance, CoordinationContinuum, Force–Time, and Range ofMotion. When training for strength, resist-ance is high, the athlete must have goodcontrol of the weight (Balance), and coordi-nation during the lift will be simultaneous.The force–time profile of strength trainingattempts to maintain large forces applied tothe bar through as much of the range of mo-tion as possible. The SSC nature of themovement should be minimized. Thiskeeps the movement slow and force outputnear the weight of the bar. High initialforces applied to the ball results in lowerforces applied to the bar later in the range ofmotion (Elliott et al., 1989). The principle ofRange of Motion in strength training tends

toward one of two extremes. First, minimizethe range of motion of joints that do not con-tribute to the movement and of those thatallow other muscles to contribute to themovement. Second, the range of motion forjoint movements or muscles that are target-ed by the exercise should be maximized.

The two principles most strongly relat-ed to exercise safety in the bench press areBalance and Range of Motion. Athletesmust control the weight of the bar at alltimes, and a lack of control will affect therange of motion used in the exercise. Theathlete in Figure 11.3 shows weaknesses inboth balance and range of motion. Since theathlete is struggling to “make weight,” thedifference in strength between the sides ofthe body manifests as uneven motion of thebar and poor balance. The athlete also hy-perextended his lumbar spine in strainingto lift the weight.

Several aspects of this performancemay have a strength coach thinking about a


Figure 11.4. The concentric phase of a bench press from an athlete struggling to make a weight goal.

risk of immediate and future injury: lateralstrength imbalance, poor control of bar mo-tion, and hyperextension of the lumbarspine. Since the athlete is “maxing-out,”some of these weaknesses can be expected,but safety is the greatest concern. Spotterscan assist lifters with poor bar control, orwho can complete the lift with only oneside of their body. Hyperextension of thespine, however, is an immediate risk to theathlete's low-back health. Hyperextensionof the lumbar spine under loading is dan-gerous because of uneven pressures on theintervertebral disks and greater load bear-ing on the facet joints. The best interventionhere is to terminate the lift with assistancefrom a spotter and return to lifting onlywhen the athlete maintains a neutral andsupported spinal posture on the bench.Here the immediate risk of injury is moreimportant than balance, skill in the exercise,or passing a screening test.

EQUIPMENT

Equipment can have quite a marked influ-ence on the training effect of an exercise.Exercise machines, “preacher” benches,and “Smith” machines are all exampleshow equipment modifies the training stim-ulus of weight-training exercises. Strengthand conditioning catalogues are full of spe-cialized equipment and training aids; un-fortunately, most of these devices have notbeen biomechanically studied to determinetheir safety and effectiveness. Garhammer(1989) provides a good summary of the ma-jor kinds of resistance exercise machines inhis review of the biomechanics of weighttraining.

Let's revisit the squat exercise usingone of these training devices. This device isa platform that stabilizes the feet and lowerlegs. A person performing the eccentricphase of a front squat with this device is de-picted in Figure 11.5. Compare the squat

technique of this subject with the techniquein the traditional squat (Figure 11.1). Whatbiomechanical principles are affected mostby the use of this device?

Inspection of Figure 11.5 shows thatthere are several Range-of-Motion differ-ences between the two squat exercises.Squatting with the device results in lessknee flexion and ankle dorsiflexion. Notehow the lower leg remains nearly vertical,and how the center of mass of theathlete/bar is shifted farther backward inthis squat. There does not appear to be anyobvious differences in trunk lean betweenthe two devices with these performers.What do you think are the training implica-tions for these small differences? Whichbody position at the end of the eccentricphase seems to be more specific to football,skiing, or volleyball: this or the front squat?

Using the device makes balancing easi-er, although it puts the line of gravity of thebody/bar well behind the feet. The largerbase of support and Inertia (body andstand) stabilizes the exerciser in the squat. Itis not possible to compare the kinetics ofthe two exercises from qualitative analysisof the movements, but it is likely there aredifferences in the loading of the legs andback (Segmental Interaction). What jointsdo you think are most affected (think aboutthe moment arm for various body segmentand shearing forces in the knee)? Whatkinds of biomechanical studies would youlike to see if you were advising the compa-ny on improving the device?

SUMMARY

Strength and conditioning professionalsuse the principles of biomechanics to quali-tatively analyze the technique of exercises,evaluate the appropriateness of exercises,and reduce the risk of injury from danger-ous exercise technique. Qualitative analysisof several free weight exercises was pre-


sented, and we examined the biomechani-cal principles in the qualitative analysis ofexercises machines. Strength and condition-ing professionals also must integrate physi-ological and psychological knowledge withbiomechanical principles to maximizeclient improvement. Since strength trainingutilizes loads closer to the ultimate mechan-ical strength of tissues, professionals needto keep safety and exacting exercise tech-nique in mind.


1. The squat and various leg-press exer-cise stations are often used interchangeably.What biomechanical principles are moreimportant in the squat than in the leg press,and how would you educate lifters whothink that the exercises do the same thing?

2. An athlete back in the weight roomafter initial rehabilitation from an injury isapprehensive about resuming their condi-tioning program. What biomechanical prin-ciples can be modified in adapting exercis-es for this athlete? Suggest specific exercis-es and modifications.

3. What aspect of exercise specificity(muscles activated or joint motions) do youthink is most important in training forsports? Why? Does analysis of the biome-chanical principles of exercises and sportmovement help you with this judgment?

4. If an athlete uses unsafe technique inthe weight room, should the coach's re-sponse be swift and negative for safety'ssake, or should they take a positive (teach-able moment) approach in teaching safertechnique? Are there athlete (age, ability,etc.) or exercise factors that affect the bestapproach?


Figure 11.5. The eccentric phase of a person doing a squat using a foot and leg stabilizing stand.

5. Athletes train vigorously, pushingtheir limits, treading a fine line betweentraining safely and overtraining. Are therebiomechanical indicators that could help thestrength and conditioning professional rec-ognize when training intensity has movedbeyond overload to dangerous? Why?

6. For a specific sport movement, deter-mine if conditioning exercises should em-phasize Force-Time or Force-Motion to bemore activity-specific.

7. What biomechanical principles arerelevant to training overarm-throwing ath-letes with upper-body plyometric exercis-es? Be sure to integrate the muscle mechan-ics knowledge summarized in chapter 4 inyour answer.

8. Strength training resistances are oftenexpressed as percentages of maximumstrength (1RM). If loads on the muscu-loskeletal system were also expressed as per-centages of mechanical strength, what train-ing loads do you think would be safe (ac-ceptable risk) or unsafe (unacceptable risk)?

9. Which is most important in selectingweight training resistances: training studiesor biomechanical tissue tolerances? Why?

SUGGESTED READING

Atha, J. (1981). Strengthening muscle. Exerciseand Sport Sciences Reviews, 9, 1–73.

Baechle, T. R., & Earle, R. W. (Eds.) (2000).Essentials of strength training and conditioning(2nd ed.). Champaign, IL: Human Kinetics.

Bartlett, R. M., & Best, R. J. (1988). The biome-chanics of javelin throwing: A review. Journal ofSports Sciences, 6, 1–38.

Garhammer, J. (1989). Weight lifting and train-ing. In C. Vaughan (Ed.), Biomechanics of sport(pp. 169–211). Boca Raton, FL: CRC Press.


Knuttgen, H. G., & Kraemer, W. J. (1987). Ter-minology and measurement in exercise per-formance. Journal of Applied Sport ScienceResearch, 1, 1–10.

Komi, P. V. (Ed.) (1992). Strength and power insport. London: Blackwell Science.

Stone, M., Plisk, S., & Collins, D. (2002).Training principles: Evaluation of modes andmethods of resistance training—A coachingperspective. Sports Biomechanics, 1, 79–103.

Wilson, G. J. (1994). Strength and power insport. In J. Bloomfield, T. R. Ackland, & B. C.Elliott (Eds.) Applied anatomy and biomechanicsin sport (pp. 110–208). Melbourne: BlackwellScientific Publications.

Zatsiorsky, V. N., & Kraemer, W. J. (2006).Science and practice of strength training (2nd ed.).Champaign, IL: Human Kinetics.


WEB LINKS

NSCA—National Strength and Conditioning Association.http://www.nsca-lift.org/menu.htm

PCPFS Research Digest—research reviews published by the President's Council onPhysical Fitness and Sports.

http://www.fitness.gov/pcpfs_research_digs.htm

Biomechanics also helps professionals inclinical settings to determine the extent ofinjury and to monitor progress during reha-bilitation. Many sports medicine programshave specific evaluation and diagnostic sys-tems for identification of musculoskeletalproblems. The physical therapist and ath-letic trainer analyzing walking gait or anorthopaedic surgeon evaluating functionafter surgery all use biomechanics to helpinform decisions about human movement.

These clinical applications of biome-chanics in qualitative analysis tend to focusmore on localized anatomical issues thanthe examples in the previous three chap-ters. This chapter cannot replace formaltraining in gait analysis (Perry, 1992), injuryidentification (Shultz, Houglum, and Per-rin, 2000), or medical diagnosis (Higgs &Jones, 2000). It will, however, provide anintroduction to the application of biome-chanical principles in several sports medi-cine professions. Biomechanical principlesmust be integrated with the clinical trainingand experience of sports medicine profes-sionals.

INJURY MECHANISMS

Most sports medicine professionals mustdeduce the cause of injuries from the histo-ry presented by patients or clients. Occa-sionally athletic trainers may be at a prac-tice or competition where they witness aninjury. Knowledge of the biomechanicalcauses of certain injuries can assist an ath-

letic trainer in these situations, in that diag-nosis of the particular tissues injured isfacilitated. Imagine you are an athletictrainer walking behind the basket during abasketball game. You look onto the courtand see one of your athletes getting injuredas she makes a rebound (see Figure 12.1).What kind of injury do you think occurred?What about the movement gave you theclues that certain tissues would be at risk ofoverload?

The athlete depicted in Figure 12.1 like-ly sprained several knee ligaments. Land-ing from a jump is a high-load event for thelower extremity, where muscle activitymust be built up prior to landing. It is like-ly the awkward landing position, insuffi-cient pre-impact muscle activity, and twist-ing (internal tibial rotation) contributed tothe injury. It is also likely that the anterior(ACL) and posterior (PCL) cruciate liga-ments were sprained. The valgus deforma-tion of the lower leg would also suggestpotential insult to the tibial (medial) collat-eral ligament. Female athletes are morelikely to experience a non-contact ACLinjury than males (Malone, Hardaker, Gar-rett, Feagin, & Bassett, 1993), and the major-ity of ACL injuries are non-contact injuries(Griffin et al., 2000). There are good recentreviews of knee ligament injury mecha-nisms (Bojsen-Moller & Magnusson, 2000;Whiting & Zernicke, 1998).

You rush to the athlete with theseinjuries in mind. Unfortunately, any ofthese sprains are quite painful. Care mustbe taken to comfort the athlete, treat pain

CHAPTER 12

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247

and inflammation, and prevent motion thatwould stress the injured ligaments. Jointtests and diagnostic imaging will eventual-ly be used to diagnosis the exact injury.What biomechanical issue or principle doyou think was most influential in thisinjury?

EXERCISE SPECIFICITY

The principle of specificity also applies totherapeutic exercise in rehabilitation set-tings. The exercises prescribed must matchthe biomechanical needs of the healingpatient. Exercises must effectively train themuscles that have been weakened by injuryand inactivity. Biomechanical research ontherapeutic exercise is even more criticalsince therapists need to know when inter-

nal loadings may exceed the mechanicalstrengths of normal and healing tissues.

Imagine that you are a physical thera-pist treating a runner with patellofemoralpain syndrome. Patellofemoral pain syn-drome (PFPS) is the current terminologyfor what was commonly called chondroma-lacia patella (Thomee, Agustsson, & Karls-son, 1999). PFPS is likely inflammation ofthe patellar cartilage since other kneepathologies have been ruled out. It isbelieved that PFPS may result from mis-alignment of the knee, weakness in themedial components of the quadriceps, andoveruse. If the vastus medialis and espe-cially the vastus medialis obliquus (VMO)fibers are weak, it is hypothesized that thepatella may track more laterally on thefemur and irritate either the patellar orfemoral cartilage. The exercises commonly


Figure 12.1. A basketball player injuring her knee during a rebound.

prescribed to focus activation on the VMOare knee extensions within 30º of near com-plete extension, similar short-arc leg press-es/squats, and isometric quadriceps settingat complete extension, and these exerciseswith combined hip adduction effort. Whileincreased VMO activation for these exercis-es is not conclusive (see Earl, Schmitz, andArnold, 2001), assume you are using thistherapeutic strategy when evaluating theexercise technique in Figure 12.2. What bio-mechanical principles are strengths andweaknesses in this exercise.

Most biomechanical principles are wellperformed. Balance is not much of an issuein a leg press machine because mechanicalrestraints and the stronger limb can com-pensate for weakness in the affected limb.There is simultaneous Coordination, andthere appears to be slow, smooth move-ment (Force–Time).

The principle that is the weakest forthis subject is the large knee flexion Rangeof Motion. This subject has a knee angle ofabout 65º at the end of the eccentric phase

of the exercise. This very flexed positionputs the quadriceps at a severe mechanicaldisadvantage, which results in very largemuscle forces and the consequent largestresses on the patellofemoral and tibio-femoral joints. This exercise technique canirritate the PFPS and does not fit the thera-peutic strategy, so the therapist shouldquickly instruct this person to decrease therange of motion. Providing a cue to onlyslightly lower the weight or keeping theknees extended to at least 120º would beappropriate for a patient with PFPS.

A better question would be: should thisperson even be on this leg press machine?Would it be better if they executed a differ-ent exercise? A leg press machine requiresless motor control to balance the resistancethan a free-weight squat exercise, so a legpress may be more appropriate than asquat. Maybe a more appropriate exercisewould be a leg press machine or a cyclethat allows the subject to keep the hipextended (reducing hip extensor contribu-tions and increasing quadriceps demand)

CHAPTER 12:APPLYING BIOMECHANICS IN SPORTS MEDICINE & REHABILITATION 249

Figure 12.2. The leg press technique of a person trying to remediate patellofemoral pain.

and limit the amount of knee flexionallowed. The differences in muscle involve-ment are likely similar to upright versusrecumbent cycling (Gregor, Perell,Rushatakankovit, Miyamoto, Muffoletto, &Gregor, 2002). These subtle changes in bodyposition and direction of force application(Force– Motion) are very important indetermining the loading of muscles andjoints of the body. Good therapists areknowledgeable about the biomechanicaldifferences in various exercises, and pre-scribe specific rehabilitation exercises in aprogressive sequence to improve function.

EQUIPMENT

Sports medicine professionals often pre-scribe prosthetics or orthotics to treat avariety of musculoskeletal problems. Pro-sthetics are artificial limbs or body parts.Orthotics are devices or braces that sup-

port, cushion, or guide the motion of abody. Shoe inserts and ankle, knee, or wristbraces are examples of orthotics. Orthoticscan be bought “off the shelf” or custom-build for a particular patient.

Shoe inserts are a common orthotictreatment for excessive pronation of the sub-talar joint. One origin of excessive pronationis believed to be a low arch or flat foot. Aperson with a subtalar joint axis below 45º inthe sagittal plane will tend to have morepronation from greater eversion and adduc-tion of the rear foot. It has been hypothe-sized that the medial support of an orthoticwill decrease this excessive pronation.

Figure 12.3 illustrates a rear frontalplane view of the maximum pronationposition in running for an athlete diag-nosed with excessive rear-foot pronation.The two images show the point of maxi-mum pronation when wearing a runningshoe (a) and when wearing the same shoewith a custom semirigid orthotic (b). Imag-


Figure 12.3. Rear frontal plane view of the positions of maximum pronation in running in shoes (a) and shoes witha semi-rigid orthotic (b) on a treadmill at 5.5 m/s.

ine that you are the athletic trainer workingwith this runner. The runner reports that itis more comfortable to run with the orthot-ic, an observation that is consistent withdecreased pain symptoms when usingorthotics (Kilmartin & Wallace, 1994). Youcombine this opinion with your visual andvideotaped observations of the actions ofher feet in running.

Inspection of Figure 12.3 suggests thatthere is similar or slightly less pronationwhen the runner is wearing an orthotic.Biomechanical research on orthotics andrear-foot motion have not as of yet deter-mined what amount of pronation or speedof pronation increases the risk of lower-extremity injuries. The research on thisintervention is also mixed, with little evi-dence of the immediate biomechanicaleffects of orthotics on rear-foot motionand the hypothesized coupling with tibialinternal rotation (Heiderscheit, Hamill, &Tiberio, 2001). In addition, it is unclear ifthe small decrease in pronation (if therewas one) in this case is therapeutic. Thecomfort and satisfaction perceived by thisrunner would also provide some supportfor continued use of this orthotic.

READINESS

Orthopaedic surgeons and athletic trainersmust monitor rehabilitation progress beforeclearing athletes to return to their practiceroutine or competition. Recovery can bedocumented by various strength, range-of-motion, and functional tests. Subjectivemeasures of recovery include symptomsreported by the athlete and qualitativeanalyses of movement by sports medicineprofessionals. Athletes will often be askedto perform various movements of increas-ing demands, while the professional quali-tatively evaluates the athlete's control ofthe injured limb. A couple of common func-tional tests for athletes with knee injuries

are multiple hops for distance or time(Fitzgerald et al., 2001).

Imagine you are an athletic trainerworking with an athlete rehabilitating anACL injury in her right knee. You ask theathlete to perform a triple hop for maxi-mum distance. The technique of the firsthop is illustrated in Figure 12.4. As youmeasure the distance hopped, you go overthe strengths and weaknesses in terms ofthe biomechanical principles of the hop inyour mind. Later you will combine thisassessment with the quantitative data. Thedistance hopped on the injured limbshould not be below 80% of the unaffectedlimb (Fitzgerald et al., 2001). What biome-chanical principles are strengths and weak-nesses, and what does a diagnosis of thishopping performance tell you about herreadiness to return to practice? Biomechan-ical technique is just one aspect of manyareas that must be evaluated in makingdecisions on returning athletes to play(Herring et al., 2002).

Most all biomechanical principles arewell performed by this athlete. This athleteis showing good hopping technique withnearly Optimal Projection for a long seriesof hops. She shows good Coordination ofarm swing, integrated with good simulta-neous flexion and extension of the lowerextremity. She appears to have good Bal-ance, and her application of the Range-of-Motion and Force–Time principles in theright leg shows good control of eccentricand concentric muscle actions. There are noapparent signs of apprehension or lack ofcontrol of the right knee. If these qualitativeobservations are consistent with the dis-tance measured for the three hops, it is like-ly the athletic trainer would clear this ath-lete to return to practice. The therapistmight ask the coach to closely monitor theathlete's initial practices for signs of appre-hension, weakness, or poor technique asshe begins more intense and sport-specificmovements.


INJURY PREVENTION

This chapter opened with the scenario ofone of the most common injuries in sports,a non-contact sprain of the ACL. The largenumbers of injuries to young female ath-letes has resulted in considerable researchon how these injuries occur in landing,jumping, and cutting. Many biomechanicalfactors have been hypothesized to be relat-ed to increased risk of ACL injuries in sport:peak vertical ground reaction force, kneeflexion angle at landing, hamstringstrength, and balance. A large prospectivestudy of the biomechanics of landing infemale adolescent athletes who then partic-ipated in high-risk sports has recently iden-tified several variables that are associatedwith risk of ACL injury (Hewitt et al., 2005).The variables that were associated withgirls that became injured were greater knee

abduction angle (lower leg valgus), andgreater ground reaction force and kneeabduction moment. It is possible that asgirls enter adolescence the increased risk ofACL injuries comes from dynamic valgusloading at the knee that results from a com-bination of factors. With adolescence infemales the limbs get longer and hipswiden, if strength at the hip and knee, coor-dination, and balance do not keep up withthese maturational changes it is likely thatrisk of ACL injury could be increased.

While sports medicine professionalshave qualitatively evaluated the strengthand balance of patients in single leg stanceand squats for many years, recent papershave proposed that simple two-dimension-al measurements of frontal plane motion ofthe lower extremity in single leg squatsmight be a useful clinical tool for identify-ing athletes that may be at a higher risk for


Figure 12.4. An athlete doing a triple hop test.

ACL injury (McLean et al., 2005; Wilson, Ire-land, & Davis, 2006). While this test is notas dynamic as landing, it is likely a saferscreening procedure that also can be quali-tatively evaluated. If screening suggests anathlete may be at risk (poor control of kneein the frontal plane), research has shownthat preventative conditioning programscan decrease the risk of ACL injuries (seereview by Hewitt, Ford, & Meyer, 2006).

Figure 12.5 illustrates the position ofthe lower extremity at the bottom of a sin-gle leg squat for two young athletes. If youwere an athletic trainer or physical thera-pist screening these athletes before a com-petitive season, which athlete would you bemost concerned about for a higher risk ofACL injury? Could you draw on the figurelines along the long axes of the leg andmeasure an angle representing the valgusorientation of the lower leg? What condi-tioning would you suggest for this athlete?

Would there be any special technique train-ing you would suggest to the coach forjumping, landing, and cutting during prac-tice?

SUMMARY

Sports medicine professionals use biome-chanical principles to understand injurymechanisms, select appropriate injury pre-vention and rehabilitation protocols, andmonitor recovery. In the specificity exam-ple, we saw that qualitative analysis ofexercise technique can help sports medicineprofessionals ensure that the client's tech-nique achieves the desired training effect.Qualitative analysis in sports medicineoften focuses on an anatomical structurelevel more often than other kinesiologyprofessions. Qualitative analysis of thera-peutic exercise also requires an interdisci-


Figure 12.5. Lower leg position of the bottom of a single leg squat for two young athletes.

plinary approach (Knudson & Morrison,2002), especially integrating clinical train-ing and experience with biomechanics.Other issues sports medicine professionalsmust take into account beyond biomechan-ical principles are pain, fear, motivation,and competitive psychology.


1. What biomechanical principle doyou think is more important in rehabilitat-ing from an ankle sprain, Balance or Rangeof Motion?

2. Patients recovering from kneeinjuries are often given braces to preventunwanted movement and to graduallyincrease allowable motion. What move-ment characteristics would indicate that apatient is ready to exercise or functionwithout a brace?

3. Sports medicine professionals look-ing for the causes of overuse injuries oftenevaluate joints distant from the affectedarea (Kibler & Livingston, 2001) because ofSegmental Interaction through the kinemat-ic chain. What biomechanical principles canprovide cues to potential overuse injuries inother parts of the body?

4. A major injury in athletic and seden-tary populations is low-back pain. Whatabdominal and back muscles are most spe-cific to injury prevention for an office work-er and a tennis player?

5. Athletes using repetitive overarmthrowing often suffer from impingementsyndrome. What biomechanical principlescan be applied to the function of the shoul-der girdle and shoulder in analyzing theexercise and throwing performance of aninjured athlete?

6. You are an trainer working with anathlete recovering from a third-degreeankle sprain. You and the athlete are decid-ing whether to use athletic tape or an anklebrace. What does a qualitative biomechani-

cal analysis suggest is the better of thesetwo options? What biomechanical studieswould you suggest to investigate the clini-cal efficacy of these options?

7. What biomechanical principlesshould be focused on when a therapist ortrainer is working with elderly clients toprevent falls?

8. An adapted physical educator hasreferred a young person who might haveDevelopmental Coordination Disorder(DCD) to a physician. Before various imag-ing and neurological tests are performed,what biomechanical principles should bethe focus of observation, and what simplemovement tests would be appropriate inthe initial physical/orthopaedic exam?

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ACSM—The American College of Sports Medicine is a leader in the clinical and scien-tific aspects of sports medicine and exercise. ACSM provides the leading professionalcertifications in sports medicine.

http://acsm.org/

APTA—American Physical Therapy Associationhttp://www.apta.org/

CGA—International Clinical Gait Analysis website, which posts interesting case stud-ies, discussions, and learning activities.

http://guardian.curtin.edu.au/cga/

FIMS—International Federation of Sports Medicinehttp://www.fims.org/

Gillette Children's Hospital Videos and CDROMshttp://www.gillettechildrens.org/default.cfm?PID=1.3.9.1

GCMAS—North American organization called the Gait and Clinical MovementAnalysis Society

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absolute angle: an angle measured to anon-moving (inertial) frame of refer-ence

acceleration: the rate of change of velocity(vector)

accelerometer: a device that measures ac-celeration

actin: the thin filaments in a myofibril thatinteract with myosin to create muscletension

accommodation: a decrease in biologicalresponse to an unchanging stimulus

action potential: the electrical potentialchange during depolarization of nervesand activated muscle fibers

active tension: the tension created by thecontractile component (actin–myosininteraction) of activated muscle

affine scaling: image scaling techniqueused to measure in a plane not perpen-dicular to the optical axis of the camerain 2D cinematography/videography

agonist: an anatomical term referring to theconcentric action of a muscle or musclegroup for presumed to create a specificmovement

aliasing: distortion of a signal by an inade-quate sampling rate

analog-to-digital (A/D) conversion: theprocess of taking a continuous signaland sampling it over time (see “sam-pling rate”) to create a digital (discretenumbers) representation

anatomy: the study of the structure of thebody

angle–angle diagram: a kinematic graph ofone variable plotted against another(not time) that is useful in the study ofcoordination of movements

angular acceleration: the rate of change ofangular velocity (vector)

angular displacement: the change in angu-lar position (vector)

angular momentum: the quantity of angu-lar motion, calculated as the product ofthe moment of inertia times the angularvelocity (vector)

angular velocity: the rate of change of an-gular displacement (vector)

angular impulse: the angular effect of atorque acting over time: the productof the torque and the time it acts (vec-tor)

anisotropic: having different mechanicalproperties for loading in different di-rections

antagonist: an anatomical term referring toa muscle or muscle group that is pre-sumed to oppose (eccentric action) aspecific movement

anthropometry: the study of the physicalproperties of the human body

aponeurosis: connective tissue within mus-cle and tendon in the form of a flatsheet

Glossary

283

APPENDIX A

Archimedes' principle: the magnitude ofthe buoyant force is equal to the weightof the fluid displaced

arthrokinematics: the major, freely move-able rotations allowed at joints

balance: a person's ability to control theirbody position relative to some base ofsupport

balance principle: a biomechanical appli-cation principle which states that thestability and mobility of a body posi-tion are inversely related

ballistic: explosive, momentum-assistedmovement

bandpass filter: a filter designed to pass arange (bandpass) of frequencies, re-moving frequencies above or belowthis desirable range

bending: a combination of forces on along body that tends to bend or curvethe body creating tensile loads onone side and compression loads on theother side

Bernoulli's principle: the pressure a fluidcan exert decreases as the velocity ofthe fluid increases

Bernstein's problem: a theory of motorcontrol in which skill learning involvesthe reduction of redundant degrees offreedombilateral deficit: simultaneousactivation of two limbs that causes lessforce generation than the sum of thetwo individually activated limbs

biomechanics: study of the motion andcauses of motion of living things

boundary layer: the layers of a fluid inclose proximity to an object suspendedin the fluid

buoyancy: the supporting or floating forceof a fluid

center of buoyancy: the point at which thebuoyant force acts

center of mass/gravity: the point that repre-sents the total weight/mass distribu-tion of a body; the mass centroid is thepoint where the mass of an object is bal-anced in all directions

center of percussion: a point on a strikingobject where impact with another ob-ject results in no reaction force at anassociated point on the grip (see“sweet spot”)

center of pressure: the location of the verti-cal ground reaction force vector; thecenter of pressure measured by a forceplatform represents the net forces insupport and the COP may reside in re-gions of low local pressure

coactivation: simultaneous activation of ag-onist and antagonist muscles (co-con-traction)

coefficient of drag: a measure of the rela-tive fluid resistance between an objectand a fluid

coefficient of friction: a measure of theresistance to sliding between the sur-faces of two materials

coefficient of lift: a measure of the lift forcethat can be created between an objectand a fluid

coefficient of restitution: a measure of therelative elasticity of the collision be-tween two objects

common mode rejection: a measure of thequality of a differential amplifier in re-jecting common signals (noise)

compression: a squeezing mechanical load-ing created by forces in opposite direc-tions acting along a longitudinal axis


compliance: the ratio of change in lengthto change in applied force, or the in-verse of stiffness (see “stiffness”); a ma-terial that is easily deformed has highcompliance

components: the breaking up of a vectorinto parts, usually at right angles

concentric muscle action: the conditionwhere activated muscles create a torquegreater than the resistance torque (mio-metric)

conservation of energy: the Law of Con-servation of Energy states that energycannot be created or destroyed; instead,energy is transformed from one formto another

contourgram: exact tracings of the body po-sitions of a movement from film/videoimages

contractile component: a part of the Hillmuscle model that represents the ac-tive tension and shortening of actinand myosin

coordination continuum: a biomechanicalapplication principle which states thatmovements requiring generation ofhigh forces tend to utilize simultaneoussegmental movements, while lower-force and high-speed movements tendto use sequential movements

couple: (1) two forces of equal size, parallellines of actions, and opposite sense; (2)a mechanical calculation tool that isemployed to represent torques withoutaffecting linear kinetics

creep: the increase in length (strain) overtime as a material is constantly loaded

cross-talk: the pick-up of EMG signals fromother active muscles aside from themuscle of interest

cut-off frequency: the cutting point of afiltering technique, where frequencies

above or below are removed; the low-er the cut-off frequency for a lowpassfilter, the greater the smoothing ofthe signal

deformable body: biomechanical modelthat documents the forces and defor-mations in an object as it is loaded

density: the mass of an object divided byits volume

degrees of freedom: the number of inde-pendent movements an object maymake, and consequently the number ofmeasurements necessary to documentthe kinematics of the object

differential amplification: EMG techniquefor amplifying the difference betweenthe signals seen at two electrodes rela-tive to a reference electrode

digital filter: a complex frequency-sensi-tive averaging technique used tosmooth or process data

digitize (video): the A/D conversion of ananalog video signal to create the dis-crete picture elements (pixels) used tomake a video image

digitize (biomechanics): the process ofmeasuring 2D locations of points on animage

direct dynamics: biomechanical simulationtechnique where the kinematics of abiomechanical model are iterativelycalculated from muscle activation orkinetic inputs

direct linear transformation (DLT): ashort-range photogrammetric tech-nique to create 3D coordinates (x,y,z)from the 2D coordinates (x,y) of two ormore synchronized camera views of anevent

displacement: linear change in position in aparticular direction (vector)

APPENDIX A: GLOSSARY 285

distance: liner change in position withoutregard to direction (scalar)

double differential amplification: EMGtechnique to eliminate cross-talk

drag: the fluid force that acts parallel to therelative flow of fluid past an object

dynamic flexibility: the increase in passivetension per increase in joint range ofmotion

dynamical systems: motor learning theorywhich argues that movement coordina-tion emerges or self-organizes based onthe dynamic properties of the body andenvironment rather than on a centralmotor program from the brain

dynamics: the branch of mechanics study-ing the motion of bodies under acceler-ation

dynamometer: a device that measures forceor torque for muscular performancetesting

eccentric muscle action: the conditionwhere an activated muscle(s) creates atorque less than the resistance (plyo-metric) torque

economy: the amount of energy needed todo a specific amount of work

efficiency: in a system, the ratio of workdone to work input

elastic: the resistance of a body to deforma-tion (see “stiffness”)

elastic (strain) energy: the potential me-chanical work that can be recoveredfrom restitution of a body that has beendeformed by a force (see “hysteresis”)

electrogoniometer: a device that makescontinuous measurements of jointangle(s)

electromechanical delay: the delay be-tween motor action potential (electricsignal of muscle depolarization orEMG) and production of muscularforce

electromyography (EMG): the amplifica-tion and recording of the electrical sig-nal of active muscle

energy (mechanical): the ability to do me-chanical work (potential, strain, and ki-netic energy are all scalar mechanicalenergies)

ergometer: machine used to measure me-chanical work

Euler angles: a way to represent the 3D mo-tion of an object using a combination ofthree rotations (angles)

excursion: the change in the length of amuscle as the joints are moved throughtheir full range of motion

external force: a force acting on an objectfrom its external environment

external work: work done on a body by anexternal force

fascicle: a bundle of muscle fibers (cells)

fast Fourier transformation (FFT): mathe-matical technique to determine the fre-quencies present in a signal

field (video): half of an interlaced video im-age (frame), composed of the even orodd horizontal lines of pixels

finite difference: calculating time deriva-tive by discrete differences in kinemat-ics divided by the time between data-points

finite-element model: advanced biome-chanical model to study how forces actwithin a deformable body

firing rate: the number of times a motorunit is activated per second


First Law of Thermodynamics: applicationof the Law of Conservation of Energyto heat systems

fluid: a substance, like water or gasses, thatflows when acted upon by shear forces

force: a push, pull, or tendency to distortbetween two bodies

force–length relationship: skeletal musclemechanical property that demonstrateshow muscle force varies with changesin muscle length (also called thelength–tension relationship)

force–motion principle: a biomechanicalapplication principle which states thatunbalanced forces are acting whenev-er one creates or modifies the move-ment of objects

force platform: a complex force transducerthat measures all three orthogonalforces and moments applied to a surface

force–time principle: a biomechanical ap-plication principle which states that thetime over which force is applied to anobject affects the motion of that object

force–time relationship: (see “electro-mechanical delay”)

force–velocity relationship: skeletal mus-cle mechanical property that showshow muscle force potential depends onmuscle velocity

Fourier series: a mathematical techniquefor summing weighted sine and cosineterms that can be used to determine fre-quency content or represent a time do-main signal

frame (video): a complete video image

free-body diagram: a technique for study-ing mechanics by creating a diagramthat isolates the forces acting on a body

frequency: the inverse of time or the num-ber of cycles of an event per second

frequency content: time-varying signalscan be modeled as sums of weightedfrequencies (see “Fourier series”)

frequency response: the range of frequen-cies that are faithfully reproduced byan instrument

friction: the force in parallel between twosurfaces that resists sliding of surfacespast each other

global reference frame: measuring kine-matics relative to an unmoving pointon the earth

Golgi tendon organ: a muscle receptor thatsenses muscle tension

goniometer: a device used to measure an-gular position

gravity: the force of attraction between ob-jects; usually referring to the verticalforce of attraction between objects andthe earth

ground reaction force: the reaction (oppo-site) forces created by pushing againstthe ground (e.g., feet in running orhands in a handstand)

harmonic: a multiple of a fundamental fre-quency (see “frequency content”)

helical (screw) axis motion: a way to repre-sent the 3D motion of an object usingan imaginary axis in space and rota-tions relative to that axis

highpass filter: a signal-processing tech-nique that removes the low-frequencycomponents of a signal

Hill muscle model: a three-componentmodel of muscle force consisting ofa contractile component, a series elas-tic component, and a parallel elasticcomponent


hypertrophy: the increase in size of musclefibers

hysteresis: the energy loss within a de-formed material as it returns to its nor-mal shape

impulse: the mechanical effect of a forceacting over time (vector); J = F • t

impulse–momentum relationship: princi-ple which states that the change in mo-mentum of an object is equal to the netimpulse applied; the original languageof Newton's second law, and equivalentto the instantaneous version: F = ma

inertia: the property of all matter to resist achange in its state of motion

inertial force: the mass acceleration (ma)term in Newton's Second Law (dynam-ics); the effect of inertia and accelera-tion on dynamic movement, but it isimportant to remember that its effect isnot a real force acting on an object fromanother object

inertia principle: A biomechanical applica-tion principle which states that inertialresistance to changes in state of motioncan be used to advantage in resistingmotion or transferring energy

information: observations or data with un-known accuracy

in situ: Latin for “in place”, or structuresisolated by dissection

integrated EMG (IEMG): the area undera rectified EMG signal; correctly,the time integral reported in units ofamplitude � time (mV•s); unfortunate-ly, some studies employ outdatedequipment and incorrect terminology,so that reported IEMGs are not reallyintegrated but filtered or smoothedEMG values (mV), which is essentiallya linear envelope detector

interdisciplinary: the simultaneous inte-grated application of several disci-plines to solution of a problem

internal force: a force within an object orbetween the molecules of an object

internal work: work done on body seg-ments by internal forces (muscles, liga-ments, bones)

inverse dynamics: biomechanics researchtechnique for estimating net forces andmoments in a linked-segment modelfrom measured kinematics and anthro-pometric data

in vitro: Latin for “in glass,” or tissues re-moved from the body but preserved

in vivo: Latin for “in the living,” or duringnatural movement

isokinetic (“same, or constant, motion”):the condition where activated musclescreate constant joint angular velocity

isometric (“same, or constant, length”): thecondition where activated muscles cre-ate a torque equal to the resistancetorque, so there is no joint motion

isotonic (“same, or constant, tension”): thecondition where activated muscleswork against a constant gravitationalresistance; muscle tension is not con-stant in these conditions

jerk: the third derivative of displacementwith respect to time

joint center: an approximation of the in-stantaneous center of rotation of a joint

joint reaction forces: the net forces acting atjoints calculated from inverse dynam-ics; these forces do not represent the ac-tual bone-on-bone forces acting atjoints, but a combination of bone, mus-cle, and ligament forces

Joule: the unit of mechanical energy andwork


kinematic chain: a linkage of rigid bodies;an engineering term used to simplifythe degrees of freedom needed to docu-ment the mechanical behavior of a sys-tem; Steindler (1955) proposed the ter-minology of a kinetic chain, and classi-fying chains as either open or closed;unfortunately, this has resulted in agreat deal of confusion and an unclearmanner of classifying movements/ex-ercises: open: one end link is free tomove; closed: constraints (forces) onboth ends of the kinematic chain

kinematics: the branch of mechanics thatdescribes the motion of objects relativeto some frame of reference

kinetic energy: the capacity to do work dueto the motion of an object

kinetics: the branch of mechanics that ex-plains the causes of motion

knowledge: the contextual, theory-basedand data-supported ideas that makethe best current explanation for reality

laminar flow: movement of fluid insmooth, parallel layers

Law of Acceleration: Newton's Second Lawof Motion, which states that the acceler-ation an object experiences is propor-tional to the resultant force, is in thesame direction, and is inversely propor-tional to the object's mass (�F = ma)

Law of Inertia: Newton's First Law ofMotion, which states that objects tendto resist changes in their state of mo-tion; formally, we say an object will re-main in a state of uniform motion (still-ness or constant velocity) unless actedupon by an external force

Law of Momentum: Newton's second lawwritten as the impulse–momentum re-lationship

Law of Reaction: Newton's Third Law ofMotion, which states that for everyforce there is an equal and opposite re-action force

lever: a simple machine used to magnifymotion or force; a lever consists of arigid object rotated about an axis

lift: the fluid force that acts at right anglesto the relative flow of fluid

linear envelope: EMG processing tech-nique where a rectified signal issmoothed with a lowpass filter

linearity: a measure of the accuracy of aninstrument, usually expressed as a per-centage of full-scale output (FSO)

linear voltage differential transducer(LVDT): a force-measuring device

linked-segment model: a rigid body modellinked together by joints

load: a force or moment applied to a mate-rial

load cell: a force-measuring device

load-deformation curve: the mechanicalbehavior of a material can be docu-mented by instantaneous measurementof the deformation and load applied it

local reference frame: measuring kinemat-ics relative to a moving point, or near-by rigid body (joint, segment, or centerof mass)

lowpass filter: a signal-processing tech-nique that removes the high-frequencycomponents of a signal

Magnus effect: the creation of lift force on aspinning sphere

markers: high-contrast reflective materialsattached to subjects to facilitate the lo-cation of segments, landmarks, or jointcenters for digitizing


mass: the resistance of an object to linear ac-celeration

maximal voluntary contraction (MVC): themaximum force/torque a person cancreate with a muscle group, usually un-der in isometric conditions

mechanical advantage: a ratio describingthe effectiveness of a lever calculated bythe moment arm for the force dividedby the moment arm for the resistance

mechanics: the branch of physics that dealswith forces and the motion they create

mechanomyography (phonomyography,vibromyograph): the amplification andrecording of the vibrations created bymuscle activation

modeling: mathematical representations ofthe biomechanical systems used for cal-culations or simulations

moment (moment of force, torque): the ro-tating effect of a force

moment arm: the leverage of a force for cre-ating a moment; the perpendicular dis-tance from the axis of rotation to theline of action of the force

moment of inertia: the resistance to rota-tion (angular acceleration) of a body

momentum: the quantity of motion of anobject calculated by the product ofmass and velocity (vector)

motor action potential: the change in elec-trical charge about a muscle fiber as it isactivated

motor unit: a motor neuron and the musclefibers it innervates

muscle action: the activation of muscle tocreate tension that contributes to jointmovement or stabilization

muscle inhibition: the inability to fully ac-tivate or achieve maximum muscleforce during maximum voluntary con-traction

muscle spindle: an intramuscular receptorthat senses changes in muscle length

myofibril: the small cylindrical filamentsthat make up a muscle fiber/cell

myosin: the large filaments in a myofibrilthat interact with actin to create muscletension

myotatic reflex: a short reflex arc that acti-vates a muscle as it is stretched

net force: the resultant force or sum of allexternal forces acting on an object

Newton: the SI unit of force; 1 Newton (N)is equal to 0.22 pounds

normal reaction: the force acting at rightangles to the surfaces of objects that arein contact

Nyquist frequency: a signal sampling the-orem which states that the minimumdigital sampling rate (Nyquist frequen-cy) needed to accurately represent ananalog signal is twice the highest fre-quency present in the signal

optimal projection principle: A biome-chanical application principle whichstates that there are ranges of optimalangles for projecting objects to achievecertain goals

orthogonal: perpendicular (at right angles)

orthotics: objects/braces that correct defor-mities or joint positioning

overuse injury: an injury created by repeti-tive movements below acute injurythresholds, but due to inadequate restand/or repetitive stress, injury devel-ops; also known as cumulative traumadisorder or repetitive motion injury


parallel elastic component: a part of theHill muscle model that represents thepassive tension from connective tissuethroughout the muscletendon unit

Pascal: the SI unit of pressure or stress(force per unit area)

passive insufficiency: the limitation ofjoint motion because of increases inpassive tension in multiarticular mus-cles stretched across multiple joints

passive tension: a component of muscletension from passive stretching of mus-cle, especially the connective tissuecomponents

pennation: the angle of muscle fiber bun-dles relative to a tendon

piezoelectric: crystals with electromechani-cal properties that can be used to meas-ure force/acceleration

point mass: a simplified mechanical modelthat represents an object as a point inspace with a given mass

potential energy: the capacity to do workof an object due to its vertical positionin a gravitational field (gravitationalpotential energy) or its deformation(strain energy)

potentiometer: a device that is used tomeasure rotation

power (mechanical): the rate of doing me-chanical work; peak mechanical powerrepresents the greatest mechanical ef-fect, the ideal combination of force andvelocity; power can be calculated asW/t or F • V

preamplification: the amplification ofsmall signals (EMG) close to theirsource before they are conducted toother devices for amplification andrecording

pressure: external force divided by areaover which the force acts

projectile: an object projected into spacewithout self-propulsion capability, sothe only forces acting on the object aregravity and air resistance

proprioceptive neuromuscular facilitation(PNF): specialized stretching proce-dures that utilize sequences of muscleactions to potentiate reflexes to relaxmuscles being stretched

prosthetics: artificial limbs

Pythagorean Theorem: the two sides of aright triangle forming the right angle (aand b) and the hypotenuse (c) are relat-ed as follows: a2 + b2 = c2

qualitative analysis: systematic observa-tion and introspective judgment of thequality of human movement for thepurpose of providing the most appro-priate intervention to improve perform-ance (Knudson & Morrison, 2002)

quantitative analysis: solving a biome-chanical problem using numericalmeasurements and calculations

quasistatic: the state of a mechanical systemwhere the accelerations are smallenough to be assumed equal to zero

radian: a dimensionless unit of rotationequal to 57.3°

radius of gyration: a convenient way tosummarize an object's moment of iner-tia, defined as the distance from the axisof rotation at which half the object'smass must be placed in both directionsto equal the object's moment of inertia

range-of-motion principle: a biomechani-cal application principle which statesthat the amount of linear and angularmotion used will affect the speed andaccuracy of human movement


reaction change: a method to calculate thecenter of gravity of static body postures

reciprocal inhibition: the inhibition of anopposing muscle group (antagonist)when a muscle group (agonist) is acti-vated

recruitment: activation of motor units ofmuscles by the central nervous system

rectified EMG: a processing technique thatconverts negative EMG voltages to pos-itive ones

redundancy (distribution) problem: amathematical problem with most kinet-ic biomechanical models, where thereare more musculoskeletal unknownsthan there are equations

relative angle: an angle measured betweentwo moving objects

residuals: difference between a smoothedand raw signal; can be used to examinethe quality of the fit of the new signal tothe pattern of the raw signal

resolution (video): the number of pixelsavailable to measure a given field ofview; a video image of a 3-meter widearea with a horizontal resolution of 640pixels has a resolution for measure-ment of about 5 mm

resonance: frequency of vibration thatmatches the physical properties of abody so that the amplitudes of the vibra-tion increase rather than decay over time

resting length: the middle of muscle rangeof motion where passive tension beginsto rise

resultant: the addition of vectors to obtaintheir net effect (see “net force”)

right-hand rule: a convention or standardfor drawing the correct direction of an-gular velocity vectors

rigid body: mechanical simplification (ab-straction) assuming the dimensions ofan object do not change during move-ment or loading

root mean square (RMS): signal processingcalculation that approximates the meanabsolute value of a time-varying signal

rotator cuff: the four deep, stabilizing mus-cles of the glenohumeral joint: the in-fraspinatus, supraspinatus, subscapu-laris, and teres minor

sampling rate: the number of discretesamples per second used to representa signal; NTSC video has an effectivesampling rate of 60 Hz or 60 fields persecond

sarcomere: the functional unit of a myofib-ril; a sarcomere is the region betweentwo Z disks

scalar: simple quantity completely definedby a single number (magnitude)

scaling: converting image measurements toactual size

science: a systematic method for testing hy-potheses with experimental evidencefor the purpose of improving our un-derstanding of reality

Second Law of Thermodynamics: no ma-chine can convert all the input energyinto useful output energy

segmental interaction principle: a biome-chanical application principle whichstates that forces acting in a system oflinked rigid bodies can be transferredthrough the links

segmental method: a research method usedto calculate the center of gravity of abody using anthropometric data, jointcoordinates, and static equilibrium


series elastic component: a part of the Hillmuscle model that represents the pas-sive tension of connective tissue in se-ries with the contractile component

shear: mechanical loading in opposite di-rections and at right angles to the sur-face of a material

shutter speed: the period of time duringwhich a photographic or video image iscaptured (e.g., 1/1000 of a second); lim-iting this period can prevent blurring ofmoving objects

simulation: use of a biomechanical modelto predict motion with given input con-ditions in order to study the factors thataffect motion (see “direct dynamics”)

size principle: the orderly recruitment ofmotor units occurs from the smallest tothe largest

smoothing: a processing technique thatsmooths data, removing rapid fluctua-tions that are not part of normal biome-chanical signals

smoothing parameter: an index of theamount of smoothing allowed insplines; the larger the smoothingparameter, the more smoothing (allow-able deviation between the raw andfitted curve)

snap: the fourth derivative of displacementwith respect to time

speed: the rate of change of distance(scalar)

spin principle: a biomechanical applicationprinciple which states that spin isput on a projectile to affect trajectoryor bounce

spline: a smoothing technique that replacesthe signal with several polynomialslinked together; cubic (third power)and quintic splines (fifth power) arecommon in biomechanics

static equilibrium: when all the forces andtorques acting on an object sum to zero,meaning that the object is motionless ormoving at constant velocity

static flexibility: the linear or angularmeasurement of the limits of motion ina joint or joint complex

statics: the branch of mechanics that stud-ies bodies at rest or in uniform motion

stiffness: the elasticity of a material, meas-ured as the slope of the elastic (linear)region of the stress–strain curve(Young's modulus of elasticity); a mate-rial's stiffness is usually approximatedusing the slope of the linear region ofthe load-deformation curve

strain (mechanical): the amount of defor-mation of a material caused by an ap-plied force, usually expressed as a per-centage change in dimensions

strain (muscular): muscular injury usuallycaused by large eccentric stretches ofmuscle fibers

strain energy: the capacity to do work of anobject due to its deformation by an ex-ternal force

strain gauge: a small array that is bondedto materials in order to sense the smallchanges in size (strain) as the materialis loaded; usually used to measureforce or acceleration

strength (mechanical): the toughness of amaterial to resist loading, usuallymeasured as the total work or peakforce required to permanently deform(yield strength) or break a material (ul-timate strength)

strength (muscular): the maximum forceor torque produced by a muscle groupin an isometric action at a specificjoint angle; research has found severaldomains of strength expression de-pending on the time, velocity, and re-sistance involved


stress (mechanical): the force per unit areain a material

stress fracture: a very small fracture in cor-tical bone caused by repetitive loadingand inadequate rest

stress relaxation: the decrease in stress in amaterial over time when subjected to aconstant force

stress–strain curve: (see “load deforma-tion”)

stretch-shortening cycle (SSC): a commoncoordination strategy where agonistsfor a movement are eccentricallyloaded in a countermovement, immedi-ately before the concentric action andmotion in the intended direction; anSSC results in larger initial forces andgreater concentric work than purelyconcentric actions

synergy: the combination of several muscleactions that serve to optimally achievea motor task

sweet spot: striking implements (bats, rack-ets, etc.) have zones where impact withother objects is most effective; the termsweet spot tends to refer to the zone withthe highest coefficient of restitution, al-though there are zones that minimizereaction forces (center of percussion),or minimize vibration (node)

technology: the tools and methods for ap-plying scientific knowledge to solveproblems or perform tasks

telemetry: a technique to send biomechani-cal signals to recording devices withoutwires, using an FM radio transmitterand receiver

tension: a pulling apart (making longer) ofmechanical loading created by forces inopposite directions acting along thelongitudinal axis of a material

tensor: a complex variable that cannot bedescribed using only magnitude anddirection

tetanus: the summation or fusion of manytwitches of muscle fibers into a smoothrise in tension

thixotropy: a property of a material tochange passive stiffness in response toprevious loading; this history-depend-ent behavior is apparent in the increas-ing stiffness of muscle with extendedinactivity

time constant: typically, an averaging/smoothing value in EMG processing;the larger the time constant the largerthe time interval averaged over, mean-ing more smoothing

torque (see “moment of force”): the rotat-ing effect of a force; mechanics of mate-rials uses torque to refer to torsion mo-ments acting on an object

torsion: opposing loads that twist an objectalong its longitudinal axis

trajectory: the path in space that an objectfollows as it moves through the air

twitch: the force response of a muscle fiberto a single stimulation

twitch interpolation (superimposition)technique: a method used to determinethe maximality of a maximum volun-tary action (MVC) where stimulation isprovided during an MVC

vector: a complex quantity requiring de-scription of size and direction

viscoelastic: the property of a materialwhere force in the material is depend-ent on time and deformation

weight: the downward (vertical) force ac-tion on an object due to gravity


Wolff's Law: bones remodel according tothe stress in the tissue

work (mechanical): work is done whena force moves an object in the di-rection of the force and is calcu-lated as the product of force and dis-placement

work–energy relationship: principle inphysics which states that the workdone on a body is equal to the netchange in energy in the body

yield point: point on the load-deformationcurve where a material continues to de-form without increasing load

Young's modulus (see “stiffness”)


Biomechanical variables are reported intraditional English units and the metricsystem (SI, International System). Theconversion factors below appendix are use-ful for converting between various meas-urement units. It is likely you will find oneunit of measurement easier to relate to,and you may need to transform some val-ues from the literature to more convenientunits of measurement.

For example, if you wanted to get a feel forhow fast a person is running at 9 m/s, youcould take 9 m/s times 2.23 to get 20.1 mph.If you wanted to know how fast you wererunning on a treadmill that reported yourpace as 8.5 minutes per mile, you wouldfirst convert the pace to an average speed inmiles per hour. Sixty minutes divided by 8.5minutes would equal 7.1 mph. Next youwould take 7.1 mph divided by the conver-sion factor (2.23) to obtain 3.2 m/s.

APPENDIX B

Conversion Factors

297

Variable SI unit � Factor = Other unit

distance m 3.28 ftkm 0.621 milesradian 57.3 degrees

speed m/s 2.23 mphkm/hr 0.62 mphm/s 3.28 ft/srad/s 57.3 deg/srad/s 9.55 rpm

acceleration m/s/s 0.102 g'smass kg 0.069 slugsmoment of inertia kg•m2 0.738 slugs•ft2

force N 0.225 poundstorque N•m 0.738 lbs•ftimpulse N•s 0.225 lbs•senergy Joules 0.738 ft•lbswork Joules 0.738 ft•lbspower Watts 1.341 horsepowermomentum (kg•m)/s 0.225 (slug•ft)/s

(kg•m2)/s 0.225 (slug•ft2)/sstress/pressure Pascals 0.00015 lbs/in2

This appendix provides initial answers to,primarily, the odd-numbered review ques-tions from chapters 1 through 8. The pur-pose of review questions is to practice andrehearse key biomechanical concepts, prin-ciples, and laws. Students are encouragedto study the topics related to each questionin greater depth. The discussion questionsin chapters 9 through 12 are designed forstudents and instructors to discuss. Dis-cussion questions are ideal for small-groupbrainstorming and practice in qualitativeanalysis of human movement.

Chapter 1

1. Biomechanics is the study of how liv-ing things move using the science of me-chanics. In the first half of the twentiethcentury this was synonymous with kinesi-ology, but now kinesiology is the academicdiscipline of the study of human move-ment.

3. The advantages of qualitative biome-chanical analysis is its ease of use and flex-ibility, but its weaknesses are related to sub-jectivity and reliability. Quantitative biome-chanical analysis may have greater preci-sion and accuracy, but its weaknesses arethe high cost in terms of equipment andtime.

5. A wide variety of journals publishbiomechanics research. These journals in-clude specialized biomechanics, engineer-ing, biology, medicine, strength and condi-tioning, and sports-medicine journals.

7. Biomechanics must be integratedwith other kinesiology sciences becausepeople are not robots that move without re-gard to environmental factors. Psycho-logical, physiological, and perceptual is-sues are all examples of factors that mightbe more important than biomechanical fac-tors in some situations.

Chapter 2

1. Biomechanics has traditionally fo-cused on rigid body and fluid mechanics.The majority of early biomechanical studiesfocused on the kinematics of movement,but there are still many studies on the caus-es (kinetics) of movement.

3. Scalars only require knowledge ofsize and units. Vector variables have size,units, and direction.

5. The nine principles of biomechanicscan be subdivided into principles related tohuman movement and projectiles.

7. Many factors affect human move-ment along with the principles of biome-chanics. Some factors might be performercharacteristics (psychological, perceptual,or social), the physical environment, thegoal of the movement, and the philosophi-cal goals of the kinesiology professional.

Chapter 3

1. There are several anatomical termsemployed to describe the location and mo-

APPENDIX C

Suggested Answers to SelectedReview Questions

299

tion of body structures. Some examples in-clude directions (anterior/posterior, medi-al/lateral, superior/inferior, proximal/dis-tal) and joint movements (flexion/exten-sion, adduction/abduction, internal rota-tion/external rotation).

3. Muscle fiber types and their architec-tural arrangement affect muscle force andrange of motion. The rise and decay ofmuscle tension is greatest in fast-twitchfibers and decreases the greater the oxida-tive or slow-twitch characteristics of thefiber. Muscle fibers arranged in parallelhave greater range of motion but create lessforce. Pennate fiber arrangements producegreater force but have less range of motion.

5. Muscle tension has active and pas-sive components. Passive tension does notappear to play a large role in the middle ofthe range of motion, but does tend to limitmotion when the muscle is stretched nearthe end of the range of motion.

7. Examples of the force–motion princi-ple can be seen anytime an object changesits state of motion. If a dumbbell reversesdirection at the bottom of an arm curl exer-cise, we can conclude an unbalanced up-ward force was applied to the dumbbell.

9. Biomechanical principles and re-search help the kinesiology professional tounderstand how human movement occursand how movement might be improved.The major areas of biomechanics researchthat are the most valuable in this area areEMG, studies of anatomical variation,linked segment interactions, and modelingand simulation.

Chapter 4

1. The primary loads on body tissuesare compression, tension, and shear. Thecombined loads are bending and torsion.

3. The tensile strengths of tendon andmuscle are about 14,500 and 60 lb/in2, re-spectively, while the tensile strength of

bone is about 18,000 lb/in2. These data areconsistent with the higher incidence ofmuscle injuries compared to that for tendonor bone.

5. The Force–Velocity Relationship hasseveral implications for resistances andspeed of movement in strength-trainingexercises. When training for muscularstrength, large resistances should be movedslowly to train the muscle where it isstrongest. Training for muscular power andendurance uses smaller resistances movedat faster speeds.

7. The Force–Time Relationship definesthe delay between neuromuscular signal-ing for creation of muscle force and a rise inthat force, while the force–time principledeals with duration of force application.While these two concepts are related, theforce–time principle involves adapting thetiming of the application of force by a per-son to the demands of the task whileelectromechanical delay is one of the fac-tors that affects how force can be applied.

9. The brain creates muscle tension byrecruitment of motor units and modifyingtheir firing rate or rate coding. Motor unitstend to have predominantly one fiber type,so that the brain generally recruits motorunits based on the size principle, fromslow-twitch motor units to fast-twitch mo-tor units.

11. Muscle spindles sense stretch andgolgi tendon organs sense muscle tension.

13. Large ranges of motion allow forgreater production of speed and force,while smaller ranges of motion tend to al-low for more accurate movement. Theweight shifts in a golf swing and baseballbatting are small because of the high accu-racy demands of these skills. Maximizingrange of motion in the countermovement injumps is not usually effective because oftiming limitations or biomechanically weakpositions in deep knee flexion.

15. A person doing a seated knee exten-sion exercise uses concentric action of the


quadriceps groups to extend the knee, andeccentric action of the quadriceps to flex theknee. The forces acting on the lower leg in-clude muscle forces from the hamstrings,quadriceps, ankle muscles, and gravity. Ifthe person were exercising on a machinethere would be forces applied to theleg/ankle from the machine.

Chapter 5

1. The frame of reference is the pointfrom where motion is measured.

3. An average velocity is a velocity esti-mate for the middle of a time intervalwhere displacement and time informationare available (V = d/t). The smaller the timeinterval used for the calculation, the moreaccurate the average velocity is and thecloser it gets to true instantaneous velocity.An instantaneous velocity is an exact esti-mate of the velocity at an instant in time,and is calculated using calculus.

5. With upward displacement as posi-tive, the average vertical velocity (V = d/t)of the dumbbell for the concentric phase is1.2/1.5 = 0.8 m/s , while the average verti-cal velocity of the eccentric phase is–1.2/2.0 = –0.6 m/s.

7. Angular kinematics are particularlysuited for analysis of human movement be-cause joint motions are primarily rotational.Markers placed on the body can by digi-tized to calculate the angular kinematics ofthe joints during human movements.

9. Since knee extension is positive (+50deg/s), the angular acceleration of her knee(�� = ��/t) is: (0 – 50)/0.2 = –250 deg/s/s.

11. The coach could use a radar gun tomeasure maximum and warm-up throwingspeeds. If the coach did not have a radargun, they could measure off the standarddistance and time of the throws with a stop-watch to calculate average velocities in eachthrowing condition.

13. To use the angular-to-linear velocityconversion formula (V =�� • r), the angularvelocity must be in radian/second: 2000deg/s divided by 57.3 deg (1 radian), whichis equal to 34.9 radian/s. The velocity of theclub head relative to the golfer's hands is:34.9 (1.5) = 52.4 m/s.

15. The vertical acceleration of a volley-ball anywhere in flight is a downward ac-celeration due to gravity of –9.8 m/s/s or–32.2 ft/s/s.

Chapter 6

1. A 6-kg bowling ball has the same in-ertia in all states of motion. The ball's iner-tia is a fundamental property of matter andis measured by its mass, 6 kg. This will notchange unless we get the ball rolling nearthe speed of light!

3. Increasing inertia is useful in move-ment when you want to maximize stability,or if there is time to get a larger inertia mov-ing in a desired direction. Increasing themass of a wrestler will make it more diffi-cult for an opponent to move the wrestler.

5. The major determining factors of dryfriction are the normal reaction and the co-efficient of friction. Since adding mass to aperson has other effects, the best strategy isto select a shoe with a higher coefficient offriction with common flooring.

7. If we move the shearing force to theleft, we create a right triangle with a 30° an-gle on the right and a hypotenuse of 1000N. The longitudinal component of the jointforce (FL) is the adjacent side, so we can usethe cosine relationship to calculate: cos 30°= FL/1000, so FL = 866 N. The sine of 30° isa special value (0.5), so we can quickly seethat FS = 500 N.

9. Muscular strength is the maximumforce a muscle group can create in certainconditions, usually an isometric action at aspecified joint angle. Muscular power is therate of doing muscular work. Maximum

APPENDIX C: SUGGESTED ANSWERS TO SELECTED REVIEW QUESTIONS 301

muscular power occurs at the combinationof velocity and force that maximizes mus-cular work. This usually occurs at moderate(about a third of maximum) velocities andmuscular force.

11. Given a 800-N climber has 81.6 kg(800/9.8) of inertia and upward displace-ment is positive, we can use Newton's sec-ond law in the vertical direction (F = ma)to calculate: –800 + 1500 = 81.6(a), so a = 8.6m/s/s.

13. Sequential coordination of high-speed movements is advantageous becauseinitial proximal movement contributes toSSC muscle actions, and mechanical energycan be transferred through segmental inter-action.

15. Given that an upward displacementis positive and a 30-kg barbell weighs –294N (30 • 9.8), we can use Newton's secondlaw in the vertical direction (F = ma) to cal-culate: –294 + 4000 = 30(a), so a = 123.5m/s/s or 12.6 g's of vertical acceleration.

Chapter 7

1. A torque or moment of force dependson the applied force and the moment arm.

3. The joints of the human body allowus to change our resistance to rotation ormoment of inertia by moving the masses ofthe body segment towards or away from anaxis of rotation. Bringing segments close toan axis of rotation decreases moment of in-ertia while extending segments away froman axis of rotation increases moment of in-ertia.

5. Newton's first angular analogue saysthat an object will stay at rest or constant ro-tation unless acted upon by an externaltorque. Newton's second angular analoguesays that the angular acceleration of an ob-ject is proportional to the torque causing it,is in the same direction, and is inverselyproportion to the moment of inertia.Newton's third angular analogue states that

for every torque acting on an object there isan equal and opposite torque this object ap-plies back on the other object creating thetorque.

7. The center of gravity of athletes do-ing a lunge-and-sprint start as illustratedbelow are likely the positions indicated bythe dot.

9. To maximize stability, a person canincrease the size of the base of support,lower the center of gravity relative to thebase of support, and position the center ofgravity relative to anticipated forces.Maximizing stability tends to decrease theability to move in all directions (mobility).

11. Given that the force applied by thestudent was 30 lb and we know the radiusof the merry-go-round, it is easiest to findthe rotary component (FR) of the force tomultiply by the radius (4 ft) to obtain thetorque applied. We can calculate: cos 55° =FR/30, so FR = 17.2 lb. Torque (T = F • d⊥)applied to the merry-go-round is: 17.2(4) =68.8 lb•ft. This is almost half the 120 lb•ft oftorque when the force is applied at an anglethat maximizes the moment arm.

13. You cannot calculate the torque be-cause the muscle angle of pull is notknown.

Chapter 8

1. The major fluid forces are buoyancy,lift, and drag. Buoyancy acts upward. Dragacts parallel to and opposing the relative


flow of fluid, while lift acts at right anglesto the relative flow of fluid.

3. The center of gravity and center ofbuoyancy of the human body move in sim-ilar manner, following the mass shifts withmoving segments. The center of gravitymoves more than the center of buoyancybecause the trunk volume dominates thevolume of the rest of the body.

5. Optimal projection angles includethe effect of fluid forces as well as the re-lease and target locations of projection ac-tivities. For example, place-kicking has anoptimal angle of projection much lowerthan 45° because of the fluid forces of drag.

7. The centers of buoyancy of a swim-mer in three flotation positions (below) arelikely the positions indicated by the dot.

9. A volleyball serve with topspin divesdownward because the Magnus Effect gen-erates a downward-and-backward-directedlift force that adds to gravity.

11. Round balls tend to curve in the di-rection of the spin. If the front of a ball isspinning to the right (as you observe it as itis coming toward you), the lift force willact to the right and make the ball curve tothe right.

13. Swimmers and cyclists shave so asto decrease surface drag, which resists theirmotion, while a rougher surface of a spin-ning baseball will create a greater lift force.The greater Magnus Effect and lift forceacting on the baseball is more importantthan the minor effect the roughness willhave on drag.

APPENDIX C: SUGGESTED ANSWERS TO SELECTED REVIEW QUESTIONS 303

Trigonometry is a branch of mathematics thatis particularly useful in dealing with right-an-gle triangles. This is important in the study ofbiomechanics because vectors are usually re-solved into right-angle components. This ap-pendix provides a brief review of four trigo-nometric relationships for two-dimensionalanalysis in the first quadrant. There are manymore trigonometric relationships that are ful-ly defined for all 360° of a circle. The four re-lationships will be defined relative to right tri-angle illustrated below.

The sides of a triangle are traditionally la-beled in two ways, with letters and names de-scribing their position relative to one of theacute angles of interest (��). The longest side ofthe triangle is the hypotenuse or c. The sidenext to the angle of interest is usually labeleda or the adjacent side. The last side is the op-posite side or b.

The first relationship is the PythagoreanTheorem, which describes the relationshipbetween the lengths of the sides in all righttriangles. If you have knowledge of any twoof the three sides of a triangle you can apply

the formula c2 = a2 + b2 to solve for the mag-nitude of the other side.

The sine, cosine, and tangent are the mostcommonly used trigonometric relationships,because they define the relationships betweenthe acute angles and the dimensions of righttriangles. The abbreviation and formula foreach relationship is:

sin �� = b/ccos �� = a/ctan �� = b/a

Suppose the right triangle depicted be-low corresponds to the following data on therelease conditions of a soccer kick: c = 40 m/sand �� = 35°. A biomechanist wanting to deter-mine the vertical velocity (b) in order to deter-mine the time of flight could write:

sin 35° = VV/40,and solving could yield

VV = 22.9 m/sNow use the cosine, tangent, or PythagoreanTheorem to see if you can confirm if the hori-zontal velocity of the ball is 32.8 m/s.

APPENDIX D

Right-Angle Trigonometry Review

305

RatingPrinciple Body part (inadequate-normal-excessive)

Balance

Coordination

Force–Motion

Force–Time

Inertia

Range of Motion

SegmentalInteraction

Optimal Projection

Spin

APPENDIX E

Qualitative Analysis ofBiomechanical Principles

307

A

Abdominal muscles, 82, 222Abduction, 43–44Absolute angle, 122Acceleration, 113–15

angular, 123–28, 178and gravity, 114–15and mass, 136–37, 139uniform, 115–17

Accommodation, 139–41Actin, 48, 51, 84Action potential, 86–87Active insufficiency, 85Active muscle tension, 48, 51–53, 84–85Active state dynamics, 87Acute injury, 148Adduction, 43–44, 189Agonist, 58Air flow, 198Air resistance and release parameters, 114, 118Airplane wing and lift force, 202–03American Alliance for Health, Physical

Education, Recreation, and Dance (AAHPERD), 14

American College of Sports Medicine (ACSM), 14, 60

American Society of Biomechanics (ASB), 14Anatomical position, 41Anatomy

concepts of, 41–49definition of, 41functional, 53–60

Angleabsolute, 122relative, 122

Angle of attack, 206Angle of projection, 117–21Angle of pull, 141–45, 154Angle of release, 119–21Angular acceleration, 123–28, 178

Angular displacement, 121, 124–25Angular inertia, 174–78Angular kinematics, 107–32Angular kinetic energy, 152Angular kinetics, 169–91Angular momentum, 164, 209Angular motion, 121–28, 178Angular speed, 123Angular velocity, 80, 122–25Animals and study of biomechanics, 12–13, 55Animation of movement, 10Anisotropic, 72Ankle, structure of, 39Antagonist, 58, 100Anterior cruciate ligament (ACL) injuries,

9, 247, 252–53Anterior direction, 42Anterior tibial stress syndrome, 148Anteroposterior axis, 41–42, 44Anthropometry, 56Aponeurosis, 47Archimedes Principle, 193, 210Arm swing transfer of energy, 164Arthrokinematics, 109Articular cartilage, 77Artificial limbs. See ProstheticsAscending limb region, 85–86Assistive devices, 9Athletic training, 60, 97. See also Strength

and conditioningAtmospheric pressure, 134–35Atrophy, 49Axis of rotation, 41–42, 126, 169–70, 189

and inertia, 171–78Axon, 94–95

B

Back, 180Balance, 180

and gender, 181, 188

Index

309

Balance principle, 33, 183–89, 243Ball

elasticity of, 155spinning, 155, 203–09surface roughness of, 199

Ballistic stretching, 75Barbell, 158Baseball. See also Softball

batting, 218–19pitching, 33, 62–63, 140, 206throwing, 227–28

Basketballand angles of projection, 120–21catching, 222–24free throw, 62–63, 219–20jump shot, 189passing, 230stiffness of, 7–8

Batting technique, 218–19Bench press, 140, 242–43Bending, 69, 71Bernoulli's Principle, 202–03Biarticular muscles, 58Bibliographic databases, 14–15Biceps

and angle of pull, 141–42brachii, 47, 53–54femoris, 169and lever, 170

Bilateral deficit, 97Biomechanical knowledge, 4, 16–20. See also

KnowledgeBiomechanics, 4

analysis of, 11–12applications of, 5–6collaborative, 15definition of, 1, 3forensic, 9, 10improving performance, 5–8principles of, 29–35reduction/treatment of injury, 9–10, 41research in, 6–7, 12–16sports, 13textbooks, 15–16and understanding muscle actions, 56–60

Bipennate muscle arrangement, 47Body composition, 136Body segments, 160Bone

biomechanics of, 76–77cancellous, 76–77

cortical, 76–77loading of, 76–77remodeling, 76

Bone density loss, 76Boundary layer, 197

in a spin, 204–05Bowling, 152, 154Buoyancy, 193–95, 210

C

Canadian Society of Biomechanics, 14Cancellous bone, 76–77Catching, 149–50, 222–24, 233–34Center of buoyancy, 194–95Center of gravity, 180–85, 188Chondromalacia patella, 248Cinematography, 231Closed motor skills, 219Coaching, 6, 227–35Coefficient of friction, 145–47Coefficient of kinetic friction, 146Coefficient of restitution, 155Coefficient of static friction, 146Collaborative biomechanics, 15Collagen, 75, 77Compliance, 74–75, 91Components of a vector, 26Compression, 69–70Computer models of biomechanics, 10Computerized literature searches,

14–15Concentric muscle action, 49–50, 79,

89–92Conditioning, 64, 230–31

and strength, 237–46Conditioning programs, 8Conservation of energy, 152–54Conservation of momentum, 152–53Contact forces, 145–47Contractile potentiation, 89–90Contraction, definition of, 49Contraction dynamics, 87Conversion factors, 297Coordination Continuum Principle, 33–34,

128–30Coordination of temporal impulses, 160Coordination Principle, 230Cortical bone, 76–77Cosine function, 143–45, 305


Creep, 74Critical thinking, 20Cross-bridge attachment sites, 84–85Cumulative trauma disorders, 15Curl-up exercise, 221–22

and angular motion, 121–22Curveball, 206–07Cycling, 97–98, 159, 199–200

D

Dartsand range of motion principle, 61

Decline squats, 65Deformable-body mechanics, 23Degrees, use in angular kinematics, 119–21Degrees of freedom, 109, 160Delay. See Electromechanical delayDeltoid, 47, 58Density

of bone, 76–77, 239of capillary, 81of electromyographic signal, 97of the human body, 194–96of water, 210

Descending limb region, 85–86Diagnosis task of qualitative analysis, 36Differentiation, 63, 115, 197–98Direct dynamics, 137Displacement, 107–08, 111

angular, 121and force, 27, 155–57by projectile, 118–20and speed, 119

Distal segment, 161–62Distance, 107–09Drafting, 200Drag, 193, 195–200, 210

surface, 196–97Drag crisis, 199Dribbling technique, 228–30Drop jump, 91, 239–40Dynamic equilibrium, 179Dynamic flexibility, 78Dynamical systems, 24, 96Dynamics, 24, 137Dynamometer, 27

isokinetic, 28, 124, 171–72

E

Eccentric force, 79, 88–92, 137–38Eccentric muscle action, 50Efficiency of movement, 159Elastic energy, 90–91Elastic limit, 71–72Elastic region, 71–72Elasticity, 27–28, 52, 154–55Elbow, 63, 124–26

flexion of, 53–54Electrogoniometer, 123Electromechanical delay, 87–88. See also

Force–Time RelationshipElectromyography (EMG), 14, 57, 86–87,

97–98EMBASE, 14Endomysium, 46Energy

conservation of, 152–54definition of, 151gravitational potential, 152loss of, 153–54mechanical, 58, 72, 151–55strain, 154–55transfer of, 164

Epimysium, 46Equilibrium, 179–80

static, 179, 181, 183Equipment, exercise, 244, 250–51

design improvements, 7–8Erector spinae, 82Error detection/correction, 35European Society of Biomechanics, 14Evaluating sources of literature, 18–19Evaluation task of qualitative analysis, 36Excitation dynamics, 87Exercise machines, 7–8, 244, 250–51

resistance, 86Exercise specificity, 240–42, 248–50Exercises, 8, 220–22, 237–46

and bone density loss, 76functional, 163

Explosive movement, 159–60, 165Extension, 43–44External force, 23, 99, 135, 154External rotation, 43, 45External work, 151, 156–57

INDEX 311

F

Failure strength, 72Fascicles, 46Fast-glycolytic muscle fiber, 81–83Fast-oxidative-glycolytic fiber, 81–83Fast twitch muscle fiber, 81–83Fatigue, 95, 99Female athlete triad, 76Fibers. See Muscle fibersFiring rate, 95, 97First Law of Motion, 33, 133–36First Law of Thermodynamics, 153–54Fitness, 220–22Flexibility and stretching, 78Flexion, 43–44, 123–26, 174, 189, 221–22Flotation, 194Fluid flow, 193–208Fluid forces, 193–208Fluid mechanics, 23, 193–211Fluids, 193Foot, 58–59Foot strike, 91Football, 34

and angles of projection, 119catching, 151, 233–34

Force, 26application, 92–93creating motion, 3development, 88–89and displacement, 27, 155–56drag, 195–96and dynamics, 24external, 23fluid, 193–208and impulse, 147inertial, 179lift, 34, 200–01and motion, 135and reaction, 137–38regulation of muscle, 95–98response of tissues, 69–75and time, 32–33and timing, 91, 149–51and torque, 169–70

Force development, 91Force–Length Relationship, 84–86Force–Motion Principle, 30–32, 63–65, 92–94,

157, 218, 222–23, 229Force plates, 139Force platform, 139, 146

Force potentiation, 90Force sensor arrays, 139Force–Time Principle, 32–33, 69, 92–94,

148–51, 165, 218, 223, 239. See alsoElectromechanical delay

Force–Time Relationship, 86–88. See alsoElectromechanical delay

Force–Velocity relationship, 51, 79–83, 158Forensic biomechanics, 9–10Frame of reference, 109Free-body diagram, 32, 63Free throw, 219–20Free weights, 59Friction, 145–47Friction drag, 196Frontal area, 199Frontal plane, 41Functional anatomy, 53–60

G

Gait, analysis of, 9–10Gait and Clinical Movement Analysis Society

(GCMAS), 10Gastrocnemius, 47, 55, 82–83, 126Gender and balance, 181, 188Genu (knee) valgus, 43Girls and sport injuries, 9Global reference frame, 109Golf

and angles of projection, 119–20and hooked shot, 206and range of motion principle, 61and segmented movement, 162swing, 105, 231–32

Golgi tendon organs, 99–100Goniometer, 121Gravitational acceleration, 114–15Gravitational potential energy, 152Gravitational torque, 186–87Gravity, 134–35

affecting acceleration, 115–17center of, 180–83

Grip strength, 27Ground reaction force, 88–89, 137,

147–48, 189Guitar strings and stress relaxation, 74Gymnastics

and center of gravity, 188and overuse injury, 148


H

Hamstringsflexibility of, 51torque of, 173

Heat, 151–52, 154Height of release, 118Helmet design, 9Hill muscle model, 51–53Hip, 217–21

abductors, 64flexion, 143–44, 179, 221–22, 238torque of, 173

Hip rotation, 63History-dependent behaviors, 90Hooke's Law, 27Horizontal adduction, 43Horizontal component in angle of pull, 143–45Horizontal displacement, 108Horsepower, 157Human movement. See MovementHydrotherapy, 195Hyperextension, 244Hypertrophy, muscular, 49, 51Hysteresis, 74–75, 154

I

Iliopsoas muscle force, 143–44Impact, 148–50Impringement syndrome, 58Improving performance, 5–8, 20Impulse, 147Impulse–momentum relationship, 33,

147–48, 164In vitro, 79–80In vivo, 80Index Medicus, 14Inertia, 33, 138–39, 164–65

angular, 174–78and force, 133–36, 179

Inertia Principle, 139–41, 164–65, 222, 227, 230Inferior direction, 42Information, 16–20Injury, 247–48

acute, 148anterior cruciate ligament (ACL), 9and eccentric muscle action, 50overuse, 9, 148prevention of, 242, 252–53

reduction/treatment of, 9–10, 41risk of, 242–44

Integration, 172Interdisciplinary approach to kinesiology, 4–5Internal force, 51Internal rotation, 43, 45, 63Internal work, 152, 154International Society for Electrophysiology and

Kinesiology (ISEK), 14International Society for the Advancement of

Kinanthropometry (ISAK), 56International Society of Biomechanics in Sports

(ISBS), 13International Society of Biomechanics (ISB), 14International Sports Engineering Association

(ISEA), 7Interventional task of qualitative analysis, 36Intervertebral disks, 180, 244Inverse dynamics, 137, 178Inward rotation, 43, 45Isokinetic, 8Isometric muscle, 26, 49–50, 56, 79–80Isotonic, 8

J

Javelin, 240–42equipment design of, 7and performance improvement, 20and range of motion principle, 61

Jointvelocity of, 119

Joint motion, 43–46, 52, 61Joint powers, 179Joint reaction forces, 137–38Joint torque, 171–72, 178–79Joule, 28, 151, 155Journals, scholarly, 16–18Jump shot in basketball, 189Jumping, 160

and center of gravity, 182and plyometrics, 91vertical, 35, 117, 128

K

Karate front kick, 51Kicking technique, 179, 215–18Kilogram as unit of measurement, 28

INDEX 313

Kinanthropometry, 56Kinematic chain, 163

closed, 163open, 163

Kinematics, 24, 87, 105, 107–32Kinesiology

definition of, 1, 3–4interdisciplinary approach to, 4–5as a profession, 4sciences of, 5

Kinetic energy, 147, 151–54Kinetic friction, 146Kinetics, 24, 105, 160

angular, 169–91laws of, 133

Kneeangle, 62direction of joint, 43extension, 123flexion, 249

Knowledge, 4, 12, 16–20. See also Biomechanicalknowledge

L

Laminar flow, 198–99Landing, 150Lateral direction, 42Law of Acceleration, 136–37Law of Conservation of Energy, 152–54Law of Inertia, 133–36, 139Law of Momentum, 136–37Law of Reaction, 137–39Leg press, 249Length tension relationship, 74, 79–80, 84–86,

98–99Levers and torque, 170Lift, 193, 200–03, 210

and angle of attack, 206as a force, 34, 94and power, 158and spinning, 203–08

Ligaments, biomechanics of, 77, 79Limb extension and slowing down, 92–93Linear displacement, 107–08Linear inertia, 139Linear kinematics, 107–32Linear kinetic energy, 151Linear kinetics, 133–67Linear motion, 107–09

Linear motion inertia, 134Linear velocity, 111, 126–27Linked segment model, 33–34, 58Load, 71–74Load deformation, 73–74Load–deformation curve, 71–73Loading response, 74–75Loads on tissue, 69Local reference frame, 141, 145Long jumping, 151

and angles of projection, 119Longitudinal axis, 41–42Low-back pain, 180

M

Machines. See Exercise machinesMagnus Effect, 203–08, 210Margaria test, 159Mass

and acceleration, 136–37and axis of rotation, 175–77definition of, 25–26and inertia, 33and momentum, 147and stability, 139–40vs. weight, 26

Maximal-effort movements, 98Maximal voluntary contraction, 97Maximum static friction, 146Mechanical advantage, 92Mechanical energy, 72, 151–55Mechanical equilibrium, 179Mechanical method of muscle action, 53–56Mechanical power, 157–60Mechanical strength, 71–72Mechanical stress, 70Mechanical variables, 25–29Mechanical work, 155–57Mechanics

basic units of, 25–29definition of, 3, 23

Medial direction, 42Medial gastrocnemius, 82–83Medicine ball, 141Mediolateral axis, 41–42, 44MEDLINE, 14Meter as unit of measurement, 28Mobility, 184–89Modeling, 59


INDEX 315

Moment arm, 169–71Moment of force, 26, 173Moment of inertia, 33, 174–78, 183, 189Momentum, 136–37, 147, 152, 241Motion, 24

changes in, 32–33forces and, 3, 161and inertia, 134of joints, 43–46linear, 107–32planes of, 41–42range of, 33range-of-principle, 60–63uniformly accelerated, 115–17

Motion segment, 180Motor action potential, 86–87Motor skills, 219–20Motor units, 94–97Movement

analysis of, 11–12animation of, 10control of, 94–98coordination of, 87–88, 128–30efficiency of, 159explosive, 159–60, 165improving, 3–4principles, 30–31, 60–63segmented, 160–64vs. training muscle, 59

Multiarticular muscles, 58Muscle

actions, 49–53, 56–60activation, 57–58agonist, 58analysis of, 53–60antagonist, 58, 174balance, 173biarticular, 58concentric action, 8–92, 49–50, 79disinhibition of, 100and eccentric force, 50, 79endurance, 83fibers, 47–49, 81–83, 95force, 47force vectors, 141–45function, 59–60groups of, 60hypertrophy, 49inhibition of, 97, 100injury, 58, 147–48mechanical characteristics, 53–60, 79–88

multiarticular, 58power, 80proprioception, 99–100regulation of force, 95–98and segmental interaction, 34strength of, 83, 97striated, 48structure of, 46–49synergy, 57tension of, 48, 51–52training vs. movement, 59

Muscle angle of pull, 141–45Muscle attachment sites, 58Muscle fibers

architecture, 46–48parallel, 47pennate, 47shortening of, 47, 79–83, 90

Muscle spindles, 90, 99–100Muscle-tendon unit (MTU), 73

passive, 75–76Muscle tension, 84–88Muscular endurance, 83Muscular strain, 71–72Muscular strength. See Muscle, strength ofMusculoskeletal system, mechanics of, 69–103Myofibrils, 48Myosin, 48, 51, 84Myotatic reflex, 90, 99–100

N

National Association for Sport and PhysicalEducation (NASPE), 14

Net force, 136Neuromuscular control, 94–100Neuromuscular training, 97Neuron, 94Newton, Isaac, 133Newton's Laws of Motion, 30, 133–39, 178, 202Normal reaction, 145–46

O

Oblique muscles, 155Observation task of qualitative analysis, 6,

35–36, 216–17Occupational biomechanics, 9–10Occupational overuse syndrome, 9, 15, 148

Occupational therapy, 9–10Olympic weight lifting, 158Open motor skills, 219Optimal Projection Principle, 34, 117–21, 229–30Orthotics, 9, 250Osteokinematics, 109Osteoporosis, 76Outward rotation, 43, 45Overarm throw, 62–63, 90, 228–28Overuse injury, 9, 148

P

Pace, 110Parallel elastic component, 52–53, 75Parallel muscle arrangement, 47Parallel squat. See SquatParallelogram of force, 142–43Pascal, 70Passive dynamics, 161Passive insufficiency, 51–52Passive muscle tension, 48, 51–53, 74–75, 84–85Patella, 248Patellofemoral pain syndrome (PFPS), 142, 248Pectoralis major, 58, 242Peer review of journals, 16–17Pennate muscle arrangement, 47Performance improvement, 5–8, 20Perimysium, 46Periosteum, 46Physical activity, benefits of, 3Physical conditioning, 162Physical education, 215–24Physical Education Digest, 18Physical Education Index, 15Physical therapy, 9, 248–52Pitching, 33, 62–63, 140, 206Planes of motion, 41–42Plastic region, 71–72Plateau region, 85–86Platform diving and center of gravity, 188–89Plyometrics, 91–92, 239Point mass, 108Position of body, 186–88Posterior cruciate ligament (PCL) injuries, 247Posterior direction, 42Potential energy, 152Power

mechanical, 157–60vs. strength, 160

Power lifting, 158Preparation task of qualitative analysis, 35Pressure, 194

atmospheric, 134–35and velocity, 202–03

Pressure drag, 197–200Principle of Inertia, 222Principle of optimal trajectory, 220Principle of Specificity, 140–41, 162Principle of Spin, 193, 208–10Projectile principles, 30–31Projectiles, 34

and gravitational acceleration, 115–17Pronation, 43–45, 250–51Proprioceptive neuromuscular facilitation

(PNF), 100Proprioceptors, 99–100Propulsion in swimming, 201Prosthetics, 9–10, 250Proximal segment, 161–62Pull, angle of, 141–45Pull-up exercise, 64Pullover exercise, 54, 242Pythagorean Theorem, 305

Q

Quadriceps, torque of, 173Qualitative analysis, 11–12, 23, 35–36, 213–24,

307Qualitative vector analysis, 141–43Quantitative analysis, 12, 36Quantitative vector analysis, 143–45Quickness, 115

R

Radian, 28, 121–23, 127Range of motion, 216–18, 221, 241–43, 249Range of Motion Principle, 33, 60–63, 94,

218–19, 223, 227, 229–30, 243Rate coding, 95, 97Rate of change, 111Rate of force development, 88–89Reaction

change, 181–82force, 137–38Law of, 137–39

Reaction board method, 181–82


Readiness, 251Reciprocal inhibition, 100Recruitment, 95, 231–32

and firing rate, 97Rectus abdominis, 47Rectus femoris, 47Reflex, 99

potentiation, 89–90Rehabilitation, 60, 247–55Relative angle, 122

height of projection, 118–21velocity, 118

Release velocity, 118–19Resistance arm, 50, 179Resting length of muscles, 71, 84Resultant, 26Reynolds numbers, 199Rhomboid muscle, 58Right-angle trigonometry, 143–45, 305Rigid-body mechanics, 23–24Rotary component, 141–42Rotation

of hip and trunk, 63and inertia, 174–78of joints, 43, 45

Running, 111biomechanics of, 7and movement efficiency, 159and overuse injury, 148and pronation, 44–45, 250–51and speed, 83

S

Sagittal plane, 41, 180Sarcomere, 47–48, 86Scalar quantity, 25Scalars, 25Scholarly societies, 13–14Science, principles of, 29Sculling hand movement, 201–02Second as unit of measurement, 28Second Law of Motion, 136–37Second Law of Thermodynamics, 153–54Segmental Interaction Principle, 34, 140, 160–64Segmented method, 181–83Semimembranosus, 47Sensors, 139Sequential Coordination, 162, 227Series elastic component, 52–53, 75

Shear, 69–70Shoes

and coefficient of friction, 146–47design, 9inserts, 250and linear inertia, 139

Shortening of muscle, 47, 79–83, 90Shoulder, rotation of, 45Simulation, 59Sine function, 143–45Sit-and-reach test, 52SI units, 28–29Size principle of motor units, 95Skating and acceleration, 136–37Skin friction drag, 196Sliding Filament Theory, 84Sliding friction, 146–47Slow-oxidative muscle fiber, 81–83Slow twitch muscle fiber, 81–83Soccer, 179

dribbling, 228–30Softball. See also Baseball

catching, 149–50throwing, 227–28oleus, 58, 82–83

Specificity principle, 124Speed, 109–12

angular, 123and displacement, 121in running, 83

Speed skate design improvement, 8Spin, 34, 203, 208–10Spine, 180, 238

hyperextension of, 244Splits, 64Sport Engineering Society, 14Sport Information Resource Center (SIRC), 14SportDiscus, 14Sports biomechanics, 13Sports medicine, 60, 247–55

and injury prevention/treatment, 9Spring and force, 27–28Sprinting, 83, 94, 114–15Squat, 128, 130, 237–39, 253

decline, 65with exercise equipment, 244–45

Stability, 184–89and mass, 139

Stability–mobility paradox, 184–90Stabilizing component, 142Static equilibrium, 179, 181, 183, 190

INDEX 317

Static flexibility, 78, 121Static friction, 145–46Static range of motion, 78Static stretching, 75Statics, 24Statistics, validity of, 19Step aerobics, 148Stiffness, 71, 73–74, 78

of spring, 27–28Strain

energy, 154–55muscular, 70–71, 75

Streamlining, 197–99Strength

and conditioning, 7, 140, 237–46mechanical, 71–72muscular, 26–27, 83, 97vs. power, 160

Strength curves, 86, 173Strength training, 129Stress, mechanical, 70Stress fracture, 76, 148Stress relaxation, 74Stress–strain curve. See Load–deformation

curveStretch reflex, 90, 100Stretch-shortening cycle (SSC), 88–92, 101Stretching

dynamic, 78and flexibility, 78and muscular hypertrophy, 49, 51static, 78and viscoelasticity, 73–74

Striated muscle, 48Summing torque, 173–74, 181Superior direction, 42Supination, 44–45Surface drag, 196–97Swimming, 199–202

and acceleration, 113–14and buoyancy, 193–95and lift, 201–02

Swing plane, 162Swing weight, 177Synergy, muscle, 57

T

Tangent, 143, 305Technology, 29

Tendinoses, 148Tendon, 46, 75

and motion, 47and muscle fibers, 91and overuse injury, 148stretching of, 73–74

Tennisand angles of projection, 119racket design improvement, 7, 177and stress relaxation, 74

Tennis elbow, 148Tension of muscle, 51–52, 69–70, 79–82,

84–88, 99Tensor, 70Tetanus, 97Textbooks, 15–16Thermodynamics, 153–54Third Law of Motion, 137–39Thixotropy, 78Throwing, 62–63, 119, 126–27, 129, 151, 227–28Tibialis posterior, 47Time and force, 32–33, 86–88, 92–94, 149–51Time and power, 157Tissue loads, 69–75Tissues and response to forces, 69–75Toe region, 73Topspin, 203–05Torque, 26, 80, 86, 169–74, 189–90

gravitational, 186–87joint, 171–72, 178–79and muscle action, 49–50, 58and spinning, 208summing, 173–74

Torque–angular velocity, 89–90Torsion, 69Training

and force–velocity relationship, 80–81

muscles vs. movements, 59neuromuscular, 97

Trajectory, 116of ball, 205–08, 220of basketball, 120–21

Transverse plane, 41Trigonometry, right-angle, 305Triple hop test, 251–52Trunk rotation, 63Turbulent flow, 198–99Twitch, 97

response of muscle fiber, 81–83, 95–97Twitch interpolation technique, 97


U

Uniformly accelerated motion, 115–17Unipennate muscle arrangement, 47Units of measurement, 25

English, 110, 297International System (SI), 28–29, 297metric, 110, 297

Unloading response, 73–74

V

Valgus, 42–43Variability, 65Varus, 42–43Vastus lateralis, 142–43Vastus medialis, 142–43Vastus medialis obliquus (VMO), 248–49Vaulting, 154Vector

analysis of, 141–45in linear motion, 107–08quantity, 25–26

Velocity, 111–13, 115, 117, 126and angles of projection, 118–19angular, 122–23and drag, 196and kinetic energy, 151–52and pressure, 202–03relationship with force, 79–83vertical, 116

Vertical component in angle of pull, 143–45Vertical displacement, 108

Vertical jumping, 35, 60–62, 88–89, 97, 128,164–65

Video, 11, 110, 231Viscoelastic, 100Viscoelasticity, 72–75Viscosity and drag, 196–97Volleyball, 34, 129, 208Vortex, 202

W

Walking. See also Gaitinverse dynamics of, 189

Warm-up, 78, 139–40Wave drag, 200Weight lifting, 94Weight training, 81Weight vs. mass, 26Wheel and inertia, 177Wolff's Law, 76Women and sport injuries, 9Work, mechanical, 155–57Work–Energy Relationship, 151–60Work-related musculoskeletal disorders,

15, 148Worldwide web, 18

links, 22

Y

Yield point, 71–72Young's modulus, 71

INDEX 319

This section of the book provides appliedlaboratory activities. These labs are de-signed to illustrate key points from thechapters of the text. The labs are also de-signed to be flexible enough to be used asfull labs for universities with 4-credit cours-es or as short activities/demonstrations for3-unit courses. The emphasis is on usingactual human movements and minimalresearch equipment. While quantitativemeasurements and calculations are part ofsome labs, most of them focus on students'conceptual understanding of biomechanicsand their ability to qualitatively analyzehuman movement. Most labs are structured

for work in small groups of three to fivestudents.

Citations of background informationare provided for students to prepare for thelabs. Space does not allow for all relevantresearch citations to be included on eachtwo-page lab. If instructors assign back-ground reading prior to labs, they shouldassign specific sections of the resourcessuggested. I am indebted to many of mypeers who have shared their teaching ideasat professional meetings, especially thosewho have attended and contributed to thelast few national conferences on teachingbiomechanics.

Lab Activities

L-1

LAB ACTIVITY 1

FINDING BIOMECHANICAL SOURCES

Biomechanics is the study of the causes of biological movement. Biomechanics is a core sub-discipline of kinesiology, the academic study of human movement. All kinesiology profes-sions use biomechanical knowledge to inform their practice. Both scholarly and profession-al journals publish biomechanical research. There are many people interested in biomechan-ics, so biomechanical literature is spread out across many traditional scholarly areas. Thislab will help you appreciate the breadth of biomechanics in your chosen career, and provideyou with experience in finding biomechanical sources.

BACKGROUND READING

Chapter 1 herein: “Introduction to Biomechanics of Human Movement”Ciccone, C. D. (2002). Evidence in practice. Physical Therapy, 82, 84–88.Minozzi, S., Pistotti, V., & Forni, M. (2000). Searching for rehabilitation articles on Medline

and Embase: An example with cross-over design. Archives of Physical Medicine andRehabilitation, 81, 720–722.

TASKS

1. Identify one professional area of interest.

2. Review one year of a journal from this area of interest for biomechanical articles.

3. Identify a potential biomechanical topic of interest from your professional interests.

4. Search a computer database (Medline or SportDiscus) for biomechanical papers on yourtopic.

5. Answer the questions.

L-2 FUNDAMENTALS OF BIOMECHANICS

Copyright © 2007 Springer Science+Business Media, LLC.All rights reserved.

LAB ACTIVITY 1 NAME _____________________________

FINDING BIOMECHANICAL SOURCES

1. What is your professional area of interest, and give a human movement topic you have abiomechanical interest in?

2. Report the name of the journal, number of articles published in a particular year, and thepercentage of articles related to biomechanics.

3. Summarize the results of two searches on a literature database like Medline orSportDiscus. Be sure to specify the exact search you used, and the number and quality ofcitations you obtained.

4. Based on all your searches, list the two citations you believe to be most relevant to yourprofessional interests.

5. Comment on the diversity of sources you observed in your search.

6. Rate the quality of the sources you found based on the hierarchy of evidence presentedin chapter.

LAB ACTIVITIES L-3


LAB ACTIVITY 2

QUALITATIVE AND QUANTITATIVE ANALYSIS OF

RANGE OF MOTION

This text summarizes many biomechanical variables and concepts into nine principles of biomechan-ics. The analysis of human movements using these biomechanical principles can be qualitative (sub-jective) or quantitative (based on numerical measurements). All kinesiology professions have usedboth qualitative and quantitative analyses of human movement, but qualitative analysis is used mostoften. This lab will explore the Range-of-Motion Principle of biomechanics, using a variety of staticflexibility tests common in physical education and physical therapy. This lab will show you there area variety of ways to quantify range of motion and that there are strengths and weaknesses of bothqualitative and quantitative analyses of human movement.

Physical therapists used to perform a standing toe touch to screen for persons with limited ham-string flexibility. Patients either passed the test by being able to touch their toes with their fingerswhile keeping their legs straight, or they failed to touch their toes, indicating poor hamstring flexibil-ity. Flexible hamstrings allows a person to tilt their pelvis forward more, making it easier to touchtheir toes. Recently, more accurate field tests of static flexibility have been developed. The tests thatwill be used are the sit-and-reach test (SRT), active knee extension (AKE), and the modified Schobertest (MST). The results of these flexibility tests can be analyzed qualitatively (judging if the subject hasadequate flexibility) or quantitatively. Quantitative analysis can either be norm-referenced (compar-ing scores to all other people) or criterion-referenced. Criterion-referenced testing compares testscores to some standard of what should be. Criteria or standards are usually based on evidence onwhat correlates with health (health-related fitness) or with physical abilities to perform jobs safely (oc-cupational screening). For example, physical therapists studying the sit-and-reach test suggested thatsubjective observation of the forward tilt of the rear of the pelvis is as effective an assessment of ham-string flexibility as the SRT score (Cornbleet & Woolsey, 1996).

BACKGROUND READING

Chapter 2 herein: “Fundamentals of Biomechanics and Qualitative Analysis”Cornbleet, S. & Woolsey, N. (1996). Assessment of hamstring muscle length in school-aged children

using the sit-and-reach test and the inclinometer measure of hip joint angle. Physical Therapy, 76,850–855.

Gajdosik, R. & Lusin, G. (1983). Hamstring muscle tightness: Reliability of an active–knee-extensiontest. Physical Therapy, 63, 1085-1088.

Gleim, G. W., & McHugh, M. P. (1997). Flexibility and its effects on sports injury and performance.Sports Medicine, 24, 289–299.

Knudson, D., Magnusson, P., & McHugh, M. (2000, June). Current issues in flexibility fitness. ThePresident's Council on Physical Fitness and Sports Research Digest, pp. 1-8.

TASKS

1. Select three volunteers for flexibility testing2. Learn how to use a sit-and-reach box, inclinometer, goniometer, and tape measure for SRT, AKE,

and MST.3. Collect the following quantitative assessments of lumbar and hamstring range of motion for one

side of the body: SRT, AKE, and MST. While these measurements are being taken, have people inyour lab group do a qualitative/categorical assessment (hypoflexible, normal, hyperflexible) of thesubject being tested.





QUALITATIVE AND QUANTITATIVE ANALYSIS OF

RANGE OF MOTION

Ratings of Hamstring Flexibility

Qualitative SRT AKESubject 1 _________ _________ _________Subject 2 _________ _________ _________Subject 3 _________ _________ _________

Ratings of Lumbar Flexibility

Qualitative SchoberSubject 1 _________ _________Subject 2 _________ _________Subject 3 _________ _________

1. Given that the healthy standard for adult (>17 years) males and females in the SRT are 17.5 and 20cm, respectively, and a passing AKE is �K = 160°, how well did your qualitative and quantitativeratings of hamstring flexibility agree?

2. Given that the passing score for the MST is 7 cm, how well did your qualitative and quantitativeratings of lumbar flexibility agree?

3. List the characteristics of the range of motion you evaluated in your qualitative ratings of hamstringflexibility.

4. Range of motion is a kinematic (descriptive) variable and does not provide kinetic (muscletendonresistance) information about the passive tension in stretching. Static flexibility measurements likethese have been criticized for their subjectivity related to a person's tolerance for stretch discomfort(Gleim & McHugh, 1997). Are there kinetic aspects of stretching performance that can be qualita-tively judged by your observations of these flexibility tests?

5. Compare and contrast the strengths and weaknesses of a qualitative versus quantitative assessmentof static flexibility.

LAB ACTIVITIES L-5


LAB ACTIVITY 3

FUNCTIONAL ANATOMY?

Anatomy is the study of the structure of the human body. The joint motions created by muscles in humans havebeen studied by anatomists several ways: cadaver dissection, and manipulation, observation, and palpation.Historically, anatomical analyses in kinesiology used the mechanical method of muscle action analysis to establishthe agonists for specific movements. This requires a detailed knowledge of the planes of movement, joint axes, at-tachments, courses of the muscles, and the classification of joints. Anatomy provides only part of the prerequisiteinformation necessary to determine how muscles create movement. A century of EMG research has clearly shownthe inadequacy of functional anatomy to explain how muscles act to create human movement (Hellebrandt, 1963).Chapter 3 summarized several areas of research that show the integration of biomechanical research electromyo-graphy (EMG, kinetics, simulation) is necessary to understand the actions of muscles in human movement. Thislab will review the mechanical method of muscle action analysis in functional anatomy and show why biomechan-ical analysis is needed to determine the actions of muscles.

BACKGROUND READING

Chapter 3 herein: “Anatomical Description and Its Limitations”

Hellebrandt, F. A. (1963). Living anatomy. Quest, 1, 43–58.

Herbert, R., Moore, S., Moseley, A., Schurr, K., & Wales, A. (1993). Making inferences about muscles forces fromclinical observations. Australian Journal of Physiotherapy, 39, 195–202.

Maas, H., Baan, G. C., & Huijing, P. A. (2004). Muscle force is determined by muscle relative position: isolated ef-fects. Journal of Biomechanics, 37, 99-110.

TASKS

1. For the anatomical plane and joint(s) specified, use functional anatomy to hypothesize a muscle involved andthe muscle action responsible for the following demos and record them on the lab report.

Demo 1 — Sagittal plane elbow joint arm curl

Demo 2 — Sagittal plane lumbar vertebrae trunk flexion

Demo 3 — Sagittal plane metacarpophalangeal passive wrist flexion

Demo 4 — Frontal plane hip joint left hip adduction2. Perform the demos:

Demo 1: Lie supine with a small dumbbell in your right hand and slowly perform arm curls.Have your lab partner palpate your upper arm, being sure to note differences in muscle acti-vation in the first 80 and last 80° of the range of motion. Analyze only the lifting phase.

Demo 2: Lie supine with your hips flexed to 90° and your quadriceps relaxed. Cross yourarms over your chest and tighten your abdominal muscles. Make a note of which end of yourbody is elevated. See if you can make either or both sides of your body rise.

Demo 3: In the anatomical position, pronate your right forearm and flex your elbow complete-ly. Totally relax your right hand and wrist. In this position (hand roughly horizontal), use yourleft hand to extend your relaxed right wrist and let gravity passively flex the wrist. Note themotion of the fingers during wrist extension and flexion.

Demo 4: From the anatomical position, stand on your left foot (flexing the right knee) andabduct your shoulders so that your arms are horizontal. Smoothly lower and raise your righthip (left hip adduction and then abduction) as many times as you can in one minute. Note themuscles that feel fatigued.





FUNCTIONAL ANATOMY?

For the anatomical plane and joint(s) specified, use functional anatomy to hypothesize a muscle andthe muscle action responsible for the following activities:

Plane Joint Movement Muscle Action

Demo 1 — Sagittal elbow joint arm curl ________ _______

Demo 2 — Sagittal lumbar vertebrae trunk flexion ________ _______

Demo 3 — Sagittal metacarpophalangeal wrist flexion ________ _______

Demo 4 — Frontal hip joint hip adduction ________ _______

1. Functional anatomy does not consider the action of other forces (other muscles or external forces)in hypothesizing muscle actions. Describe the muscle actions throughout the range of motion in thehorizontal plane arm curl, and note why an external force changes the muscle activation strategy.

2. Classifying muscle attachments as an “origin” or “insertion” is not always clear. What muscle(s) areactive in the abdominal exercise, and what attachments are being pulled?

3. What muscle(s) created metacarpophalangeal extension when the wrist was passively flexed inDemo 3? What muscle(s) created metacarpophalangeal flexion when the wrist was passively ex-tended? How does the muscle create this motion without activation?

4. Was there discomfort in the left hip adductors in Demo 4? What muscle and action was responsiblefor controlling left hip adduction?

5. Give a movement example (be specific) where functional anatomy may be incorrect because of:

External forces

Muscle synergy

Passive tension

Attachment stability changes

LAB ACTIVITIES L-7


LAB ACTIVITY 4

MUSCLE ACTIONS AND THE STRETCH-SHORTENING

CYCLE (SSC)

The forces muscles exert to create movement vary dramatically in terms of length, velocity ofshortening or lengthening, and timing of activation. The classic in vitro muscle mechanicalcharacteristics interact with other factors (activation, leverage, connective tissue stiffness,etc.) to determine the amount of torque a muscle group can create. The torque a muscle groupcreates naturally affects muscular strength, endurance, and other performance variables. Thepurpose of this lab is to demonstrate the performance consequence of muscle actions and thestretch-shortening cycle (SSC). The endurance of the elbow flexors will be examined in con-centric and eccentric actions to review the Force–Velocity Relationship. Two kinds of verticaljumps will be examined to determine the functional consequences of the SSC.

BACKGROUND READING

Chapter 4 herein: “Mechanics of the Musculoskeletal System”Komi, P. V. (Ed.) (1992). Strength and power in sport. New York: Blackwell Science.Kubo, K., Kawakami, Y., & Fukunaga, T. (1999). Influence of elastic properties of tendon

structures on jump performance in humans. Journal of Applied Physiology, 87, 2090–2096.Lieber, R., L., & Bodine-Fowler, S. (1993) Skeletal muscle mechanics: Implications for reha-

bilitation. Physical Therapy, 73, 844–856.

TASKS

1. Select five volunteers for elbow flexor endurance testing. For each subject select a dumb-bell with submaximal resistance (between 50 and 80% 1RM). Record the number or con-centric-only repetitions (partners lower the dumbbell) for the person's stronger limb andthe number or eccentric-only (partners lift the dumbbell) for their weaker limb. Attemptto keep a similar cadence for each test.

2. Perform and measure the maximum height for the countermovement jump (CMJ) and anequivalent static jump (SJ) for everyone in the lab. The SJ begins using isometric muscleactions to hold a squat position that matches the lowest point of the CMJ for that person.Observe jumps carefully since it is difficult to match starting positions, and it is difficult(unnatural) for subjects to begin the concentric phase of the SJ with virtually no counter-movement.

3. Perform the calculations and answer the questions.




MUSCLE ACTIONS AND THE STRETCH-SHORTENING

CYCLE (SSC)

Maximal Repetitions with a Submaximal ResistanceConcentric—Stronger Side Eccentric—Weaker Side

Subject 1 _________ _________Subject 2 _________ _________Subject 3 _________ _________Subject 4 _________ _________Subject 5 _________ _________

Pre-Stretch Augmentation in SSCCMJ _________ SJ _________

PA (%) = ((CMJ – SJ)/SJ) • 100 (Kubo et al., 1999)

My PA _________ Class Mean PA _________

QUESTIONS

1. Did the stronger side of the body have the most endurance? Explain the results of thiscomparison of concentric and eccentric muscles actions based on the Force–Velocity Rela-tionship of muscle.

2. Hypothesize the likely lower extremity muscle actions in the SJ and the CMJ.

3. How much improvement in vertical jump could be attributed to using a SSC?

4. What aspects of coaching jumps and other explosive movements must be emphasized tomaximize performance? Explain why your technique points may improve performancebased on muscle mechanics or principles of biomechanics.

LAB ACTIVITIES L-9


LAB ACTIVITY 5A

VELOCITY IN SPRINTING

Linear kinematics in biomechanics is used to create precise descriptions of human motion. It is importantfor teachers and coaches to be familiar with many kinematic variables (like speeds, pace, or times) that arerepresentative of various levels of performance. Most importantly, professionals need to understand that ve-locity varies over time, as well as have an intuitive understanding of where peak velocities and accelera-tions occur in movement. This lab will focus on your own sprinting data in a 40-meter dash and a world-class 100-meter sprint performance to examine the relationship between displacement, velocity, and accel-eration. These activities provide the simplest examples of linear kinematics since the body is modeled as apoint mass and motion of the body is measured in one direction that does not change.

BACKGROUND READING

Chapter 5 herein: “Linear and Angular Kinematics”Haneda, Y., et al. (2003). Changes in running velocity and kinetics of the lower limb joints in the 100m sprint

running. Japanese Journal of Biomechanics in Sports and Exercise, 7, 193-205.Mero, A., Komi, P. V., & Gregor, R. J. (1992). Biomechanics of sprint running: A review. Sports Medicine, 13,

376–392.Murase, Y., et al. (1976). Analysis of the changes in progressive speed during the 100-meter dash. In P.V.

Komi (Ed.), Biomechanics V-B (pp 200–207). Baltimore: University Park Press.

TASKS

1. Estimate how fast you can run in mph _____2. Following a warm-up, perform a maximal 40-meter sprint. Obtain times with four stopwatches for times

at the 10-, 20-, 30-, and 40-meter marks.3. Perform the calculations and answer the questions.

Kinesiology Major Normative DataTime (s)

Females Males10 20 30 40 10 20 30 40

Mean 2.3 3.9 5.4 7.0 2.0 3.3 4.6 5.9sd 0.2 0.4 0.5 0.7 0.2 0.2 0.3 0.5

Maurice Greene: 1999 World Championships Seville, Spain

Meters Seconds

0–10 1.8610–20 1.0320–30 0.9230–40 0.8840–50 0.8650–60 0.8460–70 0.8570–80 0.8580–90 0.8590–100 0.86

9.67



LAB ACTIVITY 5A NAME _____________________________

VELOCITY IN SPRINTING

Record your times in the spaces below.

10 m 20 m 30 m 40 m

t1 = _____ t2 = _____ t3 = _____ t4 = _____

QUESTIONS

1. Calculate the average horizontal velocity in each of the 10-m intervals of your 40-m sprint (V =�d/�t). Report your answers in m/s and mph (m/s • 2.237 = mph).

2. Calculate the average velocities for the intervals of Maurice Greene's 100-m sprint. Note that thetimes in the table represent the change in time (time to run the interval: �t), not the cumulativetime, as in your 40-m sprint data. Average velocities are usually assigned to the midpoints of theinterval used for the calculation.

Velocity (m/s) at the

5____ 15____ 25____ 35____ 45____ 55____ 65____ 75____ 85____ 95____

meter points.

3. Plot Greene's and your velocities on the following velocity-displacement graph:

LAB ACTIVITIES L-11


4. Give a qualitative description of the general slopes of the Greene velocity graph in question 3 (thegeneral pattern would be same if this were a true velocity–time graph) that determine the acceler-ation phases of maximal sprinting. Where is acceleration the largest and why?

LAB ACTIVITY 5B

ACCURACY OF THROWING SPEED MEASUREMENTS

Linear kinematics in biomechanics are used to create precise descriptions of human motion. It is im-portant for teachers and coaches to be familiar with many kinematic variables (like speeds, pace, ortimes) and the accuracy and consistency of these measurements. The accuracy of a speed calculatedfrom the formula s = l/t strongly depends on the time interval used and errors in measurement. Thespeed calculated is also an average over the time interval used for the calculation. The reliability of ameasurement of speed decreases with greater variation from measurement errors and subject per-formance. This lab will allow you to explore accuracy and consistency issues in the measurement ofball speed in softball throwing.

BACKGROUND READING

Chapter 5 herein: “Linear and Angular Kinematics”Atwater, A. E. (1979). Biomechanics of overarm throwing movements and of throwing injuries.

Exercise and Sport Sciences Reviews, 7, 75–80.Brody, H. (1991, March/April). How to more effectively use radar guns. TennisPro, 4–5.

TASKS

1. Estimate how fast you can throw a softball: _______

2. Following a warm-up, perform maximal and 75% effort throws to a partner or chain link fence 20m away. Measure and record the speed of the throws two ways: with a radar gun and by flight timesaveraged from four stopwatches. Be sure to note the variation in times measured by stopwatch op-erators, and record all time and radar data for all throws for everyone in the lab. Average speed ofthe throw will assume the distance of ball flight was 20 m.

3. Perform the calculations to calculate the average speed of your throws and answer the questions.

Kinesiology Major Normative Data for Maximum Effort Throws

Females MalesSpeed (mph) Speed (mph)

Mean 43.3 64.0sd 8.6 8.7



LAB ACTIVITY 5B NAME _____________________________

ACCURACY OF THROWING SPEED MEASUREMENTS

Record your times in the spaces below.

Maximal Throw 75% Effort Throw

Speed = _____ t = _____ Speed = _____ t = _____

1. Calculate the average speed of your maximal and 75% effort throw (s = Δl/Δt) from the stopwatchdata. Report your answers in m/s and mph (m/s ∗ 2.237 = mph). What factors would account fordifferences you observed between the radar and stopwatch measurements of ball speed?

2. Comment on the typical differences in stopwatch times for the four timers for maximal throws and75% effort throws. About how accurate are stopwatches for estimating softball throwing speed?

3. Comment on how consistent were the radar measurements of your maximal and 75% effort throws.Given that reliability, how much of a difference would you consider meaningful?

4. Coaches sometimes ask athletes to perform warm-ups, drills, or practice at submaximal speeds.How effective were you and the persons in your lab at throwing at 75% of maximal speed?

LAB ACTIVITIES L-13


LAB ACTIVITY 6A

TOP GUN KINETICS: FORCE–MOTION PRINCIPLE

Newton's laws of motion explain how forces create motion in objects. The application principle relat-ed to Newton's second law is the Force–Motion Principle. The purpose of this lab is improve your un-derstanding of Newton's laws of motion. As a candidate for the prestigious “Top Gun” kinetic scoot-er pilot in biomechanics class, you must not only perform the missions but use kinetics to explain yourscooter's flight. Biomechanics Top Gun is like a Naval Top Gun in that skill and knowledge are re-quired to earn the honor. It is important that you follow the instructions for each mission explicitly.Care should be taken by pilots and their ground crew to perform the task correctly and safely. Notethat your multimillion-dollar scooters provide low (not quite zero) friction conditions, so you need tomove/push briskly so you can ignore the initial effects of friction. Kinetics explains all motion: fromscooters, braces, rackets, jump shots, to muscle actions. Think about the forces, what directions theyact, and the motion observed in each mission. This lab is roughly based on a lab developed by LarryAbraham (Abraham, 1991).

BACKGROUND READING

Chapter 6 herein: “Linear Kinetics”

Abraham, L. D. (1991). Lab manual for KIN 326: Biomechanical analysis of movement. Austin, TX.

TASKS

1. Using your multimillion-dollar scooters, ropes, and spring/bathroom scales, perform the followingtraining missions:

— Sit on the scooter and maximally push off from a wall (afterburner check). Experiment with vari-ous body positions and techniques.

— Sit on your scooter and push off from a partner on another scooter.

— Loop a rope over a bathroom scale held by a partner on a scooter. Sit on your scooter and pull yourpartner, who passively holds the scale, and note the largest force exerted.

— Repeat the last mission, but have your partner also vigorously pull on the scale.




LAB ACTIVITY 6A NAME _________________________

TOP GUN KINETICS: FORCE–MOTION PRINCIPLE

1. How far were you able to glide by pushing off from the wall? What is the relationship between thedirection of your push and the direction of motion?

2. How far were you able to glide by pushing off from another scooter pilot? Explain any differencesfrom task 1 using Newton's Laws of Motion.

3. How much force was applied to pull a passive partner? Which scooter pilot moved the most andwhy?

4. How much force was applied when both partners vigorously pulled on the rope? Explain any dif-ferences in the observed motion from task 3 using Newton's Laws.

5. Assume the mass of your scooter cannot be modified, but you are charged with recommendingtechnique that maximizes scooter speed and agility. Use the Force–Motion Principle to suggest whya certain body position and propulsion technique is best.

LAB ACTIVITIES L-15


LAB ACTIVITY 6B

IMPULSE–MOMENTUM: FORCE–TIME PRINCIPLE

The timing of force application to objects affects the stress and motion created. Newton's second lawapplied to forces acting over time is the impulse–momentum relationship. The change in momentumof an object is equal to the impulse of the resultant force. This activity will allow you to experiencesome interesting real-life examples of the impulse–momentum relationship. The purpose of this lab isto improve your understanding of changing the motion of an object (specifically, it's momentum) byapplying force over a period of time. In some ways body tissues are similar to water balloons in thattoo much force can create stresses and strains that lead to injury. It is important for teachers/coachesto understand how movement technique affects the impulse and peak force that can be applied to anobject. This lab is modified from a lab proposed by McGinnis and Abendroth-Smith (1991).

BACKGROUND READING

Chapter 6 herein: “Linear Kinetics”

McGinnis, P., & Abendroth-Smith, J. (1991). Impulse, momentum, and water balloons. In J. Wilkerson,E. Kreighbaum, & C. Tant, (Eds.), Teaching kinesiology and biomechanics in sports (pp. 135–138).Ames: Iowa State University.

Knudson, D. (2001c). Accuracy of predicted peak forces during the power drop exercise. In J. R.Blackwell (Ed.) Proceedings of oral sessions: XIX international symposium on biomechanics in sports(pp. 135–138). San Francisco: University of San Francisco.

TASKS

1. Estimate how far you can throw a softball-sized water balloon. _____

2. Estimate the maximum distance you could catch a similar water balloon. ____

3. Fill several water balloons to approximately softball size (�7–10 cm in diameter).

4. Measure the maximal distance you can throw the water balloon. _____

5. Measure the maximal distance you and a partner can throw and catch a water balloon. _____





IMPULSE–MOMENTUM: FORCE–TIME PRINCIPLE

Distance of Throw _____ Distance of Toss & Catch _____

1. What technique factors were important in the best water balloon throws?

2. What technique factors were most important in successfully catching a water balloon?

3. Theoretically, if you could throw a water balloon 25 m, could you catch it? Why?

4. How are the mechanical behaviors of water balloons similar to muscles and tendons?

5. Below is a graph of the vertical force (N) measured when a medicine ball was dropped from thesame height and bounced (●) or was caught and thrown back up in a power drop exercise (◆). Usethe Force–Time Principle to explain the differences in the forces applied to the medicine ball. Datafrom Knudson (2001c).

LAB ACTIVITIES L-17


LAB ACTIVITY 7A

ANGULAR KINETICS OF EXERCISE

The positions of body segments relative to gravity determine the gravitational torques that must bebalanced by the muscles of the body. The purpose of this lab is to improve your understanding oftorque, summation of torques, lifting, and center of gravity. These biomechanical parameters are ex-tremely powerful in explaining the causes of human movement because of the angular motions ofjoints. Several classic lifting and exercise body positions are analyzed because the slow motion (verysmall or zero acceleration) in these movements comprise a quasi-static condition. In static conditions,Newton's second law can be simplified to static equilibrium: �F = 0 and �T = 0. Remember that atorque (T) or moment of force is the product of the force and the perpendicular distance between theline of action of the force and the axis of rotation (T = F• d⊥).

BACKGROUND READING

Chapter 7: “Angular Kinetics”

Chaffin, B. D., Andersson, G. B. J., & Martin, B. J. (1999). Occupational biomechanics (3rd ed.). New York:Wiley.

Hay, J. G., Andrews, J. G., Vaughan, C. L., & Ueya, K. (1983). Load, speed and equipment effects instrength-training exercises. In H. Matsui & K. Kobayashi (Eds.), Biomechanics III-B (pp. 939–950).Champaign, IL: Human Kinetics.

van Dieen, J. H., Hoozemans, M. J. M., & Toussaint, H. M. (1999). Stoop or squat: A review of biome-chanical studies on lifting technique. Clinical Biomechanics, 14, 685–696.

TASKS

1. If an athlete doubled his/her trunk lean in a squat exercise, how much more resistance would theirback feel? Estimate the extra load on the lower back if a person performed a squat with a 40° trunklean compared to a 20° trunk lean. _______ %

2. Obtain height, weight, and trunk length (greater trochanter to shoulder joint) data for a person inthe lab.

3. The amount of trunk lean primarily determines the stress placed on the back and hip extensors(Hay et al., 1983). Perform two short endurance tests to see how trunk lean affects muscle fatigue.Use a standard bodyweight squat technique. Hold the squats with hands on hips in an isometricposition for 30 seconds and subjectively determine which muscle groups were stressed the most.Test 1 is a squat with a nearly vertical trunk and a knee angle of approximately 120°. Test 2 is a squatwith a trunk lean of about 45° and a knee angle of approximately 120°. Wait at least 5 minutes be-tween tests.

4. Perform calculations on the following simple free-body diagrams of exercise and body positions toexamine how gravitational torques vary across body configurations and answer the questions.



LAB ACTIVITY 7A NAME _____________________________


1. Where were the sites of most fatigue in the two squat tests? What muscle group feels more fatiguein a nearly vertical trunk orientation? Why?

2. Kinematic measurements from film/video and anthropometric data are often combined to make an-gular kinetic calculations. A static analysis can be done when the inertial forces and torques (dynam-ic loading from high-speed movement) are small. Assume the figure below is an image of you cap-tured from video while performing bodyweight squats. Calculate a gravitational torque of your up-per body about the hip (M/L) axis. Assume your head, arms, and trunk (HAT) have mass equal to0.679 of body mass. The center of gravity of your HAT acts at 62.6% up from the hip to the shoulder.

LAB ACTIVITIES L-19


3. Calculate the gravitational torque about the hip if the bottom of your squat exercise has a trunklean of 40°. (Show free-body diagram and work.)

4. If the weight of the head, arms, and trunk do not change during the squat exercise, what doeschange that increases gravitational torque as the person leans forward?

5. How different is the load on the back/hip extensors when you double your trunk lean? Is the sizeof this difference what you expected? Why is it different?

LAB ACTIVITY 7B

CALCULATING CENTER OF GRAVITY USING ANGULAR KINETICS

The purpose of this lab is to improve your understanding of torque, summation of torques,and center of gravity. Torque is a useful kinetic variable explaining the causes of humanmovement because of the angular motions of joints. Locating the center of gravity of an ob-ject and tracking its motion is useful in understanding how the force of gravity affectsmovement and balance. The reaction board method will be used with the angular analogand static form of Newton’s second law (ΣT = 0). Remember that torque (T) or moment offorce is the product of the force and the perpendicular distance between the line of actionof the force and the axis of rotation (T = F • d⊥).

BACKGROUND READING

Chapter 7: “Angular Kinetics”Gard, S. A., Miff, S. C, & Kuo, A. D. (2004). Comparison of kinematic and kinetics methods

for computing the vertical motion of the body center of mass during walking. HumanMovement Science, 22, 597–610.

TASKS

1. Estimate the height of your center of gravity as a percentage of your height: _____.

2. Record your height and weight. Measure the length of the reaction board from one sup-porting edge to the other.

3. Measure the reaction force lying on the reaction board in your normal standing position,and in another sport/activity relevant position of interest to you. Think about where youshould you put your feet to make the calculation easier to express relative to your body.

4. Perform calculations to calculate the location of your center of gravity and answer thequestions.





Record your data in the space below:

Height ____ Weight _____ Reaction standing ____ Reaction other _____

1. Draw a free body diagram of you on the reaction board and calculate the location ofyour center of gravity.

2. Calculate the height of your center of gravity as a percentage of your height and dis-cuss any differences from normative data for your gender.

3. Calculate the location of your center of gravity in the other body position (show freebody diagram and work).

4. Explain the difference in the center of gravity location between the two body posturesyou studied, and how it might affect stability and mobility.

LAB ACTIVITIES L-21


LAB ACTIVITY 8

MAGNUS EFFECT IN BASEBALL PITCHING

Fluid forces have dramatic effects in many human movements. Fluid dynamics is of vital interest to coaches ofswimming, cycling, running, and sports where wind or ball velocities are great. The fluid forces of lift and drag in-crease with the square of velocity. The purpose of this lab is to improve your understanding of how fluid forces(specifically lift) can be used to affect a thrown balls trajectory. The example is in baseball pitching, although theSpin Principle applies to other ball sports. Pitching technique and the Magnus Effect are explored in the “rise” ofa fastball, the “break” of a slider, and the “drop” of a curveball. Skilled performance in many sports involves ap-propriate application of rotation to a ball to create fluid forces for an advantageous trajectory.

BACKGROUND READING

Chapter 8 herein: “Fluid Mechanics”Allman, W. F. (1984). Pitching rainbows: The untold physics of the curve ball. In E. W. Schrier & W. F. Allman

(Eds.), Newton at the bat: The science in sports (pp. 3–14). New York: Charles Scribner & Sons.Knudson, D. (1997). The Magnus Effect in baseball pitching. In J. Wilkerson, K. Ludwig, & M. Butcher (Eds.),

Proceedings of the 4th national symposium on teaching biomechanics (pp. 121–125). Denton: Texas Woman'sUniversity Press.

TASKS

1. Set up a mock baseball pitching situation indoors with a pitching rubber and home plate about 7 m apart. Warmup the shoulder and arm muscles and gradually increase throwing intensity with whiffle balls. Exchange thewhiffle ball for a styrofoam ball.

2. Hitters often perceive that a well-thrown fastball “rises” (seems to jump over their bat). The fastball is usuallythrown with the index and middle fingers spread and laid across the seams of a ball, with the thumb providingopposition from the front of the ball. At release, the normal wrist flexion and radioulnar pronation of the throw-ing motion create downward and forward finger pressure on the ball. These finger forces create backspin on theball. Try to increase the rate of backspin to determine if the ball will rise or just drop less than a similar pitch.Be careful to control the initial direction of the pitches by using visual references in the background. Estimatethe rise or drop of the pitch relative to the initial trajectory at release.

3. A pitch that is easy to learn after the basic fastball is a slider. A slider creates a lateral “break” that can be towardor away from a batter, depending on the handedness of the pitcher and batter. The grip for a slider (right-hand-ed pitcher) has the index and middle finger together and shifted to the right side of the ball (rear view). Thethumb provides opposition from the left side of the ball. Normal wrist flexion and pronation at release now cre-ate a final push to the right side of the ball, imparting a sidespin rotation. A typical right-handed pitcher (facinga right-handed hitter) would usually direct this pitch initially toward the center to the outside corner of homeplate, so the ball would break out of reach.

4. A pitch that can make a batter look foolish is the curveball. The common perception of hitters watching a well-thrown curveball is that the ball seems to “drop off the table.” The ball looks like it is rolling along a horizontaltable toward you and suddenly drops off the edge. The grip for a curveball is similar to a fastball grip, but witha different orientation of the seams. At release the index and middle fingers are on top of the ball, making a fi-nal push forward and downward. Common teaching cues are to pull down at release like pulling down a shadeor snapping your fingers. Research has shown that radioulnar pronation is delayed in the curveball, so that atrelease the forearm is still in a slightly supinated position. Curveballs are thrown with forearm pronation justlike other pitches; it is just delayed to near the moment of release.

5. If time is available, students can do some “show and tell” with other pitch variations. These include variationsin release (sidearm, windmill softball pitch, grips, screwball, knuckleball, etc.).





MAGNUS EFFECT IN BASEBALL PITCHING

1. Were you able to make a styrofoam fastball rise? Draw a free-body diagram of your fast-ball, showing all relevant forces and explain how it relates to the vertical motion of theball you observed.

2. Could you make a styrofoam slider break sideways? If so, how much?

3. Draw a rear view of the ball from the pitcher's (your) perspective and draw on the ballthe axis of ball rotation and Magnus force for your slider.

4. Draw a rear view of the ball from the pitcher's (your) perspective and draw on the ballthe axis of ball rotation and Magnus force for your curveball. In what direction(s) didyour curveball break?

5. Did your curveball have more lateral or downward break? Why?

6. To get a ball to curve or break to the right with the Spin Principle, describe how force isapplied to the ball? Would this be the same for curves to the right in other impact and re-lease sports?

LAB ACTIVITIES L-23


LAB ACTIVITY 9

QUALITATIVE ANALYSIS OF LEAD-UP ACTIVITIES

An effective teaching strategy for many sports skills is to provide a sequence of lead-up ac-tivities that are similar to and build up to the skill of interest. How biomechanically similarthe lead-up activities are to the sport skill of interest is important to physical educators. Aqualitative answer to the similarity question will be explored in a sport skill selected by theinstructor. The present lab will allow you to practice qualitative analysis of human move-ments using the biomechanical principles.

BACKGROUND READING

Chapter 9 herein: “Applying Biomechanics in Physical Education”

Knudson, D. V., & Morrison, C. S. (2002). Qualitative analysis of human movement (2nd ed.).Champaign, IL: Human Kinetics.

TASKS

1. For the sport skill identified by the instructor, identify two lead-up skills, activities, ordrills.

2. Select a volunteer to perform these movements.

3. Videotape several repetitions of the movements from several angles.

4. Observe and evaluate the performance of the biomechanical principles in each movementusing videotape replay.





QUALITATIVE ANALYSIS OF LEAD-UP ACTIVITIES

1. What biomechanical principles are most relevant to the sport skill of interest?

2. What was the first lead-up movement? What biomechanical principles are related to per-formance of this lead-up movement?

3. What was the second lead-up movement? What biomechanical principles are related toperformance of this lead-up movement?

4. For the volunteer in your lab, what lead-up movement was most sport-specific? Whatbiomechanical principles were most similar to the sport skill?

LAB ACTIVITIES L-25


LAB ACTIVITY 10

COMPARISON OF SKILLED AND NOVICE PERFORMANCE

Coaching strives to maximize the performance of an athlete or team in competition. A keyingredient of athletic success is motor skill. Most aspects of skill are related to the biome-chanical principles of human movement. A good way to practice the qualitative analysis ofsport skills is to compare the application of biomechanical principles of a novice and thoseof a skilled performer. The purpose of this lab is to compare the application of biomechan-ical principles in a skilled performer and a novice performer in a common sport skill.

BACKGROUND READING

Chapter 10 herein: “Applying Biomechanics in Coaching”

Hay, J. G. (1993). The biomechanics of sports techniques (4th. ed.). Englewood Cliffs, NJ:Prentice-Hall.


TASKS

1. Select a sport skill where a novice and a skilled performer can be found from students inthe lab.

2. Select two volunteers (one novice and one skilled) to perform the skill.

3. Videotape several repetitions of the skill from several angles

4. Observe and evaluate performance of the biomechanical principles in each movement us-ing videotape replay.





COMPARISON OF SKILLED AND NOVICE PERFORMANCE

1. What are the biomechanical principles most relevant to the sport skill of interest?

2. What biomechanical principles are strengths and weaknesses for the novice performer?

3. What biomechanical principles are strengths and weaknesses for the skilled performer?

4. What intervention would you recommend for the novice performer and why?

5. What intervention would you recommend for the skilled performer and why?

LAB ACTIVITIES L-27


LAB ACTIVITY 11

COMPARISON OF TRAINING MODES

Strength and conditioning coaches prescribe exercises to improve performance based on thePrinciple of Specificity. This is often called the “SAID” principle: Specific Adaptation toImposed Demands. There are a variety of free-weight, elastic, and mechanical resistancesthat coaches can prescribe to train the neuromuscular system. Qualitative analysis of exer-cise technique based on biomechanical principles can help a strength coach make two im-portant evaluations: is the exercise technique safe and is it sport-specific? This lab will fo-cus on the latter. The purpose of this lab is to compare the specificity of exercise techniquein training for a sport skill.

BACKGROUND READING

Chapter 11 herein: “Applying Biomechanics in Strength and Conditioning”


TASKS

1. Select a sport skill of interest.

2. Select three exercises that will train the main agonists for the propulsive phase of the skill.Be sure to select an elastic resistance, inertial resistance (free weight), and an exercise ma-chine. Strive to make the resistances about equal in these exercises.

3. Select a volunteer to perform the exercises.

4. Videotape several repetitions of the exercises perpendicular to the primary plane ofmovement.

5. Observe and evaluate the performance of the biomechanical principles in each exerciseusing videotape replay.





COMPARISON OF TRAINING MODES

1. What are the biomechanical principles most relevant to the sport skill of interest?

2. What was the first exercise? What biomechanical principles of this exercise are similar tothe sport skill?

3. What was the second exercise? What biomechanical principles of this exercise are similarto the sport skill?

4. What was the third exercise? What biomechanical principles of this exercise are similar tothe sport skill?

5. Which exercise was most sport-specific? Why? (Be sure to explain based on the impor-tance of certain biomechanical principles in terms of performance in the sport.)

LAB ACTIVITIES L-29


LAB ACTIVITY 12

QUALITATIVE ANALYSIS OF WALKING GAIT

Sports medicine professionals qualitatively analyze movement to find clues to injury and tomonitor recovery from injury. Walking is a well-learned movement that athletic trainers,physical therapists, and physicians all qualitatively analyze to evaluate lower-extremityfunction. There is a variety of qualitative and quantitative systems of gait analysis. This labwill focus on the qualitative analysis of two walking gaits based on biomechanical princi-ples. Professionals qualitatively analyzing gait must remember that quantitative biome-chanical analyses are needed in order to correctly estimate the loads in musculoskeletalstructures, so assumptions about muscle actions in gait from body positioning alone are un-wise (Herbert et al., 1993).

BACKGROUND READING

Chapter 12 herein: “Applying Biomechanics in Sports Medicine and Rehabilitation”

Herbert, R., Moore, S., Moseley, A., Schurr, K., & Wales, A. (1993). Making inferences aboutmuscles forces from clinical observations. Australian Journal of Physiotherapy, 39,195–202.


Whittle, M. (1996). Gait analysis: An introduction (2nd ed.). Oxford: Butterworth-Heinemann.

TASKS

1. Select a volunteer to perform the walking trials.

2. Have the volunteer walk in three conditions: their natural gait, as fast as they comfort-ably can, and simulating an injury. Injury can be easily simulated by restricting joint mo-tion with athletic tape or a brace. Antalgic (painful) gait can be simulated by placing asmall stone in a shoe.

3. Videotape several cycles of each waking gait.

4. Observe and evaluate performance related to the biomechanical principles in each gaitusing videotape replay.





QUALITATIVE ANALYSIS OF WALKING GAIT

1. What biomechanical principles are most evident in natural walking gait?

2. What biomechanical principles increased or decreased in importance relative to normalgait, during fast gait?

3. What injury did you simulate? What biomechanical principles increased or decreased inimportance relative to normal gait, during injured gait?

4. What musculoskeletal structures are affected in your simulated injury? Hypothesize thelikely changes in muscular actions and kinematics because of this injury and note whereyou might find biomechanical literature to confirm your diagnosis.

LAB ACTIVITIES L-31


Fundamentals of Biomechanics - PROGRAMA DA DISCIPLINA

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