Powered lower limb prosthesis are facing energy and efficiency challenges. This article presents an investigation into reducing the energy losses and increasing the efficiencies of energy regeneration for a powered prosthetic knee during level ground walking. The results showed that the regeneration and overall system efficiencies would dramatically increase if the negative mechanical load in the braking quadrants are within the regenerative zone of the motor. This approach reduced the energy losses in the stance and swing phases and increased the possibility of harvesting more negative mechanical energy during level ground walking

Abouhossein, A

Awad, MI

Chong, B

Dehghani-Sanij, AA

Moser, D

Richardson, R

Zahedi, S

White Rose Research Online

   Abstract—Powered lower limb prosthesis are facing energy and efficiency challenges. This article presents an investigation into reducing the energy losses and increasing the efficiencies of energy regeneration for a powered prosthetic knee during level ground walking. The results showed that the regeneration and overall system efficiencies would dramatically increase if the negative mechanical load in the braking quadrants are within the regenerative zone of the motor. This approach reduced the energy losses in the stance and swing phases and increased the possibility of harvesting more negative mechanical energy during level ground walking. I. INTRODUCTION VERY year, thousands of people around the world lose their lower limbs due to circulatory and vascular problems, complications of diabetes, cancer, or trauma. The loss of a lower extremity limb would result in the impairment of a subject’s mobility and in turn would deteriorate the quality of life of the individual with the amputated limb.  Prosthetic limbs are used to restore this loss of mobility and to assist amputees in their activities of daily living (ADLs). Current lower limb prosthetic technology has improved dramatically with the invention of microprocessor controlled knee joints and powered knees. Although these powered prostheses are able to supply positive power to assist transfemoral amputees during ADLs, they consume more power than the human joint [1]. The reason for this is that they use an external power source to generate motion and provide the required mechanical power at the joints which deteriorates the overall dynamic  performance of the system [1], while the walking process of humans is considered to be a mechanically energy-efficient cyclic activity as a consequence of effective dynamic interaction between various segments of the human body. In this work, we investigate the effect of the transmission mechanism and electrical DC motor characteristics on the energy transmission efficiency and regeneration ability of a prosthetic knee in order to reduce its power consumption and to provide assistive power during level ground walking. II. PROSTHETIC KNEE SYSTEM A. Mechanical system A 2.3 kg actuated prosthetic knee mechanism was developed  *The study is supported by EPSRC (EP/K020463/1). M. I. Awad, A. Abouhossein, B. Chong, A. A. Dehghani-Sanij, and R. Richardson are with the University of Leeds, Leeds, LS2 9JT, UK; e-mail: m.i.awad@leeds.ac.uk, a.abouhossein@leeds.ac.uk, b.chong@leeds.ac.uk,  a.a.dehghani-sanij@leeds.ac.uk, and r.c.richardson@leeds.ac.uk.  by the authors [2, 3] to provide easy back-driven action when there is negative mechanical energy applied to the prosthetic limb due to the dynamic coupling interaction between the residual limbs and the interaction with the environment. This back-driven movement was provided to the mechanism by a high efficiency ball-screw as shown in Figure 1. The ball screw was used also as a reduction gearbox to reduce the motor angular velocity and increase the torque reflected to the prosthetic knee joint. The reduction ratio (RR) of the proposed mechanism is calculated using equation 1 and 2 based on the mechanism geometry in Figure 1a. 𝑅𝑅 =2πr𝑝 (1) Where: RR: reduction ratio, r: transmission arm (equation 2), 𝑝: ball screw pitch. 𝑟 =𝑥𝐿1𝐿𝑠𝑐𝑟𝑒𝑤𝑠𝑖𝑛𝛽 =𝑥𝐿1√𝐿12 + 𝑥2 − 2𝑥𝐿1𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝛽 (2)  ACBL1Lscrewrx kRSthighshankH  (a) Schematic diagram of the prosthetic knee kinematic chain (b) The prosthetic leg attached to an amputee CAD model FIG. 1. SCHEMATIC LAYOUT OF THE PROSTHETIC LEG  B. Energy and Efficiency  In order to calculate the system efficiency and investigate the possibility of regeneration from negative mechanical energy, the clinical gait data of a 100kg healthy subject [4] was used. The overall concept of actuator sizing and motor selection is to find the smallest actuator that can successfully provide the required torque. The RR and motor specifications (RR1) were selected initially in order to provide the required peak torque, continuous torque and speed of the load profile. As shown in Figure 2, the mechanical speed-torque profile of D. Moser and S. Zahedi are with Chas A Blatchford & Sons Ltd, Lister Road, Basingstoke, Hants, UK; email: David.Moser@blatchford.co.uk and Saeed.Zahedi@blatchford.co.uk Investigation into Energy Efficiency and Regeneration in an Electric Prosthetic Knee*  M. I. Awad, A. Abouhossein, B. Chong, A. A. Dehghani-Sanij, R. Richardson, D. Moser and S. Zahedi E   a healthy subject transferred to the motor shaft based on (1) is inside the maximum winding lines zone of the selected DC motor. The quadrants II and IV (braking or negative mechanical energy quadrants) are separated by the regenerative braking limit line based on equation (3) which is derived based on Kirchhoff’s Voltage Law at steady state when there is no applied voltage. Although the load in C or F is negative (-ve) power, the motor cannot regenerate this energy as it is outside the regenerative zone (D and E) and need positive braking power to resist this load. This will increase the power loss and the positive electrical power required to drive the prosthetic knee as shown in Figure 3.  𝑇𝑚 = −𝑘𝑚𝑘𝑔𝑅𝑎𝜔𝑚 (3) Where: 𝑅𝑎 : motor’s armature resistance (Ω), 𝑘𝑔: motor speed constant (V/(rad/sec)), 𝜔𝑚: motor angular velocity (rad/sec), 𝑇𝑚: motor torque (Nm), 𝑘𝑚: torque constant (Nm/A).  FIG. 2. KNEE SPEED-TORQUE PROFILE REFLECTED TO THE MOTOR WITH RESPECT TO MOTOR CHARACTERISTICS IN RR1    FIG. 3. MECHANICAL AND ELECTRICAL POWER FOR TWO DIFFERENT ACTUATION REDUCTION RATIOS (RR1: MAX. 82 AND MIN. 67, RR2: MAX. 204 AND MIN. 167) In order to increase the regeneration efficiency and reduce the power loss in the actuation system, the load in zones C and F need to be moved to the regeneration zone (D and E). This can be implemented by selecting an actuation system with higher slope line and/or a higher reduction ratio (RR) by decreasing the pitch (𝑝) from 5mm to 2mm in (1) as in case of RR2 in Figure 3. When the actuation RR was changed to move the load points from zones C and F to zones D and E, the power losses were reduced dramatically which will increase the actuation system efficiency and reduce the electrical power consumption. III. RESULTS AND DISCUSSION Table I shows the net positive and negative energies generated and absorbed by both the mechanical and electrical systems in the case of two different configurations RR1and RR2. The overall net electrical energy is negative in RR2 which can contribute to the battery life during level ground walking. The overall and regenerative efficiencies have been improved with the RR2 configuration in both the stance and swing phases. However, RR2 has less back-driving efficiency which will affect the dynamic behavior. This change in dynamic behavior will be studied in the future work.  TABLE I: ENERGY AND EFFICIENCY Parameter RR1 RR2 Mechanical Electrical Mechanical Electrical 𝐸𝑇 (J) -23.34 12.5262 -23.34 -17.50 𝐸𝑁 (J) -29.67 -18.54 -29.67 -26.41 𝜂𝑜 (%) 40.86 83.5 𝜂𝑜𝑟 (%) 62.5 89.01 𝐸𝑁 𝑠𝑡 (J) -12.34 -4.74 -12.34 -10.17 𝐸𝑁 𝑠𝑤 (J) -20.55 -13.73 -20.55 -17.04 𝜂𝑠𝑡 (%) 38.38 82.45 𝜂𝑠𝑤 (%) 66.81 82.93 Where: 𝐸𝑇: overall net energy, 𝐸𝑁: negative energy, 𝜂𝑜: overall actuation system efficiency, 𝜂𝑜𝑟: overall regenerative energy efficiency, 𝐸𝑁 𝑠𝑡: negative energy in stance phase, 𝐸𝑁 𝑠𝑤: negative energy in swing phase, 𝜂𝑠𝑡: regenerative efficiency in stance phase, 𝜂𝑠𝑤: regenerative efficiency in swing phase. IV. CONCLUSION Choosing the right actuation configuration for powered lower limb prosthesis can increase efficiency and reduce energy consumption. This can help overcome the limited battery life challenges with current powered knee prostheses. REFERENCES [1] R. Unal, F. Klijnstra, S. M. Behrens, E. E. G. Hekman, S. Stramigioli, H. F. J. M. Koopman, et al., "The control of recycling energy strorage capacity for WalkMECHadapt," in Robot and Human Interactive Communication, 2014 RO-MAN: The 23rd IEEE International Symposium on, 2014, pp. 720-725. [2] Z. W. Lui, M. I. Awad, A. Abouhossein, A. A. Dehghani-Sanij, and N. Messenger, "Virtual prototyping of a semi-active transfemoral prosthetic leg," Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, vol. 229, pp. 350-361, May 1, 2015 2015. [3] M. I. Awad, A. A. Dehghani-Sanij, D. Moser, and S. Zahedi, "Inertia Properties of a Prosthetic Knee Mechanism," in Towards Autonomous Robotic Systems: 16th Annual Conference, TAROS 2015, Liverpool, UK, September 8-10, 2015, Proceedings, C. Dixon and K. Tuyls, Eds., ed Cham: Springer International Publishing, 2015, pp. 38-43. [4] D. A. Winter, The biomechanics and motor control of human gait : normal, elderly and pathological, 2nd ed. Waterloo, Ont.: Waterloo Biomechanics, 1991.  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Investigation into Energy Efficiency and Regeneration in an Electric Prosthetic Knee

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