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REVIEW 3 major objections 5 minor 32 references

Explosive Output to Enhance Jumping Ability: A Variable Reduction Ratio Design Paradigm for Humanoid Robots Knee Joint

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims a knee whose reduction ratio falls as it extends keeps a fixed electric motor in its high-power band through takeoff, yielding a 63 cm single-joint jump and a 0.5 m humanoid jump.

desk verdict Real hardware, genuine jump demos, but the headline 28.1% advantage over fixed-ratio knees is a simulation result built on a model with a likely missing 1/2 factor in the Jacobian. read the letter →

arxiv 2506.12314 v1 pith:CFLJLTOA submitted 2025-06-14 cs.RO cs.SYeess.SY

Xiaoshuai Ma , Haoxiang Qi , Qingqing Li , Haochen Xu , Xuechao Chen , Junyao Gao , Zhangguo Yu , Qiang Huang This is my paper · ORCID
classification cs.ROcs.SYeess.SY
keywords humanoidrobotsexplosivejumpingvariablereductionratiokneejointdesignlinearactuatorballscrewelectricactuationjumpcontrol
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

Electric humanoid robots jump poorly because a fixed gear ratio between the knee motor and the body cannot deliver both high torque at the start of a jump and high speed at the end; the motor either stalls low or spins into a high-loss speed region. This paper proposes a knee whose reduction ratio starts high and falls as the joint extends, so the motor can sit in its high-power band through the whole takeoff. The idea is realized with a linear-actuator-driven guide-rod mechanism whose geometry makes the effective ratio a tunable function of knee angle, and the paper optimizes that geometry for maximum takeoff energy. On a one-leg test platform carrying a 20 kg load, the joint jumped 63 cm, which the paper reports as a theoretical improvement of 28.1% over the best fixed-ratio joint (the conclusion states 20%). Integrated into a 45 kg humanoid, the design produced a 0.5 m vertical jump, a 1.1 m forward jump, and a 0.5 m box jump.

What carries the argument

The central object is the explosive variable reduction ratio knee (EVRR-K): a coupling law in which the transmission ratio $k(q_2)$ decreases as knee angle $q_2$ extends, so a high ratio near the crouched position amplifies torque and a low ratio near full extension keeps motor speed down. The physical implementation is a linear actuator driving a crank-guide-rod: a ball screw pushes a link that rotates the knee through a crank, and the effective ratio is a function of the crank radius $r$, frame length $S_0$, and assembly offset $\Delta\theta$, given by $k = \frac{2\pi r (S_0+r)\sin\theta}{Q \sqrt{2S_0 r - 2r^2\cos\theta + S_0^2 + 2r^2 - 2S_0 r \cos\theta}}$ with $Q$ the screw lead. The design is tuned by an optimization that maximizes takeoff mechanical energy $W_{\text{takeoff}} = \frac{1}{2}m_{\text{tot}}\dot{y}_{\text{CoM}}(t_{\text{to}})^2 + m_{\text{tot}} g y_{\text{CoM}}(t_{\text{to}})$ over $(r, S_0, \Delta\theta)$ under a maximum-torque 'explosive' control law and structural constraints. This parameterized ratio-angle coupling is what lets one fixed electric motor act as both a torque amplifier at the start of a jump and a speed-friendly drive at the end.

What would settle it

Run an A/B jump test on the same robot with the same motor, control law, and takeoff angle, swapping only the knee ratio curve: if the EVRR-K joint does not measurably out-jump the best fixed-ratio knee, or if the knee motor's speed exceeds the high-loss region before takeoff in the EVRR-K case, the central claim fails. A cheaper check: instrument the knee during the reported 0.5 m box jump and verify that motor speed stays below roughly 3000 rpm and joint power remains near 1.5 kW through the late takeoff phase.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that the knee-to-CoM transmission ratio mismatch is not a control problem but a mechanical-design problem. For a fixed-ratio knee, the ratio between motor speed and CoM speed grows steeply as the knee extends, so a motor sized for the start of the jump is forced to very high speed, and therefore high loss, at the end. The EVRR-K couples the reduction ratio to the joint angle so that the product of motor torque and speed stays close to the motor's peak-power plateau: a high initial ratio builds torque quickly, and the declining ratio caps the motor-speed rise. The paper claims that optimizing the crank length, frame offset, and angular offset of the guide-rod mechanism, using a takeoff-energy objective under maximum-torque control, yields a monotonically decreasing ratio curve whose simulated jump height beats the optimal fixed-ratio knee by 28.1% (abstract; 20% in the conclusion), and that the mechanism delivers this in hardware: a 63 cm jump on a 24.93 kg single-joint platform and, on the 45 kg humanoid BHR8-J1, a 0.5 m vertical, 1.1 m forward, and 0.5 m box jump.

Load-bearing premise

The claimed improvement is computed with a model in which the knee is the only active joint and the center of mass moves straight up, and the paper acknowledges that the ankle's role is not addressed.

Editorial extensions

If this is right

  • A single electric knee motor can cover the full explosive-jump torque-speed profile, so jump performance no longer requires a larger, heavier motor or hydraulic actuation.
  • The optimized ratio curve keeps the knee motor below about 3000 rpm during takeoff, in the high-power, low-loss band, whereas a fixed-ratio joint would need over 4000 rpm and enter the loss region.
  • Because the ratio curve is set by three geometric parameters, the same guide-rod mechanism can be re-tuned for different limb lengths, masses, and initial crouch angles.
  • On the full robot, the knee peaks at 286 Nm, 15.5 rad/s, and 1.5 kW during the box jump, with hip and ankle joints staying below 200 Nm and 1.2 kW, confirming the knee as the bottleneck the design targets.
  • The reported 0.5 m box jump was not limited by the mechanism: the paper notes neither the vertical nor the forward jump reached optimal performance, so the same joint should yield more once the control law exploits the variable ratio.

Reading between the lines

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

  • A natural extension the paper does not test: if the ankle were also given a variable-ratio treatment, takeoff energy should rise further; the paper identifies the ankle as its main unaddressed limitation, and a knee-limited model likely leaves that margin on the table.
  • The 28.1% (abstract) versus 20% (conclusion) improvement figure likely depends on which fixed-ratio baseline and initial angle is chosen; a reader comparing against other robots should focus on the absolute jump numbers rather than the single percentage.
  • The same variable-ratio principle might transfer to other explosive tasks, such as squatting lifts or stair-springing, where the load-speed profile changes over the motion, though the paper only tests jumps.
  • A direct A/B on the full robot, with the same control and motor and only the ratio curve swapped, would isolate the mechanism's contribution; the paper's evidence is a single configuration plus a simulated fixed-ratio comparison.
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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

3 major / 5 minor

Summary. The paper proposes a variable-reduction-ratio knee joint (EVRR-K) for humanoid jumping, implemented by a linear-actuator-driven guide-rod mechanism whose reduction ratio decreases as the knee extends. The authors analyze motor output limits and a simplified vertical-CoM knee kinematic model, optimize the mechanism parameters (crank length, frame length, assembly offset) by maximizing simulated takeoff energy, and compare the result with an optimized fixed-ratio knee in simulation. Experiments on a 24.93 kg single-joint platform give a 63 cm vertical jump, and the 45 kg humanoid BHR8-J1 equipped with the mechanism performs a 0.5 m vertical jump, a 1.1 m forward jump, and a 0.5 m box jump. The reported 28.1% advantage over fixed-ratio knees is a simulation-based comparison rather than a hardware measurement.

Significance. The paper's concrete hardware achievements are significant: a compact motor-driven knee enables a 63 cm jump on a 24.93 kg single-joint platform and useful multi-task jumps on a full humanoid, with motor speeds kept below about 3000 rpm and the mechanism packaged in a practical form. The design paradigm is credible and worth reporting. However, the headline quantitative superiority over fixed-ratio knees is not measured; it is a model-based prediction, and the simplified model used for that prediction appears to contain a Jacobian error that may change the reported margin. The central claim is therefore defensible but not yet established at the strength claimed.

major comments (3)
  1. [Section II-B, Eq. (5)] Equation (5) is missing a factor of 1/2. For the CoM height y_CoM = [m1 a1 + m2(l1+a2) + m3(l1+l2)] cos(q2/2)/(m1+m2+m3), differentiation gives d y_CoM/d q2 = -(1/2)[m1 a1 + m2(l1+a2) + m3(l1+l2)] sin(q2/2)/(m1+m2+m3). The magnitude, which is what Eq. (5) intends, should therefore contain the factor 1/2. Because lambda(q2)=1/J in Eq. (4) and Eq. (6) uses lambda to map joint torque to CoM force and joint rate to CoM velocity, all subsequent quantities in Section IV, including the optimized takeoff energy and the FRR-K comparison in Table II, are computed with lambda values that are a factor of two too large. The optimization should be rerun with the corrected Jacobian and the reported 28.1%/28.9% margin should be re-quantified.
  2. [Section V-A and Table II] The claimed improvement over fixed-ratio joints is not validated experimentally. Section V-A reports only the EVRR-K platform jump of 63 cm; no fixed-ratio knee was built or tested. The 'theoretical improvement of 28.1%' (abstract) and '20% improvement' (Section VI) both derive from the simulation in Table II, where the FRR-K baseline is optimized in the same simplified model. Since a model-based baseline is used to support the central quantitative claim, a hardware or whole-body-simulation comparison against a comparable fixed-ratio knee is needed before the improvement can be considered established.
  3. [Section II-B and Section V-B] The simplified model used for optimization constrains the CoM to vertical motion and treats the hip and ankle as passive, yet the full-robot validation in Section V-B uses active hip and ankle joints, and Section VI explicitly states that the ankle's role is unaddressed. The single-joint platform is consistent with the model, but the full-robot jumps cannot validate the optimized ratio curve or the simulated margin over FRR-K. A concrete resolution would be to evaluate the optimized EVRR-K parameters in a whole-body multi-joint model with active hip/ankle, or to compare hardware against a fixed-ratio knee on the same platform.
minor comments (5)
  1. [Abstract, Section IV-B, Section VI] The improvement percentages are inconsistent: 28.1% in the abstract, approximately 28.9% in Section IV-B, and 20% in Section VI. These should be reconciled and stated as simulated margins where appropriate.
  2. [Eq. (6)] The second relation in Eq. (6) appears inconsistent with Eq. (4): if lambda(q2)=qdot2/ydot_CoM, then ydot_CoM = qdot2/lambda(q2), not qdot2*lambda(q2). Please correct the printed equation or the definition.
  3. [Section I and abstract] There are typographical errors: 'Index T erms' in the abstract, 'center of mas' in Section I, and inconsistent formatting of subscripts and Greek letters in several equations. The manuscript should be proofread.
  4. [Fig. 5 caption] The caption of Fig. 5 references 'Fig. 12a' and 'Fig. 12b' when it should reference panels (a) and (b) of Fig. 5; this can confuse readers.
  5. [Section IV-B, Eq. (18)] In Eq. (18), H = W_takeoff/(m_tot g) - y_CoM,s; please clarify whether y_CoM,s is the CoM height in the fully extended pose, since this affects the reported jump height.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the 28.1% improvement over fixed-ratio knees is a same-model simulation comparison, not a fitted prediction, and the measured jump heights are independent of the parameter optimization.

full rationale

The central claim chain is not circular. The EVRR-K versus FRR-K comparison in Section IV is obtained by maximizing the same takeoff-energy objective (Eqs. 14-16) for both joint types under the simplified vertical CoM model of Section II-B; this is a model-based design comparison, not a prediction made from fitted data, and the fixed-ratio baseline is optimized within the same framework rather than selected adversarially. The experimental jump heights (63 cm platform, 0.5 m robot vertical jump, 1.1 m forward jump, 0.5 m box jump) are measured outcomes and are not used to fit the VRR parameters; the motor torque/speed envelope is external manufacturer data. The paper does reference prior work from the same group for jump control ([10], [12]), but the variable-reduction-ratio claim does not rest on those citations: the knee mechanism, the optimization, and the hardware demonstrations are self-contained evidence. The acknowledged modeling simplifications (single actuated knee, passive hip/ankle, vertical CoM in Section II-B; ankle role unaddressed in Section VI) are correctness risks rather than circularity. The possible missing factor 1/2 in the Jacobian of Eq. (5) is a mathematical modeling concern, not a step that reduces the conclusion to its inputs, so it does not affect the circularity score.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a simplified vertical jumping model, rigid-link assumptions, and manufacturer motor data. The design parameters r, S0, and Δθ are free parameters optimized via simulation. No new physical entities are introduced.

free parameters (4)
  • Crank length r = 47 mm (platform), 47-49 mm (simulation)
    Optimized via grid search (Algorithm 1) to maximize simulated takeoff energy; the optimal value depends on the simplified model and motor envelope. Not an externally measured quantity.
  • Frame length S0 = 259 mm (platform), 150 mm (simulation)
    Design parameter chosen by the same optimization; the large difference between simulation and platform indicates the optimized value is model-sensitive.
  • Assembly offset Δθ = 0 degrees
    Included in the optimization variables and set to zero in the final design, so it did not affect the result.
  • Fixed ratio k (FRR-K baseline) = 22 to 23
    Baseline ratio used in simulation comparisons; it is optimized for the fixed-ratio joint and is not a property of the proposed mechanism.
assumptions (5)
  • domain assumption The knee is the only actuated joint during takeoff; hip and ankle are passive and constrained to vertical motion.
    Used throughout Section II-B to derive the Jacobian and transmission ratio. The paper acknowledges the ankle's role is unaddressed in Section VI.
  • domain assumption All links are rigid bodies with uniform mass distribution and centroids at their geometric centers.
    Stated in Section IV-B before optimization; real humanoid links have non-uniform mass and compliance.
  • domain assumption The motor torque-speed envelope (TPE/PPE) in Fig. 1 is a correct representation of the actuator limits.
    Taken from manufacturer (TQ-8526sp) data; the optimization and the comparison rely on this external envelope, which is not independently verified in the paper.
  • domain assumption The Jacobian formula in Eq. (5) is correct as stated.
    The formula is presented without derivation and appears to be missing a factor of 1/2 (derivative of cos(q2/2)); if so, the transmission ratios are off by a constant factor, which could alter the optimized parameters.
  • domain assumption The explosive jump control applies maximum available torque according to Eq. (10).
    The optimization and experiments use this control law; the paper does not analyze whether a different control could change the optimal ratio curve.

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Cite this review

Pith. "Pith review of Explosive Output to Enhance Jumping Ability: A Variable Reduction Ratio Design Paradigm for Humanoid Robots Knee Joint." pith.science (2026). https://pith.science/paper/CFLJLTOA

@misc{pith2026250612314,
  author       = {Pith},
  title        = {Pith review of: Explosive Output to Enhance Jumping Ability: A Variable Reduction Ratio Design Paradigm for Humanoid Robots Knee Joint},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CFLJLTOA}},
  note         = {Machine review of arXiv:2506.12314}
}
read the original abstract

Enhancing the explosive power output of the knee joints is critical for improving the agility and obstacle-crossing capabilities of humanoid robots. However, a mismatch between the knee-to-center-of-mass (CoM) transmission ratio and jumping demands, coupled with motor performance degradation at high speeds, restricts the duration of high-power output and limits jump performance. To address these problems, this paper introduces a novel knee joint design paradigm employing a dynamically decreasing reduction ratio for explosive output during jump. Analysis of motor output characteristics and knee kinematics during jumping inspired a coupling strategy in which the reduction ratio gradually decreases as the joint extends. A high initial ratio rapidly increases torque at jump initiation, while its gradual reduction minimizes motor speed increments and power losses, thereby maintaining sustained high-power output. A compact and efficient linear actuator-driven guide-rod mechanism realizes this coupling strategy, supported by parameter optimization guided by explosive jump control strategies. Experimental validation demonstrated a 63 cm vertical jump on a single-joint platform (a theoretical improvement of 28.1\% over the optimal fixed-ratio joints). Integrated into a humanoid robot, the proposed design enabled a 1.1 m long jump, a 0.5 m vertical jump, and a 0.5 m box jump.

Figures

Figures reproduced from arXiv: 2506.12314 by the authors.

Figure 1
Figure 1. Motor torque performance envelope (TPE) and power [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. (a)Knee-CoM y-axis transmission ratio 𝜆(𝑞2) as a function of knee joint angle 𝑞2; (b) Ideal transmission ratio curve for motor explosive output. extension. This enables rapid entry into and maintenance within the high-power region at takeoff, significantly boosting jump performance (Fig. 3b). Furthermore, as Eq. 5, increasing the CoM height and limb lengths raises 𝐽𝑐𝑜𝑚,𝑦 (𝑞2), which lowers 𝜆(𝑞2) and the required mot… view at source ↗
Figure 4
Figure 4. Schematic of the high-explosiveness variable reduction [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figures from the paper (8 more)
Figure 6
Figure 6. Figure 6: , which drives the joint to operate at its maximum available torque. The maximum torque that the motor can provide is given by: 𝜏𝑚,𝑚𝑎𝑥 =  𝜏peak, 𝜔𝑚 ≤ 𝜔break 𝜏limit(𝐼𝑞, 𝜔𝑚), 𝜔𝑚 ∈ (𝜔break, 𝜔max] (10) where 𝜏𝑚 represents the motor torque output during control, 𝜏peak is t…
Figure 7
Figure 7. Figure 7: Numerical simulation results for explosive jumping take [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]
Figure 9
Figure 9. Figure 9: Experimental data of explosive vertical jumping motion [PITH_FULL_IMAGE:figures/full_fig_p006_9.png]
Figure 8
Figure 8. Figure 8: Vertical jump experiment on the one-DOF leg-like [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 12
Figure 12. Figure 12: The total mass is 45 kg. The control system comprises [PITH_FULL_IMAGE:figures/full_fig_p006_12.png]
Figure 10
Figure 10. Figure 10: Full-scale humanoid robot jump experiments. [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 11
Figure 11. Figure 11: The full-scale BHR8-J1 humanoid robot equipped with [PITH_FULL_IMAGE:figures/full_fig_p007_11.png]
Figure 13
Figure 13. Figure 13: Hip, knee, and ankle pitch direction data for the 50cm [PITH_FULL_IMAGE:figures/full_fig_p007_13.png]

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    M. Rigacci, R. Sato, and K. Shirase, “Experimental evaluation of mechanical and electrical power consumption of feed drive systems driven by a ball-screw,”Precision Engineering, vol. 64, pp. 280–287, 2020

    2020

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.