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Finite-step-integration:An original method for the forward kinematics analysis of parallel manipulators

Frontiers of Mechanical Engineering 2025年第1期20卷 129-146页

作者： Yuan JIANG Bo HAN Xiaohan LIU Meng HAN Jiantao YAO Yongsheng ZHAO School of Mechanical Engineering Yanshan UniversityQinhuangdao 066004China Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System Yanshan UniversityQinhuangdao 066004China College of Information Science and Engineering Northeastern UniversityShenyang 110819China

In today’s society,parallel manipulators(PMs)are widely used in industrial production,aerospace,and other fields,where their forward kinematic analyses often serve as the foundation for various tasks,such as design,calibration,and *** the past few decades,this issue has seemingly been repeatedly addressed using various numerical methods,intelligent algorithms,and algebraic *** it is undeniable that solving the equations is easier with current technology,the problem of“how to formulate solvable equations”is often *** analysis issue typically involves establishing non-linear,multi-parameter,high-dimensional,and strong-coupled mathematical equations,which,from a geometric perspective,is also considered a process of solving a spatial *** considering the temporal dimension of motion between two isomorphic polytopes,based on calculus theory,it has been found that this non-linear problem can be transformed into the superposition of multiple iteratively linear ***,we propose an original method for the forward kinematic analysis of PMs,namely the finite-step-integration(FSI)*** this study,the mathematical principles and modeling methods of the FSI method are elucidated,and the modeling and programming processes of the FSI method are demonstrated using general 6-UPS and 3-UPS/S manipulators as *** the analysis of its unique algebraic structure,the methods for singularity determination and motion tracking characteristic analysis are *** method addresses the long-standing challenges in the forward kinematic modeling of PMs,which is applicable for design,calibration,and control,while also offering novel insights for modeling and solving certain non-linear engineering problems.

关键词： finite-step-integration forward kinematic analysis parallel manipulator singularity determination motion tracking

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Design and Analysis of Single-drive Space Deployable Metamorphic Capture Manipulator

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Jixie Gongcheng Xuebao/Journal of Mechanical Engineering 2025年第1期61卷 30-43页

作者： Han, Bo Yang, Ming Luo, Mingyan Li, Mingyang Yao, Jiantao Zhao, Yongsheng School of Mechanical Engineering Yanshan University Qinhuangdao066004 China Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System Yanshan University Qinhuangdao066004 China

In order to improve the problems of large volume and complex driving of grasping mechanism in space non-cooperative target capture task, a single-drive space deployable truss capture manipulator is proposed. Based on the scissor mechanism and metamorphic principle, the structure of the deployable basic unit is designed, and the deployable unit is connected by the synchronous hinge to realize the synchronous drive of each deployable unit on the single-branch truss. The characteristics of changing the axis of the revolute joint at a specific position can be realized by using the metamorphic joint in the unit, so that the unfolding motion of the manipulator is transformed into the turning motion of the platform, and the capture action of the manipulator is completed. On the basis of considering the friction, the dynamic model of the basic deployable unit is established by using the Lagrange equation. The position, velocity and acceleration of each connecting rod are obtained by vector operation, and the relationship between the driving force and the equivalent torque is obtained. The single-branch manipulator truss is equivalent to a 4R mechanism, and the dynamic model of the manipulator truss combination is further carried out by Newton-Euler recursive method, and the correctness of the model is verified by software simulation. The proposed space capture manipulator has the advantages of expandable, metamorphic, and small number of drives, which can provide theoretical guidance and reference for the research of related technical fields. © 2025 Chinese Mechanical Engineering Society. All rights reserved.

关键词： Trusses

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Type Synthesis of Fully Decoupled Three Translational parallel Mechanism with Closed-Loop Units and High Stifness

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Chinese Journal of Mechanical Engineering 2023年第5期36卷 231-247页

作者： Shihua Li Sen Wang Haoran Li Yongjie Wang Shuang Chen Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic Systems Yanshan UniversityQinhuangdao 066004China

In order to solve the problem of weak stifness of the existing fully decoupled parallel mechanism, a new synthesis method of fully decoupled three translational (3T) parallel mechanisms (PMs) with closed-loop units and high stifness is proposed based on screw theory. Firstly, a new criterion for the full decoupled of PMs is presented that the reciprocal product of the transmission wrench screw matrix and the output twist screw matrix of PMs is a diagonal matrix, and all elements on the main diagonal are nonzero constants. The forms of the transmission wrench screws are determined by the criterion. Secondly, the forms of the actuated and unactuated screws can be obtained according to their relationships with the transmission wrench screws. The basic decoupled limbs are generated by combination of the above actuated and unactuated screws. Finally, a closed-loop units construction method is investigated to apply the decoupled mechanisms in a better way on the high stifness occasion. The closed-loop units are constructed in the basic decoupled limbs to generate a high-stifness fully decoupled 3T PM. Kinematic and stifness analyses show that the Jacobian matrix is a diagonal matrix, and the stifness is obviously higher than that of the coupling mechanisms, which verifes the correctness of the proposed synthesis method. The mechanism synthesized by this method has a good application prospect in vehicle durability test platform.

关键词： Screw theory Three translational parallel mechanism Full decoupled Closed-loop units High stifness

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Kinematics and Dynamics Hessian Matrices of Manipulators Based on Screw Theory

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Chinese Journal of Mechanical Engineering 2015年第2期28卷 226-235页

作者： ZHAO Tieshi GENG Mingchao CHEN Yuhang LI Erwei YANG Jiantao Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System Yanshan University Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of Education Yanshan University

The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling ***,the traditional representations cannot achieve this because of the absence of coordinate ***,the coordinate invariant method is an important research ***,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is *** on the twist and the rigid-body acceleration,the acceleration of the end-effector is expressed as a linear-bilinear form,and the kinematics Hessian matrix of the manipulator（represented by Lie bracket）is ***,Newton-Euler＇s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is *** formulae and the dynamics Hessian matrix are proved to be coordinate *** to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is *** index of dynamical coupling based on dynamics Hessian matrix is *** the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics *** screw theory based method can simplify the kinematics and dynamics of a manipulator,also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.

关键词： kinematics dynamics Hessian matrix parallel manipulator screw theory

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Problem of intersection of two fourth order screw systems and its application for constraint determination in hybrid mechanisms

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Applied Mathematical Modelling 2025年 147卷

作者： Bo Hu Jinjun Zhao School of Mechanical Engineering Yanshan University Qinhuangdao 066004 China Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System Yanshan University Qinhuangdao 066004 China

The intersection of fourth order screw systems is a challenging work in the field of mechanisms, which is very important for mechanism analysis especially for the constraint analysis of 2+2 type parallel+parallel lower mobility hybrid mechanisms. In this paper, aiming at the intersection problem of two fourth order screw systems, by constructing the ruled surface and the straight generatrix expressions corresponding to the third and fourth order screw systems, combining with the idea of solving the common generatrix, the direct and indirect methods for constructing the analytical intersection model are proposed. The proposed method is used to analyze the terminal constraints of a novel hybrid mechanism under different configurations. The results show that the terminal constraints of the mechanism are two constraint forces. The proposed intersection model of two fourth order screw systems has the advantages of clear geometric meaning and strong intuition. It provides a new idea for the intersection operation of two screw systems and a theory basis for the terminal constraint analysis of lower mobility hybrid mechanisms.

关键词：

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Synthesis of Branched Chains with Actuation Redundancy for Eliminating Interior Singularities of 3T1R parallel Mechanisms

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Chinese Journal of Mechanical Engineering 2016年第2期29卷 250-259页

作者： LI Shihua LIU Yanmin CUI Hongliu NIU Yunzhan ZHAO Yanzhi Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System Yanshan University Qinhuangdao 066004 China Hebei Vocationa & Technical College of Building Materials Qinhuangdao 066004 China

Although it is common to eliminate the singularity of parallel mechanism by adding the branched chain with actuation redundancy, there is no theory and method for the configuration synthesis of the branched chain with actuation redundancy in parallel mechanism. Branched chains with actuation redundancy are synthesized for eliminating interior singularity of 3-translational and 1-rotational（3T1R） parallel mechanisms. Guided by the discriminance method of hybrid screw group according to Grassmann line geometry, all the possibilities are listed for the occurrence of interior singularities in 3T1R parallel mechanism. Based on the linear relevance of screw system and the principles of eliminating parallel mechanism singularity with actuation redundancy, different types of branched chains with actuation redundancy are synthesized systematically to indicate the layout and the number of the branched chainsinterior with actuation redundancy. A general method is proposed for the configuration synthesis of the branched chains with actuation redundancy of the redundant parallel mechanism, and it builds a solid foundation for the subsequent performance optimization of the redundant actuation parallel mechanism.

关键词： parallel mechanism interior singularity hybrid screw group branched chain with actuation redundancy

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Global Dynamic Modeling of Electro-Hydraulic 3-UPS/S parallel Stabilized Platform by Bond Graph

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Chinese Journal of Mechanical Engineering 2016年第6期29卷 1176-1185页

作者： ZHANG Lijie GUO Fei LI Yongquan LU Wenjuan Hebei Provincial Key Laboratory of Heavy Machinery Fluid Power Transmission and Control Yanshan University Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of Education Yanshan University Parallel Robot and Mechatronic System Laboratory of Hebei Province Yanshan University

Dynamic modeling of a parallel manipulator（PM） is an important issue. A complete PM system is actually composed of multiple physical domains. As PMs are widely used in various fields, the importance of modeling the global dynamic model of the PM system becomes increasingly prominent. Currently there lacks further research in global dynamic modeling. A unified modeling approach for the multi-energy domains PM system is proposed based on bond graph and a global dynamic model of the 3-UPS/S parallel stabilized platform involving mechanical and electrical-hydraulic elements is built. Firstly, the screw bond graph theory is improved based on the screw theory, the modular joint model is modeled and the normalized dynamic model of the mechanism is established. Secondly, combined with the electro-hydraulic servo system model built by traditional bond graph, the global dynamic model of the system is obtained, and then the motion, force and power of any element can be obtained directly. Lastly, the experiments and simulations of the driving forces, pressure and flow are performed, and the results show that, the theoretical calculation results of the driving forces are in accord with the experimental ones, and the pressure and flow of the first limb and the third limb are symmetry with each other. The results are reasonable and verify the correctness and effectiveness of the model and the method. The proposed dynamic modeling method provides a reference for modeling of other multi-energy domains system which contains complex PM.

关键词： screw bond graph multi-energy domains 3-UPS/S parallel mechanism electro-hydraulic servo system

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Applicability and Generality of the Modified Grübler-Kutzbach Criterion

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Chinese Journal of Mechanical Engineering 2013年第2期26卷 257-263页

作者： LI Yanwen WANG Lumin LIU Jingfang HUANG Zhen Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System Yanshan University College of Environment and Chemical Engineering Yanshan University College of Mechanical Engineering and Applied Electronics Technology Beijing University of Technology

A generally applicable criterion for all mechanism mobility has been an active domain in mechanism theory lasting more than 150 years. It is stated that the Modified Grübler-Kutzbach criterion for mobility has been successfully used to solve the mobility of many more kinds of mechanisms, but never before has anyone proven the applicability and generality of the Modified Grübler-Kutzbach criterion in theory. In order to fill the gap, the applicability and generality of the Modified Grübler-Kutzbach Criterion of mechanism mobility is systematically demonstrated. Firstly, the mobility research background and the Modified Grübler-Kutzbach criterion are introduced. Secondly, some new definitions, such as half local freedom, non-common constraint space of a mechanism and common motion space of a mechanism, etc, are given to demonstrate the correctness and broad applicability of the Modified Grübler-Kutzbach criterion. Thirdly, the general applicability of the Modified Grübler-Kutzbach criterion is demonstrated based on screw theory. The mobilities of the classical DELASSUS mechanisms and a modern planar parallel mechanism, are determined through the Modified Grübler-Kutzbach criterion, which are as examples to show the practical application of the Modified Grübler-Kutzbach criterion.

关键词： mobility screw theory classical mechanism parallel mechanism

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Analysis and Optimization of a Spatial parallel Mechanism for a New 5-DOF Hybrid Serial-parallel Manipulator

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Chinese Journal of Mechanical Engineering 2018年第3期31卷 60-68页

作者： Dong-Sheng Zhang Yun-Dou Xu Jian-Tao Yao Yong-Sheng Zhao Parallel Robot and Mechatronic System Laboratory of Hebei Province Yanshan University Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education Yanshan University

Hybrid manipulators have potentially application in machining industries and attract extensive attention from many researchers on the basis of high sti ness and high dexterity. Therefore,in order to expand the application prospects of hybrid manipulator,a novel 5?degree?of?freedom(DOF) hybrid serial?parallel manipulator(HSPM) is proposed. Firstly,the design plan of this manipulator is introduced. Secondly,the analysis of this manipulator is carried out in detail,including kinematics analysis,statics analysis,and workspace analysis. Especially,an amplitude equivalent method of disposing the over?constrained force/couple to the non?overconstrained force/couple is used in the statics analysis. Then,three performance indices are used to optimize the PM. Two of them have been widely used,and the third one is a new index which considers the characteristics of the actuated force. Based on the performance indices,the performance atlas is drawn and the optimal design of the PM is investigated. In order to satisfy the anticipant kinetic characteristics of the PM,the verification of the optimized physical dimension is done and the workspace based on the optimized physical dimension is carried out. This paper will lay good theoretical foundations for application of this novel HSPM and also can be applied to other hybrid manipulators.

关键词： parallel mechanism Performance indices Optimal design Performance atlas

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Kinetostatics Analysis of a Novel 6-DOF parallel Manipulator with Three Planar Limbs and Equipped with Three Fingers

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Chinese Journal of Mechanical Engineering 2014年第5期27卷 919-927页

作者： LU Yi LI Xuepeng College of Mechanical Engineering Yanshan University Key Laboratory of Parallel Robot and Mechatronic System of Hebei Province Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education

It is significant to develop a robot hand with high rigidity by a 6-DOF parallel manipulator（PM）.However,the existing6-DOF PMs include spherical joint which has less capability of pulling force bearing,less rotation range and lower precision under alternately heavy loads.A novel 6-DOF PM with three planar limbs and equipped with three fingers is proposed and its kinematics and statics are analyzed systematically.A 3-dimension simulation mechanism of the proposed manipulator is constructed and its structure characteristics is *** kinematics formulae for solving the displacement,velocity,acceleration of the platform,the active legs and the fingers are *** statics formulae are derived for solving the active forces of PM and the finger *** analytic example is given for solving the kinematics and statics of proposed manipulator and the analytic solved results are verified by the simulation *** is proved from the error analysis of analytic solutions and simulation solutions that the derived analytic formulae are correct and provide the theoretical and technical foundations for its manufacturing,control and application.

关键词： parallel manipulator planar limbs finger kinematics statics

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