{"title":"A new formulation for the dynamics of rigid bodies with unilateral interactions","authors":"","doi":"10.1016/j.mechmachtheory.2024.105809","DOIUrl":"10.1016/j.mechmachtheory.2024.105809","url":null,"abstract":"<div><div>A new approach is introduced for modelling multibody systems with unilateral interactions. We focus on the simulation of the forward dynamics problem. The dynamic and kinematic steps are solved with two different formulations. First, a four-point-mass model is used to represent the rigid body dynamics, avoiding the use of rotational coordinates. Therefore, the nonlinear inertial terms do not appear explicitly in the formulation. However, there are constant distance constraints between the point masses. The velocities of the point masses are obtained by solving the dynamics with this model. The angular velocity of the rigid body can be calculated from such velocities. Then, the kinematic problem is solved using the rigid body representation that fully embeds the constant distance constraints. Thus, the proposed approach can improve the accuracy of the dynamic problem with unilateral contact since the nonlinear inertial terms do not enter the formulation explicitly. The constraints appear explicitly in the dynamics representation, but they are linear there. In the position update, they are embedded exactly through the model change back to the angular velocity-based minimum coordinate formulation.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441351","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":"Analysis of the tooth-root stress of external spur gears with high effective contact ratio","authors":"","doi":"10.1016/j.mechmachtheory.2024.105813","DOIUrl":"10.1016/j.mechmachtheory.2024.105813","url":null,"abstract":"<div><div>For spur gears with contact ratio close to 2, the extension of the contact interval resulting from loaded tooth deflections and local contact deformations may result in an effective contact ratio above 2. In these cases, the load is transmitted by at least two tooth-pairs, the maximum load and tooth-root stress decrease, and therefore the calculation methods of the gear rating Standards ISO and AGMA provide very conservative results. In this work, two models are applied to the calculation of the tooth-root stress of load-induced high contact ratio external gears: (i) an analytic model of load sharing, based on the minimum energy method, and (ii) a finite element model, which validates the results obtained from the previous model. Obtained values of the stress are compared with those provided by ISO and AGMA rating methods, which do not account for the stress reduction due to the higher contact ratio. A new modification coefficient is proposed to correct these conservative values, which allows the AGMA and ISO geometry factors to remain as no load-dependent factors and keep their actual calculation methods and significance.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142432041","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":"Design and analytical modeling of a double-joint flexible surgical instrument with hand-held isomorphic actuation","authors":"","doi":"10.1016/j.mechmachtheory.2024.105804","DOIUrl":"10.1016/j.mechmachtheory.2024.105804","url":null,"abstract":"<div><div>In catheter reduction surgeries, surgical instruments with multi-joint end effectors are employed to improve surgery qualities, where implementations of miniaturization design and isomorphic actuation are challenging. In this work, a miniaturized double-joint end effector is designed using a novel multi-backbone mechanism. The backbones are made of spiral-notched tubes that have good axial stiffness and large bending flexibility, and a co-placed backbone arrangement is used to avoid double-joint actuation coupling. A double-joint handle is developed to implement isomorphic actuation of the end effector, where local reinforcement design of the handle is proposed to reduce torsional disturbances on the end effector. A recursive kinematic model of the multi-backbone mechanism is firstly established by relating friction with bending angles in a beam model of the backbones, and forward kinematics from the handle to the end effector is developed. Performance tests show that the double-joint end effector has good actuation decoupling characteristics. Parameter identification is conducted and model accuracy is validated. Phantom model experiments show that the end effector can reach the target position with the double-joint configuration.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142424019","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 general method to synthesize planar overconstrained mechanism","authors":"","doi":"10.1016/j.mechmachtheory.2024.105801","DOIUrl":"10.1016/j.mechmachtheory.2024.105801","url":null,"abstract":"<div><div>Traditionally, planar overconstrained mechanisms has been explained through special geometry, which often lacks clarity and specificity. This paper addresses this challenge by introducing two explicit criteria for analyzing and synthesizing planar overconstrained mechanisms. With the criteria, one may synthesize new planar overconstrained systematically and confidently. To create new planar overconstrained mechanisms, three approaches are employed: the parallelogram-aided approach, the stretch-rotation approach, and an optimization-based method. Given that the mobility of mechanisms is independent of the choice of the ground link and that the mathematical treatment of function generation is straightforward, this paper proposes a systematic approach for synthesizing novel function cognates. By combining these approaches, new types of overconstrained mechanisms are discovered. Leveraging advanced computational tools, a special geometric condition for function cognates of inverted slider cranks is found for the first time. Through inversion, the coupler cognates for slider cranks are also identified. The success of these results indicates that the proposed criteria are explicit and crucial for discovering new mechanisms, and the concept may be extended to spherical or spatial cases.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142424017","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":"Simulation and validation of the transmission error, meshing stiffness, and load sharing of planetary spur gear transmissions","authors":"","doi":"10.1016/j.mechmachtheory.2024.105800","DOIUrl":"10.1016/j.mechmachtheory.2024.105800","url":null,"abstract":"<div><div>Although the load sharing between planets of sequentially phased planetary gear transmissions has been studied in the past, the required solving techniques based on the Finite Element Method result in long time consuming and high computational cost. This limits the possibilities of undertaking extensive studies that take into consideration a high number of cases allowing optimal solutions to be sought or general conclusions drawn. In addition, the determination of the curves of transmission error, time-varying mesh stiffness, and load sharing among tooth pairs in simultaneous contact are also complicated. In this work an analytical model has been developed for the simulation of the time-varying mesh stiffness, quasi-static transmission error, and load sharing ratio between planets and tooth pairs of planetary spur gear transmissions. It is based on similar models for external and internal spur gears previously developed and has been validated by comparison with a hybrid model based on the Finite Element Method and theoretic-experimental correlation.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142424016","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":"Kineto-static analysis of a hybrid manipulator consisting of rigid and flexible limbs with locking function for planar shape morphing","authors":"","doi":"10.1016/j.mechmachtheory.2024.105802","DOIUrl":"10.1016/j.mechmachtheory.2024.105802","url":null,"abstract":"<div><div>The incorporation of lockable passive backbones into active compliant morphing systems efficiently results in lightweight, high-load, and large deformation systems. However, there exist challenges in kineto-static analysis due to the interaction between rigid reconfigurable kinematic constraints and the nonlinear deformation of actuated flexible limbs. This paper addresses these issues by developing a kineto-static method to analyze the motion in a novel planar 3-DOF shape-morphing manipulator. The manipulator features two actuated flexible limbs with a lockable variable geometry truss (LVGT). In this study, two isostatic topologies are selected for reconfigurable motion control under external tip loads. A multi-step sequential control strategy is proposed to maneuver the manipulator's platform for desired poses. Then, a constrained-trajectory-based kinematic model is proposed for an inverse kinematic solution considering motion planning. Subsequently, a kineto-static model is introduced, considering constraints from rigid and flexible limbs, aiming to distribute distributing redundant actuation forces. Finally, nonlinear finite element analysis (FEA) and experiments are carried out to validate the effectiveness of the proposed method.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142424018","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":"Non-inertial dynamic modeling and gear mesh characteristic analysis of planetary gear train system","authors":"","doi":"10.1016/j.mechmachtheory.2024.105794","DOIUrl":"10.1016/j.mechmachtheory.2024.105794","url":null,"abstract":"<div><div>Floating offshore wind turbines experience periodical platform motions due to waves and currents, which intensify vibrations in wind turbine gearboxes. In these gearboxes, the gear mesh characteristics of the planetary gear train system (PGTS) are vulnerable to vibrations caused by platform motions. However, many PGTS models lack attention to gear mesh characteristics affected by platform motions. This study introduces a novel instantaneous multi-teeth contact model that integrates a loaded tooth contact analysis model with dynamic displacements. A rigid-flexible coupling dynamic model of PGTS that accounts for platform motions is established, and then an efficient iterative solution scheme is developed. The model is validated using the Finite Element Method, and gear mesh characteristics of PGTS are thoroughly analyzed. Simulation results show that resonance exacerbates dynamic gear meshing force and stiffness fluctuations, leading to significant deviations from static values. Platform motions disturb contact force distribution, increase peak forces and fluctuations, and pose a risk of tooth disengagement. The axial vibration frequencies and amplitudes of the ring gear tooth correlate with base motions, suggesting potential applications in gear mesh state monitoring.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142424015","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":"Exact constraint design of bridge-type displacement flexure amplifier","authors":"","doi":"10.1016/j.mechmachtheory.2024.105799","DOIUrl":"10.1016/j.mechmachtheory.2024.105799","url":null,"abstract":"<div><div>Bridge-type amplifiers are commonly used to increase the effective actuation stroke of piezoelectric stack actuators owing to their compact size. However, the traditional bridge-type amplifier has an unconstrained degree-of-freedom, which yields large parasitic motions when subject to offset loads and induces dynamic performance losses related to underconstrained resonance. This work presents an exact constraint design (ECD) of bridge-type amplifier, in which a semi-bridge is introduced for both the lower bridge and the upper bridge on the basis of the traditional bridge-type amplifier. A holistic theoretical model is established for the whole bridge-type amplifier without reducing it to a half or even a quarter by taking advantage of structural symmetry. The model is generalized so that it can be used for modeling the traditional, the compound and the ECD amplifiers. Based on the model, three different bridge-type amplifiers considering manufacturing errors are modeled and compared, and the results show that the ECD amplifier is more precise in achieving desired motion and more robust against manufacturing imperfections. All the results are verified by those of the finite element models.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318773","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":"Application of instantaneous invariants to Cardan positions for two parameters complex plane motion","authors":"","doi":"10.1016/j.mechmachtheory.2024.105798","DOIUrl":"10.1016/j.mechmachtheory.2024.105798","url":null,"abstract":"<div><div>This paper aims to represent the Cardan position in the complex plane using Bottema’s instantaneous invariants for two parameters motions. The study provides unchanging and simple quantities that simplify the analysis of complicated mechanical systems by determining complex number representations of Bottema’s instantaneous invariants for Cardan motions with two parameters. The method involves illustrating invariants based on two parameters in the complex plane, defining cycloidal and Cardan motions of two parameters, and deriving the conditions for the Cardan positions. The key results are the necessary and sufficient conditions for the Cardan position for two-parameter motions in the complex plane obtained based on these instantaneous invariants.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142310909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic inversion and optimal tracking control on the ball-plate system based on a linearized nonholonomic multibody model","authors":"","doi":"10.1016/j.mechmachtheory.2024.105795","DOIUrl":"10.1016/j.mechmachtheory.2024.105795","url":null,"abstract":"<div><div>This paper addresses the optimal control of the ball-plate system, a well-known nonholonomic system in the context of nonprehensile manipulation, using a multibody dynamics approach. The trajectory tracking control of a steady-state circular motion of the ball on the plate, for any radius and potentially off-centric with respect to the plate’s pivoting point, is achieved by designing a Linear-Quadratic Regulator. A spatial multibody model of the ball-plate system is considered. A key contribution is the analytical computation of the circular steady motion of the ball by dynamic inversion, including the control actions to achieve this reference solution. This enables the analytical computation of the linearized equations along this reference motion, resulting in a periodic linear time-varying (LTV) system, and the application of linear controllability criteria for LTV systems. A controllable linear system, involving the Cartesian coordinates of the contact point and the yaw angle of the sphere, is obtained using a convenient coordinate partition in the linearization. Compared to existing results on the same problem, closed-loop stability about the desired trajectory is achieved for any radius of the circular trajectory.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0094114X24002222/pdfft?md5=61cf4d5bbf6881351f1a0c8ae07724cd&pid=1-s2.0-S0094114X24002222-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142310908","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}