pith. sign in

arxiv: 2606.22073 · v2 · pith:EH2CMRDPnew · submitted 2026-06-20 · 💻 cs.RO

Dynamics, stability, and energy efficiency of an energy-recycling rimless wheel with spring-clutch legs

Tongchen Lin , Yanqiu Zheng , Chuhan Zhang , Ruigang Chen , Yizhar Or , Mingyi Liu This is my paper

Pith reviewed 2026-06-26 12:00 UTC · model grok-4.3

classification 💻 cs.RO
keywords rimless wheelenergy recyclingspring-clutch legscost of transportpassive walkinghybrid dynamicsgait stabilitylegged robot
0
0 comments X

The pith

A rimless wheel with spring-clutch legs recycles impact energy to achieve up to 16.13 percent lower cost of transport in simulations.

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

This paper introduces a rimless wheel equipped with spring-clutch legs that capture elastic energy from foot impacts and release it during the subsequent step. A hybrid dynamic model is built to analyze the system's behavior, and simulations compare its performance to a standard viscoelastic-legged version. The results indicate improved energy efficiency and maintained local stability of periodic gaits. Experiments with a physical prototype demonstrate passive walking on a gentle incline, validating the concept's practicality for low-energy locomotion.

Core claim

The energy-recycling rimless wheel with spring-clutch legs stores part of the impact-induced elastic energy after foot contact using a lockable clutch and reinjects it in the next gait cycle. Numerical simulations show this reduces the Cost of Transport by up to 16.13% compared to a benchmark viscoelastic-legged rimless wheel, and by more than 50% compared to a rigid one, while maintaining locally stable periodic gaits over tested ranges. Prototype experiments confirm passive walking on a 1 degree slope with a CoT of approximately 0.02.

What carries the argument

The lockable clutch in the spring legs, which stores impact-induced elastic energy after foot contact and reinjects it in the next gait cycle.

If this is right

  • Reduces CoT by up to 16.13% versus viscoelastic benchmark.
  • Reduces CoT by more than 50% versus rigid rimless wheel.
  • Maintains locally stable periodic gaits across tested slope and stiffness ranges.
  • Enables passive walking on 1 degree slope with CoT around 0.02.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The energy savings might scale to other passive dynamic walkers if clutch timing can be adapted to different terrains.
  • Unmodeled friction in the clutch could limit real-world gains below the simulated 16.13 percent.
  • Combining this with variable stiffness could further optimize efficiency on varying slopes.

Load-bearing premise

The hybrid dynamic model and clutch mechanism accurately capture energy storage and reinjection without significant unmodeled losses, delays, or friction.

What would settle it

A physical test showing that the measured energy consumption or CoT does not improve by the simulated amount due to clutch inefficiencies or model inaccuracies.

read the original abstract

This paper proposes an energy-recycling rimless wheel with spring-clutch legs. The proposed mechanism uses a lockable clutch to store part of the impact-induced elastic energy after foot contact and reinject it in the next gait cycle. First, we develop a hybrid dynamic model of the energy-recycling rimless wheel. Second, numerical simulations are used to examine the dynamics, local stability of periodic gaits, and the Cost of Transport (CoT) of the proposed mechanism. The simulation results show that the proposed mechanism reduces the CoT by up to 16.13% compared with a benchmark viscoelastic-legged rimless wheel with telescopic spring-damper legs. Compared with the rigid rimless wheel, the viscoelastic-legged and energy-recycling models reduce the CoT by more than 50%. The energy-recycling model also maintains locally stable periodic gaits over the tested slope and stiffness ranges. Finally, prototype experiments on an inclined plane are conducted to examine the feasibility of the proposed mechanism. The experimental results show that the proposed rimless wheel achieves passive walking on a shallow 1{\deg} slope, corresponding to a CoT of approximately 0.02. These results suggest that the proposed spring-clutch mechanism can improve the simulated walking efficiency of the energy-recycling rimless wheel, while the prototype experiments support the feasibility of passive walking with the mechanism.

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

2 major / 1 minor

Summary. The paper proposes an energy-recycling rimless wheel with spring-clutch legs that stores impact-induced elastic energy via a lockable clutch and reinjects it in subsequent gait cycles. It develops a hybrid dynamic model, uses numerical simulations to analyze dynamics, local stability of periodic gaits, and Cost of Transport (CoT), reporting up to 16.13% CoT reduction versus a viscoelastic-legged benchmark with telescopic spring-damper legs (and >50% versus rigid), and conducts prototype experiments showing passive walking on a 1° slope with CoT ≈ 0.02.

Significance. If the hybrid model correctly predicts net energy reinjection without substantial unmodeled losses, the approach could improve efficiency in passive dynamic walkers beyond existing viscoelastic designs. The prototype establishes basic feasibility of the clutch mechanism for passive locomotion on shallow slopes.

major comments (2)
  1. [Numerical simulations section] Numerical simulations section: the headline 16.13% CoT reduction is obtained from forward simulations of the proposed hybrid model against fixed benchmarks, but the manuscript provides no sensitivity analysis to clutch friction, backlash, or actuation delay; even modest dissipation would eliminate the reported advantage while leaving the feasibility result intact.
  2. [Prototype experiments section] Prototype experiments section: the experiments confirm passive walking on a 1° slope (CoT ≈ 0.02) but report no quantitative measurements of stored/released elastic energy, clutch timing, or direct CoT comparison against the viscoelastic benchmark on the physical hardware, so the central efficiency claim remains simulation-only.
minor comments (1)
  1. [Abstract] Abstract: the maximum 16.13% CoT reduction is stated without specifying the exact slope angle or stiffness range at which it occurs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below, indicating planned changes to the manuscript.

read point-by-point responses

  1. Referee: [Numerical simulations section] Numerical simulations section: the headline 16.13% CoT reduction is obtained from forward simulations of the proposed hybrid model against fixed benchmarks, but the manuscript provides no sensitivity analysis to clutch friction, backlash, or actuation delay; even modest dissipation would eliminate the reported advantage while leaving the feasibility result intact.

    Authors: We agree that the simulations assume idealized clutch behavior and lack sensitivity analysis for friction, backlash, or delays. In the revised manuscript we will add a sensitivity study to quantify how these factors affect the reported CoT reduction and assess robustness under realistic conditions. revision: yes

  2. Referee: [Prototype experiments section] Prototype experiments section: the experiments confirm passive walking on a 1° slope (CoT ≈ 0.02) but report no quantitative measurements of stored/released elastic energy, clutch timing, or direct CoT comparison against the viscoelastic benchmark on the physical hardware, so the central efficiency claim remains simulation-only.

    Authors: The prototype experiments were designed to establish basic feasibility of passive walking. We acknowledge that quantitative energy measurements, clutch timing data, and hardware CoT comparisons to the viscoelastic benchmark are absent, leaving the efficiency claim simulation-based. In revision we will explicitly clarify this distinction and the scope of the experiments; adding the requested hardware comparisons would require a second instrumented prototype and is outside the present study. revision: partial

Circularity Check

0 steps flagged

No circularity: CoT reduction is forward simulation output from distinct models

full rationale

The paper derives a hybrid dynamic model from first principles, runs forward numerical simulations to compute and compare CoT between the proposed spring-clutch mechanism and a separate benchmark viscoelastic model, and reports experimental feasibility on a physical prototype. The 16.13% CoT reduction is an output of those simulations on two non-identical models; no parameter is fitted to target data and then relabeled as a prediction, no self-citation chain carries the central claim, and no equation reduces to its own input by construction. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; full paper would likely specify clutch timing parameters, contact models, and slope/stiffness ranges used in simulations.

pith-pipeline@v0.9.1-grok · 5796 in / 1148 out tokens · 50214 ms · 2026-06-26T12:00:38.852952+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

27 extracted references · 1 linked inside Pith

  1. [1]

    Efficient bipedal robots based on passive- dynamic walkers,

    S. Collins, A. Ruina, R. Tedrake, and M. Wisse, “Efficient bipedal robots based on passive- dynamic walkers, ”Science, vol. 307 , no. 5712, pp. 1082–1085, 2005

    2005

  2. [2]

    Passive dynamic walking,

    T. McGeeret al., “Passive dynamic walking, ”Int. J. Robotics Res., vol. 9 , no. 2, pp. 62–82, 1990

    1990

  3. [3]

    A bipedal walking robot with efficient and human-like gait,

    S. Collins and A. Ruina, “ A bipedal walking robot with efficient and human-like gait, ” in Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 2005, pp. 1983–1988

    2005

  4. [4]

    Low-bandwidth reflex-based control for lower power walking: 65 km on a single battery charge,

    P . A. Bhounsule, J. Cortell, A. Grewal, B. Hendriksen, J. D. Karssen, C. Paul, and A. Ruina, “Low-bandwidth reflex-based control for lower power walking: 65 km on a single battery charge, ”The International Journal of Robotics Research, vol. 33, no. 10, pp. 1305–1321, 2014

    2014

  5. [5]

    Exciting engineered passive dynamics in a bipedal robot,

    D. Renjewski, A. Spröwitz, A. Peekema, M. Jones, and J. Hurst, “Exciting engineered passive dynamics in a bipedal robot, ”IEEE Transactions on Robotics, vol. 31, no. 5, pp. 1244–1251, 2015

    2015

  6. [6]

    Energy-efficient locomotion generation and theoretical analysis of a quasi-passive dynamic walker,

    L. Li, I. Tokuda, and F. Asano, “Energy-efficient locomotion generation and theoretical analysis of a quasi-passive dynamic walker, ”IEEE Robotics and Automation Letters, vol. 5, no. 3, pp. 4305–4312, 2020

    2020

  7. [7]

    Dynamics and stability of a rimless spoked wheel: a simple 2d system with impacts,

    M. J. Coleman, “Dynamics and stability of a rimless spoked wheel: a simple 2d system with impacts, ”Dynamical Systems, vol. 25, no. 2, pp. 215–238, 2010

    2010

  8. [8]

    Tensegrity-based legged robot generates passive walking, skipping, and crawling gaits in accordance with environment,

    Y . Zheng, F. Asano, C. Yan, L. Li, and I. T. Tokuda, “Tensegrity-based legged robot generates passive walking, skipping, and crawling gaits in accordance with environment, ”IEEE/ASME Transactions on Mechatronics, 2025

    2025

  9. [9]

    Dead-beat control of walking for a torso-actuated rimless wheel using an event-based, discrete, linear controller,

    P . A. Bhounsule, E. Ameperosa, S. Miller, K. Seay, and R. Ulep, “Dead-beat control of walking for a torso-actuated rimless wheel using an event-based, discrete, linear controller, ” inInter- national Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 50152. American Society of Mechanical Engineers, 2016...

    2016

  10. [10]

    Design, modeling, and control of a differential drive rimless wheel that can move straight and turn,

    S. Sanchez and P . A. Bhounsule, “Design, modeling, and control of a differential drive rimless wheel that can move straight and turn, ”Automation, vol. 2, no. 3, pp. 98–115, 2021

    2021

  11. [11]

    Development of rimless wheel with controlled wobbling mass,

    Y . Hanazawa, “Development of rimless wheel with controlled wobbling mass, ” in2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2018, pp. 4333–4339

    2018

  12. [12]

    Walking model with no energy cost,

    M. Gomes and A. Ruina, “Walking model with no energy cost, ”Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, vol. 83, no. 3, p. 032901, 2011

    2011

  13. [13]

    Quiet (nearly collisionless) robotic walking,

    M. W . Gomes and K. Ahlin, “Quiet (nearly collisionless) robotic walking, ” in2015 IEEE Interna- tional Conference on Robotics and Automation (ICRA). IEEE, 2015, pp. 5761–5766

    2015

  14. [14]

    Three uses for springs in legged locomotion,

    R. Alexanderet al., “Three uses for springs in legged locomotion, ”International Journal of Robotics Research, vol. 9 , no. 2, pp. 53–61, 1990

    1990

  15. [15]

    Energy-efficient quadruped locomotion with compliant feet,

    P . Pal, S. Kolathaya, and A. Ghosal, “Energy-efficient quadruped locomotion with compliant feet, ”arXiv preprint arXiv:2605.14411, 2026

    Pith/arXiv arXiv 2026

  16. [16]

    Stable and robust walking with compliant legs,

    J. Rummel, Y . Blum, H. M. Maus, C. Rode, and A. Seyfarth, “Stable and robust walking with compliant legs, ” in2010 IEEE International Conference on Robotics and Automation. IEEE, 2010, pp. 5250–5255

    2010

  17. [17]

    J. W . Hurst,The role and implementation of compliance in legged locomotion. Carnegie Mellon University, 2008

    2008

  18. [18]

    Reducing the energy cost of human walking using an unpowered exoskeleton,

    S. H. Collins, M. B. Wiggin, and G. S. Sawicki, “Reducing the energy cost of human walking using an unpowered exoskeleton, ”Nature, vol. 522, no. 7555, pp. 212–215, 2015

    2015

  19. [19]

    Recycling energy to restore impaired ankle function during human walking,

    S. H. Collins and A. D. Kuo, “Recycling energy to restore impaired ankle function during human walking, ”PLoS one, vol. 5, no. 2, p. e9307 , 2010

    2010

  20. [20]

    Design of an ankle ex- oskeleton that recycles energy to assist propulsion during human walking,

    C. Wang, L. Dai, D. Shen, J. Wu, X. Wang, M. Tian, Y . Shi, and C. Su, “Design of an ankle ex- oskeleton that recycles energy to assist propulsion during human walking, ”IEEE Transactions on Biomedical Engineering, vol. 69 , no. 3, pp. 1212–1224, 2021

    2021

  21. [21]

    Lower limb exoskeleton-energy optimization of bipedal walking with energy recycling-modeling and simulation,

    H. Lee and J. Rosen, “Lower limb exoskeleton-energy optimization of bipedal walking with energy recycling-modeling and simulation, ”IEEE Robotics and Automation Letters, vol. 8, no. 3, pp. 1579–1586, 2023

    2023

  22. [22]

    Elastic energy-recycling actuators for efficient robots,

    E. Krimsky and S. H. Collins, “Elastic energy-recycling actuators for efficient robots, ”Science Robotics, vol. 9 , no. 88, p. eadj7246, 2024

    2024

  23. [23]

    Birdbot achieves energy-efficient gait with minimal control using avian-inspired leg clutching,

    A. Badri-Spröwitz, A. Aghamaleki Sarvestani, M. Sitti, and M. A. Daley, “Birdbot achieves energy-efficient gait with minimal control using avian-inspired leg clutching, ”Science Robotics, vol. 7 , no. 64, p. eabg4055, 2022

    2022

  24. [24]

    Passive dynamic walking of viscoelastic-legged rimless wheel,

    F. Asano and J. Kawamoto, “Passive dynamic walking of viscoelastic-legged rimless wheel, ” in 2012 IEEE International Conference on Robotics and Automation. IEEE, 2012, pp. 2331–2336

    2012

  25. [25]

    Dynamic bipedal walking under stick-slip transitions,

    B. Gamus and Y . Or, “Dynamic bipedal walking under stick-slip transitions, ”SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, pp. 609–642, 2015

    2015

  26. [26]

    Lock your robot: A review of locking devices in robotics,

    M. Plooij, G. Mathijssen, P . Cherelle, D. Lefeber, and B. Vanderborght, “Lock your robot: A review of locking devices in robotics, ”IEEE Robotics & Automation Magazine, vol. 22, no. 1, pp. 106–117 , 2015

    2015

  27. [27]

    The effects of electroadhesive clutch design param- eters on performance characteristics,

    S. B. Diller, S. H. Collins, and C. Majidi, “The effects of electroadhesive clutch design param- eters on performance characteristics, ”Journal of Intelligent Material Systems and Structures, vol. 29 , no. 19 , pp. 3804–3828, 2018. 25

    2018