{"title":"Multi-fidelity harmonic balance method: A non-intrusive approach","authors":"Hady Mohamed , Nils Brödling , Fabian Duddeck","doi":"10.1016/j.mechmachtheory.2025.106251","DOIUrl":"10.1016/j.mechmachtheory.2025.106251","url":null,"abstract":"<div><div>This paper presents a novel non-intrusive hierarchical multi-fidelity harmonic balance method (HBM) framework for efficient uncertainty quantification (UQ) of nonlinear frequency response functions (FRFs) with application to gear transmission dynamics. The framework uniquely combines proper orthogonal decomposition (POD) to reduce the dimensionality of HBM-derived Fourier coefficients, enable efficient surrogate modeling in latent space, and retain access to both time- and frequency-domain responses. A key innovation is aligning low- and high-fidelity Fourier coefficient latent spaces via Procrustes analysis to improve the construction of a multi-fidelity surrogate using hierarchical Kriging with polynomial chaos Kriging (PCK) as the trend function. Further, computational efficiency in low-fidelity evaluations is achieved by integrating POD with linear regression for rapid compliance matrix estimation in loaded tooth contact analysis (LTCA). Numerical results demonstrate significant computational savings for uncertain FRF predictions of 5000 Monte Carlo (MC) samples. The proposed novelties represent the first application of hierarchical Kriging across aligned Fourier latent spaces and accelerated LTCA within a scalable framework for moderate-dimensional, vector-valued FRF uncertainty analysis, supporting broad applicability to nonlinear dynamical systems modeled with Frequency domain solvers.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"217 ","pages":"Article 106251"},"PeriodicalIF":4.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic characteristics of rigid-flexible coupled planetary gear-bearing-rotor system considering the tooth surface lubrication friction and roughness","authors":"Ning Liu , Hui Ma , Xiangfu Ding , Jiaqi Liu","doi":"10.1016/j.mechmachtheory.2025.106259","DOIUrl":"10.1016/j.mechmachtheory.2025.106259","url":null,"abstract":"<div><div>A novel rigid-flexible coupled planetary gear-bearing-rotor (PBR) dynamic model with bearing-gear coupling effect, modulation of the planetary carrier, roughness, and friction under different lubrication states is established. The necessity of the bearing nonlinear force, the flexible ring and the modulation of the planet carrier in the model is verified through experiments. The improved friction coefficient and the meshing stiffness with lubrication friction are proposed based on elastohydrodynamic lubrication (EHL) and the three-dimensional loaded tooth contact analysis (3D-LTCA) method. The influence of friction under different lubrication conditions on the dynamic characteristics of the PBR system is analyzed. Some interesting phenomena are as follows: friction coefficient of the mixed EHL is greater than that of the EHL at the pitch point. Compared with friction introduced into the stiffness model, the friction introduced into kinematic equations has a greater impact on the PBR system. The low-frequency energy ratio is more sensitive to friction. Meanwhile, compared with the model without friction, friction leads to an increase in the contact force, contact stiffness and contact area of the ball-race, and the dynamic meshing force (DMF).</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"217 ","pages":"Article 106259"},"PeriodicalIF":4.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145322263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Self-Locking Tendon-Driven Robotic Arm Inspired by Cubic Origami","authors":"Fengrui Liu, Tatsuro Terakawa, Zhongzheng Liang, Masaharu Komori","doi":"10.1016/j.mechmachtheory.2025.106230","DOIUrl":"10.1016/j.mechmachtheory.2025.106230","url":null,"abstract":"<div><div>The ability to transition between load-carrying and readily foldable states enables deployable structures to satisfy diverse functional requirements, such as compact storage, adaptive shape transformation, and stable load-bearing performance. Self-locking origami structures, which utilize geometric constraints to prevent the structure from collapsing under external loads, offer an effective solution for achieving these capabilities. In this study, we investigate the self-locking behavior of a Foldable Cube Origami (FC-ori) structure in its cubic configuration by analyzing its geometry and singularity. To address self-locking constraints, a tendon-driven mechanism is developed with tendons routed through the side panels, in contrast to conventional designs where tendons pass only through the top and bottom panels. By optimizing the tendon path, we reduced the maximum friction by approximately 20%. Moreover, we design and implement two multi-unit tendon-driven FC-ori robotic arms configured in series and parallel arrangements. These systems allow for programmable deployment sequences and achieve rapid transitions between folded and deployed configurations within several seconds, driven by only a single motor. By integrating a tunable stiffness origami structure with efficient actuation, this work offers enhanced potential for applications in space exploration, foldable shelters, reconfigurable robotics, and other engineering domains.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"217 ","pages":"Article 106230"},"PeriodicalIF":4.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145189711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bihai Deng , Huafeng Ding , Tao Ke , Bin Zi , Andrés Kecskeméthy
{"title":"A matrix-based configuration synthesis and design of power-split hybrid transmissions for multi-vehicle application scenarios","authors":"Bihai Deng , Huafeng Ding , Tao Ke , Bin Zi , Andrés Kecskeméthy","doi":"10.1016/j.mechmachtheory.2025.106269","DOIUrl":"10.1016/j.mechmachtheory.2025.106269","url":null,"abstract":"<div><div>This paper presents a matrix-based synthesis and design framework for power-split hybrid transmissions targeting light-duty (L-HEV), medium-duty (M-HEV), and heavy-duty (H<img>HEV) hybrid electric vehicles. A unified structural and position matrix is developed to model planetary gear mechanisms and auxiliary components. This matrix enables automated calculation of rotational speeds and torques, as well as identification of power-split operating modes. Based on this representation, an efficient enumeration algorithm is proposed to generate all feasible configurations, followed by initial screening using kinematic and control feasibility criteria. To evaluate configuration complexity, a composite index is formulated by combining planetary gear structure and shift element layout complexity. Configurations with the lowest complexity are selected and assessed using dynamic programming to analyze acceleration performance and fuel economy across standard driving cycles. The study ultimately identifies eight high-performance configurations for both <span>l</span>-HEV and M-HEV, and 47 preferred configurations for H<img>HEV, each achieving a balance between mechanical simplicity, dynamic performance, and fuel efficiency. The proposed end-to-end framework offers a systematic and practical approach for hybrid transmission design suited to various application scenarios.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"217 ","pages":"Article 106269"},"PeriodicalIF":4.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Francisco H.J. Ricardo , João D.M. Marafona , Pedro M.T. Marques
{"title":"Modelling gear mesh stiffness including axial effects: Approximate approach","authors":"Francisco H.J. Ricardo , João D.M. Marafona , Pedro M.T. Marques","doi":"10.1016/j.mechmachtheory.2025.106221","DOIUrl":"10.1016/j.mechmachtheory.2025.106221","url":null,"abstract":"<div><div>Recently, with the advancement in technology, gear mesh stiffness has been a central topic in gear design optimisation and gear dynamics. Consequently, some approximate models for spur and helical gears have been developed due to their low computational cost. However, these models disregarded the axial component of the gear mesh stiffness. To address this issue, a new approximate expression is developed accounting for the axial effect, having as starting point a previously developed approximate expression that considers only the transverse component. The new expression is validated for a random sample representative of all possible gears within a wide range of geometric parameters. The new approximate model for helical gears, based on the development of an expression for the single tooth pair slice structural mesh stiffness, revealed to be fast and accurate, confirming the applicability of the model and proving that it is capable of replacing the more time consuming methods for the same applications. Additionally, a single equation relying on a single constant aiming to convert the transverse into normal stiffness is presented.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"217 ","pages":"Article 106221"},"PeriodicalIF":4.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhongwei Tang , Yuansheng Zhou , Shuai Mo , Jinyuan Tang , Zichang Du , Wuji Zhang , Haiyu He
{"title":"A new mathematical model for the product family design of the skiving tools of spur face gears","authors":"Zhongwei Tang , Yuansheng Zhou , Shuai Mo , Jinyuan Tang , Zichang Du , Wuji Zhang , Haiyu He","doi":"10.1016/j.mechmachtheory.2025.106232","DOIUrl":"10.1016/j.mechmachtheory.2025.106232","url":null,"abstract":"<div><div>Power skiving is increasingly used in face gear manufacturing while the existing tools are limited to the face gears with specific parameters (module, pressure angle, and tooth number), which reduces flexibility and increases costs. This paper proposes a product family design method for skiving tools aimed at spur face gears. First, a mathematical model of the tooth surface is established, along with an error evaluation framework. Then, an error compensation method is introduced for a specific gear design, and errors are analyzed when using a dedicated tool to machine the face gears with different parameters. Results show that variations in tooth number cause minor errors, while differences in module and pressure angle lead to significant inaccuracies. A product family design approach is proposed to enable one tool to machine multiple gears accurately. Validated through simulations and experiments, the method achieves high precision for gear families with small variations in module and pressure angle. This work offers practical value and theoretical support for developing skiving tool libraries.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"217 ","pages":"Article 106232"},"PeriodicalIF":4.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Is the root fillet curve in involute gears trochoidal? A geometric reassessment","authors":"Alessio Artoni","doi":"10.1016/j.mechmachtheory.2025.106228","DOIUrl":"10.1016/j.mechmachtheory.2025.106228","url":null,"abstract":"<div><div>The root fillet of involute gears is commonly described as “trochoidal”, yet, to the author’s knowledge, the geometric basis for this label has never been stated explicitly. This article addresses the question from geometric first principles. Trochoids are roulettes of points attached to a circle rolling on a base curve, with two subfamilies: line-based (cycloids) and circle-based (epi-/hypotrochoids). Focusing on spur gears and working in a blank-fixed transverse plane, we derive the locus of a generic rack point: the rack tip (or the center of its rounding) traces a prolate involute of a circle, not a trochoid; explicit parametric equations are provided. By contrast, with pinion-shaped cutters the cutter tip (or the center of its rounding) traces a hypotrochoid for internal gears or an epitrochoid for external gears, and thus the nominal fillet is genuinely trochoidal. The same reasoning carries over to helical gears. These findings support clearer and more precise terminology in technical publications and standards.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"217 ","pages":"Article 106228"},"PeriodicalIF":4.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jie Ju , Jianfeng Li , Tuxian Ye , Qianhui Ma , Mingjie Dong , Shiping Zuo , Wei-Hsin Liao
{"title":"Configuration design and redundancy optimization of a novel kinematically redundant parallel external fixator for interference avoidance in foot and ankle deformity correction","authors":"Jie Ju , Jianfeng Li , Tuxian Ye , Qianhui Ma , Mingjie Dong , Shiping Zuo , Wei-Hsin Liao","doi":"10.1016/j.mechmachtheory.2025.106265","DOIUrl":"10.1016/j.mechmachtheory.2025.106265","url":null,"abstract":"<div><div>During foot and ankle deformity correction via external fixators, successful implementation of the preplanned optimal correction strategy is crucial for achieving acceptable correction outcomes. However, interference phenomena can interrupt the correction process. Owing to the inherent non-redundant mechanism properties of existing external fixators, current interference avoidance methods inevitably necessitate adjustments of the pre-determined assembly relation and/or equally-spaced correction trajectories, thereby hindering the implementability of the optimal correction strategy. To address this issue, this paper introduces the concept of kinematic redundancy in external fixator design, and a novel 2(S<u>P</u>S-<u>P</u>-S<u>P</u>S)-S<u>P</u>R kinematically redundant external fixator with configuration optimization capabilities is proposed. Subsequently, based on the algebraic solution for forward kinematics while combining the cost functions for interference avoidance tasks, the inverse kinematics of the proposed external fixator is resolved using the gradient projection method with closed-loop feedback. Clinical case simulations demonstrate the effectiveness of the external fixator in avoiding multiple interference problems while maintaining the optimal correction strategy. Comparative analyses further reveal considerable improvements in the tracking accuracy of the correction trajectory compared with the conventional velocity-level method with open-loop solutions.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"217 ","pages":"Article 106265"},"PeriodicalIF":4.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tiancheng Ouyang , Yinxuan Li , Hongyang Tian , Shaohui Qin , Yang Yang , Yong Chen
{"title":"Thermo-cavitation study of helical gears caused by vibration","authors":"Tiancheng Ouyang , Yinxuan Li , Hongyang Tian , Shaohui Qin , Yang Yang , Yong Chen","doi":"10.1016/j.mechmachtheory.2025.106239","DOIUrl":"10.1016/j.mechmachtheory.2025.106239","url":null,"abstract":"<div><div>In the context of high-precision manufacturing, filling the gap in the study of the correlation between helical gear dynamics and thermo-cavitation has a significant impact on the optimal design of transmission systems. For this purpose, a cavitation two-phase flow research system containing fluid energy, temperature and dynamic model is constructed, aiming at studying the phenomenon of vibration-cavitation under the non-constant flow and variable temperature of oil in helical gear system, analyzing the evolution law of cavitation in the meshing region and revealing the thermo-cavitation generation mechanism under the influence of vibration. Besides, the reliability of the numerical method is assessed by the relative error between the experimental and simulation results. The results show that fluid thermal effect has a significant impact on cavitation at extreme operating conditions, with high speeds being the main factor in the dramatic increase in cavitation. The load profoundly affects the fluctuation of cavitation and the contact surface temperature, but there exists an optimal value to achieve a balance between the two, the value of helix angle between 15° and 20° is a well choice.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"217 ","pages":"Article 106239"},"PeriodicalIF":4.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A novel time-optimal feedrate planning method for robots with contour error constraints","authors":"Qi Qi, Jixiang Yang, Wenhao Li, Han Ding","doi":"10.1016/j.mechmachtheory.2025.106227","DOIUrl":"10.1016/j.mechmachtheory.2025.106227","url":null,"abstract":"<div><div>Existing time-optimal feedrate planning methods for robots typically consider the robot's drive capability limitations, while neglect the limitation of the robot motion accuracy especially the contour accuracy. To address this issue, this paper proposes a novel time-optimal feedrate planning method for robots with contour error constraints. First, a joint tracking error prediction model for the robot considering the control loop and the robot end load is established, and a contour error constraint model for feedrate planning is proposed. Secondly, an improved feedrate squared B-spline is used to transform the feedrate planning problem into a linear optimization problem represented by control points. For jerk constraints, joint torque constraints and contour error constraints that cannot be directly converted into linear constraints, a scaling estimation method is proposed to linearize all nonlinear constraint equations in feedrate planning. Thirdly, a two-step linear programming (LP) method is proposed to solve the time-optimal feedrate planning considering contour error constraints. Comparative experiments conducted on a robot demonstrate that the proposed method can effectively improve the robot's motion efficiency while satisfying the contour error constraints.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"217 ","pages":"Article 106227"},"PeriodicalIF":4.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}