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REVIEW 2 major objections 5 minor 64 references

Passive knee flexion increases forward impulse of the trailing leg during the step-to-step transition

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Passive knee flexion, by delaying the start of ankle push-off until after the leading leg lands, increases the trailing leg's horizontal impulse by 87% and shifts ankle energy toward swinging the leg rather than accelerating the body.

desk verdict Direct robot result is clean and worth knowing; the stats are mispaired and the causal chain from SAPF timing to impulse is underdetermined. read the letter →

arxiv 2411.13289 v1 pith:PYWGKQM6 submitted 2024-11-20 cs.RO

Bernadett Kiss , Alexandra Buchmann , Daniel Renjewski , Alexander Badri-Spröwitz This is my paper · ORCID
classification cs.RO
keywords passivekneeflexionanklepush-offtimingstep-to-steptransitionbipedalrobotelasticcatapultcenterofmassmomentumgaiteventcosttransport
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

This paper asks whether passively letting the knee flex, rather than actively driving it, can trigger the release of the leg's 'catapult'—the elastic ankle that stores energy in stance and releases it at push-off. Using the EcoWalker-2 bipedal robot, the authors compare active knee flexion initiation (AKFI) with passive knee flexion initiation (PKFI), where the knee motor is unpowered for most of stance. They find that passive initiation delays the start of ankle plantar flexion by about 3% of the gait cycle, from just before to just after the leading leg touches down, and this delay is associated with an 87% larger horizontal impulse of the trailing leg during the step-to-step transition. The authors argue that the timing of ankle release relative to touch-down determines whether ankle energy accelerates the remaining body or swings the trailing leg forward, which matters for understanding human push-off and for designing orthoses, prostheses, and efficient robots.

What carries the argument

The central object is the EcoWalker-2, a planar biped with hip and knee motors, passive spring-loaded ankles, and biarticular GAS and SOL spring-tendons that span the ankle and also couple to the knee. Its two control modes define the comparison: in AKFI the knee motor tracks a programmed rhythmic angle trajectory for the whole gait cycle; in PKFI the knee motor outputs zero torque from 35% of the gait cycle onward, so knee flexion arises only from the GAS spring and ground reaction forces. The mechanism that carries the argument is the timing gap between the start of ankle plantar flexion (SAPF) and leading-leg touch-down (LLTD): AKFI releases the ankle 2% of the gait cycle before LLTD, PKFI releases it 2% after LLTD, and the paper attributes the momentum differences to that shift. All momentum changes are evaluated over the step-to-step transition, defined as the interval from the minimum to the maximum vertical center-of-mass velocity.

What would settle it

Run the robot in a third condition that keeps knee and hip flexion onsets identical to AKFI but commands the ankle plantar-flexion onset to occur 3% of the gait cycle later, matching PKFI's SAPF timing; if the trailing-leg horizontal impulse does not rise by roughly 87% relative to AKFI, the paper's claim that the SAPF delay drives the momentum change would be falsified.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that passive knee flexion initiation works as a gait-event timing mechanism: with the knee motor switched off during mid-to-late stance, the knee begins to flex 5% of the gait cycle later than with active control, and the ankle begins to plantarflex 3% later—after rather than before leading-leg touch-down. That shift moves the elastic recoil of the passive ankle springs from a pre-touch-down 'preemptive push-off' that mainly accelerates the rest of the body into a post-touch-down release that mainly propels the trailing leg into swing. Measured over the step-to-step transition, the trailing leg's horizontal momentum impulse is 0.14 kg m/s larger (87% larger), the center-of-mass momentum magnitude increase is 188% larger, and the remaining body's horizontal impulse decreases more in the passive condition. Both conditions walk at the same speed with sufficient toe clearance, and passive knee flexion slightly lowers the net positive cost of transport. The paper presents this as the first robotic test of the hypothesis that passive knee flexion is the 'catch' that releases the human lower-leg catapult.

Load-bearing premise

The load-bearing premise is that the later start of ankle plantar flexion—not the simultaneous differences in knee flexion onset, hip flexion onset, and leading-leg touch-down timing—is what produces the larger trailing-leg impulse.

Editorial extensions

If this is right

  • If the timing claim holds, shifting ankle push-off a few percent of the gait cycle after leading-leg touch-down is enough to redirect a large share of ankle energy toward swinging the trailing leg rather than accelerating the body.
  • A robot can maintain the same walking speed and toe clearance with no knee torque during most of stance, so passive knee dynamics can replace active knee control in that phase without losing gait functionality.
  • The small cost-of-transport reduction (0.52 vs 0.56 in net positive cost of transport) suggests that letting the knee flex passively may also be energetically beneficial, not just kinematically feasible.
  • For assistive devices, the results imply that knee-flexion timing—not just ankle power—should be a control parameter in orthoses and prostheses, since it changes where push-off energy goes.
  • The event-ordering difference (SAPF before vs after LLTD) provides a robotic confirmation of the human-like preemptive push-off pattern and gives a concrete mechanical role to the knee in the leg catapult release.

Reading between the lines

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

  • Editorial inference: The causal attribution is narrower than the experimental manipulation—AKFI and PKFI differ in knee flexion onset, hip flexion onset, and touch-down timing as well as ankle push-off timing, so a follow-up varying only the commanded ankle release time would test whether the 87% impulse change is really driven by SAPF timing.
  • Editorial inference: Applied to prosthetics, a zero-torque or low-impedance knee window timed near push-off could let users tune how much ankle energy returns to the limb versus the torso, which may matter for users with limited hip control.
  • Editorial inference: Since human gait events vary by about 1.5% of the gait cycle across strides, the 3% timing shift in this robot suggests that natural stride-to-stride variability could produce appreciable differences in how push-off energy is distributed, even at the same average speed.
  • Editorial inference: The sagittal-plane constraint and upper-body stabilization may magnify the measured effects; a free 3D walker would likely show some of the push-off impulse absorbed by lateral momentum, so the 87% figure should be read as an upper-bound estimate for unconstrained walking.
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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

2 major / 5 minor

Summary. The paper compares two knee-control modes on the bipedal robot EcoWalker-2: active knee flexion initiation (AKFI), where the knee motor follows a commanded trajectory throughout the gait cycle, and passive knee flexion initiation (PKFI), where the knee motor is commanded to zero torque from 35% of the gait cycle onward. The authors report that PKFI delays the start of knee flexion by 5% of the gait cycle (GC), the start of hip flexion by 4% GC, and the start of ankle plantar flexion (SAPF) by 3% GC, while also shifting leading-leg touch-down by 1% GC. During the step-to-step transition, PKFI increases the horizontal impulse of the trailing leg by 87% (0.14 kg·m/s), increases the magnitude of the center-of-mass momentum vector by 188%, and causes a larger decrease in remaining-body horizontal momentum, compared with AKFI. The authors interpret these findings as evidence that passive knee flexion can trigger the release of the ankle catapult and that the delayed SAPF timing is the causal driver of the impulse differences. Data and code are provided via a public repository.

Significance. If the reported effects are robust, the paper provides a valuable robotic demonstration of Perry's hypothesis that passive knee flexion can initiate the push-off sequence, and it quantifies momentum changes associated with altered gait-event timing. The strengths of the work include its use of a physical biped with passive spring-loaded ankles, the precision of the encoder-based measurements (reported SD < 0.4% GC), the inclusion of a PKFI40 robustness check, and the public release of data, code, and CAD files. However, the direct empirical contrast between AKFI and PKFI is strong, but the mechanistic interpretation that the SAPF delay specifically 'leads to' the larger impulse is underdetermined because multiple kinematic and actuation variables change simultaneously between conditions. The statistical analysis also uses a paired test on non-paired data. With corrected statistics and appropriately hedged causal claims, the study would be a solid contribution to the discussion of push-off function and knee-ankle coordination.

major comments (2)
  1. [3.4] The Wilcoxon signed-rank test is applied to 120 gait cycles from each of two separate experimental runs. These cycles are not paired: there is no one-to-one correspondence between cycle i in the AKFI run and cycle i in the PKFI run, and the two runs were performed sequentially on the same robot rather than as a matched repeated-measures design. Using a paired test on unpaired samples can inflate significance. Please re-analyze with an unpaired two-sample test (e.g., Mann-Whitney U) or a mixed-effects model that treats gait cycle as a repeated measure within each run. Because the reported p-values are extremely small, the substantive conclusions will likely survive, but the inference procedure as written is incorrect.
  2. [Abstract and Discussion] The abstract states that passive knee flexion 'resulted in a 3% of the gait cycle later onset of ankle plantar flexion, leading to 87% larger increase in the trailing leg horizontal momentum.' However, PKFI and AKFI differ simultaneously in SKF onset (5% GC later), SHF onset (4% GC later), SAPF onset (3% GC later), LLTD timing (1% GC difference), and in the knee motor being torque-free from 35% GC onward (Fig. 3, Methods 3.3). The authors themselves describe SAPF as 'indirectly manipulated' (Introduction, Fig. 1b), so the experiment does not independently vary SAPF. The observed impulse difference could plausibly be caused by any of these coordinated changes, or by the change in knee joint impedance itself. An additional condition that varies SAPF timing without changing knee torque and hip-flexion timing, or a mediation analysis that controls for the other timing variables, is needed before the causal chain can be supported. At minimum, the abstract and conclusions should be reworded to describe the observed coordinated timing shift rather than asserting that the SAPF delay alone produces the impulse increase.
minor comments (5)
  1. [3.4] In the SAPF definition, the text says 'We defined the moment of SAPF when the trailing leg's ankle plantar flexion angle reached its maximum.' Since SAPF is the start of plantarflexion after a period of dorsiflexion, the relevant event should be the maximum dorsiflexion angle. Please clarify the sign convention and event definition, as written the description is ambiguous.
  2. [Table 1 caption] The caption contains duplicated text: 'the the absolute' appears twice. Please correct.
  3. [Introduction] The phrase 'A possible release mechanism can be derives from Perry's work' contains a grammatical error; it should read 'can be derived from Perry's work.'
  4. [Discussion] The sentence 'leading leg touch-down did not happen exactly at 50 %GC in either PKFI or AKFI experiment by neither legs' uses a double negative. Please reword to 'in either leg' or 'in neither leg.'
  5. [Methods 3.1] The term 'SOLO actuator module' is used without explanation on first appearance. Please define it as a compact series-elastic actuator module or reference the appropriate prior work.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the AKFI-vs-PKFI momentum and timing differences are measured, not fitted, and no result is defined into existence.

full rationale

This is an experimental study comparing two robot control modes. The quantities claimed—SAPF timing (3% GC later), trailing-leg horizontal impulse (+87%), and CoM momentum magnitude (+188%)—are directly measured from encoder, potentiometer, and current data (Methods 3.3, 3.4), not generated by fitting a model to data. The hypothesis in the Introduction ('We hypothesize that pRB increases more and pTL increases less...') was stated before measurement and then tested with Wilcoxon tests, so the result is not a fitted parameter renamed as prediction. The phrase 'leading to 87% larger increase' in the abstract is a causal interpretation, but there is no equation in the paper that defines the impulse change as a function of SAPF onset; the causal chain (PKFI → later SAPF → larger TL impulse) is underdetermined because SKF, SHF, LLTD, and knee motor impedance also differ between conditions. Underdetermination is a threat to causal validity, not circularity. The paper itself acknowledges the indirect manipulation ('by indirectly manipulating SAPF timing', Fig. 1b) and lists limitations in the Discussion ('Our study has limitations as the experiments were done on a bipedal robot...'), explicitly noting that human transfer remains to be explored. Self-citations to the authors' prior EcoWalker work ([12], [55]) supply the robot design and cost-of-transport comparison, but the central PKFI/AKFI contrast and all outcome measurements are performed in this paper and do not depend on those citations for their content. No 'uniqueness theorem' or prior result is invoked to force the interpretation. Hence no circular step meets the evidence bar.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new theoretical entities. The central claim depends on hand-chosen control parameters that are constant across conditions, on the modeling assumption that the robot reproduces human leg catapult mechanics, and on a questionable statistical independence assumption. No fitted constants are used to generate the reported differences.

free parameters (3)
  • Knee zero-torque start time in PKFI = 35 %GC (robustness check at 40 %GC)
    Chosen by hand as the middle of stance before push-off; defines the passive condition and thus the comparison at the center of the paper.
  • Hip P gains = right: 30, left: 26
    Manually tuned to obtain matching left and right leg kinematics; identical in both conditions, so they do not explain the between-condition differences.
  • CPG control parameters = f=1 Hz, Fhip=0.6, Fknee=0.6, knee amplitude 55 deg, knee offset 8 deg, hip amplitude 26 deg, hip offset 12 deg, hip…
    Control parameters chosen for the robot; held constant across AKFI and PKFI, so they affect absolute gait but not the comparison.
assumptions (4)
  • domain assumption The EcoWalker-2 robot with passive ankles and elastic SOL/GAS springs is a valid physical model of the human lower-leg catapult.
    Invoked in the Introduction and Discussion when transferring robot results to human gait; if the robot does not capture the relevant human mechanics, the broader conclusions do not follow.
  • domain assumption The step-to-step transition can be bounded by the minimum and second maximum of vertical CoM velocity.
    Methods 3.4 defines the transition period; choosing the second of two similar peaks affects the measured momentum changes.
  • domain assumption The 120 gait cycles in each condition are independent, enabling a paired statistical test.
    Methods 3.4 uses a Wilcoxon signed-rank test with N=120; this assumption is questionable because cycles come from two separate runs and are not paired.
  • standard math Newtonian mechanics for momentum and kinetic energy computation.
    Standard physics used in calculation of segment momenta and impulses; unproblematic.

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Cite this review

Pith. "Pith review of Passive knee flexion increases forward impulse of the trailing leg during the step-to-step transition." pith.science (2026). https://pith.science/paper/PYWGKQM6

@misc{pith2026241113289,
  author       = {Pith},
  title        = {Pith review of: Passive knee flexion increases forward impulse of the trailing leg during the step-to-step transition},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PYWGKQM6}},
  note         = {Machine review of arXiv:2411.13289}
}
read the original abstract

Human walking efficiency relies on the elastic recoil of the Achilles tendon, facilitated by a "catapult mechanism" that stores energy during stance and releases it during push-off. The catapult release mechanism could include the passive flexion of the knee, as the main part of knee flexion was reported to happen passively after leading leg touch-down. This study is the first to investigate the effects of passive versus active knee flexion initiation, using the bipedal EcoWalker-2 robot with passive ankles. By leveraging the precision of robotic measurements, we aimed to elucidate the importance of timing of gait events and its impact on momentum and kinetic energy changes of the robot. The EcoWalker-2 walked successfully with both initiation methods, maintaining toe clearance. Passive knee flexion initiation resulted in a 3% of the gait cycle later onset of ankle plantar flexion, leading to 87% larger increase in the trailing leg horizontal momentum, and 188% larger magnitude increase in the center of mass momentum vector during the step-to-step transition. Our findings highlight the role of knee flexion in the release of the catapult, and timing of gait events, providing insights into human-like walking mechanics and potential applications in rehabilitation, orthosis, and prosthesis development.

Figures

Figures reproduced from arXiv: 2411.13289 by the authors.

Figure 1
Figure 1. The two main roles of push-off (a) and the expected effect of passive versus active knee flexion initiation (b). The main part of knee flexion, from 5-40 deg, occurs passively after LLTD5 . We compare PKFI and AKFI to influence energy flow into the RB and TL by indirectly manipulating SAPF timing. We aim to contribute to the debate on the primary function of ankle push-off in the human swing leg catapult mechanism16… view at source ↗
Figure 2
Figure 2. Hip, knee, and ankle angles during the full gait cycle in the experiments with active knee flexion initiation (AKFI - a), and with passive knee flexion initiation (PKFI - b). Shading shows the standard deviation of the curves. Horizontal axis shows the gait cycle percentage, 0 %GC is the touch-down of the trailing leg. In the PKFI experiment, the knee motor torque is zero from the dark pink vertical dotted line (kne… view at source ↗
Figure 3
Figure 3. Timing of the gait events in gait cycle percentage with active knee flexion initiation (AKFI), and with passive knee flexion initiation (PKFI), and by humans42 . 0 %GC is the touch-down of the trailing leg. In the PKFI experiment, knee and hip flexion start 5 %GC later than in the AKFI experiment (SKF and SHF). LLTD occurs 1 %GC earlier with PKFI than with AKFI. The ankle starts to plantarflex (SAPF) 2 %GC after LLT… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Trailing Leg (TL), Remaining Body (RB), and Center of Mass (CoM) instantaneous momentums in horizontal (a, c, and e) and vertical (b, d, and f) directions at the start of the step-to-step transition (vmin), at leading leg touch-down (LLTD), and at the end of the step-t…
Figure 5
Figure 5. Figure 5: Center of Mass (CoM) velocity vectors at the start of the step-to-step transition (vmin), at leading leg touch-down (LLTD), and at the end of the step-to-step transition (vmax) in the active knee flexion initiation (AKFI - a) and in the passive knee flexion initiation …
Figure 6
Figure 6. Figure 6: Schematic and rendering of the bipedal EcoWalker-2 robot. a: Schematic of the robot with spring-tendon routing, angle definitions, and range of motion of the joints. Segment lengths: lthigh = lshank = 160mm, lheel = 32mm, ltoe = 17mm. Pulley radii: rGAS = rSOL = 13mm. …

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.