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arxiv: 2605.13192 · v1 · pith:ABTDNUPZnew · submitted 2026-05-13 · 💻 cs.RO

Dynamics Computation of Soft-Rigid Hybrid-Link System and Its Application to Motion Analysis of an Athlete Wearing Sport Prosthesis

Sunghee Kim , Yuta Shimane , Taiki Ishigaki , Ko Yamamoto This is my paper

Pith reviewed 2026-05-14 18:16 UTC · model grok-4.3

classification 💻 cs.RO
keywords systemforcemotionhybrid-linkprosthesisanalysisdynamicsestimation
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The pith

A soft-rigid hybrid-link model enables inverse kinematics and dynamics computation for athletes wearing flexible prostheses, with 12% error reported on ground-reaction-force estimation in a human-subject trial.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The work combines two modeling traditions. Human bodies are usually treated as rigid links connected at joints, while flexible prostheses bend and store energy like soft rods. The authors merge both into one hybrid system so that the deformation of the prosthesis and the forces it exchanges with the remaining limb can be calculated together. From standard motion-capture markers they first solve an inverse-kinematics problem to recover the full pose of the hybrid chain. They then run inverse dynamics to obtain joint torques and ground-reaction forces. In a single-subject experiment the computed ground-reaction force matched measured force-plate data within roughly 12 percent. The same framework also supplies estimates of muscle forces that remain after amputation and that interact with the bending prosthesis.

Core claim

Through a human subject experiment, we show that the inverse dynamics achieved approximately 12% error on the ground reaction force estimation. Furthermore, we provide the muscle force estimation considering muscle amputation and interaction force with the prosthesis leg deformation.

Load-bearing premise

The hybrid-link formulation accurately captures the interaction force between the rigid human skeleton and the flexible prosthesis without requiring additional parameters or post-hoc tuning that would invalidate the inverse-dynamics results.

Figures

Figures reproduced from arXiv: 2605.13192 by Ko Yamamoto, Sunghee Kim, Taiki Ishigaki, Yuta Shimane.

Figure 1
Figure 1. Figure 1: Overview for the motion analysis framework based on the hybrid-link system. From a motion capture system, we reconstruct human motion and prosthesis deformation by inverse kinematics. Then, inverse dynamics calculates the joint torques, inner force in the prosthesis and the ground reaction force. From the obtained joint torques and interaction force from the prosthesis, we estimate muscle tendon forces by … view at source ↗
Figure 2
Figure 2. Figure 2: Schematic view of the PCS model H(s, t) ∈ SE(3) as H(s, t) =  R(s, t) p(s, t) 0 T 1  (4) where R(s, t) ∈ SO(3) is the rotational matrix and p(s, t) ∈ R 3 is the position vector. Hereinafter, t or s is omitted for simplicity when its meaning is obvious. Given the configuration curve H(s), a six-dimensional displacement ξ(s) ∈ R 6 is defined with the operator [ξ(s)×] as [ξ(s)×] := H(s) −1 ∂H ∂s . (5) In th… view at source ↗
Figure 3
Figure 3. Figure 3: Conceptual illustration of a hybrid-link system that consists of rigid-links and soft-segments rep￾resented by the PCS model. We consider that the base-link is not fixed to the environment and that there are multiple contacts where f C,i denote a contact force. generalized velocity vector ψ as follows: q := n H0, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schemetics for the transtibial amputation surgery by myodesis focused on muscles 2.4. Muscle Force Estimation 2.4.1. Muscle Force Optimization From the joint torques estimated by the ID, we can estimate muscle forces that actuate each joint. Because a human joint is redundantly actuated by multiple muscles, muscle forces f are usually estimated by an optimization given as follows [2]: min f 1 2 ∥τ R − J T … view at source ↗
Figure 5
Figure 5. Figure 5: Schematic of the side view of the MRI scanning for leg with transtibial amputation operated by myodesis. Gastrocnemius and Soleus [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Arrangement of the transected muscles based on the MRI image of the subject. • Anterior compartment musculature was removed. • Deep posterior musculature (Gastrocnemius and Soleus) was transected and se￾cured to the tibia via small holes. If the transtibial amputation is operated by myodesis, the side view of the MRI scan￾ning of the amputated leg can be illustrated as [PITH_FULL_IMAGE:figures/full_fig_p0… view at source ↗
Figure 7
Figure 7. Figure 7: Hybrid-link model that integrates human skeleton and a leaf-spring prosthesis leg [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Layout of optical markers for motion capture measurement. than the amputation stump. Also, the end of the muscles are secured to the front of the tibia. Therefore, these muscles has the shape as wrapping the tibia stump [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Walking motion reconstructed by the inverse kinematics of the hybrid-link system. 1st Force Plate Right (Prosthesis) 3rd Force Plate Right (Prosthesis) 2nd Force Plate Left (Foot) [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: A subject was asked to walk or run with a single stride on each force plate in the experiment The number of segments was determined based on the previous report [23], where the change ratio of strain along the central axis coordinate was large. We assume that each segment has only angular strain with 3 DOFs ignoring linear strain while qs,0 is calculated so that each segment has 6 DOFs for a precise model… view at source ↗
Figure 11
Figure 11. Figure 11: Setting of contact points in the inverse dynamics [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Reconstructed walking motion and estimated ground reaction force. for the prosthesis, as shown in [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Reconstructed running motion and estimated ground reaction force. 0 0.5 1 1.5 2 2.5 time(s) -500 0 500 1000 1500 F x(N) 0 0.5 1 1.5 2 2.5 time(s) -500 0 500 1000 1500 F y(N) Contact force for 1st force plate 0 0.5 1 1.5 2 2.5 time(s) -500 0 500 1000 1500 F z(N) Force plate ID Result 0 0.5 1 1.5 2 2.5 time(s) -500 0 500 1000 1500 F x(N) 0 0.5 1 1.5 2 2.5 time(s) -500 0 500 1000 1500 F y(N) Contact force fo… view at source ↗
Figure 14
Figure 14. Figure 14: Estimated contact force and its ground truth along xyz axes in the walking motion. W2 = O. This would degrade the precision of the estimation; however, we excluded the EMG signal factor from the estimation for a pure comparison as a trial. During the experiment, the subject wore tights to protect the connecting part be￾tween the socket and amputated leg. If the air enters inside the tights, the subject co… view at source ↗
Figure 15
Figure 15. Figure 15: Estimated contact force and its ground truth along xyz axes in the running motion [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Visualization of estimated muscle activities, in which the red part indicates higher activity, and the green part indicates lower activity. is the most affected joint from the transtibial muscle amputation. If the change of transected muscle tensions affects the knee joint torque, the action of these muscles will be altered together. Therefore, we consider that the evaluation of these two muscles is still… view at source ↗
Figure 17
Figure 17. Figure 17: Location of the muscle and EMG sensors for the experiment 0 0.2 0.4 0.6 0.8 1 Time [s] -500 -400 -300 -200 -100 0 Muscle Tension [N ] Biceps Femoris Caput Longum (Right) emg msid Single Phase (Right) Single Phase (Left) Single Phase (Right) [PITH_FULL_IMAGE:figures/full_fig_p016_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Muscle tension comparison between the estimations by the optimization and the EMG signal: Biceps Femoris Caput Longum 4. Discussions 4.1. Ground Reaction Force Estimation Tables 1 and 2 show the root mean square error (RMSE) and related root mean square error (rRMSE) between the estimated and ground truth values, which are defined as follows [24]: RMSE = sPn i=1(fi − ˆfi) 2 n , and (38) rRMSE = RMSE × 100… view at source ↗
Figure 19
Figure 19. Figure 19: Muscle tension comparison between the estimations by the optimization and the EMG signal: Semitendinosus [PITH_FULL_IMAGE:figures/full_fig_p017_19.png] view at source ↗
Figure 11
Figure 11. Figure 11: (2) Running motion result: As seen in [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
read the original abstract

This paper presents a motion analysis framework for an athlete wearing sport-specific flexible prosthesis based on the soft-rigid hybrid-link system. Such a motion analysis is a challenging problem because we need to consider the interaction force between the rigid human skeleton system and a flexible prosthesis. However, most of human musculoskeletal models are based on the computation framework of a rigid-body multi-link system. Recently in soft robotics research field, fast and efficient modeling methods were developed for a flexible rod deformation, which allows us to build a hybrid-link system that integrates rigid-link and soft-bodies in a unified formulation. We apply inverse kinematics of the hybrid-link system to motion reconstruction from a motion captured data, and also present the estimation of the joint torques and ground reaction force by inverse dynamics. Through a human subject experiment, we show that the inverse dynamics achieved approximately 12% error on the ground reaction force estimation. Furthermore, we provide the muscle force estimation considering muscle amputation and interaction force with the prosthesis leg deformation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. This paper presents a framework for motion analysis of an athlete with a sport prosthesis using a soft-rigid hybrid-link system. It integrates rigid-body dynamics with soft-body modeling to account for interaction forces, applies inverse kinematics to motion capture data, and uses inverse dynamics to estimate joint torques, ground reaction forces (GRF), and muscle forces considering amputation and prosthesis deformation. A human subject experiment reports an approximately 12% error in GRF estimation.

Significance. Should the hybrid model prove robust, the work offers a novel approach to analyzing sports movements in prosthetic users by unifying soft robotics techniques with human dynamics. It enables estimation of internal forces and muscle activations that rigid models cannot capture, potentially aiding in performance optimization and injury prevention for amputee athletes. The experimental application to real motion data is a positive step toward practical use.

major comments (3)
  1. [Human subject experiment (results)] The GRF estimation achieves approximately 12% error, but the abstract and results provide no error bars, no description of data exclusion rules, no baseline comparison to rigid models, and no count of free parameters fitted (such as prosthesis stiffness and damping coefficients). This limits assessment of the result's reliability and the hybrid formulation's specific role.
  2. [Hybrid-link formulation (methods)] The interaction force computation between the rigid skeleton and flexible prosthesis depends on stiffness and damping parameters. The paper should specify their identification method and confirm they were not adjusted post-hoc to fit the force-plate data used in validation, as this could introduce circularity in the 12% error claim.
  3. [Inverse dynamics application] While GRF error is reported, there is no independent validation of the soft-body deformation predictions, such as comparison to measured prosthesis bending or interface pressures. The integrated GRF metric alone does not isolate the accuracy of the hybrid coupling terms.
minor comments (2)
  1. [Introduction] The background on soft robotics methods for flexible rod deformation could include more specific citations to recent efficient modeling techniques.
  2. [Figures] Ensure that diagrams of the hybrid-link system clearly label rigid and soft segments and the interaction points.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below, indicating where revisions will be made to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Human subject experiment (results)] The GRF estimation achieves approximately 12% error, but the abstract and results provide no error bars, no description of data exclusion rules, no baseline comparison to rigid models, and no count of free parameters fitted (such as prosthesis stiffness and damping coefficients). This limits assessment of the result's reliability and the hybrid formulation's specific role.

    Authors: We agree that these details are important for evaluating reliability. In the revised manuscript we will add error bars computed from the temporal variation of the GRF estimation error across the movement cycle, describe the data processing pipeline and confirm that no trials were excluded, include a direct comparison against a standard rigid-body inverse-dynamics baseline, and explicitly state the number of fitted parameters (two stiffness and two damping coefficients identified in separate calibration tests). revision: yes

  2. Referee: [Hybrid-link formulation (methods)] The interaction force computation between the rigid skeleton and flexible prosthesis depends on stiffness and damping parameters. The paper should specify their identification method and confirm they were not adjusted post-hoc to fit the force-plate data used in validation, as this could introduce circularity in the 12% error claim.

    Authors: The stiffness and damping coefficients were obtained from independent material characterization experiments performed on the prosthesis prior to the motion-capture session and were held fixed during inverse-dynamics computation. They were not tuned to the force-plate recordings. We will expand the Methods section with a full description of the calibration procedure to eliminate any ambiguity regarding circularity. revision: yes

  3. Referee: [Inverse dynamics application] While GRF error is reported, there is no independent validation of the soft-body deformation predictions, such as comparison to measured prosthesis bending or interface pressures. The integrated GRF metric alone does not isolate the accuracy of the hybrid coupling terms.

    Authors: We acknowledge that the present validation relies solely on the integrated GRF metric and does not include direct measurements of prosthesis bending or interface pressure. No such auxiliary sensor data were collected in the current human-subject experiment, so an independent check of the soft-body deformation component cannot be added without new experiments. revision: no

standing simulated objections not resolved
  • Independent validation of soft-body deformation (prosthesis bending or interface pressures) is not possible because the original experiment did not record these quantities.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The hybrid-link formulation implicitly relies on standard rigid-body dynamics assumptions plus a soft-rod deformation model whose stiffness and damping parameters are not specified; no new entities are postulated.

free parameters (1)
  • prosthesis stiffness and damping coefficients
    Required to close the soft-rod deformation equations; values not reported in abstract and therefore treated as fitted or chosen parameters.
axioms (1)
  • domain assumption The interaction force between rigid skeleton and flexible prosthesis can be captured by a single unified hybrid-link formulation without additional contact constraints.
    Invoked when the authors state that the hybrid system integrates rigid and soft bodies for inverse dynamics.

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Reference graph

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