What is the effect of running-specific prostheses on long jumps? Optimization-based prediction and analysis using biomechanical models
Authors: Anna Lena Emonds, Johannes Funken, Wolfgang Potthast, Katja Mombaur
Organizations: Institute of Computer Engineering, Heidelberg University, 69120 Heidelberg, Germany · Institute of Biomechanics and Orthopaedics, German Sport University Cologne, 50933 Köln, Germany · Institute for Anthropomatics and Robotics, Optimization and Biomechanics for Human-Centred Robotics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany · Canada Excellence Research Chair in Human-Centred Robotics and Machine Intelligence, Systems Design Engineering & Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, N2L 3G1, Canada
Long jumpers with below the knee amputation (BKA) that take off from their running-specific prosthesis (RSP) improved performances significantly over the last years. The long jump biomechanics differs compared to athletes without BKA and the question arises whether the spring-like properties of the RSP facilitate achieving long jumping distances. The aim of this work is to propose a long jump model for athletes with and without BKA, to evaluate it and to apply it for comparing long jump motions with and without RSP. We establish rigid multi-body system models of one athlete with and one athlete without below the knee amputation (BKA). Long jump motions are computed by solving a specific optimal control problem (OCP) with constraints enforcing a physically correct dynamics, both for motion reconstruction or motion synthesis. With the proposed long jump model, we are able to compute realistic long jump motions. We discuss the causes of differences in measured long jumps and show directions for eliminating them. For both athletes, the synthesized solutions reveal potential for performance improvement. The jumping distance of the athlete without BKA is 64cm (6.9%) longer than the one of the athlete with BKA in the synthesized solutions.
Figures & tables
Figure 1: Overview of the study design: The computations are divided into two steps, the first reconstructing the motion dynamics based on motion capture recordings and the second predicting long jump motions based on a combination of optimization criteria. The solutions are then used to conduct two distinct comparisons, one between the reconstructed and the optimized solutions and the other between the athletes with and without BKA.
Figure 2: Subject-specific models of a non-amputee and an amputee athlete: Visualization and degrees of freedom. The coordinate system is aligned such that the x-axis points in the forward direction of the sprinting motion. Movements to the right and left are along the y-axis, and movements up and down are along the z-axis.
Figure 3: Phase description of the investigated long jump motions for a non-amputee athlete (top) and an athlete with below the knee amputation (bottom)
Figure 4: Animated sequences of the optimal control problem generated long jump motions. The upper row shows the reconstructed and the lower row the synthesized motion. The dashed vertical line indicates the take-off position and motions are aligned to it. As immediately visible, the motion capture recordings for the reconstruction end during the jump.
Figure 5: Anterior-posterior, mediolateral and vertical ground reaction forces during take-off for the reconstructedsilutions of the athlete without (a/blue) and with (b/red) BKA during the take-off. The grey lines show the measured raw force plate data and the colored lines the reconstructed forces. The time on the x-axis is given in percent of the stance time.
Figure 6: Joint torques of the stance leg (right/affected leg) during the take-off for the reconstructed solutions of the athlete with (red) and the athlete without (blue) BKA. The time on the x-axis is given in percent of the stance time and the joint torques are normalized by body mass.
Figure 7: The diagrams show the movement of the CoM in horizontal and vertical directions for the reconstructed (dashed lines) and synthesized (solid lines) long jump solutions for the athlete with (red) and without (blue) BKA. Phase durations are normalized individually per phase and the abbreviations ‘F’ and ‘C’ denote flight and contact phases (cf. Figure 3 ).
Figure 8: Ground reaction forces in horizontal and vertical direction for the reconstructed (dashed lines) and synthesized (solid lines) long jump solutions for the athletes with (red) and without (blue) BKA. Each force is normalized by the body mass of the individual athlete. Phase durations are normalized individually per phase and the abbreviations ‘F’ and ‘C’ denote flight and contact phases (cf. Figure 3 ).
Figure 9: Joint angles of the respective contact leg for the three contact phases of the reconstructed (dashed lines) and synthesized (solid lines) long jump solutions for the athletes with (red) and without (blue) BKA. Phase durations are normalized to stance time.
Figure 10: Joint torques of the respective contact leg for the three contact phases of the reconstructed (dashed lines) and synthesized (solid lines) long jump solutions for the athletes with (red) and without (blue) BKA. Phase durations are normalized to stance time. Each torque is normalized by the body mass of the individual athlete. The passively generated joint torque of the prosthetic ankle is computed via Eq. ( 1 ).
Department of Biological Sciences, The University of Tokyo, Bunkyo-ku, Tokyo, 113-0033, Japan · Institute of Systems and Information Engineering, University of Tsukuba, Ibaraki, 305-8573, Japan
Woodruff School of Mechanical Engineering, Georgia Tech, Atlanta, GA 30332-0405 USA · Woodruff School of Mechanical Engineering, Georgia Tech, Atlanta, GA 30332-0405 and with the Institute for Robotics and Intelligent Machines, Georgia Tech, Atlanta, GA 30332-0405 USA