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REVIEW 4 major objections 5 minor 46 references

Landing-Induced Viscoelastic Changes in an Anthropomimetic Foot Joint Structure are Modulated by Foot Structure and Posture

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read An arched, multi-jointed foot damps landing impacts better than flat or rigid feet

desk verdict The hardware is the contribution; the damping-ratio story is a curve fit that should not be taken at face value. read the letter →

arxiv 2601.14634 v2 pith:43QDQPZF submitted 2026-01-21 cs.RO physics.bio-ph

Satoru Hashimoto , Yinlai Jiang , Hiroshi Yokoi , Shunta Togo This is my paper · ORCID
classification cs.ROphysics.bio-ph
keywords anthropomimeticfootimpactattenuationdampingratioviscoelasticidentificationlandingposturewindlassmechanismarchspring-mass-dampermodel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Grounded in a physical replica of the human foot skeleton, this paper claims that the arch-like, multi-jointed construction itself—not just soft tissue—provides impact attenuation, and that passive posture alone can tune the balance between dissipation and rebound. The authors drop three matched feet (multi-jointed 'soft', rigid, and flat) from four heights, measure the force transmitted to the ankle, and fit a spring-damper model to each impact. The multi-jointed foot shows the lowest peak force and the highest damping ratio; toe-first ankle postures lower peak force and raise damping, while toe extension raises elastic stiffness and lowers damping, consistent with a windlass-like stiffening. These results matter because they suggest skeletal morphology and posture can be treated as design variables for robotic feet, and they offer a mechanical explanation for differing human landing strategies.

What carries the argument

The load-bearing instrument is a single-degree-of-freedom spring-mass-damper model (M ẍ = -k x - c ẋ + F; ankle force F_a = kx + c ẋ) fitted to the measured ankle force by a 400×400 grid search over k and c, with a fixed impulse input (F = 130.7 N over 0.001 s) identical across all conditions; the reported dependent variable is the damping ratio c/(2√(Mk)). In the physical model, the 'soft' foot uses 3D-printed bone shapes, nylon-rope ligaments, an internal elastic cord for joint restoring force, and a rubber sheet as plantar fascia; the flat and rigid feet are matched for mass and sole material to isolate skeletal architecture.

What would settle it

Measure impact energy dissipation directly—for instance, by instrumenting individual joints to record angular motion and friction work, or by fitting a multi-segment model that admits per-joint stiffness and damping—and check whether the multi-jointed 'soft' foot still dissipates more energy than the rigid and flat feet under matched impacts; if the extra 'damping' vanishes when the lumped assumption is relaxed, the central claim is refuted.

Watch

Extended reading notes

Core claim

The central finding is that a multi-jointed, arch-shaped skeletal structure with ligament-like constraints dissipates more landing energy than a flat or a rigid foot of the same mass and dimensions: identified from impact waveforms, the damping ratio rises from flat to rigid to soft, and peak force is lowest for the soft foot at high drop heights. The paper further shows that ankle posture systematically shifts the identified viscoelastic parameters—toe-first (plantarflexed) landings yield lower peak force and higher damping than heel-first (dorsiflexed) landings, while the heel-first foot rebounds—and that increasing toe extension under high loads increases the elastic coefficient and decre

Load-bearing premise

The whole foot is reduced to a single linear spring and damper with constant mass, and the same short impulse is assumed for every foot and posture; if real multi-joint dynamics are not captured by this lumped model, the ordering of damping ratios across conditions is not established—and the paper itself notes the model misfits the θa = -30° case.

Editorial extensions

If this is right

  • Robotic feet could be designed with arch-like multi-joint structures and adjustable toe/ankle posture to tune impact absorption without active control.
  • The identified qualitative match with human landing strategies suggests skeletal structure contributes to observed differences in heel-first vs forefoot-first landing.
  • Toe-extension stiffness, analogous to the windlass effect, could inform footwear or orthotic designs that modulate plantar fascia tension.
  • The ranking of damping ratios (soft > rigid > flat) gives a concrete target for validating more detailed computational foot models.
  • The posture-dependent parameter shifts suggest that a single passive foot mechanism can cover a range of attenuation behaviors.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the lumped spring-damper fit is replaced by a multi-segment model that resolves individual joint angles and frictional losses, the relative damping ranking across feet may change; the paper's own misfit at θa = -30° is the warning sign.
  • A direct energy audit—measuring joint angular velocities and contact forces—could test whether the extra damping is truly joint friction and arch deformation or partly an artifact of the fitting procedure.
  • The windlass-like stiffening shown here might be exploited in prosthetic feet by making toe stiffness adjustable, but the paper does not yet show this transfers to a loaded walking cycle.
  • The fact that toe-extension effects were significant only at higher drop heights suggests the mechanism is load-dependent; a testable extension is to vary plantar-fascia pre-tension independently of toe angle.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper develops a 3D-printed anthropomimetic foot with bone geometry, ligament-like ropes, elastic cords, and a plantar-fascia-like rubber sheet, together with flat and partially rigid comparison feet of matched mass and dimensions. The authors perform repeated vertical-drop impact tests at four heights and three postural conditions (skeletal structure, ankle angle, toe angle), record ankle load-cell force and foot height, and identify effective stiffness k and damping c by fitting a linear spring-mass-damper model to the measured force waveform. They report that the multi-jointed soft foot gives a higher damping ratio than flat or rigid feet, that toe-first ankle postures reduce peak force and increase damping relative to heel-first postures, and that toe extension tends to increase stiffness and reduce damping. These results are interpreted as evidence that morphology and passive posture can tune the impact-attenuation/rebound trade-off in an anthropomimetic mechanical foot.

Significance. If the viscoelastic identification were reliable, the paper would offer a useful physical testbed for studying posture-dependent foot mechanics and a tunable passive foot design for robotics. The direct measurements—peak force, rebound height, and qualitative two-phase toe-contact behavior—are credible and valuable, and the public release of CAD files and raw data is a clear strength supporting reproducibility. However, the headline claims about damping ratio and viscoelastic tuning rest entirely on the lumped-model identification, which has a momentum-consistency error and a conceded failure in the key ankle-posture condition. The toe-angle conclusions are also stronger than the reported statistics warrant. The central quantitative claim therefore needs substantial re-analysis before it can be accepted.

major comments (4)
  1. [Simplified model analysis; Eqs. (1)–(3); Fig. S1] The forcing in the identification model is not momentum-consistent. With M=0.99 kg and h=200 mm, the impact velocity is v=√(2gh)=1.98 m/s, so the actual impact momentum is Mv=1.96 N·s. The paper sets F=130.7 N with an impulse-input time width of 0.001 s, giving an impulse of only 0.131 N·s—a factor of 15 too small. In addition, the initial velocity is set to zero. A spring-mass-damper driven by this small impulse from rest cannot represent a foot that arrives at the ground with v≈2 m/s; the identified k and c will compensate for the missing momentum and therefore are not physically interpretable. The paper must re-run the identification using either the correct initial velocity or a momentum-matched impulse, and should also state explicitly which drop height(s) were used for identification, since the F value in Fig. S1 corresponds only to h=200 mm.
  2. [Discussion, ankle-angle paragraph; Fig. S2F; Table S2] The paper concedes that the simple model incurs 'substantial modeling errors' for θa=−30° and yields an 'anomalously low' viscous coefficient. Yet the damping-ratio comparison that supports the toe-first-increases-damping conclusion is significant (Table S2) only for θa=−30° versus 15° and θa=−15° versus 15°. The −30° waveform has a two-phase structure—a small toe-contact peak followed by the main sole-contact peak—that a single spring-mass-damper with one impulse cannot reproduce. If that condition is excluded as unreliable, the monotonic ankle-posture trend in damping ratio is not established. The authors should either re-identify −30° with a model capable of representing two-phase contact or explicitly drop it from the quantitative claim and report the conclusion as restricted to the −15° to 15° range.
  3. [Toe-angle results; Table S2; Fig. 7J] The abstract and Conclusion state that toe extension 'systematically shifted' the identified parameters and reduced the damping ratio, but the reported statistics do not support this. For toe angle, the Friedman test for damping ratio is p=0.019, and none of the pairwise Wilcoxon tests after Bonferroni correction reach significance (smallest p=0.014); elastic coefficient p=0.069 and viscous coefficient p=0.086 are not significant. The 'windlass-like stiffening effect' is therefore a directional trend, not a demonstrated effect. The text should be revised to present this as an exploratory observation, and the abstract should not list toe extension as a systematic modulator.
  4. [Results; Figs. 5–7; statistical methods] The plotted means for elastic coefficient, viscous coefficient, and damping ratio are presented without error bars, confidence intervals, or any measure of fit uncertainty. Because each trial's k and c come from a 400×400 grid search, the reported point estimates may be sensitive to the arbitrary weighting exponent 0.05 in Eq. (6) and to the 300 Hz sampling of a ~35–80 ms transient. The authors should report per-condition dispersion (e.g., interquartile ranges) and, ideally, a sensitivity analysis for the weighting scheme and sampling rate, so the reader can judge whether the identified parameter differences exceed the identification uncertainty.
minor comments (5)
  1. [Experimental design; Fig. 2D] The 'rigid foot' still contains movable MTP joints, so the name is misleading. Please rename it, e.g., 'partially rigid foot,' or at least define in the text that only the small joints are fused while the toes retain five degrees of freedom.
  2. [Methods; Experimental apparatus] The load cell and infrared sensors sample at 300 Hz, which yields only about 10–25 samples across the main impact transient. A brief statement acknowledging this temporal resolution and its effect on the identified parameters would be appropriate.
  3. [Simplified model analysis; Eq. (6)] The weighting exponent of 0.05 is described but not justified. A sentence explaining how this value was chosen, or a reference to a standard method, would improve reproducibility.
  4. [Results; Figs. 5–7] Some figures show significance asterisks without a key explaining which test and comparison they refer to. Adding a caption note or a supplementary table mapping the asterisks to the p-values would help the reader.
  5. [Introduction] The statement that no prior work has 'both precisely reproduced the shape of human bones or directly mimics the musculoskeletal structure' is strong and hard to verify. It would be safer to say 'to our knowledge, the combination of bone shape, ligament constraints, and landing-impact viscoelastic identification in a physical foot has not been reported.'

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: viscoelastic parameters are empirical identification outputs, and the sole self-citation is non-load-bearing.

full rationale

The paper's derivation chain is transparent and self-contained. Impact waveforms are measured for three foot structures across ankle/toe postures; k and c are then identified by fitting the spring-mass-damper model (Eqs. 1-3, Fig. S1) to each measured waveform, and the damping ratio is computed from the fitted pair. The claims about posture/structure modulating 'apparent' viscoelastic behavior are reports of differences in these identified parameters, not predictions generated from the same parameters. No quantity is defined in terms of the conclusion, and no fitted parameter is relabeled as a prediction of unseen data. The model uses a fixed impulse input (F=130.7 N, 0.001 s width) that is not momentum-consistent with the drop heights, and the authors concede the lumped model misfits theta_a=-30 deg ('anomalously low viscous coefficient... substantial modeling errors,' Fig. S2F); these are correctness/fit-quality limitations, not circularity, because they do not make the fitted outcomes equal to inputs by construction. The only author-overlap citation (Ref. 31) is used as a design-inspiration pointer for 3D-printed flexible mechanisms and is not load-bearing for the central empirical result. Accordingly, no circular step is identified.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central results rest on treating a complex multi-jointed foot as a two-parameter spring-mass-damper with a fixed impulse input. The damping-ratio ordering, the main headline, is not a direct measurement but a derived quantity from that fitted model; the key upstream choices (Δt, impulse width, weighting, zero initial velocity) are hand-set rather than independently constrained.

free parameters (5)
  • Elastic coefficient k (per trial) = 10^3–10^7 N/m grid; best fit
    Identified by weighted grid-search fit to the measured force waveform; all damping-ratio claims are derived from fitted k.
  • Viscous coefficient c (per trial) = 1–10^4 N·s/m grid; best fit
    Identified in the same grid search; directly feeds the damping ratio c/(2√Mk).
  • Impact duration Δt = 0.015 s
    Hand-set from the width of the main force peak; determines the amplitude of F in Eq. (3), changing the input to the identification model.
  • Impulse input time width = 0.001 s
    Ad hoc value in Fig. S1; the model delivers F for 1 ms while initial velocity is zero, mixing an impulse input with arbitrary support.
  • Weighting exponent 0.05 in Eq. (6) = 0.05
    Hand-chosen increment that up-weights post-peak oscillation peaks in the identification cost; affects which (k,c) minimizes the error.
assumptions (5)
  • domain assumption The foot can be modeled as a linear time-invariant spring-mass-damper with a single mass M and constant k,c during the landing transient.
    Simplified model analysis, Eqs. (1)-(2). Non-linear joint friction and arch kinematics are absorbed into effective constants.
  • domain assumption The force transmitted to the ankle equals kx + c·ẋ (Eq. 2) and the load cell measures exactly this force.
    Eq. (2); ignores multi-DOF coupling and the apparatus between ankle and load cell.
  • ad hoc to paper The ground-contact force F is the same known impulse M√(2gh)/Δt for every foot type and posture.
    Eq. (3) and Fig. S1; actual contact kinematics differ strongly between flat/rigid/soft and toe-first/heel-first landings.
  • ad hoc to paper Initial displacement and initial velocity are zero at the moment of impact.
    Fig. S1 lists x(0)=0 and ẋ(0)=0; a foot arriving from a drop height has downward velocity, so the impulse is a proxy.
  • domain assumption Ten repeated trials per condition are independent and representative enough for non-parametric comparisons.
    Experimental procedure; manual release may introduce unreported trial-to-trial variation.

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Cite this review

Pith. "Pith review of Landing-Induced Viscoelastic Changes in an Anthropomimetic Foot Joint Structure are Modulated by Foot Structure and Posture." pith.science (2026). https://pith.science/paper/43QDQPZF

@misc{pith2026260114634,
  author       = {Pith},
  title        = {Pith review of: Landing-Induced Viscoelastic Changes in an Anthropomimetic Foot Joint Structure are Modulated by Foot Structure and Posture},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/43QDQPZF}},
  note         = {Machine review of arXiv:2601.14634}
}
read the original abstract

How skeletal architecture and landing posture shape the immediate post-impact viscoelastic response of the foot remains incompletely understood, in part because cadaveric specimens are ill-suited to repeated impact testing across postures. In this study, we developed an anthropomimetic foot joint structure aimed at replicating the skeletal geometry of the human foot. Using a vertical drop apparatus that simulates landing and a viscoelastic system-identification model, we investigated how skeletal structure and posture modulate the apparent post-impact viscoelastic response. The results show that the multi-jointed anthropomimetic structure exhibited a higher damping ratio than simplified flat and rigid feet. Moreover, ankle dorsiflexion and toe extension systematically shifted the identified parameters, reducing the damping ratio under the tested conditions. Taken together, these findings indicate that an arch-like, multi-jointed skeletal architecture can enhance impact attenuation in an anthropomimetic mechanical foot, and that morphology and passive posture alone can tune the trade-off between attenuation and rebound. The observed trends are qualitatively consistent with reported differences in human landing strategies, and highlight the engineering advantage of anatomically informed skeletal design for achieving tunable impact attenuation through postural adjustment.

Figures

Figures reproduced from arXiv: 2601.14634 by the authors.

Figure 1
Figure 1. Overview of the anthropomimetic foot joint structure and experimental apparatus. (A) Photograph of the fabricated anthropomimetic foot joint structure. (B) Schematic of the anthropomimetic foot joint structure. Nylon braided ropes are attached at positions corresponding to human ligaments to restrict the range of motion. Joint restorative force is incorporated into each joint by threading elastic cords through the h… view at source ↗
Figure 2
Figure 2. Design of each foot structure used in the experiments. (A) Design and attachment positions of the ligaments, tendons, and plantar fascia in the anthropomimetic foot joint structure (Soft foot). The attachment positions and shapes of each biological structure are designed based on anatomical illustrations from anatomical references. (B) Design of the ankle socket for adjusting ankle angles. The ankle socket is fixed … view at source ↗
Figure 3
Figure 3. Three comparative conditions in the impact loading experiments. (A) Differences in the skeletal structure. The landings of three types of foot structures—flat foot, rigid foot, and soft foot (anthropomimetic foot joint structure)—are compared. (B) Differences in the ankle angle. Landings with varying ankle angles 𝜃! are compared. The ankle angle 𝜃! is defined as zero degrees when the sole is horizontal, with dorsifl… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Overview of the experimental apparatus. (A) Photograph and dimensions of the experimental apparatus. The apparatus is equipped with linear rails, a load cell, and infrared distance sensors, which allow the foot structures to be dropped vertically while measuring the im…
Figure 6
Figure 6. Figure 6: Viscoelastic changes caused by differences in the ankle angle. (A) Snapshots of the experiments at a drop height of ℎ = 200 mm for 𝜃! = −30°, (B) 𝜃! = −15°, (C) 𝜃! = 0°, and (D) 𝜃! = 15°. Time-series data of (E) foot height and (F) impact forces during landing. Each ti…
Figure 7
Figure 7. Figure 7: Viscoelastic changes caused by differences in the toe angle. (A) Snapshots of experiments at a drop height of ℎ = 200 mm for 𝜃" = 0°, (B) 𝜃" = 15°, (C) 𝜃" = 30°, and (D) 𝜃" = 45°. Time￾series data of (E) foot height and (F) impact forces during landing. Each time-serie…

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.