{"title":"Driving rotational motion with Euler parameters: a constraint formulation for multibody systems","authors":"Madalena Antunes, João Folgado, Carlos Quental","doi":"10.1016/j.mechmachtheory.2025.106315","DOIUrl":"10.1016/j.mechmachtheory.2025.106315","url":null,"abstract":"<div><div>The formulation of rotational driving constraints using angular variables (angle-based formulation) may introduce numerical instabilities and redundancy among kinematic constraints, which can compromise the robustness of multibody analyses. This study proposes an alternative Euler-based formulation, in which Euler parameters, describing the relative orientation between joint-connected bodies, are used to define rotational driving constraints. This formulation avoids singularities, enables full range of motion evaluation, and eliminates redundancy. Both angled-based and Euler-based formulations were applied to different joints within both open and closed kinematic chains using an in-house multibody model of the human body. Kinematic and inverse dynamic analyses were conducted across several movements from multiple subjects, and the results were compared between the two formulations and literature data. The Euler-based formulation provided independent kinematic constraints and showed good agreement with joint kinematics and torques from established methods. In addition, it improved computational efficiency. Overall, the use of Euler parameters offers a robust and efficient alternative to angle-based formulations for rotational driving constraints in multibody system dynamics.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106315"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737134","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":"Corrigendum to “Kinematics of rolling contact: Derivation, misconceptions, and generalisations” [Mechanism and Machine Theory 216 (2025) 106201]","authors":"Luigi Romano, Sweden Linköping","doi":"10.1016/j.mechmachtheory.2025.106298","DOIUrl":"10.1016/j.mechmachtheory.2025.106298","url":null,"abstract":"","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106298"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145925079","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 concept of the metamodel based on the dynamics analysis results of the eccentric crank-rocker mechanism","authors":"Andrzej Urbaś, Jacek Stadnicki","doi":"10.1016/j.mechmachtheory.2025.106333","DOIUrl":"10.1016/j.mechmachtheory.2025.106333","url":null,"abstract":"<div><div>This paper presents the concept of using the metamodel of the dynamics of the crank-rocker mechanism with eccentricity for its synthesis. The formalism of joint coordinates, homogeneous transformation matrices, and Lagrange equations are used to derive the mathematical model of the mechanism, which considers the flexibility of the drive and connecting rod. Using the mathematical model of the mechanism, the function of which is to compact the raw material using a rocker, the simulation of many dimensional variants of the mechanism is performed. Next, based on the results, a metamodel of the mechanism is proposed, with the design criterion being the maximal value of the rocker kinetic energy, which is adopted as a measure of the efficiency of raw material compaction. The metamodel is used in practice to determine the lengths of links of the mechanism that met the adopted design criteria. A comparison of options of the analysis of mechanism models with and without the flexibility of the drive or/and connecting rod is also presented.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106333"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884206","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":"Design and analysis of a Bricard-inspired dexterous hand based on generalized parallel mechanisms","authors":"Hongzeng Li , Bo Wang , Chunxu Tian , Dan Zhang","doi":"10.1016/j.mechmachtheory.2025.106340","DOIUrl":"10.1016/j.mechmachtheory.2025.106340","url":null,"abstract":"<div><div>This paper proposes a novel generalized parallel dexterous hand with the aim of enhancing dexterity and stability. First, by using topological synthesis and number synthesis methods, an analysis is conducted on the degrees of freedom (DOF), number of loops, and link combinations of the topological structures of the dexterous hand. This analysis helps to identify effective non-isomorphic Contracted Graphs (CGs). Then, the configuration of a multi-mode deployable dexterous hand is designed based on the threefold-symmetric Bricard mechanism. A reconfigurable base is incorporated into this design to enhance the adaptability of the dexterous hand. Additionally, Lie group theory is employed to analyze the motion modes of the dexterous hand. Through simulation analysis, the grasping and motion performance under different motion modes are evaluated. Moreover, the forward and inverse kinematics of the dexterous hand are analyzed. Coordinate transformation methods are used to reduce the computational complexity. Finally, the workspace and motion force transmission performance of the dexterous hand are evaluated through simulation analysis.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106340"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884207","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}
Zhigang Wu , Xuan Li , Qi Sun , Minglu Zhu , Tao Chen , Lining Sun
{"title":"Integrated geometric modeling, meshing behavior analysis, and experimental prototype validation of arc-cycloid external gear pairs","authors":"Zhigang Wu , Xuan Li , Qi Sun , Minglu Zhu , Tao Chen , Lining Sun","doi":"10.1016/j.mechmachtheory.2025.106323","DOIUrl":"10.1016/j.mechmachtheory.2025.106323","url":null,"abstract":"<div><div>This study presents theoretical design methods and conducts systematic performance analysis for an arc-cycloid external gear pair. The pairing consists of a circular-arc pinion and an enveloping-generated cycloid gear, achieving conjugate meshing via continuous line contact. This design prevents undercutting observed in involute gears and enables higher transmission ratios under identical center distance and structural constraints. Mathematical models of the gears are established using differential geometry and spatial meshing theory. Spatial contact trajectories, pressure angles, and induced normal curvature are computationally analyzed with dependencies quantified. A hybrid loaded tooth contact analysis (LTCA) methodology is developed through the integration of Boussinesq’s elastic half-space theory and the influence coefficient method. This approach enables precise calculation of contact stress distributions across loaded tooth surfaces. The theoretical LTCA model is validated by finite element analysis (FEA), with computational results showing excellent agreement against analytical solutions. Experimental verification is conducted on a purpose-built test rig. Transmission stability and band-shaped contact patterns are confirmed through precise measurements. Consistency is demonstrated between experimental measurements and simulation predictions, independently validating the proposed methodology. The gear pair demonstrates significant potential for applications demanding compact, high-ratio power transmission.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106323"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790275","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 , Hongyang Tian , Yang Yang , Shaohui Qin , Yong Chen
{"title":"Cavitation mechanism of high-speed gears with misalignment","authors":"Tiancheng Ouyang , Hongyang Tian , Yang Yang , Shaohui Qin , Yong Chen","doi":"10.1016/j.mechmachtheory.2025.106319","DOIUrl":"10.1016/j.mechmachtheory.2025.106319","url":null,"abstract":"<div><div>In high-speed gear transmissions, cavitation is prone to occur, leading to vibration deterioration and tooth surface erosion. Vibration and engagement characteristics become abnormal when misalignment inevitably occurs due to mounting errors, deformation and long-term wear. However, current gear cavitation studies are set to ideal alignment and it is not clear how misalignment affects cavitation. To investigate the cavitation mechanism in misaligned gears, a kinetic model of misaligned gears is combined with a turbulence model with cavitation for the first time. First, the abnormal vibration responses that derived from the gear finite element model are validated against existing experimental results, and they are applied as boundary rotation conditions for the flow field. Subsequently, the effects of vibration and meshing discrepancies caused by different misalignments on cavitation are comprehensively analyzed. Vapor and pressure distributions in the meshing zone are examined to evaluate the impacts of misalignment degree, rotational speed, vibration, and tooth surface meshing. Results indicate that gear pairs with misalignment exhibit significant cavitation phenomena during high-speed operation. Specifically, vibration amplification induced by radial and yaw misalignments exacerbate the severity of cavitation.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106319"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790364","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":"Rigid-foldable tapered origami patterns derived from type III Bricard octahedra","authors":"Yucai Hu, Yongliang Luo","doi":"10.1016/j.mechmachtheory.2025.106325","DOIUrl":"10.1016/j.mechmachtheory.2025.106325","url":null,"abstract":"<div><div>While origami has long served as physical analogs for classical mechanisms, few large origami patterns are directly derived from these kinematic systems. This paper presents single-degree-of-freedom rigid-foldable tapered origami patterns based on the type III Bricard octahedron (BOIII), a foundational flexible polyhedral mechanism. Building on extending BOIII into tubular structures, we demonstrate how kinematic equivalence and interchangeability between isogram and antiisogram enable the development of rigid-foldable configurations with bilateral origami-patterned surfaces. The rigid foldability of the BOIII and its derived crease patterns is validated through the consistent application of facet compatibility conditions. Using symmetric BOIII units, tapered origami patterns of spiral, zigzag, and hybrid profiles are constructed. Notably, the spiral pattern featuring two tapering vertices mimics natural spirals in ammonites and snails. An inverse design approach is established to generate tapered crease patterns, ensuring their bottom boundary edges conforms to the target planar curve at a prescribed fold angle. This mechanism-based approach expands the design space of rigidly and flat-foldable quadrilateral mesh origami patterns by incorporating the tapering feature, offering potential applications in deployable aerospace structures, reconfigurable robotics, and metamaterials.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106325"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790276","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}
Qixing Yue , Xiaoting Rui , Jianshu Zhang , Kuankuan Gang , Baichen Yang , Shengwei Miao
{"title":"An efficient algorithm for evaluating kinematic closed-loop constraint forces of flexible multibody systems","authors":"Qixing Yue , Xiaoting Rui , Jianshu Zhang , Kuankuan Gang , Baichen Yang , Shengwei Miao","doi":"10.1016/j.mechmachtheory.2025.106324","DOIUrl":"10.1016/j.mechmachtheory.2025.106324","url":null,"abstract":"<div><div>The formulation of closed-loop flexible multibody systems can be accomplished via the reduced transfer matrix method, which employs joint coordinates, elastic modal coordinates, and a tree-based topology description achieved by imaginarily cutting specific joints, resulting in a minimal set of generalized coordinates for the forward dynamic analysis utilizing recursive procedures. An efficient algorithm is proposed in this paper to eliminate redundant evaluations for kinematic closed-loop constraint forces within these recursive procedures. The transfer equations and recursive relationship of the accelerations for flexible body components are reformulated in lightweight forms characterized by the minimal sets of closed-loop constraint forces. Complementarily, the kinematic closed-loop constraint equations are reformulated in lightweight manners upon the minimal sets of closed-loop constraint forces, whereby the corresponding constraint forces are evaluated through redundancy-free computations. Three numerical examples are finally presented to illustrate the effectiveness, versatility, and efficiency of the proposed algorithm. It can be concluded that the proposed algorithm provides a computationally efficient alternative to the recursive solution procedures for the forward dynamic analysis of flexible multibody systems.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106324"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790277","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":"Nonlinear topology optimization design of compliant mechanisms with tailored input/output stiffness","authors":"Yueyou Tang , Meng He , Zhen-Pei Wang , Liang Xia","doi":"10.1016/j.mechmachtheory.2025.106330","DOIUrl":"10.1016/j.mechmachtheory.2025.106330","url":null,"abstract":"<div><div>Topology optimization of compliant mechanisms (CMs) typically seeks to maximize input stiffness while minimizing output stiffness to achieve optimal geometric advantage (GA). However, simultaneously tailoring input and output stiffness inherently conflicts with these objectives, a challenge that is exacerbated under nonlinear conditions. To address this, we propose a nested optimization framework incorporating geometric and material nonlinearities, which decouples the problem into two levels: the outer loop maximizes GA, while the inner loop enables precise input/output stiffness customization. An adaptive volume control strategy is further introduced to suppress hinge-like features and improve material efficiency. Numerical examples demonstrate that the method yields hinge-free topologies with input and output stiffness closely matching the targets. Finally, a series of CMs with varying stiffness ratios were designed and fabricated. Experimental results confirm the effectiveness of proposed method in tailoring input/output stiffness, while verifying the output-end resistance to external excitations and the required input actuation force. The method is applicable to mechanisms with specific performance demands, such as low-actuation, high-output-stability robotic grippers and medical instruments with both high input and output stability.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106330"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884205","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}
Zhaojin Liu , Jiawei Li , Yuxiao Li , Shaoming Yao , Gang Wang
{"title":"Design of jerk model and optimal time trajectory planning method based on smooth continuous oscillatory type curves","authors":"Zhaojin Liu , Jiawei Li , Yuxiao Li , Shaoming Yao , Gang Wang","doi":"10.1016/j.mechmachtheory.2025.106342","DOIUrl":"10.1016/j.mechmachtheory.2025.106342","url":null,"abstract":"<div><div>This paper presents a jerk-segmented trajectory planning method based on continuous oscillatory-type curves to address the requirements for smooth and rapid maneuvering of modern industrial robots. The method replaces the traditional step oscillatory curve with a continuous oscillatory curve as the foundational model for the jerk trajectory. Furthermore, the jerk-segment curve is extended to fully exploit the kinematic capabilities. Concurrently, an optimal time solution strategy for jerk-segmented trajectories, informed by effective order, is developed. This strategy enables flexible adjustment of the solution process based on the effective order. Additionally, we introduce a coordination factor to manage the relationship between the initial jerk and its kinematic constraints during continuous changes, thereby maximizing effective drivability and maintaining continuous control time for the jerk. A velocity synchronization strategy is proposed to coordinate multi-axis motion, further establishing the applicability of this method in industrial robotic systems. Numerical simulation analysis results indicate that this method exhibits superior performance in terms of time optimality, vibration generation, and suppression. The method's effectiveness has been field experimentally validated using a complex hybrid robot prototype.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106342"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884209","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}