Towards a Fully Passive Transfemoral Prosthesis for Normal Walking

Transcription

1 The Fourth IEEE RAS/EMBS International Conference on Biomedical Robotics and Biomechatronics Roma, Italy. June 24-27, 2012 Towards a Fully Passive Transfemoral Prosthesis for Normal Walking R. Unal, R. Carloni, S.M. Behrens, E.E.G. Hekman, S. Stramigioli and H.F.J.M. Koopman Abstract In this study, we present the principle design of a fully-passive transfemoral prosthesis for normal walking, inspired by the power flow in human natural gait. The working principle of the mechanism is based on three parts, which are responsible of the energetic coupling between the knee and ankle joints. The design parameters of the prosthesis have been determined according to the energy absorption intervals of the natural human gait. Simulation results show that significant amount of energy can be stored to deliver for ankle push-off generation. The CAD representation of the prototype that is under tests is also presented. I. INTRODUCTION Transfemoral amputation and the consequently use of prostheses have drastic consequences in human life, mainly in terms of metabolic energy consumption due to the loss of muscle connections between the hip, knee and ankle joints. Therefore, one of the open challenges in the design of a prosthesis is that it should provide mobility and efficiency in terms of both metabolic energy and external actuation. Existing lower limb prostheses can be classified as passive, controlled and powered. Passive prostheses exploit the dynamics of walking thanks to their special kinematic configuration. With this kind of prosthesis, amputees consume a large amount of metabolic energy (approximately 60% extra) to compensate the lack of energy transfers from the lost muscles [1]. Controlled prostheses have internal actuators in order to control their dynamics. Therefore, these prostheses are better in terms of mobility, such as the ones presented in [2], [3]. Powered prostheses are capable of injecting power into the gait cycle in order to support pushoff generation and to reduce the extra metabolic energy consumption [4], [6], [7], [8]. Commercial transfemoral prostheses, as a representative of these three groups, are also available, such as the Mauch GM [9], 3R80 [10] (passive), RheoKnee [9], Smart Adaptive [11] and C-Leg [10] (microprocessor controlled), and the PowerKnee [9] (active). Some of the studies in this field have been focused on combining the advantages of all the three types, with the aim of obtaining an optimum design. As in [12], [13], [14], energy can be stored in the knee joint during flexion motion of the prosthesis and can be released in another phase of gait in order to support the energy requirement during walking. In particular, energy storage and release are provided by using a spring, which can be adjusted thanks This work has been funded by the Dutch Technology Foundation STW as part of the project REFLEX-LEG under the grant no {r.unal,r.carloni,s.stramigioli}@utwente.nl, Robotics And Mechatronics Laboratory, University of Twente, The Netherlands. {r.unal,s.m.behrens,e.e.g.hekman,h.f.j.m.koopman}@utwente.nl, Biomechanical Engineering Laboratory, University of Twente, The Netherlands. to its particular shape. The control has been realized by electro-magnetic drum brakes similar to the micro-processor controlled ones. In [5], an electrically powered transfemoral prosthesis, which is incorporated with a spring in parallel to the ankle motor unit, has been presented and initial tests of the self-contained version of this prosthesis have been conducted with transfemoral amputees in [15]. According to research studies, a passive prosthesis, which can store and release energy while exploiting the dynamics of walking, would provide the capability of normal walking without using external actuators and brakes. In our previous work [16], we presented the conceptual design of a passive transfemoral prosthesis based on the energetics of walking. The design is able to cover most of the energetic behavior of the knee and ankle joints by means of three elastic elements. As a proof of concept, we built a prototype with two elastic elements [17]. Initial test results showed that almost 50% of the required energy for the natural ankle push-off generation is provided. Towards the design of a fully passive transfemoral prosthesis for normal walking, in this paper, we present the next generation of our fully passive prosthesis. It contains three distinct elements, which provide 76% of the required energy for the ankle push-off generation. To derive such kind of mechanism, the kinematic relations between the ankle and the knee joints and the power flow during the natural human gait have been analyzed. In particular, we introduce an additional linkage element that is employed in the phase between heel-off and toe-off (push-off phase), when there is a simultaneous power absorption on the knee and power generation on the ankle joint. The design parameters of the prosthesis have been determined according to human biomechanical data for normal walking. The power flow of the mechanism is evaluated by simulation and promising results have been obtained. The CAD design of the prototype of the transfemoral prosthesis is also shown. The paper is organized as follows: Section II introduces the power analyses of the knee and ankle joints in human natural gait and identifies the functions of the joints during walking. The conceptual design of the prosthesis and the working principles of each element are explained in Section III. Section IV identifies the parameters of the mechanism according to biomechanical human data and is followed by the simulations and the discussion of the results in Section V. Finally, Section VI presents conclusions and future work. II. POWER FLOW IN HUMAN GAIT The design is inspired by the power analysis of human gait [19]. In particular, Fig. 1 depicts the power flow at the /12/$ IEEE 1949

2 Fig. 2. Conceptual design of the proposed mechanism (given separately for better interpretation) - The design presents three storage elements: C 2, one elastic element between the foot and upper leg; C 3, one elastic element between the foot and lower leg (left); C L, a linkage system between the knee and ankle joints (right). Fig. 1. The power flow of the healthy human gait normalized in body weight in the knee (top) and the ankle (bottom) joints during one stride (Winter, 1991). The areas A1,2,3 indicate the energy absorption, whereas G indicates the energy generation. The cycle is divided into three phases (stance, push-off and swing) with three main instants (heel-strike, heel-off and toe-off). knee (top) and ankle (bottom) joints during one complete stride of a healthy human, normalized in body weight. The figure highlights three instants, i.e. heel strike, heel-off and toe-off, and three main phases: Stance: the knee absorbs a certain amount of energy during its flexion and returns as much as the same amount of energy for its extension. In the meantime, the ankle joint absorbs energy due to the weight bearing, represented by A 3 in the figure. Push-off: the knee starts absorbing energy, represented by A 1 in the figure, while the ankle generates the main part of the gait energy for the push-off, represented by G, which is about the 80% of the overall generation. Swing: the knee absorbs energy, represented by A 2 in the figure, during the late swing phase, while the energy in the ankle joint is negligible. These energy intervals show that there is almost a complete balance between the generated and the absorbed energy, since the energy for push-off generation (G) is almost the same as the total energy absorbed in the three intervals A 1,2,3. Therefore, it is theoretically possible to design a completely self-supporting transfemoral prosthesis which mimics healthy gait, using storage elements with coupling of the two joints for transferring the stored energy. III. CONCEPTUAL DESIGN OF THE PROSTHESIS In this Section, the conceptual design of the transfemoral prosthesis is presented. First the functions of each element are described and, then, the working principle of these elements is explained. In this study, we present a mechanism that can cover the energy absorption phases and deliver the total energy of these intervals at the ankle joint for push-off generation. This mechanism has three distinct parts, as summarized in Fig. 2: One element couples the knee and ankle joints kinematically and is responsible for the transfer of a part of A 1 to the ankle push-off generation (G) - Linkage mechanism, C L. One element couples the upper and lower leg, responsible for the absorption and transfer A 2 and for a part of absorption A 3 during stance phase - Coupling elastic element, C 2. One element connects the foot and lower leg, responsible for the main part of the absorption A 3 - Ankle elastic element, C 3. As supported by the study in [19], it is assumed that the knee joint absorbs and generates the same amount of energy during stance phase. Therefore, for this phase, the knee joint is not considered as a contributor to the ankle push-off generation and no elastic element is included in the conceptual design to mimic this behavior. A. Energy transfer during push-off phase If one takes a closer look at the power flow around the knee and ankle joints during the push-off phase, the challenge for the realization of this part can be easily seen. In this phase, the knee joint absorbs the kinetic energy of the lower leg due to ankle push-off. Since the generation and absorption take place simultaneously, having this storage and release mechanism into one system leads to a complex design. In order to avoid this drawback, we introduce a mechanism that fulfills the function of this phase by coupling the two joints energetically and kinematically. This mechanism is basically a link, C L, that couples the knee and ankle joints and is designed to keep the kinematic relation of these joints during push-off generation, as depicted in Fig. 3. At the moment of push-off (around 44% of the gait cycle), when the ankle starts plantar flexing, the knee joint starts flexing. This relation can be realized with a connection of two pulleys having different radii, r k and r a on the knee and ankle joints, respectively. The relation is given by r a θ a = r k θ k (1) 1950

3 Fig. 3. Angular positions of the knee and ankle joints during one gait cycle at natural cadence [18]. Fig. 4. Angular relation between the knee and ankle joints between pushoff and toe-off. Note that, the dashed line is the linear approximation. where θa and θk are the joint angles. The transmission ratio r, defined as ra r= (2) rk can be computed according to the relation of the natural joint angles between push-off and toe-off (44% - 60% of stride), as shown in Fig. 4. It can be seen that the relation between the knee and ankle angles at this interval is almost linear, so we can actually define a constant transmission ratio for the first stage to achieve normal walking. Therefore, the power flow between the joints during this phase is pre-determined from the natural gait kinematics. By this connection, also the transfer of the energy from the pre-swing absorption interval to the ankle push-off generation interval. The transfer of the energy is accomplished by the the kinematic relation, with this transmission ratio, i.e., τa = Fa ra (3) τk = Fa rk (4) τa τk = (5) r where Fa is the push-off force from the ankle joint, which is transferred via the mechanism to the knee joint. A similar torque relation between the knee and ankle joints during this interval occurs during natural gait. Therefore, this kinematic constraint provides the natural walking kinematics while it is also providing an energy contribution, namely A1, to the ankle push-off generation from the knee joint as a consequence of closed-loop kinematic chain, as depicted in Fig. 5. B. Energy storage during swing phase The swing phase of the human gait is an energy absorption phase for the knee joint and, therefore, the energy absorbed at the knee joint has to be transferred to the ankle joint. For the storage purpose, a coupling elastic element C2 is employed during this phase. This element stores the kinetic energy of the lower leg (A2 ) during swing motion. Fig. 5. Sketch representation of linkage mechanism between the knee and ankle joints. We explained that, A1 is transferred directly to the ankle joint during push-off to support the ankle push-off generation. For the same purpose, also A2 has to be transferred from the knee to the ankle joint. At the beginning of the swing phase, the attachment point of the spring C2 is changed from the heel (P1 ) to the upper part of the foot (P2 ). At the end of the swing, the spring is loaded and its position changes back to the P1. This change of configuration is realized along a trajectory that keeps the length of the spring constant and, therefore, the potential energy stored in the spring is constant, i.e. no dissipations occur [16]. The working principle of this part is depicted in Fig. 6. C. Energy storage during stance phase The stance phase of the human gait is an energy absorption phase mainly for the ankle joint. The energy is stored at the ankle joint by means of the elastic element C3, as shown in Fig. 7. During the stance phase, i.e. while the ankle is in dorsiflexion motion, a braking torque is applied to the ankle in order to bear the weight of the body. Instead of dissipating the energy by using a brake system, we proposed a design in which the storage element provides the brake torque and, therefore, stores the energy (A3 ) during stance phase for delivering to the ankle for the push-off. In order 1951

4 The transmission ratio for the linkage system is obtained from the linear fit that is shown in Fig. 4. A. Swing Phase The elastic constant, k 2, of the coupling element, C 2, employed for swing phase energy storage is derived from the energy values of the absorption interval A 2, i.e.: A 2 = 1 2 k 2δs 2 2, (6) Fig. 6. The working principle at swing phase - After push-off phase, the attachment point of the spring C 2 is changed from the heel (P 1 ) to the upper part of the foot (P 2 ) (left). At the end of the swing, the spring is loaded and its position changes back to the P 1 (right). The point P 3 is the attachment point of the spring on the lever arm of the upper leg. Note that the configuration changes of element C 2 take place over a predefined trajectory, which keeps the length of the element constant. Fig. 7. The working principle at stance phase - At the beginning of the stance phase, both elements C 2 and C 3 are ready for the storage of absorption A 3 (left). At the end of the stance phase, both springs are loaded (right). to achieve this, a spring is connected between the heel and the lower leg. Due to the kinematic relations between the lower and upper leg, the element C 2 is also employed after mid-stance (22% of stride) to build up a resisting torque around the ankle joint in order to achieve a torque profile similar to the natural ankle joint. At the end of the stance phase, the storage elements C 2 and C 3 are loaded and, therefore, are ready to release the total energy of absorption phases (A 2,A 3 ) for the ankle push-off. Note that, the linkage mechanism C L is only active during push-off phase. The stance storage element C 3 is only active during the stance phase. Therefore, there is no undesirable interference of the storage elements during the motion. Since the activation and deactivation of the storage elements can be realized when the velocities of the related joints (during walking) are zero, ideally no dissipation is present. IV. DESIGN PARAMETERS In this Section, we derive the design parameters for the conceptual mechanism by using the energy absorption values of the healthy human gait. In particular, for both swing and stance phases, we identify the storage elements by using the bio-mechanical data for a human of 1.8 m height and 75 kg weight [20]. where δs 2 is the deflection of the elastic element C 2 and is given by δs 2 = P P 3P 2 s 20, (7) where the magnitude of P P 3P 2 is the length of the C 2 element when it is attached between P 3 and P 2 (see Fig. 6) and s 20 is its initial length, which is 0.43 m in the beginning of the swing phase. It follows that k 2 = N/m kg. B. Stance Phase As stated in Section III, during stance phase, the energy is stored in both C 2 and C 3. It should be noted that, this parallel structure leads to smaller elastic constant for the element C 3, which can be considered as an advantage for the design. The elastic constants k 3 of the elastic element C 3 is derived from the energy value of the absorption interval A 3. During the stance phase, the deflection, δs 2, of the coupling element C 2 is given by, δs 2 = P P 3P 1 s 20, (8) in which the magnitude of P P 3P 1 is the length of the element C 2 when it is attached between P 3 and P 1 (see Fig. 7) and s 20 is its initial length, which is 0.52 m at the end of swing. The deflection δs 3 of the stance storage element is given by, δs 3 = P P 6P 4 s 30, (9) in which the magnitude of P P 6P 4 is the length of the element C 3, attached between P 6 and P 4 (see Fig. 7), and s 30 is its initial length, which is 0.16 m at the beginning of roll-over. The elastic constant k 3 of the stance storage element C 3 can be found from the energy value of the absorption interval A 3, i.e.: A 3 = 1 2 k 2δs k 3δs 3 2, (10) where k 2 is the elastic constant of the storage element C 2. It follows that k 3 = 1375 N/m kg. V. SIMULATION AND RESULTS In this Section, we simulate the conceptual mechanism in MATLAB Simulink environment. The dynamic model has been derived by using Kane s method [21]. Since all the elements work only in distinct phases of normal walking, the parameterizations of the system have been done according to these phases of interest. Therefore, simulations have been implemented for the swing and stance phases separately. The model of the prosthesis mechanism during swing phase is considered in a sagittal plane with the torso fixed 1952

5 Fig. 8. Comparison of the torque profile of the knee and ankle joints of the mechanism (thick line) and natural leg during normal walking [18]. Fig. 9. The power flow of the healthy human gait [18] and the power flow for the mechanism (thick line) during one stride of normal walking. in the Newtonian reference frame. Since the elastic element C 3 for the stance phase is not active in this phase, it has not been considered in the model. For the simulation of the swing phase, the hip torque from healthy human data has been assumed as a reference to the system. The model of the prosthesis mechanism during stance phase is considered in a sagittal plane with the foot fixed in the Newtonian reference frame. Since the linkage element, C L, is not active in this phase, it has not been considered in the model. For the simulation of the stance phase, in addition to the hip torque, forces from the other leg, which are assumed to be acting on the torso, have been applied to the system as an external input. Note that, since the model has been built to see the feasibility of the conceptual mechanism, all the mechanical losses and masses of elastic elements are neglected. Fig. 8 illustrates the comparison for the torque profile of the knee and ankle joints with the mechanism (thick line) and the natural leg [18]. Note that a close match has been obtained by means of a fully passive mechanism that only uses simple elastic elements compared to the complex nature of the human leg. In order to observe the energetic performance of the mechanism, comparison of the power flow on the knee and ankle joints of the mechanism (thick line) with the human leg is depicted in Fig. 9. The figure shows that the energy stored during stance phase in the system is almost the same as the natural human joint. However, during the pushoff phase, the profile of the power flow of the conceptual mechanism is different from the biological data: this is due to the power generation of element C L, whereas the energy storage success of the element C 2 is quite similar to the biological one. Overall, the performance can be quantified with the energy provided for push-off, which is 76% of the energy that is required for the natural ankle push-off generation. On top of this energy, extra energy should be injected to the system in order to realize the ankle pushoff generation. Since the system is fully passive, this energy will be generated with extra torque from the hip and the extra forces from the sound leg. The application of the forces and torques to compensate this energy is dependent on the human adaptation and the concept is evaluated with simulation under the ideal conditions. These results also show the efficiency of the human walking in terms of mechanical work and the possibility to design such kind of mechanisms for normal walking without using external actuators and brakes. Even though this is a result from a simulation, the match between the prosthetic mechanism and the natural human leg for the torque profile and the power flow of the knee and ankle joints show promising improvement towards a fully-passive transfemoral prosthesis. Moreover, we showed in our prototype design study with two elastic elements [17] that almost 50% of the required energy for the natural ankle push-off generation can be provided with a simple design. Therefore, with the second prototype, improved results are expected in real conditions. The CAD design of the assembled prototype is presented in Fig. 10 to illustrate most of the elements of the knee and ankle joints and the foot complex. In order to see the working principle of the mechanism, the animation for one gait cycle of a 3D CAD representation is presented in Fig. 11 and in the movie attached to this paper. The mechanical details of the design have been presented in [22]. Referring to the Fig 11, frames (1-5) represent the stance phase till push-off generation, with only the ankle elastic element active during this interval. Frames (4-6) represent the rollover phase and at frame (6) sliding elastic element configuration changes for the transfer of stored energy during swing phase to the ankle push-off generation. At push-off (6), the linkage mechanism is activated and the torque created around the knee joint is transferred to the ankle joint with the natural gait relations between the ankle and knee joints. 1953

6 subjects and amputees will provide more realistic results on the performance and the feasibility of the design. Fig D CAD representation of the prototype. Fig. 11. Animation of one stride (from heel-strike to heel-strike) of the 3D CAD representation of the prototype. After toe-off (8), the linkage mechanism disengages and the slider goes to front (9). Frame (11) shows the dorsiflexion of the ankle for sufficient ground clearance and this frame is the start of swing phase energy storage, which goes up to frame (14). Stride is finishing at frame (14) with heel-strike. VI. CONCLUSIONS AND FUTURE WORKS In this study, we proposed a mechanism inspired by the power flow in the human gait for a fully-passive transfemoral prosthesis. The conceptual design of the mechanism consists of three distinct parts for the three absorption intervals of the human gait. The working principle of each parts, i.e., linkage element C L, coupling element C 2, and stance storage element C 3, have been described throughout the natural gait. Simulations have been implemented to examine the power flow of the mechanism during normal gait. Simulation results showed similar profile with the torque profile of the natural knee and ankle joints. Moreover, it is also shown that the power flow of the mechanism has been improved with this new mechanism with respect to the previous one that has been realized with only two elastic elements. Since the system is fully passive, the rest of the energy should be provided by the human as metabolic energy. A prototype based on average human dimensions has been designed and CAD representation has been presented. Construction of the prototype and an appropriate test bed to evaluate the mechanism in real conditions is under development at this stage. After completing the construction, tests on healthy REFERENCES [1] R. Waters, J. Perry, D. Antonelli and H. Hislop, Energy Cost of Walking Amputees: The Influence of Level of Amputation, Jour. Bone and Joint Surgery, vol. 58A, pp , [2] J.H. Kim and J.H. Oh, Development of an Above Knee Prosthesis Using MR Damper and Leg Simulator, IEEE Int. Conf. on Robotics and Automation, [3] H. Herr and A. Wilkenfeld, User-adaptive Control of a Magneto Rheological Prosthetic Knee, Industrial Robot: An Int. Jour., vol. 30, pp , [4] F. Sup, A. Bohara and M. Goldfarb, Design and Control of a Powered Transfemoral Prosthesis, Int. Jour. Robotics Research, vol. 27, pp , [5] F. Sup, H.A. Varol, J. Mitchell, T. Withrow and M. Goldfarb, Design and Control of an Active Electrical Knee and Ankle Prosthesis, IEEE/RAS-EMBS Int. Conf. on Biomedical Robotics and Biomechatronics, [6] W.C. Flowers, A Man-Interactive Simulator System for Above-Knee Prosthetics Studies, PhD Thesis, MIT, [7] D. Popovic and L. Schwirtlich, Belgrade Active A/K Prosthesis, in de Vries, J. (Ed.), Electrophysiological Kinesiology, Int. Congress, Excerpta Medica, pp , [8] S. Bedard and P. Roy, Actuated Leg Prosthesis for Above-Knee Amputees, US Patent, [9] [10] [11] smart adaptive.php [12] A. Rovetta, M. Canina, P. Allara, G. Campa and S.D. Santina, Biorobotic design criteria for innovative limb prosthesis, Int. Conf. Advanced Robotics, [13] A. Rovetta, T. Chettibi and M. Canina, Development of a Simple and Efficient Above Knee Prosthesis, IMECE Int. Sym. Advances in Robot Dynamics and Control, [14] M. Canina and A. Rovetta, Innovatory Bio-robotic System for the Accumulation of the Energy of Step in a Limb prosthesis, Int. Workshop Robotics in Alpe-Adria-Danube Region, [15] F. Sup, H.A. Varol, J. Mitchell, T. Withrow and M. Goldfarb, Self- Contained Powered Knee and Ankle Prosthesis: Initial Evaluation on a Transfemoral Amputee, IEEE Int. Conf. on Rehabilitation Robotics, [16] R. Unal, R. Carloni, E.E.G. Hekman, S. Stramigioli and H.F.J.M. Koopman, Conceptual Design of an Energy Efficient Transfemoral Prosthesis, IEEE/RSJ International Conference on Intelligent Robots and Systems, [17] R. Unal, S.M. Behrens, R. Carloni, E.E.G. Hekman, S. Stramigioli and H.F.J.M. Koopman, Prototype design and realization of an innovative energy efficient transfemoral prosthesis, IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics, [18] D.A. Winter, The Biomechanics and Motor Control of Human Gait: Normal, Elderly, and Pathological, University of Waterloo Press, [19] D.A. Winter, Knee Flexion During Stance as a Determinant of Inefficient Walking, Jour. of the American Physical Therapy Assoc., vol. 63, no. 3, pp , [20] J. Rose and J.G. Gamble, Human Walking, Williams & Wilkins, [21] T.R. Kane, Dynamics, Theory and Applications, McGraw-Hill, [22] S.M. Behrens, R. Unal, E.E.G. Hekman, R. Carloni, S. Stramigioli and H.F.J.M. Koopman, Design of a Fully-Passive Transfemoral Prosthesis Prototype, IEEE/EMBS International Conference on Engineering in Medicine and Biology Society,