Introduction to BiomaterialsFinal Project

“Pneumatic Artificial Muscle Characterization”Austin Frazer, Danny McCormick

Introduction

Pneumatic artificial muscles, known colloquially as “air muscles”, are devices that contract or expand

when supplied with air at a different pressure than ambient. This air fills a pneumatic bladder, causing the

device to contract and produce a force that can be harnessed for a variety of applications. A popular usage of air

muscles is in biological applications due to the characteristics they share with natural skeletal muscle. Like

natural muscle, air muscles exhibit inherent compliant behavior as a result of the compressibility of air. This

trait is critical when considering interactions between man and machine where delicate tasks may need to be

performed as a matter of safety. These pneumatic devices are preferable in many applications to the relatively

rigid behavior of hydraulic and electric drives, which have the tendency to introduce unwanted phenomena to

the system such as backlash. These applications include but are not limited to orthotic and rehabilitation

mechanisms. For example, the Active Ankle-Foot Orthotic, an MSD project still in the planning stage, intends

to use these devices for the actuation of a biological assisting mechanism. Air muscles are an ideal device for

this application due to their compact size, relative simplicity, and high strength to weight ratio. A quantitative

measure for the fatigue behavior of pneumatic artificial muscles will prove to be beneficial to them and future

MSD teams who wish to incorporate these devices into their design.

Background Information

The particular air muscle type under scrutiny for this analysis is the McKibben-type air muscle. The

McKibben PAM was invented in the 1950’s by a physician named Joseph L. McKibben for use in an artificial

limb for the handicapped (Wickrumatunge). These devices consist of a pneumatic bladder encased in a textile

shell of helically wound fibers. When the bladder expands as a result of an applied pressure, it pushes on the

wound fibers causing the muscle to contract. McKibben air muscles are distinguished from other types of

braided muscles by their construction. In McKibben muscles, the bladder and fibers are connected to the end

fittings, whereas other designs leave the bladder unattached. In either case, these fibers tighten to apply an axial

force when pressure is applied to the inner pneumatic bladder. Typically a polymer such as latex or soft

silicone is used for the material of this bladder. Of the two materials, silicone is the hypothetically favorable

biomaterial due to the potential for an allergic reaction associated with latex, which affects approximately 3

million Americans (Tondu).

Several models have been generated in an effort to predict the behavior of these air muscles given

different material properties and operating conditions, however the results remain largely inaccurate. It is

thought that this inaccuracy is attributed to the visco-elastic nature of the bladder material as well as a disregard

for the relaxation in the bladder, compressibility of the air, friction between the fibers, and damping within the

system. Research surrounding the use of air muscles has been increasing at a rapid pace, in part due to the

projected demand for the devices as the baby boomer population retires. Most of the research has been focused

on the McKibben type braided muscles; however a different type of pneumatic muscle known as the “pleated

Frazer, McCormick 2

pneumatic artificial muscle” is also gaining popularity. Up to this point, McKibben muscles have been preferred

due to their simple design, ease of assembly, and low cost (Daerden). Unfortunately, this type of muscle also

suffers from a somewhat low life expectancy that may be exacerbated inherently by its’ design, which relies on

pressure transfer from the bladder to the fibers and results in stress concentrations at the end fittings. The

pressure transfer also results in a transfer of friction and heat that is manifested as hysteresis and contributes to

the demise of the device. The Pleated PAM improves on this device by utilizing a pleated membrane to reduce

unnecessary material strain of the bladder, thus improving efficiency and control. However, there is a relative

lack of research into the viability of pleated PAM’s and the cost is high compared to the McKibben actuators.

In summary, the goal of this analysis is to determine what material properties are ideally suited for

application in a McKibben-style pneumatically actuated artificial muscle in order to improve its’ performance.

Determining the material factors that are critical to the performance of this device will allow for an improved

design while maintaining the cost effectiveness that made the McKibben style actuator popular to begin with. A

close review of a selection of previously published academic literature will guide our process that will aim to

determine these critical characteristics.

Shadmehr and Wise characterize the observed behavior of real muscle in their paper “A Simple Muscle

Model” and lay the groundwork for how to think about muscle actuation. The force generated by a real muscle

can be broken into active and passive forces, which can be modeled with varying complexity using elastic and

viscous elements (of a spring or dampener perhaps) in parallel or series arrangement. It is important to note that

this article simply describes a method by which skeletal muscle may be modeled mathematically. That is, the

combinations of elastic and viscous elements do not represent how muscles actually generate force. Many

characteristics of real muscle introduced by this study are similar to the observed characteristics of

pneumatically actuated muscles outlined in the following academic papers. This article also goes into detail

about the impact of nervous system components on the behavior of real muscle; however those details are

outside of the scope of our study.

Kothera, in his paper “Experimental Characterization and Static Modeling of McKibben Actuators”,

attempts to more accurately characterize the behavior of McKibben actuators, and to improve upon the accuracy

of previous models by including data resulting from tests utilizing actuators of differing lengths, diameters, and

thicknesses. Two modeling approaches were used and the effects of elastic energy storage of the bladder, the

noncylindrical tendency of the actuator, and variable thicknesses were all taken into consideration. This

information is particularly useful to us, as we intend to vary the bladder material to study the results on the

performance of the actuator. This article will also be useful because it outlines the steps taken to ensure/improve

accuracy during the testing process to get meaningful data, which will aid in streamlining our test setup. This

model appears to be somewhat accurate, as the experimental data lines up well with the data predicted via force

balance and energy balance equations. In order to apply this model to dynamic cases, however, relaxation of the

Frazer, McCormick 3

rubber bladder, compressibility of the air, and various sources of friction would need to be taken into account,

which was outside the scope of this study.

In “Mathematical Model of Pneumatic Artificial Muscle Reinforced by Straight Fibers”, Saga and Yaegashi

attempt to quantify, via a mathematical model, the behavior of pneumatically actuated muscles. Many

characteristics of the artificial muscle observed in this study are analogous with the characteristics observed of

real muscle in article #1. A focus of this article is improving precision by better understanding the muscular

characteristics of the actuator, which involve studying the interaction between the inner bladder and outer

fibrous weave that we will concern ourselves with in our study.

In “Modeling and Control of McKibben Artificial Muscle Robot Actuators”, Tondu and Lopez attempt to

outline the objective strengths and weaknesses of humans and robots as they relate to completing industrial

tasks. For example, a human arm is inaccurate when compared to a robot arm, but its advantage is in lightness

and joint flexibility. Conversely, a robot arm is heavy and inflexible; however it has the potential to be precise.

McKibben actuators are introduced via a brief history, and it is surmised that an actuator of this type is suitable

for industrial robot applications because of its human-like compliance and force modulation. Visual aids are

also utilized to illustrate different components of the actuator. A detailed explanation of the working principle

of the McKibben muscle in static and dynamic settings, as well as a breakdown of the sources of inefficiency in

the McKibben muscle is presented. A disadvantage of this particular study is that the model does not take into

consideration that the muscle does not perfectly maintain its cylindrical shape. The muscle takes a conic shape

at both ends as it contracts, and this behavior is not represented in the model.

Wickrumatunge and Leephakpreeda examine the behavior of pneumatic artificial muscles in their academic

journal “Study on Mechanical Behaviors of Pneumatic Artificial Muscle” In this article, models are derived and

experimental results show a nonlinear relationship between contraction magnitude, air pressure, and pulling

force within the PAM. This study does attempt to characterize the dynamic properties of the actuator, which is

an improvement over the static Kothera model. The model proposed is primarily based on the elastic behavior

of a mechanical spring system, as proposed by Shadmehr, with visco-elastic effects observed in the

experimental results. This study adds to the knowledge from the previous studies by stating that the stiffness

parameter of the model is dependent on the stretched length of the PAM as well as the air pressure inside of the

PAM. As predicted intuitively, the longer PAM yielded a larger working range and PAM’s with a larger

diameter are capable of producing larger forces. This article also suggests that the dynamic behavior of the

muscle is linked to the stiffness parameter, which be controlled via precise control of the air supply.

Sanchez and Tondu propose a unique approach to estimate the parameters of the nonlinear model of the

McKibben actuator in “Nonlinear parametric identification of a McKibben artificial pneumatic muscle using

flatness property of the system”. In this case, the approach used was applied based on the derivation of the

Gauss-Newton equations applied to the flat differential model of a process, as opposed to the standard method,

which involves direct differentiation of the classic representation of the system by differential equations.

Frazer, McCormick 4

Because this approach is sensitive to noise, it was determined that the flat differential model is inaccurate for

most real applications. The flat model method is much quicker than the direct model method however, so it may

be suitable for a first-cut solution in some cases. It is hypothesized that more advanced filtering may aid in the

accuracy of this process while maintaining its efficiency.

Though not as directly applicable as the previous academic sources, the thesis “Scalability Study for

Robotic Hand Platform” was written by an RIT graduate student that has a fair amount of exposure to

pneumatic actuators in industrial settings. This student studied and reported out on appropriate sizing of air

muscles for specifically scaled applications and was able to predict how the force of the air muscle was to be

transmitted through the robotic hand. It was determined that air muscle actuation was appropriate/reasonable

down to the ¼ scale robotic hands. A smaller scale than this would have required alternative manufacturing

methods. In general, this paper provides a good overview of the reasonable range of physical sizes of actuators

we can expect to encounter during our testing.

The article “Pneumatic Artificial Muscles: actuators for robotics and automation” narrates a general

overview of pneumatic artificial muscles for robotic applications, outlining many factors from concept and way

of operation to properties observed in service environments. Unlike the other articles, this article goes on to

explain, in the opinion of the author, the reasons that pneumatic muscles have not been in widespread use. The

author also expresses reserved optimism about the future of McKibben PAM’s, stating that the main drawbacks

of the McKibben type actuators in particular can be reduced considerably by improving the design and material

composition of the device.

Methods

In order to harness the

hysteresis data from the air

muscle, a test rig consisting of

a Velmex 9000 controller and

slide mated to an Interface 10lb

load cell was utilized. The rig

was manipulated via a specially

written Labview code written

by John Wellin that allows the

user precise control over the

movement of the slide and data

logging functions1. The device

is pictured in Figure 2.

1 Labview file can be found at http://people.rit.edu/jdweme/labview.htmFrazer, McCormick 5

Figure 1: Labview Front Panel of the Pneumatic Muscle Cycler Program

Figure 2: The Major Components of the Test Setup

The silver cross member on the left side of the slide is stationary and serves as the mounting location for the

load cell. The mount on the right is mobile, and receives input via a worm gear connected to the motor at the

left. The air muscle force was gathered in conjunction with displacement for 7 constant supply air pressures at 5

psi intervals between 30 psi and 60 psi. The latex air muscle assembled for analysis has a bladder length of

approximately 4 inches. The Labview program was configured to take force measurements at 0.0025 inch

intervals from the home position of zero extension up to 0.25 inches of displacement, and back to the home

location. This level of resolution was chosen as a happy medium between creating an unnecessarily large data

file and collecting enough data points to create a realistic curve. These data curves were then plotted, and best-

fit lines were created in Microsoft Excel for the testing at each pressure for the extension and contraction

portions individually. The area between the lines of extension and contraction at each pressure represent the

amount of energy lost to hysteresis, and can be computed using an integral and the respective best-fit equations.

Figure 3: A Closer Look at the Test Setup

Frazer, McCormick 6

The fundamental formula used for calculating this area is A = ∫a

b

f ( x )−g (x ) dx, where f is the extension curve, g

is the contraction curve, and a and b represent the lower and upper bounds of x which in this case are 0 and

0.25in., respectively. The area has units of lb-in, which is a form of work and/or energy. This computation was

performed utilizing the trapezoidal rule via a specially written Matlab script below:%Script to compute the area between two curves f(x) and g(x)

x=0:0.0001:0.25;A=130218; B=-100583; C=29807; D=-4263.8; E=316.14; F=22.293; G=-0.0648;A1=270917; B1=-207482; C1=61062; D1=-8645; E1=626.48; F1=10.105; G1=-0.0448;

f=(A*x.^6) + (B*x.^5) + (C*x.^4) + (D*x.^3) + (E*x.^2) + (F*x + G);g=(A1*x.^6) + (B1*x.^5) + (C1*x.^4) + (D1*x.^3) + (E1*x.^2) + (F1*x + G1);

plot(x,f);plot(x,g);AREA1=trapz(x,f);AREA2=trapz(x,g);

AREA = AREA1-AREA2

Where coefficients A-G and A1-G1 are tabulated in the results section. This testing method provides a

quantitative analysis that allows for comparison of the hysteresis characteristics of a pneumatic air muscle under

loading at various supply air pressures that has been, to the best of our knowledge, previously unexamined.

Results

Figure 4: Force vs. Extension of the Air Muscle at Various Supply Pressures

Frazer, McCormick 7

When best-fit lines were created for the respective data sets, it was determined that a 6th order polynomial of the

form F = Ax6+ Bx5+ Cx4+ Dx3+ Ex2+ Fx+G fit the curves suitably well, yielding an R2 value of 1. The

following table contains the coefficients.

Figure 5: Table Outlining the 6th Order Polynomial Coefficients for the Curve-Fits

Given these equations, it was then possible to compute the area contained between the curves of expansion and

contraction, which represent the total amount of energy lost during one extension and contraction cycle of the

pneumatic muscle due to

hysteresis friction. A third

order polynomial fit the

data well, yielding an R2

value of 0.9997. The

supply air pressure was

kept relatively constant

(+/- 1.5 psi) during the

testing via a pressure

regulator permanently

installed in the

Biomaterials Lab between

the supply air and our test

rig.

Discussion

At the Literature Review phase of this project, the initial goal was to characterize the differences in

performance (as it relates to hysteresis) between latex and silicone McKibben-type pneumatic air muscles.

When it came time for testing, however, the air muscle with the silicone bladder had unexpected complications

that prevented us from taking data. Though the silicone tubing was approximately of the same size Frazer, McCormick 8

Figure 6: Observed Hysteresis vs. Air Muscle Supply Pressure

and construction as the latex tubing, it did not bulge like the latex muscle when supplied with air pressure. It did

bulge slightly, albeit unevenly, up to its’ failure point at about 80 psi of air pressure without producing a

recordable force. It is possible that the silicone tubing used for the bladder had a prohibitively thick wall or was

composed of a harder compound than expected. Both of these factors result in higher energy storage in the

muscle, and therefore less observed actuation (Kothera). Thus, our focus was shifted more towards

characterizing the hysteresis of the latex muscle only in order to aid in future studies.

The data recorded of the latex muscle provided some interesting insight as to its hysteresis properties.

Figure 6 indicates that there is a positive correlation between the air pressure supplied to the muscle and its

observed hysteresis. A cubic trend line fits this data quite well, indicating that there may be a “sweet spot” of

muscle air pressure that results in the least amount of energy lost, and therefore higher efficiency at around 30

psi. Further testing and a more precise curve fitting procedure would be required to confirm this prediction.

Intuitively, this result makes sense. McKibben-type air muscles rely on the pressure generated in the interior

bladder to press on an outer mesh, which contracts axially. Friction is introduced at the interface between the

two components and increases proportionally with the amount of pressure applied. When the muscles contract,

some of their active force is wasted because of a necessity to overcome the inherent resistance introduced at this

interface (Shadmehr). The third-order behavior observed experimentally also supports this statement, indicating

the presence of some additional viscous resistance when compared to a first order perfectly elastic spring

model. Shadmehr also suggests that additional testing to determine the creep/slow relaxation characteristics

would be beneficial to our understanding of these devices. Given more time, the scope of this experiment could

be extended to include hysteresis testing at varying rates of displacement to determine the effect of this variable

on observed energy losses. In order to preserve the cost-effectiveness of the McKibben-type PAM’s, the

structure must not be changed much from the original design, however modifications to the design can be

performed that would potentially increase the performance of the device without heavily impacting the cost.

One of these modifications, as suggested by Saga and Nakumura, is to reduce the friction at the bladder-weave

interface by introducing some kind of lubricant. The inherent complication with this suggestion is that the

introduction of an additional material to the unit could result in complications. The traditional air muscle

without external lubrication is very clean, making it suitable for sensitive environments where precision is

required such as robot-assisted surgery, or as an implant in vivo. When a lubricant is introduced, there may be

issues with biocompatibility or consistency of performance as the lubrication is swept away or disintegrated.

Research by Bridgestone indicates that the ratio of the inner bladder thickness to the radius of the outer

weave must be at least 1:10 in order to assume that all the pressure forces are transmitted to the braided shell

(Tondu). This assertion aligns well with our test data, which shows that at small pressures (where the outer

weave radius is smaller relative to the bladder thickness) a smaller amount of hysteresis is present than when

higher pressures are used.

Frazer, McCormick 9

One major issue with McKibben actuators is the lack of an ability to precisely control the position of the

device under various loading conditions. A better understanding of the hysteresis characteristics in the air

muscle will aid in better controlling the position and increasing the precision of the device, which becomes very

important in machines such as autonomous robots meant to replace a human’s touch. It would also be

interesting to study how the observed hysteresis scales with the size of the muscle itself. Smaller scale air

muscles are being used more commonly in surgical and robotic applications, however there is not much data

available on how the properties of the full scale air muscles compare to their miniature counterparts. One such

paper that touches on this topic was written by Melissa Monahan, an RIT graduate student, for her master’s

thesis in 2010. The paper on the robotic hand scalability is very thorough, however there is plenty of room to

continue with and build on her research by studying not just the manufacturing limitations of the framework,

but the physical limitations of the air muscle actuators as well.

Conclusion

There is much research yet to be done in the field of pneumatic artificial muscles. As more and more

applications are discovered, there is an ever-increasing demand for additional information on the behavioral

characteristics of these devices. PAM’s will continue to be a viable solution for a myriad of applications

because of their high force to weight ratio, flexible structure, very low mechanical wear, compact size, superior

reliability and low cost. As we gain more knowledge of these devices, these characteristics that make the air

muscle so beneficial will continue to be improved.

Frazer, McCormick 10

Bibliography

Shadmehr R., Wise S.P. “A Simple Muscle Model”. Computational Neurobiology of Reaching and

Pointing”. 2004.

Kothera C.S., Jangid M., Sirohi J., Wereley N.M. “Experimental Characterization and Static Modeling of

McKibben Actuators”. ASME. 2009.

Saga N., Nakumura T. Yaegashi K. “Mathematical Model of Pneumatic Artificial Muscle Reinforced by

Straight Fibers”. Journal of Intelligent Material Systems and Structures. 2007.

Tondu B., Lopez P. “Modeling and Control of McKibben Artificial Muscle Robot Actuators”. IEEE Control

Systems Magazine. 2000.

Wickrumatunge K.C., Leephakpreeda T. “Study on mechanical behaviors of pneumatic artificial muscle”.

International Journal of Engineering Science. 2009.

Sanchez A., Mahout V., Tondu B. “Nonlinear parametric identification of McKibben artificial pneumatic

muscle using flatness property of the system”. Proceedings of the 1998 IEEE International Conference

on Control Application. 1998.

Monahan, M. “Scalability Study For Robotic Hand Platform”. Thesis. 2010.

Daerden, F., Lefeber, D. “Pneumatic Artificial Muscles: Actuators for Robotics and Automation”. Brussels

University Mechanical Engineering Department. 2006.

Hemingway, S. “Investigation of Pneumatic Muscle Actuators as Underwater Actuators”. Rochester Institute

of Technology.

Hemingway, S. Thesis Proposal. Rochester Institute of Technology

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