人体简化机构动力学3

Department of Veterans Affairs Journal of Rehabilitation Research and Development Vol . 34 No . 2, April 1997 Pages 203-213 An experimental device for investigating the force and power requirements of a powered gait orthosis Brent J. Ruthenberg, MSME; Neil A. Wasylewski, BSME ; John E. Beard, PhD Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, Houghton, MI 49931 Abstract—The Powered Gait Orthosis (PGO) is a powered exoskeleton developed as an experimental device to provide bipedal locomotion to individuals with physical impairment. The current prototype consists of a single degree of freedom (DOF) system for each leg, providing power and proper dis- placement required for bipedal locomotion . It is the goal of this research to obtain the forces that are present in the device while it is in normal operation . In addition, the time ratio of the hip function generator has been varied to determine the effect that different time ratios have on system forces and required user energy. The time ratio is the relationship between the time period that the thigh is in swing phase and when it is in support phase . Knowing the forces in the system and the optimal time ratio will allow for the design and construction of a feasible device for the rehabilitation and assistance of individuals who have lost the ability to walk. Key words : bipedal locomotion, gait, ground reaction forces, hip torque, multiple sclerosis, orthosis, powered walking exoskeleton. INTRODUCTION For a powered exoskeleton to be used as an aid in walking it must be lightweight, easy to don and doff, sim- ple to maintain, inexpensive, unobtrusive, quiet, and have This material is based upon work supported, in part, by funding provided by the Whitaker Foundation, Mechanicsburg, PA 17055. Address all correspondence and requests for reprints to : John E . Beard, PhD, Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295; email: jebeard@mtu.edu . sufficient walking distance on a single charge . To design such a device, one of the requirements is an understand- ing of the forces transmitted through the device to the user so the weight and power requirements can be mini- mized. The forces and power that occur during gait can be divided into two components : those transmitted through the individual (skeletal loading), and those transmitted through the brace . This article will focus on a study con- ducted at Michigan Technological University (MTU) to determine quantitatively the amount of force that such a device must support during gait and the power needed as a function of step cycle. Background Currently, researchers at MTU are studying the design of a device known as the Powered Gait Orthosis (PGO) as shown in Figure 1 . This particular configura- tion of the PGO is the fourth generation of prototypes. Table 1 details the significance of each prototype used in the research program . The long-term goal of the pro- gram is to develop an orthosis that would be used in a home or work environment as an alternate to the wheel- chair for certain tasks . The physical profile of the users would probably fit characteristics defined by Seireg and Grundman (1) : "full upper extremity strength capabili- ty ; moderate to full trunk stability ; the patient can shift body mass with conscious effort ; the patient can stand with bracing ." Many researchers have investigated the feasibility of exoskeleton type walking braces, including externally powered, patient-powered, and hybrid systems . A brief history of these devices would include Handyman and 203 204 Journal of Rehabilitation Research and Development Vol . 34 No . 2 1997 Figure 1. Powered gait orthosis. Table 1. Prototype progression of PGO. Na . Highlights/Aeromplishments 1 Swing gait, pendulum-like device with fixed knee investigated power requirements tested different function generators established state testing approval helped in recruiting of test subjects 2 Added power for knee flexion found that minimal power is needed at knee, as predicted by Inman (2) found no advantage in varying motor speed, decreased battery life 3 Hydraulically actuated design provided an accurate, semi-programmable, repeatable gait system friction prevented torque determina- tion (many variables) found that a large percentage of forces were carried by skeletal loading 4 Mechanized hip and knee design added cam-modulated linkage for knee function generator able to vary time ratio to investigate effect on gait performed complete force analysis Hardirnan, cybernetic anthropomorphous machines developed by General Electric for the military, to be worn as exoskeletons for strength multiplication (3) . Kato et al. did extensive research in powered prosthetics for persons with transfemoral amputation (4) . Thring built an exoskeleton for arthritics to transfer the load from the knee joints to a leg brace through a bicycle type seat attached to the leg braces (5) . As reported by Vukobratoivic, powered exoskeleton systems that were capable of climbing stairs were developed in Warsaw, Poland (6). Popovic and Schwirtlich, with their self-fitting mod- ular orthosis (SFMO), proposed a nonmotorized device to 205 RUTHENBERG et al . Powered Gait Orthosis restore locomotion (7) . Through his earlier work, Popovic concluded that a totally powered external brace was an inappropriate technique for gait restoration in subjects with spinal cord injury (SC!) . The ORLAU ParaWalker TM was developed as a practical patient-powered device and is established with an extensive patient performance base (8,9) . The Louisiana State University (LSU) reciprocat- ing gait orthosis (RGO) was initially developed for use by children and is now used as a patient-powered device for both children and adults (10). Stallard et al . added func- tional neuromuscular stimulation (ENS) to the ORLAU ParaWalker for a hybrid system with success in decreas- ing the energy requirements of the user (11) . Solomonow has also been successful in adding ENS to the RGO (12). Seirig and Grundman have concluded, in contrast to Popovic, that an externally powered device is feasible, although their device was primarily used as a research tool (1). METHODS Design Each leg of the current PGO prototype is a one degree of freedom (DOE) system that produces a repeat- able gait. A one DOE system requires a single input (motor) to control the positions of all of the links in the system. In the case of the PGO, the input for each leg is created by a 13 .2 volt DC motor that turns the input gear, Link 2 (Figure 2) . The battery pack and control circuit for the motors can be fastened to the back of the corset. The walking cycle is initiated when the user or lab assistant pushes the start button on the control pad . Once motion for a particular leg is initiated, the control circuit allows it to go through exactly one cycle (toe-off to heel- strike), at which time the button for other leg is pushed. This causes the leg initially at rest to proceed to heel- strike from toe-off. As familiarity increases with the device, it is possible for the user to initiate the motion of the second leg before that of the first is complete . This process is very similar to natural gait in form. The con- trols for automatic repetitive motion will be used during the next testing stage to insure that users will take a con- tinuous, full stride as they transverse the length of the laboratory. The hip is controlled by a class one, four-bar (i .e ., crank-rocker) mechanism that consists of Links 1, 2, 3, and 4, where I is attached to the user's torso (which acts as the reference link or kinematic ground for the mecha- nism) . The knee is actuated with the use of a cam-modu- lated linkage, the cam profile being machined into the face of Link 8 (lower gear) and the follower attached to Link 5 . Link 2 (upper gear) is the crank of the four-bar mechanism, and it also causes the rotation of the lower gear, which in turn drives the cam-modulated linkage. Since the cam follower is captured in a slotted cam pro- file, it always remains in contact with the cam during flexion and extension . This produces a fixed effect: though the knee function is always changing, at each instant in time (percent of cycle) the knee is at a specific fixed point, unable to change from its intended function. Since it is the primary goal of this project to mechanically approximate natural human gait, it is nec- essary to have a quantitative definition of natural gait. Inman provided the knee and thigh angles needed as boundary conditions for the evolution of the PLO's hip and knee function generators (1) . Inman's work consid- ered bipedal locomotion of many nondisabled test sub- jects . Figures A-1 and A-2 of the Appendix compare the gait angles defined by Inman and those produced by the PGO. Notice in Figure A-2 that the knee output of the PGO shows no discernible difference to that defined by Inman. Due to its simplicity and nature, the four-bar link- Figure 2. Kinematic sketch of the PGO . 206 Journal of Rehabilitation Research and Development Vol . 34 No . 2 1997 age used for the hip function is not able to achieve the same degree of replication found at the knee . It was deter- mined that a compact cam modulated linkage was not feasible for the hip due to the large power requirements there . A feasible cam mechanism, and hence better accu- racy, was possible at the knee because of the relatively low power requirements of that joint. Subjects Two test subjects have participated in the experi- ments conducted on the PGO . Testing began at LSU with an individual who has an incomplete SCI at the C2 level and was a quadriplegic in the rehabilitation stage . The majority of the work conducted at LSU was in determin- ing power requirements of the PGO (13) . The other test subject participated at MTU ; he is in the advanced stages of multiple sclerosis and has minimal use of his legs. These subjects may not have been the ideal candidates for testing of the PGO, but both volunteered, lived in close proximity to the testing labs, and had experience walking with the RGO or leg braces . Additional candi- dates with disabilities better suited for use of the PGO are available and will be tested when local living arrangements can be made. Force and Torsional Analysis Weight reduction of the PGO requires that all forces and torques induced in the system during normal opera- tion be known. It was determined that six full bridge axial transducers and two torsional transducers would be suffi- cient to completely define the loading conditions at all of the joints in each leg (14) . Since the PGO is symmetric about the sagittal plane, it was assumed that each leg experiences the same type of loading ; therefore, only the right leg of the PGO was strain gaged. Once the strain gages were installed and calibrated, a multichannel data acquisition board was used to simul- taneously record all force and torsional data. This was done repetitively for both the swing and support phases to assure accuracy. After the data were compiled, a repre- sentative average was found and used for further analysis. Comparison of Results Obtained to Previous Work A considerable amount of research has been per- formed to determine the ground reaction forces that occur in natural human gait . Most of these studies have involved having nondisabled test subjects walking or run- ning across a force platform. The platform is used to mea- sure the vertical and horizontal components of force in the direction of forward motion . By comparing force plat- form results to PGO forces, an understanding as to how the weight of the PGO affects the function of the device can be asserted. Using the data obtained by Alexander and Jayes (15), a comparison can be made with the PGO forces . In this study, the reaction forces were recorded for the time peri- od from heel-strike to toe-off and the data reported as the magnitude of the vertical and horizontal forces measured. Normalizing their data to the weight of their subjects yields the dashed curve of Figure 3e Note that the forces during the swing phase are not shown in that figure. Fraction of Stride Figure 3. Ground reaction forces in natural gait and those supported by the PGO . Using only the data from the MTU PGO study where the foot is in contact with the ground, the two addi- tional curves of Figure 3 were formulated . In order to compare the PGO results to those of Alexander and Jayes, the MTU results needed to be normalized to weight . The lower curve has been normalized to the weight of the user, which, except for its basic shape, does not reflect the force platform results . Therefore, in an effort to better understand the force distribution between the PGO and user, the results were normalized solely to the weight of the PGO. This curve, shown as the heavy line in the fig- ure, closely follows the results of Alexander and Jayes' force platform. This would suggest that the PGO carries its own weight while the user's weight is carried through skeletal loading (i.e ., the user is not carrying the weight of the device). Effect of Varying the Time Ratio In the initial design of the PGO, along with the thigh and knee angles mentioned above, the time ratio was used as an invariant for design comparisons . The time ratio of gait can be defined as the ratio of the time the foot is unsupported, the swing phase, to the time the foot is in Vertical Force Normalized to: —User's Weight ®PLO's Weight 207 RUTHENBERG et al . Powered Gait Orthosis contact with the floor, the support phase (16) . For opti- mization purposes, it was important to know how this affected the forces induced in the system and the energy required by the user. It was decided to vary the timing ratio between 1 .0 and 1 .2 for this study. Figure A-3 of the Appendix is a sketch showing the four vectors that compose the thigh function generator of the PGO that controls the time ratio. An attribute of the design illustrated in Figure A-3 is that the thigh input link is perpendicular to the vector r 4 . This allows the torque at the hip joint to be measured easily, since it is simply the product of a constant scalar multiple (the length of r4) and the axial load on the thigh input link. RESULTS Figure 4 is a plot of the hip torque determined by multiplying each of the force measurements by their respective moment arm lengths and normalized to the user's weight. The curves follow the same general trends, but the maximum values decrease with increasing time ratio. The angular velocity of the motor that drives the PGO is relatively constant, varying by only ± 1 .6 percent throughout the cycle . Since power is the product of torque and angular velocity, it is, therefore, a reasonable assumption that the average power consumption of the PGO is proportional to the average hip torque. Given that the average hip torque increases, and that the thigh transducer forces decrease with increasing time Figure 4. Hip torque for three different time ratios. ratio, there should be an optimal value that best satisfies the choice of power reduction or force reduction. If the trends described are plotted so that their scales are com- patible, there will be a point of intersection providing the time ratio that would give the minimum forces with the lowest power consumption . In an attempt to determine the optimal time ratio, the data obtained were plotted in the fashion shown in Figure 5 . 0 Time Ratio Optimization Optimal Zone Figure 5. Time ratio optimization plot . 1 .1 Time Ratio Torque --- Thigh Transducer Force - -Turnbuckle Force 1 .2 208 Journal of Rehabilitation Research and Development Vol . 34 No . 2 1997 By considering both the hip and knee function gen- erators, an optimal zone can be established in Figure 5. The optimal zone includes time ratios from 1 .106 to 1 .139, where: a time ratio of 1 .106 corresponds to minimum forces in the hip function generator with minimum power requirements ® a time ratio of 1 .139 corresponds to minimum forces in the knee function generator with minimum power requirements. Patient Energy Expenditure The torque results above are not significant if they are considered independent of other variables . Because the PGO is a device that is designed to assist people, the amount of energy that is needed from the user is of great significance. Low forces and torques could mean a very light, inexpensive design, but if it requires excessive energy from an already weak user, that design will not be feasible . As an easy method to monitor the exertion of the human body, pulse and blood pressure data were record- ed before and after each of the time ratio tests . Although it is not the best method for energy expenditure determi- nation, it has been shown by Stallard (17) that there is a well-defined linear relationship between oxygen uptake and heart rate . Therefore, for the initial phases of this study, the intra-subject comparison of pulse and blood pressure data was used to evaluate the user's energy input. This method would not be used as a comparison between patients, and eventually, oxygen consumption will be used to quantify the user's energy expenditure. Figure 6 plots pulse and blood pressure data. As one would expect, the pulse did increase after each test was completed . It can also be seen that the change was inde- pendent of the time ratio used, and the change in pulse was 6 beats/min for each test. Although there does appear to be a change in the blood pressure with changing time ratios, the randomness of this change may suggest that it is within the natural variation associated with blood pressure . Even though a detailed relationship can not be determined from this data between energy expenditure and time ratio, one important observation can be made : there is not an apparent nega- tive relationship between user energy input and time ratio selected ; therefore, this selection can be based on the kinematics and power concerns of the system . Change in Pulse For Varying Time Ratios Change In Blood Pressure For Varying Time Ratios Figure 6. Pulse and blood pressure before and after each test. DISCUSSION A complete force and power analysis of the PGO has been achieved. The forces were obtained with proven strain gage techniques, making it possible to accurately measure specific force and moment components in regions of combined loading. The forces obtained agree with the results published by Alexander and Jayes, sug- gesting valid results . These force and moment results suggest that a lightweight design of the PGO is possible, making it seem even more feasible for rehabilitative and 150 1 40 = 130 E - E 120 1 10 100 80 1 1 .1 1 .2 Time Ratio a Before Testing - After Testing 209 ROTHENBERG et al. Powered Gait Orthosis assisted walking . However, since it was determined that the PGO carries its own weight and this weight is not transferred to the user, so long as the device does not become overly cumbersome, in terms of this research, a larger device will only affect the motor selection, not user energy requirements . For that reason, the device was purposely over-designed in areas not considered in this study, such as the torso interface . This minimizes the chance that these areas will influence results in more critical areas . Obviously, when the device leaves the lab- oratory for home use, the size and weight of the device will be more important, especially during donning and doffing. The effect of varying the time ratio of the hip func- tion generator has been studied. The results show that the time ratio of the hip function generator is of significant importance on both the power requirements o