Research on Intelligent Manufacturing

Editors-in-chief

Han Ding, Huazhong University of Science and Technology, Wuhan, ChinaRonglei Sun, Huazhong University of Science and Technology, Wuhan, China

Series editors

Kok-Meng Lee, Georgia Institute of Technology, Atlanta, GA, USAYusheng Shi, Huazhong University of Science and Technology, Wuhan, ChinaJihong Liu, Beijing University of Aeronautics and Astronautics, Beijing, ChinaHanwu He, Guangdong University of Technology, Guangzhou, ChinaYuwang Liu, Chinese Academy of Sciences, Shenyang, ChinaJiajie Guo, Huazhong University of Science and Technology, Wuhan, ChinaHaibin Yin, Wuhan University of Technology, Wuhan, ChinaJunzhi Yu, Chinese Academy of Sciences, Beijing, ChinaWenfeng Li, Wuhan University of Technology, Wuhan, ChinaJingjing Ji, Huazhong University of Science and Technology, Wuhan, China

Research on Intelligent Manufacturing (RIM) publishes the latest developmentsand applications of research in intelligent manufacturing—rapidly, informally andin high quality. It combines theory and practice to analyse related cases in fieldsincluding but not limited to:

Intelligent design theory and technologiesIntelligent manufacturing equipment and technologiesIntelligent sensing and control technologiesIntelligent manufacturing systems and services

This book series aims to address hot technological spots and solve challengingproblems in the field of intelligent manufacturing. It brings together scientists andengineers working in all related branches from both East and West, under thesupport of national strategies like Industry 4.0 and Made in China 2025. With itswide coverage in all related branches, such as Industrial Internet of Things (IoT),Cloud Computing, 3D Printing and Virtual Reality Technology, we hope this bookseries can provide the researchers with a scientific platform to exchange and sharethe latest findings, ideas, and advances, and to chart the frontiers of intelligentmanufacturing.

The series’ scope includes monographs, professional books and graduatetextbooks, edited volumes, and reference works intended to support education inrelated areas at the graduate and post-graduate levels.

More information about this series at http://www.springer.com/series/15516

Jiajie Guo • Kok-Meng Lee

Flexonics for Manufacturingand RoboticsModeling, Design and Analysis Methods

123

Jiajie GuoSchool of Mechanical Science andEngineering

Huazhong University of Science andTechnology

Wuhan, China

Kok-Meng LeeThe George W. Woodruff School ofMechanical Engineering

Georgia Institute of TechnologyAtlanta, GA, USA

ISSN 2523-3386 ISSN 2523-3394 (electronic)Research on Intelligent ManufacturingISBN 978-981-13-2666-0 ISBN 978-981-13-2667-7 (eBook)https://doi.org/10.1007/978-981-13-2667-7

Jointly published with Huazhong University of Science and Technology Press, Wuhan, ChinaISBN: 978-7-5680-4054-9

The print edition is not for sale in China Mainland. Customers from China Mainland please order theprint book from: Huazhong University of Science and Technology Press.

Library of Congress Control Number: 2018956272

© Huazhong University of Science and Technology Press, Wuhan and Springer Nature Singapore PteLtd. 2019This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publishers, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publishers nor theauthors or the editors give a warranty, express or implied, with respect to the material contained herein orfor any errors or omissions that may have been made. The publishers remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd.The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721,Singapore

Preface

With the increasing demands for smart machines and intelligent equipmentadaptable to humans and environments, compliant structures and flexible elec-tronics have been widely developed in robotics and thin-wall components with alarge strength-to-weight ratio are common in manufacturing. Among differentchallenges in flexible mechatronics (flexonics), modelling, design and analysis arestill critical issues to be dealt with because of the nonlinear complexity of con-tinuum. This book formulates distributed models in both time and spatial domainsusing a geometric approach, along with practical field-based sensing methods forrobotics and manufacturing. Applications are illustrated by examples of exoskele-tons, mobile sensor network, intelligent sensing, and so on. This book is written foruniversity researchers, R&D engineers and graduate students in engineering andscience, who wish to learn the core principles, theories, technologies, and appli-cations of flexonics. It can be served as a textbook or reference for a graduate levelcourse on mechatronics, which may require prerequisites of linear algebra,mechanics of materials, ordinary and partial differential equations, numericalmethods, and vibrations.

The text is organized into seven chapters. Chapter 1 is an introduction to flex-onics with basic concepts, problems and reviews of related work. Chapter 2 pre-sents fundamentals of mathematics for modelling, design and analysis of flexonics.Chapter 3 formulates the boundary value problems for basic flexible elements ofbeams and plates. Application examples are given in the last four chapters. Chapter4 illustrates the design of a mobile node as an application of flexonics for structuralhealth monitoring, where design concepts, functionalities, experimental validationand demonstrative examples are included. Chapter 5 presents a distributed-parameter method for intelligent sensing of displacement and strain distributionsacross a flexible thin-wall workpiece and their field reconstruction for real-timemanufacturing applications. Chapter 6 provides a bio-joint model to capture thekinematic and dynamic features of a biological joint, based on which an adaptiveexoskeleton is designed to eliminate negative effects associated with the closedleg-exoskeleton kinematic chain on a human knee. Chapter 7 presents a modellingmethod to capture musculoskeletal deformations and its immediate application is

v

illustrated with poultry meat deboning in food processing. As a unified modellingand analysis approach is developed in Chaps. 2 and 3, readers can find commonsamong the various examples in subsequent chapters and may probably extend thepresented method to applications that are not covered in this book. Chapters 4–7 aresomewhat independent from each other, so some of them can be skipped or chosenbased on readers’ application needs and interests.

Many findings in this book are based on the last decade of research conducted atGeorgia Institute of Technology and Huazhong University of Science andTechnology, and they were obtained under research grants supported by theGeorgia Agricultural Technology Research Program, National Science Foundation(Grant CMMI-0928095) and more recently, the National Basic Research Programof China (973 Program, Grant 2013CB035803) and the National Natural ScienceFoundation of China (Grants 51505164, 51875221). The authors wish toacknowledge with great appreciation the colleagues and graduate students for theircollaboration or suggestions in the presented research, like Prof. Yang Wang, Dr.Dapeng Zhu, Dr. Xiaohua Yi and Yang Xie for Chap. 4, Prof. Kun Bai, Prof.Jingjing Ji, Man Yu, Wuguang Liu, Ruochu Liuand Bo Wang for Chap. 5, Dr.Donghai Wang for Chap. 6, and Dr. Jungyoul Lim and Mark Claffee for Chap. 7.The writing of this book is funded by Hubei Academic Works Publishing SpecialFund and National Science and Technology Academic Works Publishing Fund.The authors would also like to thank Daokai Yu from HUST Press and all thecommittee members for their efforts to organize this book series which makespublication of this book possible.

Wuhan, China Jiajie GuoAtlanta, USA Kok-Meng Lee

vi Preface

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem Description and Objectives . . . . . . . . . . . . . . . . . . . . . . 11.3 Review of Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3.1 Modeling of Compliant Mechanisms . . . . . . . . . . . . . . . . . 31.3.2 Joint Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.3 Numerical Methods for Boundary Value Problems . . . . . . 71.3.4 Flexible Robotics for Structural Health Monitoring . . . . . . 71.3.5 Human-Centered Equipment (Exoskeleton) . . . . . . . . . . . . 91.3.6 Process State Monitoring for Manufacturing . . . . . . . . . . . 101.3.7 Poultry-Meat Processing . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4 Book Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Fundamentals of Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.1 Basics of Differential Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2 Curvature of a 3D Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3 Kinematics of a 3D Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4 Kinematics of an Annular Plate . . . . . . . . . . . . . . . . . . . . . . . . . . 332.5 Multiple Shooting Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3 Flexible Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.1 Two-Dimensional Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2 Three-Dimensional Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.3 Annular Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.4 General Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

vii

4 Flexonic Mobile Node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.1 Design Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.1.1 Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.1.2 Attachment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.1.3 Flexibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.2 Functionalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.2.1 Sensor Attachment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.2.2 Convex Corner Negotiation (2D) . . . . . . . . . . . . . . . . . . . 774.2.3 Convex Corner Negotiation (3D) . . . . . . . . . . . . . . . . . . . 804.2.4 Concave Corner Negotiation . . . . . . . . . . . . . . . . . . . . . . . 834.2.5 Environment Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.3 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.3.1 First Prototype of FMN . . . . . . . . . . . . . . . . . . . . . . . . . . 884.3.2 Second Prototype of FMN . . . . . . . . . . . . . . . . . . . . . . . . 96

4.4 Structural Health Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.4.1 Steel Frame Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.4.2 Space Frame Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5 Intelligent Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.1 Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.1.1 Parametric Effects on |A(xnm)| (DC1) . . . . . . . . . . . . . . . . 1115.1.2 Illustrative Example (DC1) . . . . . . . . . . . . . . . . . . . . . . . . 1125.1.3 Numerical Verification (DC1 and DC2) . . . . . . . . . . . . . . 115

5.2 Parameter Identification and Sensing Configuration . . . . . . . . . . . 1155.2.1 Modal Damping Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.2.2 Step Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.2.3 Robustness of Sensor Performance . . . . . . . . . . . . . . . . . . 1205.2.4 Sensor Configuration Design . . . . . . . . . . . . . . . . . . . . . . 122

5.3 Formulation of Field Reconstruction . . . . . . . . . . . . . . . . . . . . . . 1235.3.1 Field Reconstruction Algorithm . . . . . . . . . . . . . . . . . . . . 1255.3.2 Numerical Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 1265.3.3 Numerical Evaluation of Reconstruction Algorithm . . . . . . 129

5.4 Experiment Results and Illustrative Application . . . . . . . . . . . . . . 1305.4.1 Free Vibration of Non-rotating Plate . . . . . . . . . . . . . . . . . 1315.4.2 Field Reconstruction for Machining . . . . . . . . . . . . . . . . . 134

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

6 Bio-inspired Exoskeleton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.1 Human Knee Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.2 Knee Joint Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

viii Contents

6.3 Knee-Exoskeleton Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1466.3.1 Coupled Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1486.3.2 Coupled Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

6.4 Experimental Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1506.4.1 Design Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . 1506.4.2 Experimental Test Bed . . . . . . . . . . . . . . . . . . . . . . . . . . . 1526.4.3 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 1526.4.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 156

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

7 Musculoskeletal Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1657.1 Musculoskeletal System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

7.1.1 Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1677.1.2 Bio-joint Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1687.1.3 Clavicle Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1707.1.4 Soft Tissue Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

7.2 Experimental Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1757.2.1 Elastic Modulus of Clavicle . . . . . . . . . . . . . . . . . . . . . . . 1767.2.2 Ligament Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

7.3 Illustrative Application to Wing Manipulation . . . . . . . . . . . . . . . 1837.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Contents ix

About the Authors

Jiajie Guo received the B.S. degree from theDepartment of Engineering Mechanics and Science atPeking University, Beijing, China, in 2006, and M.S.and Ph.D. degrees from Mechanical Engineering,Georgia Institute of Technology, Atlanta, GA, USA,in 2009 and 2011, respectively. He is currently anAssociate Professor in the State Key Lab of DigitalManufacturing Equipment and Technology and theSchool of Mechanical Science and Engineering atHuazhong University of Science and Technology,Wuhan, Hubei, China. He is IEEE and ASME memberand a program committee member of IEEE/ASMEInternational Conference on Advanced IntelligentMechatronics. His current research interests includehuman-centered robotics, flexible mechatronics, manu-facturing, and system dynamics/control. He has pub-lished more than thirty peer-reviewed technical papersin journals and conferences and has been awarded thebest paper award from IEEE/ASME Transaction onMechatronics in 2015 and the “Most Practical SHMSolution for Civil Infrastructures” Video Award inAction session of the 8th International Workshop forStructural Health Monitoring in 2011.

xi

Kok-Meng Lee received the B.S. degree from theState University of New York, Buffalo, NY, USA, in1980, and the S.M. and Ph.D. degrees from theMassachusetts Institute of Technology, Cambridge,MA, USA, in 1982 and 1985, respectively. Currently,he is a Professor in the George W. Woodruff School ofMechanical Engineering at the Georgia Institute ofTechnology, Atlanta, a member of the ThousandTalents Plan in the Organization Department of theCentral Committee, and a Distinguished Professor inthe School of Mechanical Science and Engineering atHuazhong University of Science and Technology,Wuhan, China. His research interests include systemdynamics/control, robotics, automation, and mecha-tronics. He is a world renowned researcher with morethan 30 years of research experience in magnetic fieldmodeling and design, optimization and implementationof electromagnetic actuators. He has published over150 peer-reviewed papers and he holds eight patents inmachine vision, three degrees of freedom (DOF)spherical motor/encoder, and live-bird handling system.He is IEEE/ASME Fellow and was the Editor-in-Chieffor the IEEE/ASME Transactions on Mechatronicsfrom 2008 to 2013. Recognitions of his researchcontributions include the National Science Foundation(NSF) Presidential Young Investigator, Sigma XiJunior Faculty Research, International Hall of FameNew Technology, and Kayamori Best Paper awards.

xii About the Authors

Abbreviations

2D Two dimensional3D Three dimensionalAWM Automated wing manipulationBJC Bio-joint constraintBVP Boundary value problemCBM Curvature-based beam modelDOF Degrees of freedomFEA Finite element analysisIVP Initial value problemMSM Multiple shooting methodODE Ordinary differential equationPDE Partial differential equationSHM Structure health monitoring

xiii

Symbols

Capitalized SymbolsA Cross-sectional areaC An instantaneous contact pointE Young’s modulusG Shear modulusI1, I2, I3 Moment of inertiaJ Moment of inertiaL Beam lengthNr Number of rigid bodies in a multi-body systemNc Number of compliant beam in a multi-body systemPs Material point on the initial beam axisQs Material point on the deformed beam axisXYZ Global reference coordinate frameE1, E2, and E3 Unit vectors along global reference frame X, Y, and

Z axes, respectivelyF = [F1 F2 F3]

T External force acting on a compliant beamK(0) Curvature of the initial beamK(e) Curvature change due to elastic deformationK Curvature of the deformed beamSkew(K) 0 k3 �k2

�k3 0 k1k2 �k1 0

24

35

M = [M1 M2 M3]T External moment acting on a compliant beam

R, R(0) Rotational matrixX State variables

xv

Lower Case Symbolsa, b, c Length of principal axis of an ellipsoidb Beam widthh Beam thicknessk Curvaturem Massp Pitchr Radius of an osculating circle at contact pointrw Wheel radiuss Undeformed path length from the beam root to the

reference pointt Timexs, ys, and zs xs is the longitudinal axis; ys and zs are the principal

axes of the cross-sectional area in the initial beam

eð0Þ1 ; eð0Þ2 and eð0Þ3Unit vectors along principal axes of xs, ys, and zs,respectively

e1; e2 and e3 Unit vectors along principal axes of ns, ηs, and fs,respectively

[eT, eN, eB] Frenet–Serret frame where eT is the tangent unitvector, eN is the normal unit vector, and eB is thebinormal unit vector

f External force acting on a rigid bodyqF Distributed forceqM Distributed moment

xð0Þ ¼ xð0Þ1 xð0Þ2 xð0Þ3

h iT Global nodal coordinates of initial beam shape

x = [x1 x2 x3]T Global nodal coordinates of deformed beam shape

Greek SymbolsC Boundary of a rigid bodya, b Anglesj Curvatures Torsion, external moment acting on a rigid bodyw, h and u Euler anglesns, ηs, and fs ns is the longitudinal axis; ηs and fs are the principal

axes of the cross-sectional area in the deformed beamq Densityt Poisson ratiox Angular velocitye Longitudinal strain on the beam axisl Friction coefficient

xvi Symbols

Subscripts and Superscripts(e) Elastic deformation(0) Initial state

Symbols xvii

List of Figures

Fig. 2.1 A 3D curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Fig. 2.2 Verification with a planar curve (non-constant curvature) . . . . . 30Fig. 2.3 Verification with a helix curve (constant curvature) . . . . . . . . . 31Fig. 2.4 Verification with a 3D curve with non-constant curvatures . . . . 32Fig. 2.5 An element in a compliant plate . . . . . . . . . . . . . . . . . . . . . . . 33Fig. 2.6 Multiple shooting method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Fig. 3.1 Two-dimensional deformations of a flexible beam . . . . . . . . . . 40Fig. 3.2 Formulation of a beam model . . . . . . . . . . . . . . . . . . . . . . . . . 40Fig. 3.3 Coordinates for a 3D compliant beam . . . . . . . . . . . . . . . . . . . 43Fig. 3.4 Equilibrium of a beam segment. . . . . . . . . . . . . . . . . . . . . . . . 45Fig. 3.5 Lateral deflection under axial compression. . . . . . . . . . . . . . . . 49Fig. 3.6 Normalized deformed shape of the twisted ring . . . . . . . . . . . . 51Fig. 3.7 Effect of aspect ratios and materials. . . . . . . . . . . . . . . . . . . . . 51Fig. 3.8 An element in a thin-wall plate . . . . . . . . . . . . . . . . . . . . . . . . 51Fig. 3.9 Multi-body compliant mechanism . . . . . . . . . . . . . . . . . . . . . . 58Fig. 3.10 Bio-joint constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Fig. 3.11 Snapshots illustrating the formulation . . . . . . . . . . . . . . . . . . . 62Fig. 3.12 Effect of shapes on the osculating circle . . . . . . . . . . . . . . . . . 62Fig. 3.13 Ellipse—cylinder contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Fig. 3.14 Effect of sliding on contact kinematics . . . . . . . . . . . . . . . . . . 64Fig. 3.15 Effect of sliding on orientation . . . . . . . . . . . . . . . . . . . . . . . . 64Fig. 3.16 Snapshots illustrating the effect of shape . . . . . . . . . . . . . . . . . 65Fig. 3.17 Effect of XB on XA position/orientation . . . . . . . . . . . . . . . . . . 66Fig. 3.18 Effect of aspect ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Fig. 4.1 Flexonic mobile node for structural health monitoring . . . . . . . 70Fig. 4.2 Robot dimension compared to obstacles . . . . . . . . . . . . . . . . . 70Fig. 4.3 Comparison of two magnetic wheel configurations . . . . . . . . . . 71Fig. 4.4 Design concept of an FMN. . . . . . . . . . . . . . . . . . . . . . . . . . . 73Fig. 4.5 Effect of gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Fig. 4.6 Relationship between normalized force and displacements . . . . 76Fig. 4.7 Convex corner negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

xix

Fig. 4.8 Simulation of corner negotiation . . . . . . . . . . . . . . . . . . . . . . . 78Fig. 4.9 Relation between rotation angle h, required moment Mr

and normalized force Fn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Fig. 4.10 Relation between rotation angle a and normalized force Fn. . . . 79Fig. 4.11 Turning within a limited space . . . . . . . . . . . . . . . . . . . . . . . . 80Fig. 4.12 Snapshots of the deformed beam. . . . . . . . . . . . . . . . . . . . . . . 82Fig. 4.13 Normalized displacement and force . . . . . . . . . . . . . . . . . . . . . 83Fig. 4.14 Concave corner negotiation. . . . . . . . . . . . . . . . . . . . . . . . . . . 84Fig. 4.15 Front axle yawing and pitching . . . . . . . . . . . . . . . . . . . . . . . . 84Fig. 4.16 Deformed beam shapes for a pitching camera . . . . . . . . . . . . . 86Fig. 4.17 Required input of the rear axle for different of w and h . . . . . . 87Fig. 4.18 The first prototype FMN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Fig. 4.19 Sensor attachment and obstacle negotiation . . . . . . . . . . . . . . . 90Fig. 4.20 Validation of the beam model . . . . . . . . . . . . . . . . . . . . . . . . . 92Fig. 4.21 Model validation with FEA and experiment . . . . . . . . . . . . . . . 93Fig. 4.22 Validation of sensor attachment. . . . . . . . . . . . . . . . . . . . . . . . 94Fig. 4.23 Convex right corner negotiation . . . . . . . . . . . . . . . . . . . . . . . 96Fig. 4.24 The second prototype of FMN . . . . . . . . . . . . . . . . . . . . . . . . 97Fig. 4.25 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98Fig. 4.26 Experimental validation for relation between displacement

and rotation angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Fig. 4.27 Comparison of flexible and rigid design configurations [3] . . . . 100Fig. 4.28 Steel frame structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Fig. 4.29 FFT of vertical vibration in the steel frame . . . . . . . . . . . . . . . 102Fig. 4.30 Picture of the space frame bridge on Georgia Tech campus . . . 103Fig. 4.31 Experimental setup for the bridge testing . . . . . . . . . . . . . . . . . 105Fig. 4.32 Pictures of four FMNs navigating on the space

frame bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Fig. 4.33 Hammer impact test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Fig. 4.34 Example vibration records and corresponding

FRF/PSD plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Fig. 5.1 Fixation of a thin annular workpiece . . . . . . . . . . . . . . . . . . . . 110Fig. 5.2 Effects of X and h on normalized natural frequencies . . . . . . . . 112Fig. 5.3 Distribution of natural frequencies and mode shapes (DC1) . . . 113Fig. 5.4 Mode shapes of an annular plate subjected

to DC1 constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Fig. 5.5 Mode shapes of an annular plate subjected

to DC2 constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Fig. 5.6 Experimental vibration test setup using eddy-current sensors. . . 117Fig. 5.7 Vibration test of impulse response (DC2) . . . . . . . . . . . . . . . . 119Fig. 5.8 Transient response with analysis and experiment . . . . . . . . . . . 120Fig. 5.9 Robustness of an eddy-current sensor with various media. . . . . 121Fig. 5.10 Stability of eddy-current sensing with various media . . . . . . . . 122

xx List of Figures

Fig. 5.11 Models for circular thin-wall components . . . . . . . . . . . . . . . . 124Fig. 5.12 Field reconstruction verified with FEA . . . . . . . . . . . . . . . . . . 128Fig. 5.13 Reconstruction efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Fig. 5.14 Experimental setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Fig. 5.15 Validation of the reconstructed displacement field (RDF) . . . . . 132Fig. 5.16 Reconstruction of time-varying strain distributions . . . . . . . . . . 133Fig. 5.17 Effect of eddy-current damper . . . . . . . . . . . . . . . . . . . . . . . . . 134Fig. 5.18 Reconstruction at (X, Y) = (94 mm, 0 mm)

during machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Fig. 5.19 Field reconstructions during machining . . . . . . . . . . . . . . . . . . 136Fig. 6.1 MRI of a cadaver knee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Fig. 6.2 Comparison of current contact point C . . . . . . . . . . . . . . . . . . 141Fig. 6.3 Rolling and sliding velocities of the current contact point

(Model 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141Fig. 6.4 Coordinates illustrating the knee joint rotation . . . . . . . . . . . . . 144Fig. 6.5 Kinematics of the tibia mass-center . . . . . . . . . . . . . . . . . . . . . 144Fig. 6.6 Comparing snapshots of an exoskeleton between two knee

joint models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Fig. 6.7 Force and torque comparison between two knee joint

models (with/without exoskeleton). . . . . . . . . . . . . . . . . . . . . . 146Fig. 6.8 Knee-exoskeleton kinematic and dynamic models . . . . . . . . . . 147Fig. 6.9 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153Fig. 6.10 Flowchart illustrating the computation of the

analytical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156Fig. 6.11 Verification of computed mass-center displacements. . . . . . . . . 157Fig. 6.12 Experiment and simulated contact kinematics

in a knee joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159Fig. 6.13 Knee rolling and sliding analyses . . . . . . . . . . . . . . . . . . . . . . 160Fig. 6.14 Illustrative results of cam profile designs . . . . . . . . . . . . . . . . . 160Fig. 6.15 Effects of different design configurations (Table 6.3)

on human knee joint internal forces fr, fh . . . . . . . . . . . . . . . . . 161Fig. 6.16 Effects of different design configurations (Table 6.3)

on human knee joint internal torque sa . . . . . . . . . . . . . . . . . . 161Fig. 7.1 Chicken skeleton. Adapted from [5] . . . . . . . . . . . . . . . . . . . . 166Fig. 7.2 Ligament-skeletal structure of a chicken carcass . . . . . . . . . . . . 167Fig. 7.3 Change of shoulder height due to Dhy . . . . . . . . . . . . . . . . . . . 169Fig. 7.4 Change of shoulder position due to Dhx. . . . . . . . . . . . . . . . . . 169Fig. 7.5 Clavicle deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171Fig. 7.6 Structural hierarchy of ligament or tendon [2] . . . . . . . . . . . . . 175Fig. 7.7 Experimental setup with a calibrated linear motor . . . . . . . . . . 176Fig. 7.8 Calibration of the linear motor for the force-voltage relation . . . 177Fig. 7.9 Relation between pulling force and deflection on clavicles . . . . 178Fig. 7.10 Tests on samples of full clavicles . . . . . . . . . . . . . . . . . . . . . . 179

List of Figures xxi

Fig. 7.11 Tests on samples of half clavicles . . . . . . . . . . . . . . . . . . . . . . 180Fig. 7.12 Uniaxial extension of ligaments [3] . . . . . . . . . . . . . . . . . . . . . 181Fig. 7.13 Ligament/tendon characteristic relation . . . . . . . . . . . . . . . . . . 182Fig. 7.14 Ligament-skeletal structure of a chicken-shoulder joint . . . . . . . 184Fig. 7.15 Observations of wing manipulation on shoulder location . . . . . 185

xxii List of Figures

List of Tables

Table 1.1 Joints and corresponding models . . . . . . . . . . . . . . . . . . . . . . 5Table 3.1 Boundary conditions for a two-dimensional beam . . . . . . . . . . 42Table 3.2 Boundary conditions for a three-dimensional beam . . . . . . . . . 48Table 3.3 Spring specification and boundary conditions . . . . . . . . . . . . . 49Table 3.4 Ring specification and boundary conditions. . . . . . . . . . . . . . . 50Table 3.5 Algorithm for bio-joint kinematics . . . . . . . . . . . . . . . . . . . . . 61Table 3.6 Simulation parameter values. . . . . . . . . . . . . . . . . . . . . . . . . . 61Table 3.7 Dimension of XA and XB. . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Table 4.1 Comparison of degrees of freedom . . . . . . . . . . . . . . . . . . . . . 72Table 4.2 Mechanical properties and thickness of the spring

steel laminate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Table 4.3 Slope angle and critical values . . . . . . . . . . . . . . . . . . . . . . . . 76Table 4.4 Parametric values for simulation . . . . . . . . . . . . . . . . . . . . . . . 86Table 4.5 Steel frame material properties and robot dimensions. . . . . . . . 101Table 4.6 Comparison of frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Table 4.7 Dimensions of the steel bridge . . . . . . . . . . . . . . . . . . . . . . . . 104Table 4.8 Comparison of modal characteristics extracted

from FMN data and static sensor data. . . . . . . . . . . . . . . . . . . 108Table 5.1 Plate specifications in simulation . . . . . . . . . . . . . . . . . . . . . . 111Table 5.2 Comparison of xnm against FEA (DC1), units in Hz . . . . . . . . 116Table 5.3 Comparison of xnm against FEA (DC2), units in Hz . . . . . . . . 116Table 5.4 Specifications of sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Table 5.5 Comparison of natural and damped frequencies. . . . . . . . . . . . 120Table 5.6 Values of coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Table 5.7 Mode shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Table 6.1 Geometry approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Table 6.2 Physical parameters of human’s lower leg. . . . . . . . . . . . . . . . 144Table 6.3 Specifications of exoskeleton designs . . . . . . . . . . . . . . . . . . . 151Table 6.4 Specifications of the lower leg and link . . . . . . . . . . . . . . . . . 156Table 6.5 Comparison of force/torque (mean, RMS,

Max Abs values) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

xxiii

Table 7.1 Dimensions of coracoid-keel joint and bones. . . . . . . . . . . . . . 168Table 7.2 Force sensor and sample dimensions. . . . . . . . . . . . . . . . . . . . 181Table 7.3 Measured data and simulation results . . . . . . . . . . . . . . . . . . . 185

xxiv List of Tables