Introduction to Biomaterials
Final 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, howeverthe 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 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 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 Leephakpreedaexamine 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. 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 functions[1]. The device is pictured in Figure 2.
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 betweencreating 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 atthe Test Setup
The fundamental formula used forcalculating this area is A = , 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
When best-fit lines were created for the respective data sets, it was determined that a 6th order polynomial of the form F = A+B+C+D+E+Fx+G fit the curves suitably well, yielding an 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 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 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.