This article focusses on the problem of interference among the links of a parallel robot, namely, the Stewart-Gough platform manipulator. The geometry of the legs is approximated by capsules, leading to the detection of collision among any pair of legs in terms of tangency of the corresponding capsules. Analytical conditions for the said cases of tangency are derived in closed-form, which manifest geometrically as certain quadrics in space. Through a thorough study and explicit characterisation of these surfaces, novel analytical methods are developed to find the largest spheres in space which are tangent to these surfaces. Such spheres are free of possibilities of link collisions, and they can be derived analytically for a given orientation of the moving platform of the manipulator. The analysis is subsequently extended to the orientation workspace of the manipulator by repeating the above-mentioned computations over a large number of discrete samples. The results obtained are verified numerically by comparing them with those generated from other sources. A parametric study is performed to demonstrate the utility of the proposed analysis in practice.
{"title":"A semi-analytical approach towards determining the largest collision-free sphere in R3 inside the effective regular workspace of a 6-6 Stewart-Gough platform manipulator corresponding to a given orientation workspace","authors":"Bibekananda Patra, Nishanth Adithya Chandramouli, Sandipan Bandyopadhyay","doi":"10.1016/j.mechmachtheory.2025.106331","DOIUrl":"10.1016/j.mechmachtheory.2025.106331","url":null,"abstract":"<div><div>This article focusses on the problem of interference among the links of a parallel robot, namely, the Stewart-Gough platform manipulator. The geometry of the legs is approximated by <em>capsules</em>, leading to the detection of collision among any pair of legs in terms of tangency of the corresponding capsules. Analytical conditions for the said cases of tangency are derived in closed-form, which manifest geometrically as certain quadrics in space. Through a thorough study and explicit characterisation of these surfaces, novel analytical methods are developed to find the largest spheres in space which are tangent to these surfaces. Such spheres are free of possibilities of link collisions, and they can be derived analytically for a given orientation of the moving platform of the manipulator. The analysis is subsequently extended to the orientation workspace of the manipulator by repeating the above-mentioned computations over a large number of discrete samples. The results obtained are verified numerically by comparing them with those generated from other sources. A parametric study is performed to demonstrate the utility of the proposed analysis in practice.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"220 ","pages":"Article 106331"},"PeriodicalIF":4.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927894","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}
Pub Date : 2026-04-01Epub Date: 2026-01-08DOI: 10.1016/j.mechmachtheory.2025.106344
Peter Pacsonyi , Csaba Budai , Gabor Stepan
Vibration isolation is one of the most important aspects of mechanical engineering, and various methods are available for protecting vibration-sensitive equipment. This paper focuses on vibration isolation using antiresonance effects provided by inerters. It is concluded that the spring strut complemented with an inerter can substitute the tuned mass damper, thus reducing the number of auxiliary elements and the additional mass of the vibration isolating system. If the inertance is variable, it can modify the frequency response of the system. With an appropriate nonlinear control strategy, it is achievable to tune the frequency of the antiresonance to the dominant frequency of the external excitation, thus reducing the vibration amplitudes. This paper presents the modeling and analysis of the variable inerter as well as developing a feedback linearization-based control algorithm.
{"title":"Analysis and control of a variable inerter-based vibration mitigation system","authors":"Peter Pacsonyi , Csaba Budai , Gabor Stepan","doi":"10.1016/j.mechmachtheory.2025.106344","DOIUrl":"10.1016/j.mechmachtheory.2025.106344","url":null,"abstract":"<div><div>Vibration isolation is one of the most important aspects of mechanical engineering, and various methods are available for protecting vibration-sensitive equipment. This paper focuses on vibration isolation using antiresonance effects provided by inerters. It is concluded that the spring strut complemented with an inerter can substitute the tuned mass damper, thus reducing the number of auxiliary elements and the additional mass of the vibration isolating system. If the inertance is variable, it can modify the frequency response of the system. With an appropriate nonlinear control strategy, it is achievable to tune the frequency of the antiresonance to the dominant frequency of the external excitation, thus reducing the vibration amplitudes. This paper presents the modeling and analysis of the variable inerter as well as developing a feedback linearization-based control algorithm.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"220 ","pages":"Article 106344"},"PeriodicalIF":4.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927893","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}
Pub Date : 2026-04-01Epub Date: 2026-01-22DOI: 10.1016/j.mechmachtheory.2026.106362
Ziming Zhao , Yezhuo Li , Jian S Dai , Jianxu Wu , Yan-an Yao , Peng Jin , Zibin Wang
The purpose of this paper is to put forward a novel cubical deformable mobile mechanism with URU chains. This new mobile mechanism with the external cube shape is composed of eight platforms and twelve URU chains. A unified analytical method is proposed for the analysis of the degree of freedoms (DoFs) and kinematics of this kind of mechanism. The DoFs are obtained based on screw theory. The coordinates of points are obtained through homogeneous transformation matrixes and closed-loop equations. Meanwhile, the results of DoFs analysis in each chain are used to find and verify the number of constraint equations. Furthermore, the workspaces of the center of mass (CM), platforms, chains, and loops of the mechanism are solved, the results of which are used to design a tracked-rolling gait. A series of dynamic simulations are conducted and analyzed to test the performance of the mechanism, including the verification of its folding, tracked-rolling, climbing capability spheroidal-rolling capability, and the climbing capability in vertical cracks. An experimental prototype is fabricated and constructed to verify the motion capability and the tracked-rolling gait.
{"title":"Design and analysis method of a cubical deformable mobile mechanism based on URU chains","authors":"Ziming Zhao , Yezhuo Li , Jian S Dai , Jianxu Wu , Yan-an Yao , Peng Jin , Zibin Wang","doi":"10.1016/j.mechmachtheory.2026.106362","DOIUrl":"10.1016/j.mechmachtheory.2026.106362","url":null,"abstract":"<div><div>The purpose of this paper is to put forward a novel cubical deformable mobile mechanism with URU chains. This new mobile mechanism with the external cube shape is composed of eight platforms and twelve URU chains. A unified analytical method is proposed for the analysis of the degree of freedoms (DoFs) and kinematics of this kind of mechanism. The DoFs are obtained based on screw theory. The coordinates of points are obtained through homogeneous transformation matrixes and closed-loop equations. Meanwhile, the results of DoFs analysis in each chain are used to find and verify the number of constraint equations. Furthermore, the workspaces of the center of mass (CM), platforms, chains, and loops of the mechanism are solved, the results of which are used to design a tracked-rolling gait. A series of dynamic simulations are conducted and analyzed to test the performance of the mechanism, including the verification of its folding, tracked-rolling, climbing capability spheroidal-rolling capability, and the climbing capability in vertical cracks. An experimental prototype is fabricated and constructed to verify the motion capability and the tracked-rolling gait.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"220 ","pages":"Article 106362"},"PeriodicalIF":4.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023471","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}
Pub Date : 2026-04-01Epub Date: 2026-01-30DOI: 10.1016/j.mechmachtheory.2026.106368
Siqi Guo , Wenzhong Wang , Rui Tang , He Liang , Haibo Zhang
As a critical supporting component of aero-engine main shafts, the three-point angular contact ball bearing (TPACBB) is subjected to complex external loads, leading to time-varying contact characteristics that significantly influence its dynamic behavior and service life. This study establishes a universal, nonlinear, multi-degree-of-freedom dynamic model applicable to TPACBB. It employs the Lankarani-Nikravesh model for more accurate contact force calculation and comprehensively accounts for the interactions among the balls, cage, raceways, and lubricant. The relationship between axial/radial loads and multi-point contact states is investigated, and the dynamic performance under different contact conditions is analyzed. Additionally, the critical load ratio inducing multi-point contact variations is determined under varying loading conditions and structural parameters. The results reveal that the critical axial-to-radial load ratio governing the transition between three-point and two-point contact depends on the bearing's structural parameters. Specifically, the shim angle exhibits a positive correlation with the critical load ratio, whereas the inner raceway groove radius demonstrates a negative correlation. This research provides valuable insights for the structural optimization and fault diagnosis of TPACBB.
{"title":"The effect of external load on multi-point contact transitions of three-point angular contact ball bearing","authors":"Siqi Guo , Wenzhong Wang , Rui Tang , He Liang , Haibo Zhang","doi":"10.1016/j.mechmachtheory.2026.106368","DOIUrl":"10.1016/j.mechmachtheory.2026.106368","url":null,"abstract":"<div><div>As a critical supporting component of aero-engine main shafts, the three-point angular contact ball bearing (TPACBB) is subjected to complex external loads, leading to time-varying contact characteristics that significantly influence its dynamic behavior and service life. This study establishes a universal, nonlinear, multi-degree-of-freedom dynamic model applicable to TPACBB. It employs the Lankarani-Nikravesh model for more accurate contact force calculation and comprehensively accounts for the interactions among the balls, cage, raceways, and lubricant. The relationship between axial/radial loads and multi-point contact states is investigated, and the dynamic performance under different contact conditions is analyzed. Additionally, the critical load ratio inducing multi-point contact variations is determined under varying loading conditions and structural parameters. The results reveal that the critical axial-to-radial load ratio governing the transition between three-point and two-point contact depends on the bearing's structural parameters. Specifically, the shim angle exhibits a positive correlation with the critical load ratio, whereas the inner raceway groove radius demonstrates a negative correlation. This research provides valuable insights for the structural optimization and fault diagnosis of TPACBB.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"220 ","pages":"Article 106368"},"PeriodicalIF":4.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078172","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}
Pub Date : 2026-04-01Epub Date: 2026-01-03DOI: 10.1016/j.mechmachtheory.2025.106347
Onur Can Kalay , Fatih Karpat
Gearboxes oftentimes operate under time-varying operating conditions (TVOC). Some studies on TVOC assessed the fluctuations in vibration data through computer simulations, while others appraised healthy gearboxes or piecewise constant operating conditions. Besides, these studies all focus on gears with symmetric tooth profiles. From this standpoint, the present experimental study combined a one-dimensional convolutional neural network (1-D CNN) with a long short-term memory (LSTM) algorithm for diagnosing divergent crack degrees that vary from 0% to 100% with an increment of 25% under TVOC for spur gear pairs with symmetric (20°/20°) and asymmetric (20°/30°) teeth. A series of vibration experiments was performed, considering two TVOC scenarios: (1) variable speed and constant load, and (2) constant speed and variable load. Using an asymmetric profile amplified the amplitude difference between the vibration response of healthy and cracked gears, facilitating fault diagnosis. For different TVOC scenarios, overall accuracies calculated for symmetric gears ranged between 90.005% and 98.654% and between 93.932% and 99.908% for asymmetric ones. The results revealed that the overall classification accuracy could be improved by up to 4.633% using gears with asymmetrical teeth.
{"title":"Vibration-based crack diagnosis for asymmetric gears under time-varying operational conditions using a 1-D CNN-LSTM model","authors":"Onur Can Kalay , Fatih Karpat","doi":"10.1016/j.mechmachtheory.2025.106347","DOIUrl":"10.1016/j.mechmachtheory.2025.106347","url":null,"abstract":"<div><div>Gearboxes oftentimes operate under time-varying operating conditions (TVOC). Some studies on TVOC assessed the fluctuations in vibration data through computer simulations, while others appraised healthy gearboxes or piecewise constant operating conditions. Besides, these studies all focus on gears with symmetric tooth profiles. From this standpoint, the present experimental study combined a one-dimensional convolutional neural network (1-D CNN) with a long short-term memory (LSTM) algorithm for diagnosing divergent crack degrees that vary from 0% to 100% with an increment of 25% under TVOC for spur gear pairs with symmetric (20°/20°) and asymmetric (20°/30°) teeth. A series of vibration experiments was performed, considering two TVOC scenarios: (1) variable speed and constant load, and (2) constant speed and variable load. Using an asymmetric profile amplified the amplitude difference between the vibration response of healthy and cracked gears, facilitating fault diagnosis. For different TVOC scenarios, overall accuracies calculated for symmetric gears ranged between 90.005% and 98.654% and between 93.932% and 99.908% for asymmetric ones. The results revealed that the overall classification accuracy could be improved by up to 4.633% using gears with asymmetrical teeth.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"220 ","pages":"Article 106347"},"PeriodicalIF":4.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886041","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}
Pub Date : 2026-03-01Epub Date: 2025-12-27DOI: 10.1016/j.mechmachtheory.2025.106337
Zhihao Xia , Xinhua Lao , Chunxu Tian , Dan Zhang
Generalized parallel mechanisms (GPMs) with multiloop coupling have garnered considerable attention because of their structural attributes, including high strength, superior stability, and strong scalability. However, existing synthesis methods face limitations when addressing multiloop coupled structures. Conventional approaches are typically confined to scenarios with fewer loops, involving complex and inefficient analysis processes. To overcome these challenges, this paper proposes a novel synthesis method based on a topological mapping neural network (TMNN). By mapping the topological structure of a GPM onto a neural network, the motion transmission process of the mechanism is equivalent to the forward propagation of neurons, thereby transforming a traditionally intractable problem into a trainable optimization task within a neural network. This paper elaborates on the theoretical foundation and network architecture design of the proposed method. Its feasibility and effectiveness are validated through experiments. While future work will focus on enhancing computational efficiency, this innovative topological mapping approach provides a crucial theoretical and practical foundation for the efficient synthesis of multiloop coupled GPMs.
{"title":"Mapping mechanical synthesis to a trainable task: A neural network approach for generalized parallel mechanisms","authors":"Zhihao Xia , Xinhua Lao , Chunxu Tian , Dan Zhang","doi":"10.1016/j.mechmachtheory.2025.106337","DOIUrl":"10.1016/j.mechmachtheory.2025.106337","url":null,"abstract":"<div><div>Generalized parallel mechanisms (GPMs) with multiloop coupling have garnered considerable attention because of their structural attributes, including high strength, superior stability, and strong scalability. However, existing synthesis methods face limitations when addressing multiloop coupled structures. Conventional approaches are typically confined to scenarios with fewer loops, involving complex and inefficient analysis processes. To overcome these challenges, this paper proposes a novel synthesis method based on a topological mapping neural network (TMNN). By mapping the topological structure of a GPM onto a neural network, the motion transmission process of the mechanism is equivalent to the forward propagation of neurons, thereby transforming a traditionally intractable problem into a trainable optimization task within a neural network. This paper elaborates on the theoretical foundation and network architecture design of the proposed method. Its feasibility and effectiveness are validated through experiments. While future work will focus on enhancing computational efficiency, this innovative topological mapping approach provides a crucial theoretical and practical foundation for the efficient synthesis of multiloop coupled GPMs.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106337"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145839998","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}
Pub Date : 2026-03-01Epub Date: 2025-12-11DOI: 10.1016/j.mechmachtheory.2025.106316
Bo Wang , Qing Wu , Hailiang Yu , Weihua Ma , Feng Lin , Xiangyu Li , Xueqiang Zhang
To analyze the derailment mechanism of a subway train under air spring failure conditions and to identify improvement measures, this study first establishes a dynamic train model according to the actual train formation. Subsequently, equivalent models for air spring failure are introduced. Finally, based on wheel–rail derailment theory and vehicle system dynamics, a comparative analysis is conducted under both normal (inflated) and failed air spring conditions to investigate key factors influencing the derailment mechanism. Corresponding improvement measures are then proposed. The results indicate that: (1) with air spring failure, curve transition derails the train; (2) multiple factors can effectively lower derailment risks; (3) large lateral creep force and attack angle are not necessary conditions for flange climbing; and (4) installing guard rails at curve exits and applying lubrication to the rails can effectively reduce flange climbing risk under air spring failure. This study provides valuable insights for subway track design and for mitigating derailment risks in the event of air spring failure.
{"title":"Derailment mechanism analysis of subway vehicles under air spring failure","authors":"Bo Wang , Qing Wu , Hailiang Yu , Weihua Ma , Feng Lin , Xiangyu Li , Xueqiang Zhang","doi":"10.1016/j.mechmachtheory.2025.106316","DOIUrl":"10.1016/j.mechmachtheory.2025.106316","url":null,"abstract":"<div><div>To analyze the derailment mechanism of a subway train under air spring failure conditions and to identify improvement measures, this study first establishes a dynamic train model according to the actual train formation. Subsequently, equivalent models for air spring failure are introduced. Finally, based on wheel–rail derailment theory and vehicle system dynamics, a comparative analysis is conducted under both normal (inflated) and failed air spring conditions to investigate key factors influencing the derailment mechanism. Corresponding improvement measures are then proposed. The results indicate that: (1) with air spring failure, curve transition derails the train; (2) multiple factors can effectively lower derailment risks; (3) large lateral creep force and attack angle are not necessary conditions for flange climbing; and (4) installing guard rails at curve exits and applying lubrication to the rails can effectively reduce flange climbing risk under air spring failure. This study provides valuable insights for subway track design and for mitigating derailment risks in the event of air spring failure.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106316"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737135","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}
Pub Date : 2026-03-01Epub Date: 2025-12-02DOI: 10.1016/j.mechmachtheory.2025.106302
Nils Brückmann , Christian Mirz , Mathias Hüsing , Yukio Takeda , Burkhard Corves
This paper proposes an optimal control approach to reduce frame vibrations in robotic pick and place tasks, caused by rapid acceleration and deceleration of the robot. The objective of the proposed optimal control approach is to determine time-optimal trajectories that cancel out residual frame vibrations after trajectory execution. The control problem is defined for a delta robot but can be adapted to any type of robot used for pick and place tasks. To solve the optimal control problem numerically, it is transformed into a nonlinear programming problem using the Legendre-Gauss-Lobatto collocation method. To validate the approach, experiments are conducted to compare the residual frame vibrations of optimized trajectories with typical pick and place trajectories. The novelty of the paper is the vibration reduction with an optimization-based approach on a complex multi-degree-of-freedom robot system whose dynamic parameters are identified with experimental data. In addition, a mathematical description of all constraints required for a robotic pick and place task is proposed for the optimization.
{"title":"Optimal control approach for trajectory determination to suppress residual frame vibrations of delta robots in pick and place tasks","authors":"Nils Brückmann , Christian Mirz , Mathias Hüsing , Yukio Takeda , Burkhard Corves","doi":"10.1016/j.mechmachtheory.2025.106302","DOIUrl":"10.1016/j.mechmachtheory.2025.106302","url":null,"abstract":"<div><div>This paper proposes an optimal control approach to reduce frame vibrations in robotic pick and place tasks, caused by rapid acceleration and deceleration of the robot. The objective of the proposed optimal control approach is to determine time-optimal trajectories that cancel out residual frame vibrations after trajectory execution. The control problem is defined for a delta robot but can be adapted to any type of robot used for pick and place tasks. To solve the optimal control problem numerically, it is transformed into a nonlinear programming problem using the Legendre-Gauss-Lobatto collocation method. To validate the approach, experiments are conducted to compare the residual frame vibrations of optimized trajectories with typical pick and place trajectories. The novelty of the paper is the vibration reduction with an optimization-based approach on a complex multi-degree-of-freedom robot system whose dynamic parameters are identified with experimental data. In addition, a mathematical description of all constraints required for a robotic pick and place task is proposed for the optimization.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106302"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685303","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}
Pub Date : 2026-03-01Epub Date: 2025-12-17DOI: 10.1016/j.mechmachtheory.2025.106320
M. Verotti
Recently, the instantaneous geometric invariants have proved to be a fundamental tool for the analysis of the motion generated by flexure hinges. In this paper, the invariants are applied to the synthesis of compliant mechanisms at the output port level. The motion of the moving plane associated to the output port is described through fundamental geometric entities, that are the inflection circle, the cubic of stationary curvature, and its derivative. The proposed synthesis procedure aims to reshape the output port to embody the special points on the plane, that are the Ball’s and the Burmester’s points, approximating straight and circular paths to the third and to the fourth order, respectively. The method is implemented for the design of a compliant mechanism and numerical simulations are conducted to verify the theoretical results. A discussion of the advantages and disadvantages of the method is presented.
{"title":"Synthesis at the output port of compliant mechanisms through the instantaneous geometric invariants","authors":"M. Verotti","doi":"10.1016/j.mechmachtheory.2025.106320","DOIUrl":"10.1016/j.mechmachtheory.2025.106320","url":null,"abstract":"<div><div>Recently, the instantaneous geometric invariants have proved to be a fundamental tool for the analysis of the motion generated by flexure hinges. In this paper, the invariants are applied to the synthesis of compliant mechanisms at the output port level. The motion of the moving plane associated to the output port is described through fundamental geometric entities, that are the inflection circle, the cubic of stationary curvature, and its derivative. The proposed synthesis procedure aims to reshape the output port to embody the special points on the plane, that are the Ball’s and the Burmester’s points, approximating straight and circular paths to the third and to the fourth order, respectively. The method is implemented for the design of a compliant mechanism and numerical simulations are conducted to verify the theoretical results. A discussion of the advantages and disadvantages of the method is presented.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106320"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790360","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}
Pub Date : 2026-03-01Epub Date: 2025-12-16DOI: 10.1016/j.mechmachtheory.2025.106317
Pello Alberdi, Aitor Arana, Aitor Oyanguren, Jon Larrañaga, Ibai Ulacia
Ball screw mechanisms are widely used in precision applications due to their high stiffness and efficiency. However, unlike ball bearings, the helical geometry of ball screws leads to multidirectional contact kinematics, which significantly influence friction, wear, and overall performance. In the classical contact kinematic formulation, the velocity components of the ball are not fully projected onto the contact interface, resulting in significant errors in the calculation of contact kinematics.
This work presents a revised contact kinematic formulation considering all the missing components, and revealing substantial differences in the prediction which alters the conventional understanding of contact kinematics in ball screws. The contact kinematics are broken down into their fundamental components-rolling, side, and spinning slip-and analytical expressions for each are introduced. A new characterisation framework based on three independent variables is proposed, quantifying the distinct effects of rolling, side, and spinning motion more comprehensively than traditional single SRR.
The proposed model is first validated against a well-established ball bearing formulation (i.e. ball screw with no lead), confirming its accuracy under such geometry. At the ball screw scale, the results reveal substantial deviations from existing models. Side slip emerges as the dominant mechanism, fundamentally revising the conventional interpretation of contact kinematics. Furthermore, the new three-variable framework enables a more complete and accurate characterisation of the contact behaviour, offering valuable insights for tribological modelling and performance optimisation. Finally, a parametric analysis is conducted to examine the influence of key kinematic constraints on the sliding behaviour, highlighting the independent role of each in defining the contact kinematics.
{"title":"A revised framework for ball-screw contact kinematics","authors":"Pello Alberdi, Aitor Arana, Aitor Oyanguren, Jon Larrañaga, Ibai Ulacia","doi":"10.1016/j.mechmachtheory.2025.106317","DOIUrl":"10.1016/j.mechmachtheory.2025.106317","url":null,"abstract":"<div><div>Ball screw mechanisms are widely used in precision applications due to their high stiffness and efficiency. However, unlike ball bearings, the helical geometry of ball screws leads to multidirectional contact kinematics, which significantly influence friction, wear, and overall performance. In the classical contact kinematic formulation, the velocity components of the ball are not fully projected onto the contact interface, resulting in significant errors in the calculation of contact kinematics.</div><div>This work presents a revised contact kinematic formulation considering all the missing components, and revealing substantial differences in the prediction which alters the conventional understanding of contact kinematics in ball screws. The contact kinematics are broken down into their fundamental components-rolling, side, and spinning slip-and analytical expressions for each are introduced. A new characterisation framework based on three independent variables is proposed, quantifying the distinct effects of rolling, side, and spinning motion more comprehensively than traditional single <em>SRR</em>.</div><div>The proposed model is first validated against a well-established ball bearing formulation (i.e. ball screw with no lead), confirming its accuracy under such geometry. At the ball screw scale, the results reveal substantial deviations from existing models. Side slip emerges as the dominant mechanism, fundamentally revising the conventional interpretation of contact kinematics. Furthermore, the new three-variable framework enables a more complete and accurate characterisation of the contact behaviour, offering valuable insights for tribological modelling and performance optimisation. Finally, a parametric analysis is conducted to examine the influence of key kinematic constraints on the sliding behaviour, highlighting the independent role of each in defining the contact kinematics.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":"219 ","pages":"Article 106317"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790363","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}
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