Simulation of Squat Exercise Effectiveness Utilizing a Passive Resistive Exoskeleton in Zero Gravity

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2 Simulation of Squat Exercise Effectiveness Utilizing a Passive Resistive Exoskeleton in Zero Gravity A thesis submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE In the School of Aerospace Systems of the College of Engineering and Applied Science April 2016 by Eric J. Stetz Bachelor of Science University of Cincinnati, June 2012 Committee Chair: Grant Schaffner, Ph.D.

3 Simulation of Squat Exercise Effectiveness Utilizing a Passive Resistive Exoskeleton in Zero Gravity Abstract Weightlessness induced bone loss is an unsolved health risk to anyone spending long duration stays in space. It causes returning astronauts to face months of recovery time, and years of heightened risk of fracture. Effective countermeasures must be developed to ensure the safety of future long term missions to an asteroid or Mars. The capability to simulate an exercise countermeasure and analyze its usefulness for bone loss mitigation will greatly advance the ability to design countermeasures for specific missions. This study succeeded assessing the performance of a prototype exoskeleton exercise countermeasure device, and creating a simulation model of it. This model was successfully used to demonstrate the capability to analyze the relative osteogenic performance of an exercise in weightlessness. Evidence for the use of exoskeleton based exercise countermeasures was shown by the results, as well as the improved osteogenic potential of dynamically loaded exercises over statically loaded ones. Several deficiencies in the models and simulations were also found, and areas to improve were outlined. Further research must be done to optimize the musculoskeletal models for resistive exercise, and improve the modeling of interfaces between man and machine. i

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5 Acknowledgements I owe a debt of gratitude to the numerous individuals whose support helped me throughout this project. First my advisor, Dr. Grant Schaffner, who was instrumental obtaining this project for me. His constant support kept me on the right track and toward making progress. Also to Roger Rovekamp, who was gracious enough to provide the exoskeleton this project is centered on, provide feedback and ideas throughout the project, and serve on my thesis committee. I also owe thanks to the engineers at NASA John Space Center and IHMC for building the exoskeleton prototype and loading it to me for my research. I would also like to thank Dr. Kelly Cohen for taking the time to serve on my thesis committee. I owe a tremendous thanks to Gaurav Mukherjee for introducing me to biomechanics, and always pushing me to do my best work, even back when I was an undergraduate. He served as a constant inspiration of hard work and creativity, and provided invaluable advice for successfully navigating graduate school and life. I would like to thank Dr. Daniel Humpert and Curtis Fox for providing support with lab equipment that was invaluable with our limited resources. I would like to thank my colleagues in the HSSL lab, Brandon Brown, Siddharth Sridhar, Prashanth Balasubramaniam, and Satya Siri Mummidivarapu, for all of your assistance with motion capture and OpenSim. A special thanks goes to Siddharth Sridar and John Martin for helping with the tireless work of setting my experiment up, as well as to all of the anonymous subjects who volunteered to make my study possible. I am grateful for the support of my girlfriend Venicia. I would not have been able to complete my degree without her unwavering support, compassion, and understanding. I am also grateful iii

6 for the support of my parents. Their unyielding trust and belief in me allows me to do what I love. Thank you. iv

7 Table of Contents Abstract... i Acknowledgements... iii Table of Contents... v Acronyms and Symbols... vii List of Figures... viii List of Tables... xi 1 Introduction Background and Motivation Research Goals and Approach Thesis Outline Literature Review Effects of Microgravity Exercise Countermeasures Measuring Exercise Effectiveness Osteogenic Potential Daily Load Stimulus Exercise Simulation Experimental Methods Passive Resistive Exoskeleton Data Acquisition Kinematic Data Acquisition External Force Collection Experimental Protocol Modeling and Simulation Human Modeling Calculation of Muscle Forces and Joint Contact Forces Exoskeleton Modeling Defining Geometry and Properties Resistive Band Calibration Creating OpenSim Model Validation of Exoskeleton model Exoskeleton Exercise Design and Analysis Results Kinematics Muscle and Joint Reaction Forces from Experimental Conditions Simulated Exoskeleton vs Experimental Exoskeleton Zero Gravity Exercise Effectiveness Comparison Discussion Kinematics Muscle and Joint Reaction Forces from Experimental Conditions Simulated Exoskeleton vs Experimental Exoskeleton v

8 6.4 Zero Gravity Exercise Effectiveness Comparison Conclusion and Recommendations Exoskeleton Simulation Findings Zero Gravity Exercise Findings Suggestions for Future Work References vi

9 Acronyms and Symbols abmd Areal Bone Mass Density ARED Advanced Resistive Exercise Device BMD Bone Mass Density CEVIS Cycle Ergometer with Vibration Isolation CMC Computed Muscle Control COLBERT Combined Operational Load-Bearing External Resistance Treadmill DLS Daily Load Stimulus DXA Duel-energy X-ray Absorptiometry EDLS Enhanced Daily Load Stimulus ID Inverse Dynamics IK Inverse Kinematics ired Interim Resistive Exercise Device ISS International Space Station OI Osteogenic Index QCT Quantitative computer tomography RRA Residual Reduction Algorithm TVIS Treadmill with Vibration Isolation and Stabilization vbmd Volumetric Bone Mass Density vii

10 List of Figures Figure 1-1. Experiment and simulation data workflow...4 Figure 3-1. Passive Resistive Exoskeleton...15 Figure 3-2. Front and side views of marker set...17 Figure 3-3. Exoskeleton marker set...18 Figure 3-4. Design rendering of the foot mounting apparatus, shown with models of the force plates and the exoskeleton ankle brackets attached. One force plate is shown transparent in the rendering to show how the beams wrap underneath it...20 Figure 3-5. Exoskeleton attached to the foot mounting apparatus and the experimental setup...20 Figure 3-6. Correcting shoulder forces...25 Figure 3-7. Squat to stand motion from subject 1 kinematic data...30 Figure 3-8. Stand to squat motion from subject 1 kinematic data...30 Figure 4-1. Unscaled human full body lower extremity model...32 Figure 4-2. CAD model of the Exoskeleton created in SolidWorks...38 Figure 4-3. Center of gravity and moment of inertia calculation using SolidWorks...38 Figure 4-4. Resistive band test setup...41 Figure 4-5. Resistive band force vs length experimental data...41 Figure 4-6. Exoskeleton Dynamic Model...43 Figure 5-1. Squat Kinematics for Subject Figure 5-2. Squat Kinematics for Subject Figure 5-3. Squat Kinematics for Subject Figure 5-4. Squat Kinematics for Subject Figure 5-5. Residual Forces at the pelvis in the X, Y and Z directions, for all subjects...52 Figure 5-6. Residual Moments at the pelvis about the X, Y and Z axes, for all subjects...52 Figure 5-7. Right and left leg quadriceps femoris force for all subjects from the simulation using experimental data...53 Figure 5-8. Right and left leg plantar flexors force for all subjects from the simulation using experimental data...54 Figure 5-9. Right and left leg hamstrings force for all subjects from the simulation using experimental data...54 Figure Right and left leg glutei force for all subjects from the simulation using experimental data...55 Figure Right and left leg hip joint reaction force resultant for all subjects from the simulation using experimental data...56 Figure Right and left leg tibiofemoral joint reaction force resultant for all subjects from the simulation using experimental data...56 Figure Right and left leg ankle joint reaction force resultant for all subjects from the simulation using experimental data...57 Figure Right and left leg lumbar joint reaction force resultant for all subjects from the simulation using experimental data...57 Figure Residual Forces at the pelvis in the X, Y and Z directions for all subjects...59 Figure Residual Moments about the X, Y, and Z axes for all subjects...60 Figure Exoskeleton model reserve forces for subject viii

11 Figure Exoskeleton model reserve forces for subject Figure Exoskeleton model reserve forces for subject Figure Exoskeleton model reserve forces for subject Figure Subject 1 quadriceps femoris force comparison...62 Figure Subject 1 plantar flexors force comparison...63 Figure Subject 1 hamstrings force comparison...63 Figure Subject 1 glutei force comparison...63 Figure Subject 2 quadriceps femoris force comparison...64 Figure Subject 2 plantar flexors force comparison...64 Figure Subject 2 hamstrings force comparison...64 Figure Subject 2 glutei force comparison...65 Figure Subject 3 quadriceps femoris force comparison...65 Figure Subject 3 plantar flexors force comparison...65 Figure Subject 3 hamstrings force comparison...66 Figure Subject 3 glutei force comparison...66 Figure Subject 4 quadriceps femoris force comparison...66 Figure Subject 4 plantar flexors force comparison...67 Figure Subject 4 hamstrings force comparison...67 Figure Subject 4 glutei force comparison...67 Figure Subject 1 hip joint reaction force comparison...68 Figure Subject 1 tibiofemoral joint reaction force comparison...68 Figure Subject 1 ankle joint reaction force comparison...68 Figure Subject 1 lumbar joint reaction force comparison...69 Figure Subject 2 hip joint reaction force comparison...69 Figure Subject 2 tibiofemoral joint reaction force comparison...69 Figure Subject 2 ankle joint reaction force comparison...70 Figure Subject 2 lumbar joint reaction force comparison...70 Figure Subject 3 hip joint reaction force comparison...70 Figure Subject 3 tibiofemoral joint reaction force comparison...71 Figure Subject 3 ankle joint reaction force comparison...71 Figure Subject 3 lumbar joint reaction force comparison...71 Figure Subject 4 hip joint reaction force comparison...72 Figure Subject 4 tibiofemoral joint reaction force comparison...72 Figure Subject 4 ankle joint reaction force comparison...72 Figure Subject 4 lumbar joint reaction force comparison...73 Figure Subject 1 shoulder force comparison...75 Figure Subject 1 foot force comparison...75 Figure Subject 2 shoulder force comparison...76 Figure Subject 2 foot force comparison...76 Figure Subject 3 shoulder force comparison...77 Figure Subject 3 foot force comparison...77 Figure Subject 4 shoulder force comparison...78 Figure Subject 4 shoulder force comparison...78 Figure 5-61: Subject 1 resultant joint reaction forces for the hip, tibiofemoral, ankle, and lumbar joints...79 ix

12 Figure 5-62: Subject 2 resultant joint reaction forces for the hip, tibiofemoral, ankle, and lumbar joints...80 Figure 5-63: Subject 3 resultant joint reaction forces for the hip, tibiofemoral, ankle, and lumbar joints...81 Figure 5-64: Subject 4 resultant joint reaction forces for the hip, tibiofemoral, ankle, and lumbar joints...82 Figure 5-65: Subject 1 resultant joint reaction forces for the hip, tibiofemoral, ankle, and lumbar joints...83 Figure 5-66: Subject 2 resultant joint reaction forces for the hip, tibiofemoral, ankle, and lumbar joints...84 Figure 5-67: Subject 3 resultant joint reaction forces for the hip, tibiofemoral, ankle, and lumbar joints...85 Figure 5-68: Subject 4 resultant joint reaction forces for the hip, tibiofemoral, ankle, and lumbar joints...86 Figure Osteogenic index at each joint, for all subjects and both exercise cases...88 x

13 List of Tables Table 3-1. De-identified subject information. Height and weight percentiles calculated from National Center for Health Statistics data [38]...26 Table 3-2. Summary of experimental trials performed with each subject...27 Table 4-1. Summary of simulation cases performed for each subject...31 Table 4-2. Mass and center of gravity data for each exoskeleton part...39 Table 4-3. Moment of inertia data for each exoskeleton part...39 Table 5-1. Peak muscle forces for each muscle group from all subjects...58 Table 5-2. Peak resultant joint reaction force for each joint from all subjects...58 Table 5-3. Simulated Exoskeleton peak muscle forces for each muscle group for all subjects...73 Table 5-4. Simulated Exoskeleton peak joint reaction forces at each joint for all subjects...73 Table 5-5. Static Load exercise peak joint reaction forces at each joint for all subjects...86 Table 5-6. Dynamic Load exercise peak joint reaction forces at each joint for all subjects...87 Table 5-7. Osteogenic Index at each joint for each subject. Average osteogenic index for each joint is also calculated, as well as the overall osteogenic index...87 Table 5-8. Osteogenic Index at each joint for each subject. Average osteogenic index for each joint is also calculated, as well as the overall osteogenic index...88 Table 5-9. Daily Load Stimulus...88 xi

14 1 Introduction 1.1 Background and Motivation Bone loss due to long duration exposure to zero gravity is an important unsolved problem in manned spaceflight [4,5,6]. Development of improved devices to allow for astronauts to get required exercise during spaceflight is a priority for continued research and exploration into space. Currently, recovery of bone mass after flight is long, and some level of bone mass density loss may even be permanent [4]. This opens astronauts up to high risks of injury after flight. The loss of bone and muscle mass from atrophy due to unloading during long duration missions could also endanger the safety of missions to far away destinations such as asteroids, or Mars, where the astronauts would need their strength to perform mission critical tasks months after exposure to microgravity. While many exercise devices for use during spaceflight have been developed and used, so far their effectiveness in preventing bone loss has been poor [5,6]. Recent, more complex exercise devices have been developed, such as the ARED, which have shown increased ability to prevent bone mass density atrophy [22]. However, these devices are large, heavy, and require complex vibration isolation systems that make them impractical for use on a spacecraft. An exoskeleton is a smaller, more portable device that could potentially provide the capability to perform similar exercises as the current countermeasures. If an exoskeleton based design could be proven to provide the loading to prevent bone mas density loss, it could be applied to more demanding missions. The ability to simulate the effects of exercise with an exoskeleton device, and assess its effectiveness in retaining bone mass density would allow for faster and cheaper design optimization than costly experimental testing aboard the space station. 1

15 1.2 Research Goals and Approach The long term goal of this research is to assess the applicability of a bone loading exoskeleton as an exercise countermeasure to zero gravity induced bone mass density loss. This study works toward this goal by developing a method to simulate the exoskeleton s use by a human subject, and demonstrating a method to determine the usefulness of an exercise with the exoskeleton to retaining or growing the user s bone mass density. Bone mass density loss in astronauts is an ongoing problem. Advanced exercise equipment to combat this problem will be needed. The ability to simulate exercise devices and their impact on the user in the spaceflight environment is needed in order to lower their development time and cost. To work toward this need, the specific aims of the study are as follow: Specific Aim 1. Determine the muscle and joint contact forces of a subject performing a squat exercise while wearing the passive exoskeleton using experimental kinematic and kinetic data. Specific Aim 2. Develop a simulation model of the passive exoskeleton, and compare the muscle and joint reaction forces generated by it in a subject to those generated by the experimental kinematic and kinetic data. Specific Aim 3. Use the simulation model of the exoskeleton to compare the osteogenic potential of different proposed zero gravity exercises utilizing the exoskeleton. 2

16 1.3 Thesis Outline First, chapter 2 will review the research in zero gravity induced bone loss, the history of exercise countermeasures developed for spaceflight, methods developed to assess the osteogenic potential of exercise, and past research in exercise simulation. Then, chapter 3 will cover the details of the passive exoskeleton, as well as the experimental hardware and the experimental protocol used. Chapter 4 will detail the use of the OpenSim software to model the experimental results, and the development of a model to simulate the performance of the exoskeleton. The exercise protocols designed for the exoskeleton to be used in zero gravity are also described. Chapter 5 will cover the results of the simulations of each case, including muscle and joint reaction forces for muscle groups and joints of interest, comparisons between the experimental case and simulation model s results, and the zero gravity exercise s osteogenic potential. Chapter 6 discusses these results, the validity of the exoskeleton model, and the implications of the zero gravity exercise results. Lastly, chapter 7 covers overall conclusions of the study, as well as addressing any drawbacks, how they could be improved, and what future work can be done. This is followed by the references used in the study. Figure 1-1 shows the overall workflow of data in the study. 3

17 Figure 1-1. Experiment and simulation data workflow 4

18 2 Literature Review 2.1 Effects of Microgravity The accelerated loss of bone mass density (BMD) of astronauts during long duration spaceflight is well established [1,2,3,4,5,6,7]. Since the beginning of manned spaceflight, scientists have been interested in the physiological effects of microgravity on the human body. Prior to manned spaceflight, bedrest studies predicted that skeletal calcium would be lost during prolonged weightlessness. This was verified when metabolic studies conducted on urinary and fecal samples during the United States Gemini missions, as well as the USSR Soyuz missions, showed increases in calcium excretion from the body. These were further supported by similar studies during the Apollo program [1]. Studies from the USA Skylab program collected urine and fecal samples during flights of 28, 59, or 84 days. Data showed that urine calcium content increased progressively through the first weeks of microgravity exposure, and plateaued after approximately 1 month to 81% of the post flight value [1]. Direct scans measuring bone mineral content in the radius and ulna showed no significant changes, but the calcaneus did show significant decreases on some astronauts [1]. This reinforces that the majority of bone mass density is lost in the lower, load bearing bones, rather than the upper body. Later studies done on cosmonauts performing long duration stays of 4-12 months aboard the Russian MIR space station used Duel-energy X-ray absorptiometry (DXA) to measure areal bone mass density (abmd) [3]. They found abmd loss rates of 1.01% per month from the spine, and 1.15% per month from the femoral neck, 1.56% per month from the trochanter, 1.35% per month from the pelvis, and 0.04% per month from the arm [3]. A similar study from the MIR also indicates that 97% of all abmd loss occurred in the pelvis and legs [8]. A recent study conducted on 14 5

19 astronauts aboard the International Space Station (ISS) for 4-6 months used DXA and Quantitative computer tomography (QCT) scans preflight and post-flight to measure BMD loss. The DXA scans allowed for measurement of abmd for comparisons to previous studies, and QCT scans were used to measure volumetric bone mass density (vbmd), which allows for measurement of both trabecular and cortical BMD separately. They found abmd loss rates of 0.8% per month at the spine and % per month at the hip, which agreed with previous results from the MIR studies. The QCT results showed hip vbmd loss rates of % per month in integral bone, % per month in cortical bone, and % per month in trabecular bone [4]. While the loss rate of trabecular bone was the greatest, cortical vbmd loss was the largest in terms of mass, due to cortical bone making up the largest percentage of bone in the body. These abnormally high loss rates are caused by the drastically lower level of mechanical stresses and strains applied to the body while in microgravity, rather than when on earth. Studies done on in shoe measured foot forces experienced by astronauts aboard the ISS show that they experience far lower regular loading on the lower extremities than when on earth [9,10,11]. Using the Enhanced Daily Load Stimulus model, astronauts experience 25% less loading on the lower body during a typical day aboard the ISS, than they do during a typical day on earth. This includes the use of exercise countermeasures during spaceflight [9,10,11]. The link between mechanical loading and BMD was first established by Whedon et al. through experiments in long duration bed rest [12]. The human skeleton system is dynamically changing throughout a person s life. Bone mineral is constantly being resorbed by osteoclast cells, and reformed by osteoblast cells. An estimated 10% of a human s entire skeleton is renewed per year. Changes in the level of experienced mechanical stress can disrupt the balance of bone mass creation and resorption, 6

20 leading to a net resorption of bone mass and a weakening of the skeletal system. [6,7,13]. Measures of bone turnover point toward the unbalance being caused primarily by an increase in the osteoclast s level of resorption of bone mass, with bone formation being mostly unchanged [6,13]. Recovery of bone mass post-flight, after returning to earth has been shown to be slow. One study of BMD on ISS astronauts showed incomplete recovery of the femoral neck 1 year after returning to earth, indicating that recovery time is longer than flight time [14]. A study of postflight BMD data of astronauts and cosmonauts who spent 4-6 months in space aboard either the MIR or ISS curve fit the recovered BMD percentage verses time plot to determine a predicted rate of recovery. Recovery time to 50% of preflight BMD varied between skeletal sites from 3 months at the pelvis, to 8.5 months at the trochanter [5]. Using this data a total recovery time period of 3 years was determined for a 4-6 month spaceflight. This indicates that BMD loss during spaceflight not only has immediate physiological risks, but long term detriments as well. 2.2 Exercise Countermeasures The primary countermeasure for bone and muscle depletion during spaceflight has been exercise. Numerous exercise devices have been developed and employed throughout the history of manned spaceflight. The earliest countermeasures were tested aboard the Gemini missions, where a bungee cord was used to exercise the arms and legs [7]. The Skylab space station initially was equipped with a bicycle ergometer for cardiovascular training. After several missions, there was a desire for an exercise with a higher load on the body. Therefore a pseudo treadmill was created using bungee cords to hold an astronaut down against a low friction Teflon surface that they could run on [7,15,16]. During the space shuttle era, a passive treadmill was developed by astronaut and physician William Thorton for exercise use [7,17]. It once again used 7

21 bungee cords to ideally apply a body weight level of force to the astronaut against the treadmill surface. However, the actual foot forces produced by the exercise were never measured. The USSR/Russian space station MIR was also equipped with a passive treadmill using bungee cords, which was used for walking and running exercises as well as calisthenics and upper body resistance exercises. The cosmonauts aboard the MIR were reported to have performed 3 hours of exercise a day using this machine. However, as the BMD scans from the MIR have shown, the exercises were not effective at completely reducing loss of BMD. The ISS has been equipped with numerous much more advanced exercise devices. The first ISS treadmill was the Treadmill with Vibration Isolation and Stabilization (TVIS) [18,19,7]. One problem with the treadmill used aboard the space shuttle was that it would impart large structural vibrations into the vehicle from the ground reactions forces of the astronaut using it. Therefore the ISS treadmill was designed with a vibration isolation system to limit the vibrations imparted on the space station. The system applies load by a harness connected to the Subject Load Device, a set of linear springs that provide an adjustable force that pushes them down onto the treadmill, with the tethering load reported by a digital display. The treadmill could be used in an active or passive mode. The astronauts typically adjusted the weight to be two-thirds of their body weight and ran at speeds between 1-7 mph [19]. The ISS also was supplied with a bicycle ergometer, called the Cycle Ergometer with Vibration Isolation (CEVIS) [19]. A prototype resistive exercise machine called the interim resistive exercise device (ired) was installed on the ISS to allow for resistance exercises training. The ired produces resistance through two elastomer resistance canisters, each able to produce up to 150lb (667N) of force [18,20]. The canisters are connected via a cable to each end of a bar, allowing multiple exercises to be performed, including squats, heel raise, and dead lifts. The elastomer based resistance has several drawbacks, in that 8

22 resistance varies throughout the range of motion, with the peak resistance only occurring at the edge of the motion. Many astronauts using the ired complained too low of a max resistance and it was further augmented with bungee cords [18,20]. Astronauts aboard the ISS were allowed approximately 2.5 hours per day to work out using the TVIS, CEVIS, and ired, including equipment setup time. Studies on BMD loss from astronauts aboard the ISS while these countermeasures were in use show that they were still ineffective at preserving BMD. The ired was subsequently replaced in 2008 by the Advanced Resistive Exercise Device (ARED). The ARED is intended to be an improved version of the ired, and was designed to impart much greater loading to the user. Like the ired, it can be used to perform a variety of resistance exercises including squat, heel raise, and dead lift, while applying loads between 0 and 600lb to the user. Rather than using the elastomer canisters of the ired to generate resistance, adjustable vacuum chambers allow for even and constant loading. However, the system is very large and requires a vibration isolation system to isolate it from the space station [21]. A study was done comparing BMD and BMC measurements in astronauts who worked out with the ARED to astronauts using the ired during spaceflight [22]. It was found that the astronauts using the ARED showed lower signed of BMD degradation than the ones using the ired, showing for the first time that exercise can be used to mitigate BMD loss. In 2009 the ISS s TVIS was replaced with the Combined Operational Load-Bearing External Resistance Treadmill (COLBERT) [21]. Studies on the effectiveness of the COLBERT are still forthcoming. 2.3 Measuring Exercise Effectiveness Finding the appropriate loading profile to prevent bone resorption and promote BMD growth is an ongoing topic of research. Various animal studies have been conducted, testing alternate loading profiles against control groups to find what load levels, load frequencies, and loading 9

23 protocols are most effective. These studies have resulted in the formulation of some mathematical relations that can be used to characterize the effectiveness of an exercise. In this context, the effectiveness of an exercise is defined only as its relative proclivity toward bone growth as determined by a predefined mathematical relationship. Two of these relations that will be used are the Osteogenic Potential, and the Daily Load Stimulus Osteogenic Potential Through an examination of a number of previous studies into the effects of mechanical loading on bone remodeling, Robling et al. developed an equation that can be used to quantify the relative effectiveness of a given exercise for retaining/promoting bone strength [23,24]. Several different relationships between mechanical loading and osteogenesis are taken into consideration. First, while increasing the load force is well understood to increase the osteogenic potential of an exercise, it is also shown that dynamic loading, rather than static loading, is necessary to promote bone growth [25,23,26,24]. Experiments on rat and turkey bones commonly applied loads at frequencies ranging from 1 10Hz, and found higher rates of bone growth for the higher frequency loads. It is even shown that the peak strain needed to initiate osteogenesis tends to decrease with increasing frequency [23,26]. This may counter the thought that high, body weight replacement loads are necessary to retain bone mass. Secondly, it has been shown that bone can become desensitized to mechanical loading over a single session of exercise. Studies have shown that increasing the number of cycles of exercise have a diminishing effect on the bone growth, indicating that simply extending a single session of exercise will not improve its effectiveness. Data indicates that the sensitivity decreases with each load cycle proportional to 1/(N+1), where N is the number of load cycles. [23,24,27,28]. 10

24 Therefore, the best way to increase exercise time is to separate it into different exercise sessions with rest periods in between [23,24,29,30]. A study on separated exercise sessions found that the bone s sensitivity to mechanical loading is recovered slowly during rest. It was found it took 24 hours for 98% of sensitivity to be recovered, indicating that sensitivity is recovered at a much slower rate than it is lost [23, 24, 29]. Using these relationships, Robling et al. formulated equation 1 for the Osteogenic Index, or OI [23]. This is a value representing the effectiveness of an exercise based on the exercise intensity,, and the number of load cycles,. (1) According to Robling et al. the exercise intensity should be calculated by multiplying the peak load applied to the bone by the loading frequency. However, this was approximated as simply the peak ground reaction force in their study, as they did not have the bone force and frequency data. Equation 1 will calculate the OI for a single exercise session, but for multiple separate exercise sessions a correction factor needs to be added to the equation to account for the level of recovery since the last session. Therefore for multiple session the equation for OI is shown in equation 2, where t is the time since the last session and is a time constant, usually set to 6 hours. (2) The consequences of this model is that multiple short exercises with rest periods in between are far more effective than single, long exercise sessions. If exercise time is at a premium, as it is commonly during spaceflight, it would be better to shorten each exercise session than skip sessions. 11

25 However, there may be some issues with the model based on this research. There seems to be an inconsistency between how the loading frequency is understood to influence the effectiveness of an exercise protocol. Some studies on bone sensitivity to loading found that inserting rest periods of 8-14s between load cycles was more effective than back to back load cycles [31, 32]. This seems to contradict the thought that higher frequencies loading is better, as other studies had found. More research into the mechanism between mechanical loading and osteogenesis is needed Daily Load Stimulus Another method of characterizing loading is the Daily Load Stimulus (DLS). It is hypothesized that in order to maintain BMD, a daily mechanical stimulus must be met or exceeded, otherwise net bone resorption will begin. Carter et al. derived a relationship called the Daily Load Stimulus to characterize the total loading experienced by an individual over the course of a day [33,34]. The calculation of the DLS is shown in equation 3, where effective load stress, stress states, and is the effective load stress magnitude, is the number of load cycles at the is the number of distinct daily is the relative contribution of the stress magnitude, typically assigned as 4 [33]. (3) Later on, Genc et al. modified the DLS to create the Enhanced Daily Load Stimulus (EDLS), shown in equation 4, which replaces, the effective load stress magnitude, with, the peak ground reaction force magnitude. This allows for easily collectable ground reaction forces from 12

26 exercises to be used in place of actual bone strain values, which the ground reaction forces are assumed to be proportional too [33]. (4) The EDLS also assumes that saturation occurs after either 5 minutes of running or 20 minutes of walking, and then applies the recovery coefficient to any loading which occurs after saturation [33]. Data from a bedrest study has shown that maintaining an EDLS value comparable to preflight values through treadmill exercise can prevent hip region bone loss. Studies have shown that astronauts using countermeasures aboard the ISS only achieve 74% of preflight EDLS, showing that current exercise countermeasures are insufficient by these standards [9]. 2.4 Exercise Simulation The computational simulation of exercise using biomechanical models is a growing field. The open source program OpenSim, is seeing increasing used for simulating biomechanics in difficult to test conditions, such as in space and on other planets [35,36]. A study using OpenSim simulation calculated the joint moments and muscle forces required to perform a lifting task on Earth versus the reduced gravity levels of the Moon and Mars [35]. NASA has been increasingly interested in utilizing simulation to optimize their exercises. The Digital Astronaut Project is an ongoing project being conducted at the NASA Glenn Research Center to simulate several different resistance exercises in order to aid countermeasure development [37]. 13

27 3 Experimental Methods In order to create an accurate simulation model of the exoskeleton, the model would have to be validated against experimental data from a subject exercising with it. This required the design and construction of experimental hardware, as well as design of the experimental protocol. These are detailed in this chapter. 3.1 Passive Resistive Exoskeleton The passive exoskeleton that is the subject of this experiment is a prototype designed by engineers at NASA Johnson Space Center and IHMC. It is primarily made from aluminum and 3D printed plastic parts, and uses rubber elastic bands to provide a partially adjustable level of resistance to the wearer. Details of the exoskeleton design can be seen in figure 3-1. The exoskeleton interfaces with wearer using the shoulder pads, hip belt, and foot plates. For this experiment, the hip belt was not used, so that the majority of contact between the exoskeleton and wearer occurs only at the shoulder pads and foot plates. The exoskeleton is designed to allow the wearer to perform a squat exercise by starting from a squatting position, extending to a standing position, and then squatting back down again. The elastic resistance bands are attached to a point on the upper and lower leg. The legs are designed in a way so that the resistance increases as the subject moves from a squatted to a standing position. The resistance bands apply a force between the upper and lower leg that is transferred through the exoskeleton body and applies a compressive force on the subject, between their shoulders and their feet. The upper and lower leg each have two rings for attachment of the elastic resistance bands. This allows the band length to be slightly adjusted. The height of the exoskeleton can also be adjusted by telescoping a tube in the back to one of several 6 settings. Due to the exoskeleton s prototype plastic joints, it 14

28 cannot support a high load of resistance. It is not able to support the high resistance forces typically used in exercise countermeasures, but the resistance used is high enough to show how the exoskeleton distributes a load force across the subject, and allow for a validation between the experiment and simulation. Figure 3-1. Passive Resistive Exoskeleton 3.2 Data Acquisition In order to calculate muscle and joint reaction forces from OpenSim, full kinematics and all external forces of the human subject must be known. 15

29 3.2.1 Kinematic Data Acquisition To collect the required kinematic data of the exoskeleton and human while performing the exercise, an 8 camera motion capture system (BTS Bioengineering, Milan, Italy) was used. The system collected marker position data at 100Hz. The system tracks motion through retroreflective markers, which were attached with temporary adhesive pads on to each body part and exoskeleton part to be tracked. The subject marker set used was a based on a default OpenSim marker set, modified to allow for good marker visibility while wearing the exoskeleton. On the subject a total of 36 markers were used, 2 of which were only used during the static trial. These tracked the subject s torso, pelvis, upper legs, lower legs, and feet. Figure 3-2 shows the placement of the markers on the subject. On the exoskeleton a total of 10 markers were used to track the torso/back, upper legs, and lower legs. Figure 3-3 shows the exoskeleton marker s placement. The motion capture system s coordinate system was set up to conform to the standard for motion capture data collection defined in the OpenSim user s guide. The origin is located on the ground between the subject s feet, the x-axis is pointing in the direction the subject is facing, the y-axis is pointing directly up, and the z-axis points to the right of the subject. 16

30 Figure 3-2. Front and side views of marker set 17

31 Figure 3-3. Exoskeleton marker set External Force Collection In order to properly model the exoskeleton s effect on the subject, all external forces applied to the subject had to be collected, as well as the position of the force s application. This includes the force between the subject s feet and exoskeleton s feet, as well as the force between the subject s shoulders and the exoskeleton s shoulder pads. Due to budget and equipment restrictions, force sensors that could be placed between the human and exoskeleton feet were not 18

32 available. Therefore, to collect foot force data two existing force plates (Bertec Inc, Columbus, Ohio, USA) were used. The force plates interfaced with the motion capture system s data acquisition software, so all data collected from the two systems was automatically synchronized. They were placed so that the subject could stand with one foot placed on each plate, so that separate sets of data were collected for each foot. The force plates measured force magnitude in the x, y and z directions, the position of the center of the force applied to the plate in the motion capture system coordinate system, and the torque applied about the z, y and z axis. In order to properly measure the force between the subject s feet and the exoskeleton s feet, the subject had to stand directly on the force plates, while the exoskeleton feet would be isolated from the force plate. An apparatus was designed and constructed that allowed for the exoskeleton s feet to be connected directly to the ground, bypassing the force plates that the subject stood on. Design renderings of the foot mounting apparatus and finished product are shown in figure 3-5 below. The exoskeleton s feet are removed, and the ankles are bolted to the foot mounting apparatus. The apparatus then has a structure that wraps around the edges of the force plate, and contacts the floor. 19

33 Figure 3-4. Design rendering of the foot mounting apparatus, shown with models of the force plates and the exoskeleton ankle brackets attached. One force plate is shown transparent in the rendering to show how the beams wrap underneath it Figure 3-5. Exoskeleton attached to the foot mounting apparatus and the experimental setup 20

34 Equipment constraints did not allow for the direct measurement of the force between the subject s shoulders and the exoskeleton shoulder pads. Therefore, a method was developed to computationally determine the shoulder forces from the foot force data collected by the force plates. The forces measured by the force plates can be assumed to be composed only of the force from the subject s weight, the force exerted by the exoskeleton on the subject s shoulders, and any inertial forces as a results of movement by the subject and exoskeleton. Using the force plate data from the static, non-resistance, and resistance trials, along with some basic assumptions, the approximate shoulder forces were calculated. First, the subject s total mass was determined by taking an average of the sum of both feet s y direction force data during the static trial. This is shown in equation 1, where is the weight of the subject, is the number of samples taken, is the y direction force measured by the left foot force plate during the static trial, and is the y direction force measured by the right foot force plate during the static trial. Then, it is assumed that during the non-resistance trial, the total force measured by the force plates while the subject is unmoving is equal to the subject s mass plus the force of the exoskeleton s mass applied on the subjects shoulders. The supported exoskeleton s mass is found by subtracting the subject s mass from an average of the sum of both plate s Y direction force data during a time period where the subject is not moving. This is shown in equation 2, where is the weight of the exoskeleton that acts on the subject s shoulders, is the y direction force from the left foot force plate taken during the nonresistance trial, and is the y direction force from the right foot force plate taken during the non-resistance trial. This is only true while the subject is unmoving, because while they are moving there will also be a component of force due to the inertia of their body accelerating. 21

35 (1) (2) As there is no added resistance from the elastic bands during the non-resistance trials, the y component of the total shoulder force is equal to only the mass of the supported exoskeleton s mass. As this value is the combined shoulder force, this value had to be split between each shoulder. Rather than split the force evenly for the duration of the trial, the force was divided as to equal the ratio of the ground reaction forces. The subject usually does not stand so that their weight is evenly split between each foot. The total shoulder force was split between each shoulder in the same ratio as the ground reaction forces were measured in. Equations 3 and 4 show the formulas used to calculate each data point of the right and the left shoulder forces, respectively. is the y component of the right shoulder force, is the y component of the left shoulder force. (3) (4) The x and z components of the force were handled separately. Theoretically, the x and z ground reaction forces should be equal to zero when summed between the two feet. Therefore, any residual net force in those direction is assumed to have been caused by the exoskeleton on the shoulder. So, for all cases the x and z components of the shoulder forces were calculated by taking the negative value of the measured x or z ground reaction force data from the force plates. Equations 5, 6, 7, and 8 show the formula s used to calculate each data point of the x and z 22

36 component shoulder forces, where,,, and are the shoulder forces, and,,, and are the directional forces measured from the force plates from either the non-resistive or resistive trials. (5) (6) (7) (8) For the resistive trials, it is assumed that the total force measured by the force plate is composed of the subject s mass, the force from the exoskeleton s mass exerted on the subject s shoulders, the force from the resistive bands applied to the subject s shoulders, and inertial forces from the subject s acceleration while moving. The subject s weight is subtracted from the raw ground reaction force data using equations 9 and 10, where is the y component of the right shoulder force including inertial forces, and is the y component of the left shoulder force including inertial forces. As the force data calculated from these equations still includes the inertial component of the force data, this component must be removed from the data set in order to obtain the true shoulder force data. (9) (10) While some of the inertial force measured is from the exoskeleton, the vast majority is from the subject, and therefore needs to be removed from this data in order to generate an accurate representation of the shoulder forces. The subject masses ranged from approximately kg, 23

37 whereas the exoskeleton mass supported by the shoulder is only 5.5 kg. Since these inertial forces are constantly varying with the motion of the subject, they cannot be easily calculated and subtracted like the exoskeleton mass. In order to extract this extra force signal from the calculated force signal, an inverse dynamics analysis using Opensim had to be performed. Procedures described in chapter 4 were used to generate a model of the subject and obtain model kinematics from the motion capture data. Using the subject model, motion from the resistive trial, the ground reaction forces measured, and the shoulder forces calculated from equations 9 and 10, an inverse dynamics simulation was run. The residual forces output from this simulation produces large forces in the y direction while the subject is moving, in order to offset the inertial force signal that shouldn t be in the shoulder forces. As the other forces applied to the model are correct, the residuals contain only the extraneous inertial forces. Their signal can be then subtracted from the initially calculated shoulder forces, resulting in accurate shoulder force data. Figure 3-6 shows plots of the initially calculated shoulder forces, the inverse dynamics residuals from using those forces, then the corrected shoulder force data and the updated inverse dynamics residuals from using the corrected shoulder forces. 24

38 Figure 3-6. Correcting shoulder forces To determine the position of the shoulder forces, location data from the exoskeleton shoulder markers, as well as the subject s acromion markers were used. The z component of the location is taken from the exoskeleton shoulder markers. The x and z components are taken from the subject s acromion markers data, as these markers were found to be closer to where the exoskeleton shoulder pads interface with the subject than the exoskeleton shoulder markers. 3.3 Experimental Protocol A convenience population sample of 6 subjects was selected from students of the University of Cincinnati. All subjects in the study were male, in order to reduce any variability in kinematic data due to gender-based physiological differences. As shown in table 3-1, all subjects were 25

39 between the ages of 23 and 32, and height and weight were targeted to be between the 5th and 95th percentile. Unfortunately, it was found that subjects 5 and 6 were not within both the height and weight requirements according to the latest NCHS data. Therefore these subject s data was omitted from the results. Race was not considered during subject selection. No vulnerable subjects participated in this study, and all subject s had a good history of musculoskeletal health. No current injuries, nor active treatment were reported at the time of the study. The study was approved by the Institutional Review Board at the University of Cincinnati. Table 3-1. De-identified subject information. Height and weight percentiles calculated from National Center for Health Statistics data [38] Subject ID Height (m) 1.83 Height (in) Weight (kg) Weight (lb) Sub01 Age (yrs) Percentile Height Percentile Weight Sub Sub Sub Sub <5.00 <5.00 Sub <5.00 Subjects were required to wear either tight fitting clothing, a short sleeve or no shirt, and shorts during the study to reduce issues with marker placement errors. First the experimental procedure was explained in detail to the subject, and they were presented with the consent form to read and sign. The subject was asked for their height, weight, and age, which were then recorded. The subject was outfitted with all markers, including those used for the static trial. A photograph of the subject was taken for marker reference only. A summary of each trial performed by the subject during the experiment is shown in table

40 Figure 3-2. Summary of experimental trials performed with each subject Trial Exoskeleton Resistance Ground Reaction Force Motion Static None None Human Standing still Bodyweight Squat None None Human Squatting Non-Resistance Exo Yes None Human Squatting Resistance Exo Yes Yes Human Squatting Resistance Full Exo Yes Yes Human + Exoskeleton Squatting The first trial run was a static trial for scaling the OpenSim human model. The subject was instructed to stand upright with their arms down at their sides on the force plates, one foot on each plate, and stay still. The exoskeleton was not worn for this trial, and was removed from the force plate apparatus. Motion capture and ground reaction force data was taken for approximately 5 seconds with the subject unmoving. This was repeated 1 to 2 times if necessary. This data was collected for use in scaling the human model, and determining the subject s mass. Next, the static trial markers were removed, and a trial was done with the subject performing a simple body weight squat, also without the exoskeleton attached. The subject was instructed to begin in a squatted position, with their upper legs above parallel to the ground, at approximately a 30 or 45 degree angle. They would then move to an upright position, stand for 3 seconds, and then squat back down into their original position. The subject was instructed to take approximately 1 second to perform the standing up and squatting down movements. Motion capture and ground reaction force data was captured while verbal commands were given to tell the subject when to begin, when to move, and when the trial was over. The subject was instructed to stand upright at 3 seconds into the capture, and squat down at 7 seconds into the capture. Data was collected for approximately 10 seconds. Trials were repeated until the subject had mastered the position and timing of the squat. This step was performed to allow the subject 27

41 to practice the timing of the squat, as well as possibly compare results to a bodyweight squat. This data ended up not being used for simulation. Next, a trial is performed with the subject performing the squat while wearing the exoskeleton without any resistance. The subject was instructed to rest while the exoskeleton was prepared and mounted to the force plate apparatus. With the resistive bands detached, the subject was then fitted into the exoskeleton, and the back was adjust if necessary so that the exoskeleton hip joint is as closely aligned with the subject s hip joint as possible. A photograph of the subject wearing the exoskeleton is taken for marker reference only. Motion capture and ground reaction force data was captured while the subject performed the same exercise as the previous trial, while wearing the exoskeleton. Verbal commands were once again used to instruct the subject when to begin, to stand upright at 3 seconds into the trial, to squat down at 7 seconds into the trial, and when the trial was over. Data is collected for 2 to 3 trials. This step was performed in order to determine the forces the exoskeleton exerted on the subject without resistance applied. It was used in the calculation of the shoulder forces. Next, a trial is performed with the subject performing the squat while wearing the exoskeleton with resistance. The resistive bands on the exoskeleton s legs are attached, and motion capture data and ground reaction force data was captured while the subject was instructed to perform the squat exercise again, with verbal commands instructing the subject when to move. Data is collected for 2 to 3 trials. This step was performed to determine the forces applied by the resistive bands, as well as collect data for use in simulating the muscle and joint reaction forces in the subject when using the exoskeleton prototype to exercise. This data serves as the experimental conditions in which the simulation model will be compared. 28

42 Next, a trial is performed with the subject performing the squat exercise while wearing the exoskeleton again, but while using the exoskeleton feet to stand directly on the force plates, without using the force plate apparatus. The subject removes the exoskeleton, and the exoskeleton is removed from the force plate apparatus, which is also removed entirely from the force plates. Then, the exoskeleton s feet at reattached to the ankles. The subject then puts the exoskeleton on once again, and is strapped into the foot plates, and the resistive bands are attached. Motion capture and ground reaction force data is captured while the subject is instructed to perform the squat exercise again, with verbal commands instructing the subject when to move. Data is collected for 2 to 3 trials. This data is collected to obtain motion capture and ground reaction force data to setup the exoskeleton simulation model with real kinematics and accurate ground reaction forces from the entire subject and exoskeleton. This data will be used on the simulation model that is compared to the experimental conditions. It will also be modified for use with the zero gravity exercise simulations. The subject is then instructed to remove the exoskeleton and remove the markers. Figures 3-7 and 3-8 below show key frames of the squat motion as performed by subject 1, wearing the exoskeleton. Figure 3-7 shows the initial squat to stand movement, and figure 3-8 shows the stand to squat movement. The kinematics are depicted using the OpenSim models, as actual video was not obtained during the experiment. 29

43 Figure 3-7. Squat to stand motion from subject 1 kinematic data Figure 3-8. Stand to squat motion from subject 1 kinematic data 30

44 4 Modeling and Simulation The open source musculoskeletal dynamic modeling and simulation program Opensim (3.3, Stanford, CA) was utilized to model and simulate the dynamics of both the subjects of the study and the exoskeleton. This allowed for the computation of muscle and joint reaction forces of the subject while performing the exercise, the simulation of the exoskeleton s dynamics, and its effects on the user. Four different simulation cases were completed for each subject in order to meet the aims of this study. A summary of each case can been seen in table 4-1. The first two cases, Experimental Conditions and Simulated Exoskeleton, are done to find the results from the experimental exercise and compare the ability of the exoskeleton model recreate those results. The last two cases simulate exercises with the exoskeleton in zero gravity with a static and a dynamic loading profile in order to compare the osteogenic potential of the two, and assess the usefulness of the exoskeleton as a zero gravity exercise device. Many tasks had to be completed in order to create, validate, and assess the effectiveness of the exoskeleton design using OpenSim. This chapter covers these steps. Table 4-1. Summary of simulation cases performed for each subject Simulation Case Experimental Conditions Simulated Exoskeleton Zero Gravity Exercise: Static Load Zero Gravity Exercise: Dynamic Load Model Human Human + Exoskeleton Human + Exoskeleton Human + Exoskeleton Kinematics Resistance Exo Resistance Full Exo Resistance Full Exo Resistance Full Exo External Forces Gravity GRF + Shoulder Forces Earth GRF + Resistive Band Earth Modified GRF and Knee Actuator Static Torque Modified GRF and Knee Actuator Dynamic Torque Zero Zero 31

45 4.1 Human Modeling To accurately model the human subject, a standard torso and lower extremity musculoskeletal model included with OpenSim, and intended for analyzing human movement of the lower extremities, is modified to match the subject anthropometry using the motion capture and subject mass data. The model, shown in figure 4-1, possess 10 bodies, 23 degrees of freedom, and 92 muscle-tendon actuators. The scaling tool in OpenSim is used to rescale the body lengths to match the subject s proportions, referencing the motion capture data obtained during the static trial. The model s mass is also adjusted so that the total body mass is equal to the subject s mass, while preserving the mass ratio of each body part. Figure 4-1. Unscaled human full body lower extremity model 32

46 4.2 Calculation of Muscle Forces and Joint Contact Forces The scaled human model is then used to compute the muscle and joint reaction forces in the subject during the squatting trials, through the use of the Inverse Kinematics (IK), Inverse Dynamics (ID), Residual Reduction Algorithm (RRA), and Computed Muscle Control (CMC) tools in OpenSim. Inverse Kinematics steps through the motion capture data and calculates a set of generalized coordinates, e.g. joint angles and model translations, which best fit the experimental data by minimizing marker and coordinate error. The best fit is characterized by a weighted least squares problem, shown in equation 1, where for, is the vector of the generalized coordinates being solved is the experimental position of marker i, marker on the model, and is the position of the corresponding is the experimental value for coordinate j. This is solved in OpenSim by a general quadratic programming solver, using a convergence criterion of and a limit of 1000 iterations. (1) for all prescribed coordinates j The resulting generalized coordinate data from Inverse Kinematics is used by Inverse Dynamics, RRA and CMC to prescribe the motion of the model. Inverse Dynamics calculates the generalized forces at each joint required to perform the prescribed motion. This does not directly generate the muscle and joint reaction forces, but is useful for checking for any errors in the model, motion data, or external forces applied. ID works by taking the motion data, external forces, and equations of motion for the model and solves these for the net forces and torques at each joint. Motion capture and external force measurement errors, as well modeling inaccuracies, can lead to dynamic inconsistencies where the acceleration 33

47 from the motion and the forces on the model do not satisfy newton s second law. Therefore, residual forces and moments are applied to the model s pelvis to account for any inconsistencies. Minimizing the residual forces is essential to producing accurate results. If higher than desired residual forces are encountered when running ID, the Residual Reduction tool can be run to attempt to improve the model s accuracy. RRA also uses the motion and external force data to calculate generalized forces at each joint, but it also alters the torso mass center and allows for adjustment in the kinematics of the model in order to minimize the magnitude of force and torque residuals. To do this, rather than using an inverse dynamics approach to solve for the forces, actuators at the model s joints are controlled with a tracking simulation to have the model complete the prescribed motion. The model begins at the generalized coordinates specified at the initial time from the IK results, then steps the model through small time periods where force values for each actuator are calculated in order to make the model move from the current coordinates to those at the end of the time step. The actuator forces and torques are calculated by minimizing an objective function. After the simulation, the x and z moment residuals are used to recommend adjustments to the torso mass center. The y force residual is used to calculate recommended adjustments to the model mass. The simulation is repeated with limited and low weighted residuals in order to produce altered kinematics that may still provide a realistic simulation, but with lower residuals. My simulation produced low enough moment residuals that adjustment of the mass and center of mass was not needed. However, the kinematic adjusts were used for all my simulations, as they produced only very small changes in the model kinematics, but did decrease many residual force peaks to below acceptable limits. 34

48 Computed Muscle Control calculates a complete set of muscle excitations that can be used to drive a dynamic musculoskeletal model to track a prescribed motion. These excitations can be used to directly calculate the muscle forces, as well as the joint reaction forces. Like RRA, CMC simulates the motion of the model during discrete time intervals, and computes the muscle activation level that will drive the generalized coordinates of the musculoskeletal model from the initial coordinates to the final coordinates. The muscle activations are calculated through a combination of proportional-derivative (PD) control and static optimization. Starting with the initial model states, CMC uses the first 0.03 seconds of time to compute the initial muscle states. Then during each time interval, the first step is to use the PD control law shown in equation 2 to compute a set of desired accelerations that will drive the model coordinates toward the prescribed coordinates. Here, is the set of desired accelerations, is the model coordinates, is the set of prescribed coordinates, is the feedback gain for velocity, and is the feedback gain for position. (2) As muscle forces cannot change instantaneously, the accelerations are computed for a time in the future. This time constant is 0.01s by default, but as that constant was found to cause unstable activation oscillations in the ankle for these simulations, a shorter time constant of was chosen, which corrected the unstable oscillations. The default feedback gains of and were used, which satisfy the relationship needed for critical dampening. To calculate the actuator controls, static optimization is used to distribute the load across synergistic actuators. Two different formulations of static optimization are supported in OpenSim, the slow target and the fast target. The slow target, shown in equation 3, consists of a 35

49 performance criterion J that is a weighted sum of squared actuator controls plus the sum of desired acceleration errors. (3) The fast target, shown in equation 4, is a sum of squared controls augmented by a set of equality constraints C that requires the desired accelerations to be within the tolerance set for the optimizer. (4) The default formulation is the fast target, as it generally produces both faster and better tracked results. However, there is a chance that the fast target will fail if the constraints cannot be met, resulting in failure of CMC. To prevent the fast target from failing, reserve actuators are usually placed on each joint of the model, to provide extra torque if the model s muscle are not strong enough to properly actuate the model. These reserve actuators are usually made very weak, so that the optimizer will not use them unless necessary. For all simulations with only the human model, the fast target was used in CMC to compute muscle forces. However, during the human and exoskeleton simulations the fast target would fail, likely from the complexity of the model and connections. Therefore, the slow target was used for all simulations with the exoskeleton model. 4.3 Exoskeleton Modeling To be able to assess the effectiveness of the exoskeleton for alternate exercises in different environments, a full dynamic model of the exoskeleton had to be created in OpenSim and 36

50 attached to the human model modified for each subject. As the exoskeleton model had to be created from scratch, its geometry, joint degrees of freedom, mass, and inertial properties all had to be completely characterized. The stiffness properties of the resistive bands also had to be found in order to properly model their effects on the exoskeleton. This sections details the steps taken to create the exoskeleton model Defining Geometry and Properties To characterize the geometry of the exoskeleton, it was disassembled and each limb was weighed and measured very carefully with a tape measure or calipers. Then, each part was recreated using the SolidWorks CAD program (Dassault Systems), seen in figure 4-2. A mass density was applied to each part based on the materials it was composed of and the measured part mass. SolidWorks could then calculate the center of gravity and moments of inertia for each part based on their geometry and mass, as shown in figure 4-3. These are shown below in table 4-1 and 4-2. OpenSim also allowed for export of the geometry files into the.stl format, which OpenSim can read and use graphically in models. The exoskeleton has 6 joints, each with 1 rotational degree of freedom. These are located at the exoskeleton s hips, knees, and ankles. 37

51 Figure 4-2. CAD model of the Exoskeleton created in SolidWorks Figure 4-3. Center of gravity and moment of inertia calculation using SolidWorks 38

52 Table 4-2. Mass and center of gravity data for each exoskeleton part Mass and Center of Mass (wrt to origin of part) Body Pelvis-Back Sub 1 Pelvis-Back Sub 2-3 Pelvis-Back Sub 4 Pelvis-Back Sub 5-6 UpperLeg-Left UpperLeg-Right LowerLeg-Left LowerLeg-Right AnkleFoot-Left AnkleFoot-Right Mass (kg) X (m) Y (m) Z (m) Table 4-3. Moment of inertia data for each exoskeleton part Moments of Inertia (kg m2) (wrt to center of mass) Body Pelvis-Back Sub 1 Pelvis-Back Sub 2-3 Pelvis-Back Sub 4 Pelvis-Back Sub 5-6 UpperLeg-Left UpperLeg-Right LowerLeg-Left LowerLeg-Right AnkleFoot-Left AnkleFoot-Right Ixx Iyy Izz Ixy Ixz Iyz Resistive Band Calibration To model the resistive bands the force/distance relationship of the bands had to be experimentally determined and fit to a function that could be modeled in OpenSim. The force exerted by the bands when held at a range of lengths was recorded. An Omega LC202-1K load cell was used, with excitation provided by a Vishay 2310 Signal Conditioner. Data acquisition was performed with a National Instruments USB-6009, connected to a lab computer running 39

53 MATLAB, with a custom script that interfaced with the data acquisition board to sample and record data. The load cell was attached to one of the resistive bands, and clamps were used to hold either end of the band firmly at any required position. An image of the setup is shown in figure 4-4. The band was started at 8 inches (0.20m), just above its resting length, and data was collected at 100Hz for approximately 5 seconds. Then, the band was stretched 1 inch to 9 inches, clamped down, and data was collected again. This was repeated until the band length reached 14 inches (0.36m). Then, the band was relaxed down 1 inch to 13 inches, and data was collected again. This was repeated until the band length was 8 inches. This way, force data was collected while the band was being stretched and relaxed, so any hysteresis in the bands would be detected. The data for each length was averaged over the collection time and plotted in figure 4-5. Data for 8 inches (0.20m) and 9 inches (0.23m) while relaxing the band is missing, as they were clear outliers likely caused by errors in the load cell. As seen in figure 4-5 there was no clear hysteresis in the results, so no attempt to model it was necessary. Microsoft Excel was used curve fit an equation to the data. A polynomial equation with an R 2 =0.9968, shown in figure 4-5, was found to provide the best fit, as the data was clearly nonlinear. This equation will allow for accurate modeling of the resistive bands in OpenSim. 40

54 Figure 4-4. Resistive band test setup Figure 4-5. Resistive band force vs length experimental data 41

55 4.3.3 Creating OpenSim Model Once all of the properties of the exoskeleton were characterized, the OpenSim model could be created. OpenSim models are made up of objects, such as bodies, joints, and muscles. These are defined in a text file utilizing the xml code structure, which can be created or edited with any text editor. The exoskeleton model was created as a text file, and was added to each subject s scaled model. Body objects were created for each of the exoskeleton s separately moving parts, with the mass and inertial properties determined from the measurements and CAD model calculations. The CAD graphics for each part are imported for visual representation of each body. Bodies that are attached must be created with a defined joint to another parent body. The exoskeleton s base body was defined as the back/pelvis. From this body the right and left lower leg bodies were created with 1 degree of freedom rotational joints located at their attachment point. Each upper leg then had its respective lower leg body attached with a 1 degree of freedom joint, and a foot body attached to each lower leg body with a 1 degree of freedom joint. An image of the exoskeleton model is shown in figure

56 Figure 4-6. Exoskeleton dynamic model (left), Exoskeleton model attached to human model (right) In order to simulate the resistive bands, the ExpressionBasedPointToPointForce object was used. It allows a spring object to be attached at any point to two separate bodies, and allows for a nonlinear function to be used to define the force/length property of the object. The points for the attachment of the object were set as the location of attachment for the resistive bands on the upper leg and lower leg bodies. The only drawback of the object, is that it will exert a negative force if the object s length is lower than the resting length of the bands. However, the bands never went below the resting length by a more than a negligible amount during any subject s trials, so this did not cause an issue. As the exoskeleton model s bodies were not attached by any joint properties to the human model, a method of modeling the interface between the two models had to be developed. This was not a trivial task, and several approaches had to be tested in order to find an appropriate connection. 43