{"title":"Celebrating 50 years of the groundbreaking Hunt and Crossley contact force model","authors":"Paulo Flores , Hamid M. Lankarani","doi":"10.1016/j.mechmachtheory.2025.106223","DOIUrl":"10.1016/j.mechmachtheory.2025.106223","url":null,"abstract":"<div><div>The Hunt and Crossley contact force model, published in 1975, marked a key transformative milestone in the field of contact mechanics. Compared with previous formulations, this pioneering model offered a more realistic and dynamic representation of the contact forces due to the incorporation of energy dissipation during collisions between solid materials. Over the past 50 years, the Hunt and Crossley contact force model has significantly influenced a wide range of disciplines, such as multibody dynamics, machines and mechanisms, robotics, biomechanics, vehicle dynamics, crashworthiness, and materials science, just to mention a few. This paper celebrates the golden jubilee of the Hunt and Crossley revolutionary approach, revisiting its theoretical foundations and tracing its historical development and impact. The Hunt and Crossley contact force model is probably the most well-known and useful approach to investigate contact-impact events in dynamical systems.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"216 ","pages":"Article 106223"},"PeriodicalIF":4.5,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158748","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 gravity compensation mechanism for orthogonal DoFs with coupled springs","authors":"Yiwei Wang , Peiji Chen , Shunta Togo , Hiroshi Yokoi , Yinlai Jiang","doi":"10.1016/j.mechmachtheory.2025.106220","DOIUrl":"10.1016/j.mechmachtheory.2025.106220","url":null,"abstract":"<div><div>A novel gravity compensation mechanism for orthogonal DoFs (degrees of freedom) comprised of springs, wires, and pulleys is proposed and validated on a previously developed humanoid waist. The mechanism utilizes two groups of springs coupled with wires and pulleys to counterbalance gravitational potential energy in a coupling way. It provides high versatility for existing robotic systems and high freedom in design without being restricted by the location of the springs. Nine implementation methods are illustrated based on the location of the springs and the placement of the spring-side pulleys. The mechanism was validated on a fixed-base humanoid waist with adjustable springs for different load demands. A current consumption experiment was conducted to quantify the compensation rate based on motor current, showing a static compensation rate of <span><math><mo>≥</mo></math></span>90% at maximum tilt angles. A path repetition experiment showed that the Euclidean distance between reference and measured paths was reduced by 57.8% with gravity compensation. These results indicate that the mechanism effectively reduces actuator burden and improves robot performance.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"216 ","pages":"Article 106220"},"PeriodicalIF":4.5,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158749","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":"Research on meshing performance of a novel internal revolution surface enveloping toroidal worm drive","authors":"Zhenglin Yang, Yonghong Chen, Jinhong Jiang, Zhongtao Li, Bingkui Chen","doi":"10.1016/j.mechmachtheory.2025.106219","DOIUrl":"10.1016/j.mechmachtheory.2025.106219","url":null,"abstract":"<div><div>This paper introduces a novel internal revolution surface enveloping toroidal worm drive (IRT worm drive), comprising a revolution surface gear and its corresponding enveloping toroidal worm. The meshing geometry model of the IRT worm drive is established. The induced normal curvature and sliding angle along contact lines are computed to evaluate meshing performance. Finite element analyses reveal that the IRT worm drive exhibits lower meshing stress than helical gear. The manufacturability of the revolution surface gear via injection molding is analyzed using the cavity inverse design and thermal shrinkage theory. An efficient internal whirling process is proposed for manufacturing the IRT worm. The revolution surface gear and the IRT worm were fabricated and subjected to contact pattern tests. Performance tests reveals that IRT drive achieves 86.4 % efficiency and 33.33 % higher load capacity than a helical gear pair. The proposed drive demonstrates excellent manufacturability for mass production with high drive performance.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"216 ","pages":"Article 106219"},"PeriodicalIF":4.5,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099582","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}
Hong Guan , Na Zhou , Hui Ma , Ang Gao , Xupeng Wang , Qinqin Mu , Yao Zeng , Yanyan Chen
{"title":"Dynamic modeling and natural characteristic analysis of discontinuous rotor systems with multiple joint structures","authors":"Hong Guan , Na Zhou , Hui Ma , Ang Gao , Xupeng Wang , Qinqin Mu , Yao Zeng , Yanyan Chen","doi":"10.1016/j.mechmachtheory.2025.106217","DOIUrl":"10.1016/j.mechmachtheory.2025.106217","url":null,"abstract":"<div><div>Bolts, splines, and spigot joints are typical joint structures widely employed in the disk-drum combined rotor systems of aero-engines. In existing research on the dynamic characteristics of such systems, components such as spigot joints and splines are often modeled as integrated parts, so the influences of the joint interfaces on the rotor's dynamic behavior are neglected. To address this limitation, a refined dynamic model that incorporates joint structures is developed to investigate the effect of joint stiffness on the modal characteristics of disk-drum rotor systems. First, the stiffness of bolts, splines, and spigot joints is calculated and then the joint stiffness is incorporated into the finite element (FE) model of a rotor system using a beam-shell hybrid element approach. The results indicate that the variation in rotational speed induces complex mode coupling and frequency veering (FV) phenomena in the rotor system, including mode shape interaction and multiple veering points across different traveling wave modes. Furthermore, the axial and transverse stiffness of typical joint structures significantly affects the natural frequencies of the system with threshold effects. These findings highlight the multi-level and variable nature of frequency veering in response to changes in joint parameters.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"216 ","pages":"Article 106217"},"PeriodicalIF":4.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099581","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":"Kinematic and static characterization of everting Möbius kaleidocycles with slightly incongruent links","authors":"Claudio Boni , Eliot Fried , Gianni Royer-Carfagni","doi":"10.1016/j.mechmachtheory.2025.106185","DOIUrl":"10.1016/j.mechmachtheory.2025.106185","url":null,"abstract":"<div><div>A Möbius kaleidocycle is a closed kinematic chain of <span><math><mrow><mi>n</mi><mo>≥</mo><mn>7</mn></mrow></math></span> identical links connected by revolute joints, forming a linkage with the nonorientable topology of a Möbius band. If its joints are set at a critical, <span><math><mi>n</mi></math></span>-dependent twist angle — the smallest that allows closure without forcing — then, despite formally having <span><math><mrow><mi>n</mi><mo>−</mo><mn>6</mn></mrow></math></span> internal degrees of freedom, the linkage admits only a single one: a reversible, periodic everting motion. Focusing on the case <span><math><mrow><mi>n</mi><mo>=</mo><mn>7</mn></mrow></math></span>, we determine the kinematic matrix via the Denavit–Hartenberg construction, under closure and congruence constraints. A geometric mechanism arises alongside the topological one due to a matrix-rank deficiency, accompanied by a corresponding state of self-stress. The geometric mechanism is <em>infinitesimal</em> and stiffened by self-stress, while eversion is enabled by the <em>finite</em> mechanism. Using a variational argument, we confirm that the sum of squared joint rotations remains constant throughout eversion. We further categorize the states of self-stress, identifying conserved quantities — including the sum of twisting moments raised to any positive integer power <span><math><mrow><mi>λ</mi><mo>≥</mo><mn>1</mn></mrow></math></span> — which enable estimates of self-stresses in moderately incongruent linkages requiring elastic forcing to close.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"216 ","pages":"Article 106185"},"PeriodicalIF":4.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099613","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}
Ruiyu Bai , Haoyu Zhang , Nan Yang , Zilun Yu , Bo Li , Qingsong Xu , Guimin Chen
{"title":"Optimization of a near-zero-center-shift compliant pivot for large motion range and high bearing stiffness","authors":"Ruiyu Bai , Haoyu Zhang , Nan Yang , Zilun Yu , Bo Li , Qingsong Xu , Guimin Chen","doi":"10.1016/j.mechmachtheory.2025.106218","DOIUrl":"10.1016/j.mechmachtheory.2025.106218","url":null,"abstract":"<div><div>Compliant pivots are employed in mechanical systems to achieve precise motions through the elastic deflections of the flexible elements, serving as substitutes for rigid joints. However, these pivots often encounter challenges such as a limited range of motion, significant axis shift, and low radial stiffness due to the distributed compliance of the flexible elements. To address these issues, this study introduces a novel design. This design is composed of three identical building blocks arranged in a circle array. The extended range of motion is achieved by serially connecting the flexible beams within the building blocks. The design’s symmetry ensures the nearly zeros axis shift, while the single degree of freedom and the virtual constraint enhances radial stiffness. A pivot with optimal combination properties is obtained through kinetostatic modeling and optimization, and experimental results validated its performance.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"216 ","pages":"Article 106218"},"PeriodicalIF":4.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099612","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}
Shuiguang Tong , Xiaoyan Yan , Zheming Tong , Hu Dai
{"title":"A hybrid cooperative-competitive evolutionary algorithm with non-dominated sorting for gear profile dynamic optimization in split-path transmission systems","authors":"Shuiguang Tong , Xiaoyan Yan , Zheming Tong , Hu Dai","doi":"10.1016/j.mechmachtheory.2025.106215","DOIUrl":"10.1016/j.mechmachtheory.2025.106215","url":null,"abstract":"<div><div>Split-path gear transmission systems (SPGTs) are widely employed in construction machinery, valued for their power-splitting capabilities and high torque density. The dynamic characteristics critically impact overall mechanical performance. This study proposes a hybrid cooperative-competitive evolutionary algorithm with non-dominated sorting (CCNS) for tooth profiles dynamic optimization in SPGTs. A nonlinear dynamic model for multi-gear pair SPGTs is first developed, incorporating time-varying mesh stiffness, damping, backlash, and enabling micro-geometric tooth profile modifications. This model is then integrated within the CCNS algorithm to minimize vibration acceleration RMS and dynamic transmission error peak-to-peak by optimizing modification parameters. The dynamic model’s validity is confirmed experimentally on a self-developed test rig under the constant torque and varying input speeds (450–1800 r/min). Results show predicted acceleration trends closely match measurements, exhibiting RMS errors of 4 % to 11.7 %. Leveraging this validated model, the influence of tooth profile modification parameters on dynamic characteristics is analyzed. This analysis reveals non-monotonic parameter effects, underscoring the necessity of multi-objective optimization. For the high-dimensional design space of SPGTs, CCNS demonstrates faster convergence and delivers superior Pareto solutions compared to other widely used optimization algorithms.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"216 ","pages":"Article 106215"},"PeriodicalIF":4.5,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145059929","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":"Kinematics of rolling contact: Derivation, misconceptions, and generalisations","authors":"Luigi Romano","doi":"10.1016/j.mechmachtheory.2025.106201","DOIUrl":"10.1016/j.mechmachtheory.2025.106201","url":null,"abstract":"<div><div>Rolling contact kinematics plays a foundational role in understanding the dynamic behaviour of a wide range of mechanical systems, from pneumatic tyres and railway wheels to tribological interfaces and robotic joints. Classical derivations of rolling contact kinematics often rely on vague or implicit assumptions about body elasticity or adopt non-rigorous arguments that can lead to incorrect or incomplete interpretations of slip and spin phenomena. This paper presents a unified and rigorous treatment of rolling contact, systematically addressing the cases of incommensurably elastic and similarly elastic bodies. Particular attention is dedicated to correcting several misconceptions widespread in the literature, including the misdefinition of rolling velocity and its pathological consequences. Based on the two limiting elastic cases, the paper further introduces a generalised elasto-kinematic framework combining kinematic constraints with local linear elastic equations. The resulting model is shown to be a symmetric hyperbolic system, and the novel theory is applied to an illustrative example to emphasise the role played by the bodies’ elasticity in the correct definition of slip and spin variables and in the calculation of the frictional forces and moments.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"216 ","pages":"Article 106201"},"PeriodicalIF":4.5,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046686","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}
Haichen Zhao, Haifeng Zhang, Zihao Wang, Tengfei Tang, Qinchuan Li
{"title":"Stiffness optimization strategy for cable-driven redundant manipulators considering configurations and cable tension","authors":"Haichen Zhao, Haifeng Zhang, Zihao Wang, Tengfei Tang, Qinchuan Li","doi":"10.1016/j.mechmachtheory.2025.106202","DOIUrl":"10.1016/j.mechmachtheory.2025.106202","url":null,"abstract":"<div><div>Cable-driven Redundant manipulators(CDRMs) have demonstrated superior performance in medical, industrial, and aerospace applications due to their unique capability to navigate obstacles and flexibly capture targets in complex environments. However, these manipulators' inherent multiple degrees of freedom and cable-driven characteristics also result in relatively insufficient resistance to external forces. This study proposes a stiffness optimization strategy based on the manipulator's motion redundancy and actuation redundancy properties to address this limitation. The proposed approach systematically accounts for the combined effects of manipulator configuration and cable tensions on overall stiffness performance. Furthermore, we design a stiffness index to evaluate stiffness characteristics across different operational configurations accurately. By applying a nonlinearly constrained optimization algorithm to inverse solution optimization, the optimal stiffness configuration of the manipulator can be determined for specific tasks. This optimization ensures the manipulator's end-effector achieves the desired position and orientation and maintains enhanced stiffness. Finally, the effectiveness of the proposed stiffness optimization algorithm and the accuracy of the stiffness model are thoroughly validated through both simulation and experimental studies. Results demonstrate that the implemented optimization strategy significantly improves the CDRM's capability to withstand external disturbances.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"216 ","pages":"Article 106202"},"PeriodicalIF":4.5,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046685","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 tailored approach for the comprehensive design of a multimode power-split e-CVT powertrain for a full-hybrid electric vehicle","authors":"Antonella Castellano, Marco Cammalleri","doi":"10.1016/j.mechmachtheory.2025.106214","DOIUrl":"10.1016/j.mechmachtheory.2025.106214","url":null,"abstract":"<div><div>The comprehensive design of a hybrid electric vehicle powertrain with a multimode power-split transmission is complicated by the driveline constructive complexity. The design approaches available in the literature are often based on mere explorative numerical methods mainly focused on the topological structure of the transmission without integrating the sizing of the engine or the electric unit. This paper aims to fill this literature gap by providing a tailored physical-based design procedure that, starting from a blank sheet and knowing only the vehicle parameters and desired performance, leads to the overall definition of the powertrain. The design approach is hierarchical, whereby each phase is decoupled from the others and the designer is made aware of cause-effect relationships at any design stage. Step by step, the power size of engine, battery, and electric machines is defined, and the functional and constructive arrangement of a multimode power-split transmission is synthesised, identifying the best operating range for input-, output-, and compound-split modes. The application on a C-segment full-hybrid electric car, which resulted in different but comparable solutions, proved the effectiveness of the method.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"216 ","pages":"Article 106214"},"PeriodicalIF":4.5,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020293","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}