Source-linked AI summary
What is the effect of running-specific prostheses on long jumps? Optimization-based prediction and analysis using biomechanical models
Anna Lena Emonds, Johannes Funken, Wolfgang Potthast, Katja Mombaur
TL;DR
The study addresses how running-specific prostheses affect long-jump motion and performance. Using subject-specific biomechanical models and optimal control, it finds that synthesized jumping distance is 64 cm longer without BKA than with BKA.
Problem
The study examines limited evidence on how running-specific prostheses affect long-jump motions and distances compared with non-amputee athletes.
Method
The authors use subject-specific rigid multi-body models and constrained optimal-control formulations to reconstruct, synthesize, and compare long-jump motions.
Results
64 cm longer was the synthesized jumping distance for the athlete without BKA than for the athlete with BKA.
Takeaways & Limitations
Synthesized solutions indicate individual performance-improvement potential for both athletes, including more efficient take-off without BKA and greater approach velocity with BKA.
Takeaways & Limitations
The comparison involved only two distinct athletes, so the observed difference cannot be generalized to jumping with and without running-specific prostheses.
Abstract
from arXiv · showhide
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.
Introduction
The study addresses how running-specific prostheses affect long-jump motions and performance in athletes with and without below-knee amputation. It proposes subject-specific biomechanical models and optimal-control formulations to generate and evaluate realistic motions, compare predictions with reality, and identify performance-improvement directions.
- Biomechanical understanding of long jumping supports prosthesis design, assistive-device development, therapy, and performance improvement.
- Run-up, take-off, and landing all influence long-jump performance, requiring optimal horizontal velocity, take-off positioning, and high vertical velocity.
- Measurements alone cannot establish general effects of RSPs because few athletes with BKA compete at world level and within-athlete comparisons are impossible.
- Computer simulations enable comparisons between amputee and non-amputee model versions of the same athlete and have been applied to sprinting and amputee long-jump improvement.
- The proposed model uses subject-specific athletes with and without BKA and optimal-control formulations to predict realistic long-jump motions and assess RSP advantages, disadvantages, and improvement directions.
- Model validity is assessed by comparing predicted and real jump distances, ground reaction forces, joint angles, and center-of-mass motion.
Materials and Methods
The study uses subject-specific rigid multi-body models and a multiphase optimal-control framework to reconstruct and synthesize long-jump motions with and without BKA. Motion capture data support dynamics reconstruction, while physically constrained equations model flight, contact, touchdown, and lift-off.
- Subject-specific models: The study models one non-amputee and one unilateral-BKA athlete with subject-specific rigid multi-body systems based on de Leva data.The non-amputee model has 16 segments, while the amputee model replaces the right foot and part of the right shank with a three-segment prosthesis model.
- Motion phases: The modeled motion covers the final two approach steps, take-off, flight, and landing within Hay’s four-part long-jump division.The model distinguishes airborne phases from unilateral point-ground-contact phases.
- Multiphase dynamics: The equations enforce physically constrained rigid-body dynamics, including non-sliding ground contact, holonomic constraints, ground-reaction forces, touchdown impulses, and lift-off.Touchdown is treated as completely inelastic, whereas lift-off begins when the vertical ground-reaction force vanishes.
- Optimal control: An optimal control problem computes trajectories that minimize selected criteria while respecting system dynamics and variable bounds.The solution includes generalized positions, velocities, joint torques, torque-rate controls, parameters, and phase durations.
- Dynamics reconstruction: Motion reconstruction uses marker trajectories from motion-capture recordings of one athlete with BKA and one non-amputee athlete.The recordings were collected at the German Sport University Cologne, and accompanying force-plate data were not used in reconstruction.
Numerical Results
The optimal-control solutions produced realistic long-jump reconstructions and synthesized motions for athletes with and without BKA. Reconstruction errors were small, while synthesized jumps were longer for both athletes than reconstructed jumps, with distinct take-off distances and angles.
- Dynamics reconstruction: RMSE remained below 2 cm for translational and 0.036 rad (≈2°) for rotational degrees of freedom across both athletes’ motions.The errors were computed between OCP generalized positions and reference motion-capture data, normalized by the number of degrees of freedom and multiple-shooting nodes.
- Dynamics reconstruction: Reconstructed and measured ground-reaction forces fit well in course and magnitude during take-off for both athletes.Both models produced an anterior-posterior braking component followed by a propulsive component.
- Dynamics reconstruction: 7.58 m and 8.29 m were the estimated reconstructed jumping distances for the athletes without and with BKA, respectively.The estimates assumed a parabolic center-of-mass flight curve based on center-of-mass positions and velocities at lift-off and landing.
- Motion synthesis: 9.86 m versus 9.22 m were the synthesized jumping distances for the athletes without and with BKA, respectively, with take-off angles of 20.09° and 16.85°.These synthesized distances exceeded reconstructed distances by 2.28 m without BKA and 0.93 m with BKA.
- Motion synthesis: 9.85 ms−1 and 9.99 ms−1 were the synthesized horizontal center-of-mass velocities at take-off for the athletes without and with BKA, respectively.Reconstructed horizontal velocities remained nearly constant over the final approach steps, whereas synthesized solutions showed differing approach behavior described in the results.
Discussions
The proposed model reproduces measured long-jump motions sufficiently well for analysis and synthesis, while optimization reveals performance gains and biomechanical differences between athletes with and without BKA. The synthesized athlete without BKA jumps 64 cm farther, although this comparison cannot be generalized beyond the two athletes studied.
- Model evaluation: Reconstructed solutions agree well with motion-capture, force-plate, literature, and measured long-jump data, supporting the model’s use for analysis and synthesis.Small RMSEs indicate good kinematic fit, while ground-reaction forces and joint torques generally agree with force-plate and literature values.
- Reconstruction versus synthesis: Synthesized solutions look realistic but produce significantly larger jumping distances for both athletes than reconstructed motions and measurements.The optimization considers the entire motion and adjusts variables to optimize the objective function, creating discrepancies from reconstruction.
- Reconstruction versus synthesis: Larger synthesized distances arise from higher approach velocities and less forward center-of-mass velocity loss during take-off, without a direct linear relationship to take-off angle.Whether real athletes can implement the model’s higher approach velocities given their muscular prerequisites remains open.
- RSP mechanics: 24% smaller peak take-off force occurs for the athlete with BKA in synthesis, while the prosthetic approach contact uses greater spring-like RSP behavior to generate larger vertical forces.During approach, synthesized motion shows similar or greater prosthetic flexion and torque; during take-off, it shows less flexion and smaller torque.
- Athletes with and without BKA: 64 cm longer synthesized jumping distance occurs for the athlete without BKA, but the result cannot be generalized because only two distinct athletes were compared.The athlete with BKA had better approach preconditions, whereas the athlete without BKA used take-off more efficiently.
Conclusions
The proposed long jump model generates physically correct and realistic motions, while optimized solutions indicate performance-improvement potential for athletes with and without BKA. Comparisons between athletes differ between reconstructed and synthesized solutions, potentially because their body and muscle parameters differ.
- Model validity: The proposed long jump model generates physically correct and realistic long jump motions, with reconstructed and synthesized solutions showing similar overall patterns.The reconstructed solutions represent measured motion.
- Performance potential: For both athletes, synthesized jumping distances exceed reconstructed distances, indicating individual opportunities to improve performance.The athlete without BKA may improve take-off efficiency, whereas the athlete with BKA may approach the board with greater horizontal velocity.
- Athlete comparison: The BKA athlete jumps farther in reconstructed solutions but shorter in synthesized solutions than the athlete without BKA.Because the comparison involves two distinct athletes, differing body and muscle parameters may underlie these differences.
Author contributions statement
The authors divided responsibilities across model development, results analysis, motion capture and biomechanical expertise, manuscript drafting, and review.
- AE and KM prepared the models, motion description, and optimal control problem.
- AE computed and analyzed the results, while JF and WP provided motion-capture recordings and biomechanical expertise.
- All authors discussed the results, and AE wrote the first draft before the other authors reviewed it and provided detailed feedback.
Funding declaration
The research did not receive funding.
- This research did not receive funding.