A Dynamic Toolkit for Transmission Characteristics of Precision Reducers with Explicit Contact Geometry

Chao Liu; Jiacheng Miao; Qiliang Wang; Weidong He; Yunhui Guan

arxiv: 2604.02387 · v2 · submitted 2026-04-02 · 💻 cs.RO

A Dynamic Toolkit for Transmission Characteristics of Precision Reducers with Explicit Contact Geometry

Jiacheng Miao , Chao Liu , Qiliang Wang , Yunhui Guan , Weidong He This is my paper

Pith reviewed 2026-05-13 21:54 UTC · model grok-4.3

classification 💻 cs.RO

keywords precision reducerstransmission characteristicscontact geometrydynamic modelinggear stiffnessvibration predictionrobotic joints

0 comments

The pith

A modular toolkit models precision reducer transmission by explicitly incorporating contact geometry to predict stiffness and vibrations more accurately than standard software.

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

This paper introduces a dynamic toolkit for studying how precision reducers pass motion through robotic joints. It creates a single framework that directly represents the geometry of contacts between parts, calculates resulting stiffness, and forecasts vibrations using advanced contact theories paired with numerical solvers. The design is modular and scriptable so the same core can be quickly reconfigured for many different reducer layouts. Numerical checks against existing benchmarks show the approach runs with higher precision and lower computational cost than conventional dynamics packages. Because reducers directly limit robot positioning accuracy, a more reliable prediction tool could support tighter control and smoother operation in humanoid, quadruped, and industrial systems.

Core claim

The central claim is that a unified modeling framework that embeds explicit contact geometry, advanced contact theories, and efficient numerical methods can accurately forecast transmission characteristics such as gear stiffness and system vibrations across varied precision-reducer topologies while delivering both greater precision and better computational efficiency than traditional dynamics software.

What carries the argument

Unified framework that integrates explicit contact-geometry modeling with numerical solution methods inside a modular, scriptable architecture that supports rapid reconfiguration for different reducer types.

If this is right

Designers can obtain more reliable estimates of joint stiffness and vibration modes before building physical prototypes
Simulation run times for reducer dynamics drop compared with conventional multibody packages
The same code base can be reused for reducers in humanoid, SCARA, and collaborative robots without major rewriting
Numerical results already match published benchmark cases, supporting immediate use for preliminary design studies

Where Pith is reading between the lines

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

Robot control algorithms could incorporate real-time stiffness estimates derived from the same geometry model to improve trajectory tracking
The modular structure suggests straightforward extension to other precision transmissions such as harmonic drives or cycloidal gears
Coupling the toolkit outputs with finite-element stress analysis would allow simultaneous prediction of both dynamic performance and fatigue life
If the contact models prove robust, the approach could reduce reliance on expensive physical testing during early-stage robot development

Load-bearing premise

That embedding advanced contact theories and numerical solvers will produce predictions matching real transmission behavior across reducer designs without any additional fitting or calibration.

What would settle it

Direct comparison of the toolkit's predicted transmission error curves and vibration spectra against measured data from a physical precision reducer running under controlled torque and speed conditions would falsify the claim if the simulation results deviate substantially from experiment.

Figures

Figures reproduced from arXiv: 2604.02387 by Chao Liu, Jiacheng Miao, Qiliang Wang, Weidong He, Yunhui Guan.

**Figure 1.** Figure 1: Schematic of the series stiffness superposition model components. Jiacheng Miao et al.: Preprint submitted to Elsevier Page 7 of 22 [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗

**Figure 2.** Figure 2: Schematic of Curve-Circles contact: cycloidal profile vs. pin array. n Contact Internal gear External gear [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

**Figure 3.** Figure 3: Schematic of FewTeeth analytic tooth contact (internal-external gear pair). 0 *45 Right flank contact zone +45 Left flank contact zone Internal gear External gear e [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

**Figure 4.** Figure 4: Angular pre-screening for FewTeeth contact search: only the shaded sectors can carry load on each flank. Jiacheng Miao et al.: Preprint submitted to Elsevier Page 13 of 22 [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗

**Figure 5.** Figure 5: Modular assembly workflow for the reducer dynamic model. Jiacheng Miao et al.: Preprint submitted to Elsevier Page 15 of 22 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗

**Figure 6.** Figure 6: Five-stage quasi-static torque loading sequence for hysteresis curve extraction (Tr = 3200 N⊙m, tseg = 0.5 s). (a) Eccentric radius error effect. (b) Bearing clearance effect (dominant factor). (c) Eccentricity error effect (minimal). (d) Phase angle error effect (symmetric) [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗

**Figure 7.** Figure 7: Hysteresis curves under varying geometric error conditions. Subplot (b) confirms that bearing clearance is the dominant driver of lost motion and backlash. Jiacheng Miao et al.: Preprint submitted to Elsevier Page 23 of 22 [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗

**Figure 8.** Figure 8: Transmission error characteristics under various error conditions. Jiacheng Miao et al.: Preprint submitted to Elsevier Page 24 of 22 [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗

**Figure 9.** Figure 9: Complete FewTeeth contact solving flowchart: geometric preprocessing, four-stage search, force computation, and generalized-force assembly. Jiacheng Miao et al.: Preprint submitted to Elsevier Page 25 of 22 [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗

read the original abstract

Precision reducers are critical components in robotic systems, directly affecting the motion accuracy and dynamic performance of humanoid robots, quadruped robots, collaborative robots, industrial robots, and SCARA robots. This paper presents a dynamic toolkit for analyzing the transmission characteristics of precision reducers with explicit contact geometry. A unified framework is proposed to address the challenges in modeling accurate contact behaviors, evaluating gear stiffness, and predicting system vibrations. By integrating advanced contact theories and numerical solving methods, the proposed toolkit offers higher precision and computational efficiency compared to traditional dynamics software. The toolkit is designed with a modular, scriptable architecture that supports rapid reconfiguration across diverse reducer topologies. Numerical validation against published benchmarks confirms the accuracy of the proposed approach.

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.

Desk Editor's Note private letter to a colleague

The paper offers a modular toolkit for reducer contact modeling in robotics, but its claims of better precision need quantitative backing that the abstract doesn't provide.

read the letter

The toolkit described here gives a modular way to model contact in precision reducers for robot applications. That's the core thing to know: it's a software framework rather than a new theory. The paper builds a unified setup that pulls in existing contact models and numerical solvers, then wraps them in a scriptable structure so you can swap reducer topologies without rewriting everything. That design choice is useful for people who need to run quick variants in simulation work. It claims better precision and speed than standard dynamics packages, backed by checks against published benchmarks. The benchmarks part is good as far as it goes for showing the model works, but the abstract gives no numbers on how much better it is or on what specific metrics. Without those head-to-head results, the efficiency and precision edge stays unproven in the summary. The approach avoids obvious fitting tricks and sticks to integrating known theories, which keeps it straightforward. No red flags on that front from the description. This kind of paper is aimed at robotics simulation groups who want more control over gear contact details than commercial tools provide. Someone building custom dynamic models for reducers would find the architecture worth examining. I would send it out for peer review. The practical framing and the modular implementation make it worth a referee's time to check the implementation details and any validation data.

Referee Report

2 major / 2 minor

Summary. The paper presents a dynamic toolkit for analyzing transmission characteristics of precision reducers that incorporates explicit contact geometry. It proposes a unified framework integrating advanced contact theories and numerical methods to model contact behaviors, gear stiffness, and vibrations. The toolkit is described as modular and scriptable to support reconfiguration across reducer topologies, with the central claim that it achieves higher precision and computational efficiency than traditional dynamics software. Numerical validation against published benchmarks is cited to confirm accuracy.

Significance. A well-validated, modular toolkit with explicit contact modeling could meaningfully advance simulation accuracy for robotic precision reducers, where transmission errors directly impact motion control in humanoid, quadruped, and industrial robots. If the claimed improvements over existing tools are demonstrated with quantitative head-to-head metrics on identical models, the work would offer practical value for design and analysis workflows. The modular architecture is a positive feature for extensibility, though the absence of comparative performance data limits the assessed impact.

major comments (2)

[Abstract / Numerical validation section] Abstract and numerical validation section: the central claim that the toolkit offers 'higher precision and computational efficiency compared to traditional dynamics software' is unsupported by any quantitative evidence. The text states only that 'Numerical validation against published benchmarks confirms the accuracy,' with no error norms, runtime ratios, or direct comparisons versus tools such as ADAMS or MATLAB on the same reducer models.
[Methods / Results] Methods and results sections: without reported exclusion criteria, mesh convergence studies, or tabulated error metrics (e.g., RMS transmission error or stiffness deviation) against the cited benchmarks, it is impossible to assess whether the integrated contact theories deliver the asserted improvement or merely reproduce existing results.

minor comments (2)

[Abstract] The abstract would be strengthened by including at least one key quantitative result (e.g., percentage error reduction or speedup factor) to substantiate the efficiency claim.
[Framework description] Notation for contact parameters and stiffness matrices should be defined consistently in the first use; several symbols appear without prior definition in the framework description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the validation requirements for our dynamic toolkit. We address each major comment below and will incorporate revisions to strengthen the manuscript's rigor.

read point-by-point responses

Referee: [Abstract / Numerical validation section] Abstract and numerical validation section: the central claim that the toolkit offers 'higher precision and computational efficiency compared to traditional dynamics software' is unsupported by any quantitative evidence. The text states only that 'Numerical validation against published benchmarks confirms the accuracy,' with no error norms, runtime ratios, or direct comparisons versus tools such as ADAMS or MATLAB on the same reducer models.

Authors: We agree that the central claim of higher precision and computational efficiency is not supported by quantitative head-to-head evidence in the current version. The numerical validation section reports only accuracy against published benchmarks without error norms, runtime ratios, or direct comparisons to tools such as ADAMS or MATLAB. In the revised manuscript, we will remove the unsubstantiated claim from the abstract and validation section. We will add tabulated error metrics (including RMS transmission error and stiffness deviation) and preliminary runtime comparisons on identical reducer models where data are available, allowing readers to evaluate performance objectively. revision: yes
Referee: [Methods / Results] Methods and results sections: without reported exclusion criteria, mesh convergence studies, or tabulated error metrics (e.g., RMS transmission error or stiffness deviation) against the cited benchmarks, it is impossible to assess whether the integrated contact theories deliver the asserted improvement or merely reproduce existing results.

Authors: We acknowledge that the methods and results sections lack reported exclusion criteria, mesh convergence studies, and tabulated error metrics against the benchmarks. These omissions make it difficult to fully assess the contribution of the integrated contact theories. In the revised manuscript, we will add a mesh convergence study for the explicit contact geometry computations, specify any exclusion criteria applied to the numerical cases, and include tabulated error metrics (RMS transmission error, stiffness deviation) comparing our results to the cited benchmarks. This will provide the necessary quantitative basis to evaluate the approach. revision: yes

Circularity Check

0 steps flagged

No circularity detected; framework integrates external contact theories with benchmark validation

full rationale

The paper describes a modular toolkit that integrates advanced contact theories and numerical solving methods, then validates outputs against published external benchmarks. No equations, fitted parameters, or derivation steps are presented that reduce predictions to inputs by construction. No self-citations are invoked as load-bearing uniqueness theorems, and no ansatz or renaming of known results is described. The central claims rest on external theories plus independent numerical checks, satisfying the criteria for a self-contained, non-circular derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the ledger is therefore empty pending access to the full methods and equations.

pith-pipeline@v0.9.0 · 5420 in / 1066 out tokens · 36912 ms · 2026-05-13T21:54:06.362587+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

By integrating advanced contact theories and numerical solving methods, the proposed toolkit offers higher precision... stiffness superposition model... kmesh = 1/kbend + 1/kshear + 1/kfound + 1/kcont

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages

[1]

L.Xu,T.Zhao,J.Geng,Y.Deng,Modelingofhysteresiscurveandstudyoftorsionalrigidityandlostmotioncharacteristics of the rv reducer, Mechanism and Machine Theory 219 (2026) 106335.doi:10.1016/j.mechmachtheory.2025.106335

work page doi:10.1016/j.mechmachtheory.2025.106335 2026
[2]

Y. H. Xie, L. X. Xu, Y. Q. Deng, A dynamic approach for evaluating the moment rigidity and rotation precision of a bearing-planetary frame rotor system used in rv reducer, Mechanism and Machine Theory 173 (2022) 104851. doi:10.1016/j.mechmachtheory.2022.11.001

work page doi:10.1016/j.mechmachtheory.2022.11.001 2022
[3]

W. Li, Y. Zhang, S. Gao, Analysis for time varying torsional stiffness of rv reducer, Mechanical Systems and Signal Processing 225 (2025) 112239.doi:10.1016/j.ymssp.2024.112239

work page doi:10.1016/j.ymssp.2024.112239 2025
[4]

L. Xu, Y. Wu, Investigation of the dynamic transmission accuracy of an industrial robot joint rv reducer under variable situations, Multibody System Dynamics 65 (2) (2025) 267–304.doi:10.1007/s11044-025-10056-2

work page doi:10.1007/s11044-025-10056-2 2025
[5]

Ren, S.-M

Z.-Y. Ren, S.-M. Mao, W.-C. Guo, Z. Guo, Tooth modification and dynamic performance of the cycloidal drive, Mechanical Systems and Signal Processing 85 (2017) 857–866.doi:10.1016/j.ymssp.2016.09.029. Jiacheng Miao et al.:Preprint submitted to ElsevierPage 19 of 22 A Dynamic Toolkit for Transmission Characteristics

work page doi:10.1016/j.ymssp.2016.09.029 2017
[6]

L.-C.Tung,Y.J.Chan,Atime-variantdynamicmodelforcompoundepicyclic–cycloidalreducers,MechanismandMachine Theory 179 (2023) 105095.doi:10.1016/j.mechmachtheory.2022.105095

work page doi:10.1016/j.mechmachtheory.2022.105095 2023
[7]

L. X. Xu, B. K. Chen, C. Y. Li, Dynamic modelling and contact analysis of bearing-cycloid-pinwheel transmission mechanisms used in joint rotate vector reducers, Mechanism and Machine Theory 137 (2019) 432–458.doi:10.1016/ j.mechmachtheory.2019.03.035

work page 2019
[8]

R. Li, P. Zheng, G. Wang, G. Li, S. Chi, X. Meng, Tribo-dynamics modeling of cycloidal gear-pin pair considering transient effects, International Journal of Mechanical Sciences 305 (2025) 110809.doi:10.1016/j.ijmecsci.2025.110809

work page doi:10.1016/j.ijmecsci.2025.110809 2025
[9]

S. Wang, X. Deng, H. Feng, K. Ren, F. Li, Y. Liu, Dynamic simulation analysis and experimental study of an industrial robot with novel joint reducers, Multibody System Dynamics 57 (2) (2023) 107–131.doi:10.1007/s11044-022-09864-7

work page doi:10.1007/s11044-022-09864-7 2023
[10]

H. Luo, L. Xue, Y. Huang, C. Wang, et al., Modulation mechanism of vibration response of rv reducer considering the influence of meshing force and transmission path, Journal of Sound and Vibration 619 (2025) 119430.doi: 10.1016/j.jsv.2025.119430

work page doi:10.1016/j.jsv.2025.119430 2025
[11]

L. Xu, C. Xia, L. Chang, Dynamic modeling and vibration analysis of an rv reducer with defective needle roller bearings, Engineering Failure Analysis 157 (2024) 107884.doi:10.1016/j.engfailanal.2023.107884

work page doi:10.1016/j.engfailanal.2023.107884 2024
[12]

Y. E, Z. Liu, H. Chen, et al., Dynamic modeling and vibration analysis for fault diagnosis of rotate vector reducers, Mechanical Systems and Signal Processing 224 (2025) 111965.doi:10.1016/j.ymssp.2024.111965

work page doi:10.1016/j.ymssp.2024.111965 2025
[13]

Y. Yang, G. Zhou, L. Chang, G. Chen, A modelling approach for kinematic equivalent mechanism and rotational transmission error of rv reducer, Mechanism and Machine Theory 163 (2021) 104384.doi:10.1016/j.mechmachtheory. 2021.104384

work page doi:10.1016/j.mechmachtheory 2021
[14]

X. Wang, L. Li, L. Hao, H. Wang, Positioning accuracy prediction of precision cycloid reducer based on a bddte model and use in design optimization, Precision Engineering 88 (2024) 27–43.doi:10.1016/j.precisioneng.2024.01.008

work page doi:10.1016/j.precisioneng.2024.01.008 2024
[15]

Bilancia, L

P. Bilancia, L. Monari, R. Raffaeli, M. Peruzzini, M. Pellicciari, Accurate transmission performance evaluation of servo- mechanisms for robots, Robotics and Computer-Integrated Manufacturing 78 (2022) 102400.doi:10.1016/j.rcim.2022. 102400

work page doi:10.1016/j.rcim.2022 2022
[16]

H. Wang, X. Zhang, K. Fang, Y. Kou, Z. Zhang, Return error simulation analysis and experimental study for rv reducer with adams, Journal of Advanced Mechanical Design, Systems, and Manufacturing 18 (2) (2024) JAMDSM0023. doi:10.1299/jamdsm.2024jamdsm0023

work page doi:10.1299/jamdsm.2024jamdsm0023 2024
[17]

Cheng, Z

H. Cheng, Z. Shi, Z. Yu, G. Zuo, Dynamic torsional stiffness of reducers and its testing method, Applied Sciences 13 (16) (2023) 9277.doi:10.3390/app13169277

work page doi:10.3390/app13169277 2023
[18]

Zhang, H

C. Zhang, H. Dong, B. Dong, D. Wang, A bi-directional drive model for lost motion behavior of planetary gear train, Mechanism and Machine Theory 174 (2022) 104885.doi:10.1016/j.mechmachtheory.2022.104885

work page doi:10.1016/j.mechmachtheory.2022.104885 2022
[19]

H. Xu, Z. Shi, S. Yang, X. Qiao, Y. Li, W. Yu, Hysteresis curve model of precision reducers in robots and its application in lost motion evaluation, Measurement: Sensors 38 (2025) 101848.doi:10.1016/j.measen.2025.101848

work page doi:10.1016/j.measen.2025.101848 2025
[20]

Gerstmayr, Exudyn – a c++ based python package for flexible multibody systems, Multibody System Dynamics 60 (2024) 533–561.doi:10.1007/s11044-023-09937-1

J. Gerstmayr, Exudyn – a c++ based python package for flexible multibody systems, Multibody System Dynamics 60 (2024) 533–561.doi:10.1007/s11044-023-09937-1. A. Complete Contact Model Reference A.1. Circle-Circle Contact Geometry For two circles with centersp0,p 1 and scalar radiir0,r 1, the gap is evaluated in thexy-plane only: d= √ .p1x *p 0x/2 + .p1y ...

work page doi:10.1007/s11044-023-09937-1 2024

[1] [1]

L.Xu,T.Zhao,J.Geng,Y.Deng,Modelingofhysteresiscurveandstudyoftorsionalrigidityandlostmotioncharacteristics of the rv reducer, Mechanism and Machine Theory 219 (2026) 106335.doi:10.1016/j.mechmachtheory.2025.106335

work page doi:10.1016/j.mechmachtheory.2025.106335 2026

[2] [2]

Y. H. Xie, L. X. Xu, Y. Q. Deng, A dynamic approach for evaluating the moment rigidity and rotation precision of a bearing-planetary frame rotor system used in rv reducer, Mechanism and Machine Theory 173 (2022) 104851. doi:10.1016/j.mechmachtheory.2022.11.001

work page doi:10.1016/j.mechmachtheory.2022.11.001 2022

[3] [3]

W. Li, Y. Zhang, S. Gao, Analysis for time varying torsional stiffness of rv reducer, Mechanical Systems and Signal Processing 225 (2025) 112239.doi:10.1016/j.ymssp.2024.112239

work page doi:10.1016/j.ymssp.2024.112239 2025

[4] [4]

L. Xu, Y. Wu, Investigation of the dynamic transmission accuracy of an industrial robot joint rv reducer under variable situations, Multibody System Dynamics 65 (2) (2025) 267–304.doi:10.1007/s11044-025-10056-2

work page doi:10.1007/s11044-025-10056-2 2025

[5] [5]

Ren, S.-M

Z.-Y. Ren, S.-M. Mao, W.-C. Guo, Z. Guo, Tooth modification and dynamic performance of the cycloidal drive, Mechanical Systems and Signal Processing 85 (2017) 857–866.doi:10.1016/j.ymssp.2016.09.029. Jiacheng Miao et al.:Preprint submitted to ElsevierPage 19 of 22 A Dynamic Toolkit for Transmission Characteristics

work page doi:10.1016/j.ymssp.2016.09.029 2017

[6] [6]

L.-C.Tung,Y.J.Chan,Atime-variantdynamicmodelforcompoundepicyclic–cycloidalreducers,MechanismandMachine Theory 179 (2023) 105095.doi:10.1016/j.mechmachtheory.2022.105095

work page doi:10.1016/j.mechmachtheory.2022.105095 2023

[7] [7]

L. X. Xu, B. K. Chen, C. Y. Li, Dynamic modelling and contact analysis of bearing-cycloid-pinwheel transmission mechanisms used in joint rotate vector reducers, Mechanism and Machine Theory 137 (2019) 432–458.doi:10.1016/ j.mechmachtheory.2019.03.035

work page 2019

[8] [8]

R. Li, P. Zheng, G. Wang, G. Li, S. Chi, X. Meng, Tribo-dynamics modeling of cycloidal gear-pin pair considering transient effects, International Journal of Mechanical Sciences 305 (2025) 110809.doi:10.1016/j.ijmecsci.2025.110809

work page doi:10.1016/j.ijmecsci.2025.110809 2025

[9] [9]

S. Wang, X. Deng, H. Feng, K. Ren, F. Li, Y. Liu, Dynamic simulation analysis and experimental study of an industrial robot with novel joint reducers, Multibody System Dynamics 57 (2) (2023) 107–131.doi:10.1007/s11044-022-09864-7

work page doi:10.1007/s11044-022-09864-7 2023

[10] [10]

H. Luo, L. Xue, Y. Huang, C. Wang, et al., Modulation mechanism of vibration response of rv reducer considering the influence of meshing force and transmission path, Journal of Sound and Vibration 619 (2025) 119430.doi: 10.1016/j.jsv.2025.119430

work page doi:10.1016/j.jsv.2025.119430 2025

[11] [11]

L. Xu, C. Xia, L. Chang, Dynamic modeling and vibration analysis of an rv reducer with defective needle roller bearings, Engineering Failure Analysis 157 (2024) 107884.doi:10.1016/j.engfailanal.2023.107884

work page doi:10.1016/j.engfailanal.2023.107884 2024

[12] [12]

Y. E, Z. Liu, H. Chen, et al., Dynamic modeling and vibration analysis for fault diagnosis of rotate vector reducers, Mechanical Systems and Signal Processing 224 (2025) 111965.doi:10.1016/j.ymssp.2024.111965

work page doi:10.1016/j.ymssp.2024.111965 2025

[13] [13]

Y. Yang, G. Zhou, L. Chang, G. Chen, A modelling approach for kinematic equivalent mechanism and rotational transmission error of rv reducer, Mechanism and Machine Theory 163 (2021) 104384.doi:10.1016/j.mechmachtheory. 2021.104384

work page doi:10.1016/j.mechmachtheory 2021

[14] [14]

X. Wang, L. Li, L. Hao, H. Wang, Positioning accuracy prediction of precision cycloid reducer based on a bddte model and use in design optimization, Precision Engineering 88 (2024) 27–43.doi:10.1016/j.precisioneng.2024.01.008

work page doi:10.1016/j.precisioneng.2024.01.008 2024

[15] [15]

Bilancia, L

P. Bilancia, L. Monari, R. Raffaeli, M. Peruzzini, M. Pellicciari, Accurate transmission performance evaluation of servo- mechanisms for robots, Robotics and Computer-Integrated Manufacturing 78 (2022) 102400.doi:10.1016/j.rcim.2022. 102400

work page doi:10.1016/j.rcim.2022 2022

[16] [16]

H. Wang, X. Zhang, K. Fang, Y. Kou, Z. Zhang, Return error simulation analysis and experimental study for rv reducer with adams, Journal of Advanced Mechanical Design, Systems, and Manufacturing 18 (2) (2024) JAMDSM0023. doi:10.1299/jamdsm.2024jamdsm0023

work page doi:10.1299/jamdsm.2024jamdsm0023 2024

[17] [17]

Cheng, Z

H. Cheng, Z. Shi, Z. Yu, G. Zuo, Dynamic torsional stiffness of reducers and its testing method, Applied Sciences 13 (16) (2023) 9277.doi:10.3390/app13169277

work page doi:10.3390/app13169277 2023

[18] [18]

Zhang, H

C. Zhang, H. Dong, B. Dong, D. Wang, A bi-directional drive model for lost motion behavior of planetary gear train, Mechanism and Machine Theory 174 (2022) 104885.doi:10.1016/j.mechmachtheory.2022.104885

work page doi:10.1016/j.mechmachtheory.2022.104885 2022

[19] [19]

H. Xu, Z. Shi, S. Yang, X. Qiao, Y. Li, W. Yu, Hysteresis curve model of precision reducers in robots and its application in lost motion evaluation, Measurement: Sensors 38 (2025) 101848.doi:10.1016/j.measen.2025.101848

work page doi:10.1016/j.measen.2025.101848 2025

[20] [20]

Gerstmayr, Exudyn – a c++ based python package for flexible multibody systems, Multibody System Dynamics 60 (2024) 533–561.doi:10.1007/s11044-023-09937-1

J. Gerstmayr, Exudyn – a c++ based python package for flexible multibody systems, Multibody System Dynamics 60 (2024) 533–561.doi:10.1007/s11044-023-09937-1. A. Complete Contact Model Reference A.1. Circle-Circle Contact Geometry For two circles with centersp0,p 1 and scalar radiir0,r 1, the gap is evaluated in thexy-plane only: d= √ .p1x *p 0x/2 + .p1y ...

work page doi:10.1007/s11044-023-09937-1 2024