{"title":"Design optimization and validation of a permanent-magnet array for gravity compensation in long-stroke linear motion","authors":"Xiangxian Zeng, Chin-Hsing Kuo, Emre Sariyildiz","doi":"10.1016/j.mechmachtheory.2025.105990","DOIUrl":"10.1016/j.mechmachtheory.2025.105990","url":null,"abstract":"<div><div>Conventional gravity compensation methods, such as spring- or counterweight-based approaches, often introduce additional friction and/or inertia and require auxiliary force transmission components. Although magnet-based designs mitigate these drawbacks through non-contact magnetic forces, their effectiveness in long-stroke linear motion remains limited. This paper presents a permanent-magnet array for passive gravity compensation in linear motion, enabling payload balancing over a vertical motion range several times the side length of the employed cubic magnet. The design process optimizes the positions and orientations of magnets anchored to the frame, which interact with a magnet attached to the payload to generate the necessary counteracting force. Two illustrative examples demonstrate the proposed design. The first achieves over 92 % gravity reduction for a payload weighing 20 times the magnet's weight, with a travel range six times the magnet's height. The second example enhances balancing capacity by incorporating additional magnets on the payload. One of these designs was experimentally validated. Finally, the study explores optimal magnet distribution patterns, the ideal magnet-to-travel-range ratio, methods to amplify balancing capacity, and the scalability of the proposed concept.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"209 ","pages":"Article 105990"},"PeriodicalIF":4.5,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Karim Moussa , Maxime Thieffry , Fabien Claveau , Philippe Chevrel , Stéphane Caro
{"title":"Dynamic models for simulation of Cable-Driven Parallel Robots with elasticity and sagging","authors":"Karim Moussa , Maxime Thieffry , Fabien Claveau , Philippe Chevrel , Stéphane Caro","doi":"10.1016/j.mechmachtheory.2025.105972","DOIUrl":"10.1016/j.mechmachtheory.2025.105972","url":null,"abstract":"<div><div>Cable-Driven Parallel Robots (CDPRs) are a type of parallel robots that uses cables instead of rigid links, making accurate modeling complex due to intricate cable dynamics. For simulation and control applications, it is appropriate to employ simplifying hypotheses to account for cable deformations. However, when high precision is necessary, models capturing the cable deformation become compulsory, making it challenging to balance model fidelity with computation time. This paper addresses this challenge, by proposing and comparing dynamic models of CDPRs that are both accurate and suitable for controller design. Leveraging recent advances in Finite Element Method (FEM) modeling for robotics, this paper extends recent findings and adapts them to the specific case of CDPRs. Additionally, a second model based on the assumed mode approach is extended to 3D context. The accuracy of both models is then compared with that of a lumped parameter model provided by the commercial software MapleSim, focusing on pick-and-place tasks to highlight the strengths and limitations of each approach for establishing a common benchmark. Following initial experimental validation of the models’ precision in a single-cable setup, the FEM model was selected as a comparison reference. Finally, simulation results for an eight-cable 3D suspended robot are presented.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"209 ","pages":"Article 105972"},"PeriodicalIF":4.5,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628228","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 slider-crank spring gravity balance module for 1-DOF rotary link and its application to serial manipulators","authors":"Cheng-Hsuan Hsu, Chi-Shiun Jhuang, Dar-Zen Chen","doi":"10.1016/j.mechmachtheory.2025.105991","DOIUrl":"10.1016/j.mechmachtheory.2025.105991","url":null,"abstract":"<div><div>This paper presents a slider-crank spring gravity balance module for a rotary link and its application to serial manipulators. The spring is arranged in a slider-crank mechanism, its elastic energy is a quadratic function of the crank angle. The gravitational energy of a rotary link can be expressed as a quadratic function of half the link angle. It shows energies matched when the crank angle is half the link angle with a phase difference and the spring stiffness is a function of the link mass. Thus, the balance module is formed. In a serial manipulator, the gravitational energy of a remote link is expressed as the sum of quadratic functions of the angle of itself and preceding links. It can be matched by the elastic energy of the modules on the link itself and the preceding links respectively. Thus, the balance module can be applied to serial manipulators. Torque measurement tests for balancing a rotary link and a 2-DOF serial manipulator by balance modules are performed and show the driving torques are reduced by over 90 % by the balance module.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"209 ","pages":"Article 105991"},"PeriodicalIF":4.5,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628079","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":"Effect of gear tooth root crack on the dynamic response of a planetary geared rotor system","authors":"Eduardo Henrique de Paula, Helio Fiori de Castro","doi":"10.1016/j.mechmachtheory.2025.105970","DOIUrl":"10.1016/j.mechmachtheory.2025.105970","url":null,"abstract":"<div><div>This research presented a dynamic model of a planetary geared rotor system and investigated the influence of tooth root cracks on the system’s response. The rotor components were modeled using the finite element method, while the planetary gearbox members were modeled with the lumped parameter method. The model assumed a non-rotating planetary carrier and planet gears equally spaced. Different parameters were considered for cracks at the tooth root of the ring, sun, and first planet gears. The system’s response was analyzed by comparing the frequency domain acceleration response, the acceleration signal’s power spectrum, and the intrinsic mode functions obtained via empirical mode decomposition of the acceleration signal for the healthy and cracked system. Results indicated that crack size is the most significant parameter in altering the system’s response. The signal’s power spectrum enabled clear crack detection, size differentiation, and identification of the affected gear. The empirical mode decomposition of the acceleration signal proved to be particularly advantageous in distinguishing between crack sizes in higher frequency ranges, with the first intrinsic mode function showing significant differences depending on the crack size.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"209 ","pages":"Article 105970"},"PeriodicalIF":4.5,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143591621","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":"IK-Geo: Unified robot inverse kinematics using subproblem decomposition","authors":"Alexander J. Elias, John T. Wen","doi":"10.1016/j.mechmachtheory.2025.105971","DOIUrl":"10.1016/j.mechmachtheory.2025.105971","url":null,"abstract":"<div><div>We present IK-Geo, a highly capable and computationally efficient open-source robot inverse kinematics (IK) solver. In this unifying approach, IK for any 6-DOF all-revolute (6R) manipulator is decomposed into six canonical geometric subproblems solved by intersecting circles with other geometric objects. Subproblems are efficiently solved in all cases including in a continuous and sometimes least-squares sense when a solution does not exist. This continuity requirement means IK-Geo finds all IK solutions including singular solutions and sometimes least-squares solutions. Robots with three intersecting or parallel axes are solved in closed form. All other commercially available robots have at least one pair of intersecting or parallel axes and are solved by searching over one joint angle. Fully general robots are solved by searching over two joint angles. Search solutions may be converted to a system of three or four polynomials in terms of the end effector pose in the tangent half-angle of one joint. A comparison with IKFast and the MATLAB Robotics Toolbox IK solver demonstrates that IK-Geo has faster computation and can solve more classes of robots.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"209 ","pages":"Article 105971"},"PeriodicalIF":4.5,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143591518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sérgio B. Gonçalves , Ivo Roupa , Paulo Flores , Miguel Tavares da Silva
{"title":"Kinematic and dynamic analysis of spatial multibody systems based on a formulation with fully Cartesian coordinates and a generic rigid body","authors":"Sérgio B. Gonçalves , Ivo Roupa , Paulo Flores , Miguel Tavares da Silva","doi":"10.1016/j.mechmachtheory.2025.105955","DOIUrl":"10.1016/j.mechmachtheory.2025.105955","url":null,"abstract":"<div><div>This work introduces the Fully Cartesian Coordinates Formulation with a Generic Rigid Body (FCC-GRB), a novel global multibody formulation for three-dimensional mechanical system analysis. The formulation's intrinsic characteristics are thoroughly detailed and compared with other widely-used global formulations, enabling its application in both kinematic and dynamic analysis of complex mechanical systems and as a teaching tool in advanced multibody dynamics courses.</div><div>FCC-GRB formulation is founded on two main premises: multibody systems are described using only Cartesian coordinates, and the rigid bodies are modeled with a fixed and predetermined structure. Consequently, the kinematic constraints are described by lower-degree equations and the system mass matrix is highly sparse. Additionally, the introduction of the generic rigid body simplifies the modeling process by making the definition of the bodies independent of system topology. To reduce the number of generalized coordinates, a reduced modeling approach using less coordinates for describing the generic rigid body is also introduced and compared with the fully-defined alternative.</div><div>The formulation's accuracy was validated through forward dynamic analysis of benchmark problems. Simulations demonstrated excellent agreement with reference data, with both modeling approaches yielding comparable kinematic results. The reduced approach offered faster computational performance, particularly in more complex models.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"209 ","pages":"Article 105955"},"PeriodicalIF":4.5,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yibo Jiang , Shuiguang Tong , Zheming Tong , Sheng Li , Xianmiao Yang
{"title":"Tribo-dynamic modelling and analysis of gear-rotor system: Effects of stationary and nonstationary conditions","authors":"Yibo Jiang , Shuiguang Tong , Zheming Tong , Sheng Li , Xianmiao Yang","doi":"10.1016/j.mechmachtheory.2025.105982","DOIUrl":"10.1016/j.mechmachtheory.2025.105982","url":null,"abstract":"<div><div>As crucial indicators of stability and service reliability, dynamic and tribological behaviors of gear-rotor system are investigated under both stationary and nonstationary conditions based on a new tribo-dynamic modelling approach. In the global dynamic model, the shaft compliance is considered with the gyroscopic effect, and the dynamic meshing force formulations under elastohydrodynamic and hydrodynamic lubrication states are integrated. The stepwise coupling strategy is developed to describe the two-way interaction between vibration and lubrication parameters in each time step. The methodology is validated numerically and experimentally. The investigation shows that high-speed and light-load conditions result in chaos, accompanied by extremely high subsurface stress. Higher additional torque during the acceleration and deceleration brings about rotating speed oscillation and more complex frequency components. Faster torque fluctuation contributes to multi-periodic and chaotic motions. The non-monotonic relationship with maximum pressure and minimum film thickness is also observed. Disturbing loads in the forms of sudden load variation and random load disturbance have limited impacts on system tribo-dynamic performance generally. The methodology and results provide useful guidelines for the tribo-dynamic design of gear-rotor system.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"209 ","pages":"Article 105982"},"PeriodicalIF":4.5,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143550457","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":"Quaternions in Kinematics","authors":"J. Michael McCarthy","doi":"10.1016/j.mechmachtheory.2025.105949","DOIUrl":"10.1016/j.mechmachtheory.2025.105949","url":null,"abstract":"<div><div>This paper examines Hamilton’s quaternions, dual quaternions and Clifford’s biquaternions in order to show how they are related to the kinematics of rotations in space, spatial displacements and rotations in four dimensional space. The three algebras are constructed in the same way as the even Clifford Algebras for these spaces, and their quaternion products are shown to provide a formula for spherical triangulation, spatial triangulation of lines, and double triangulation of two spherical triangles, respectively. In the process, we obtain the spherical triangle of relative rotations axes and the spatial triangle of relative screw axis, which are important generalizations of the planar pole triangle in Kinematics. We conclude with applications of double quaternions as approximations to spatial movement, which simplify calculations that rely on distance metrics for spatial positions, such as spatial motion interpolation.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"209 ","pages":"Article 105949"},"PeriodicalIF":4.5,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143550458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust motion control synthesis with essential dynamics for hybrid-driven continuum robots","authors":"Jun Yang, Haoyong Yu","doi":"10.1016/j.mechmachtheory.2025.105973","DOIUrl":"10.1016/j.mechmachtheory.2025.105973","url":null,"abstract":"<div><div>Incorporating system dynamics into the design of centralized control architectures is increasingly recognized as an effective approach to improve the motion control of continuum robots. However, the huge computational demands of most existing dynamic models pose significant challenges for their application in real-time control scenarios. In this paper, for hybrid-driven continuum robots, we first develop two simplified dynamic models that capture the essential dynamic characteristics while ensuring high computational efficiency. Subsequently, by incorporating the simplified models into feedback control, a robust dual-loop control framework suitable for real-time applications is presented. Specifically, the inner loop adopts these simplified models to counteract the inherent nonlinear dynamics of systems, thereby achieving a linear input/output relationship. The outer loop focuses on stabilizing the entire closed-loop system. Moreover, an extra robust term is designed and incorporated into the outer loop to mitigate the effects induced by modeling errors. Comparative experiments based on a hybrid-driven continuum robot with two segments are implemented to validate the effectiveness of these simplified models and their control synthesis.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"209 ","pages":"Article 105973"},"PeriodicalIF":4.5,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529805","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":"An overview of higher-order kinematics of rigid body and multibody systems with nilpotent algebra","authors":"Daniel Condurache","doi":"10.1016/j.mechmachtheory.2025.105959","DOIUrl":"10.1016/j.mechmachtheory.2025.105959","url":null,"abstract":"<div><div>This paper proposes a framework for a new computational method based on multidual nilpotent algebra calculus of the higher-order acceleration fields of the rigid body motion and multibody systems. A closed-form coordinate-free solution is presented, this result being generated by the morphism between the Lie group of the rigid body displacements and the Lie groups of the multidual homogenous matrix, orthogonal hyper-multidual tensors and, respectively, the hyper-multidual unit quaternions. The solution is implemented for higher-order kinematics analysis of lower-pair serial chains by a specific product of the exponential formula. A general method for studying the vector field of arbitrary higher-order accelerations is described. The “automatic differentiation” feature of the multi dual and hyper-multidual functions is used to obtain simultaneously a higher-order derivative of a rigid body pose. The methodologies are obtained without further differentiation of the body pose concerning time. It is proved that all information regarding the properties of the distribution of higher-order accelerations is contained in the specified multi dual homogenous matrix, or orthogonal hyper-multidual tensors, and, respectively, the unit hyper-multidual quaternions. In the case of closed kinematic chains, equations that provide higher-order kinematic constraints in the compact form are given in general form.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"209 ","pages":"Article 105959"},"PeriodicalIF":4.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519902","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}