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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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Configuration Design and Size Optimization of a High-Precision Novel parallel Pointing Mechanism Based on Interference Separation

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Chinese Journal of Mechanical Engineering 2024年第5期37卷 365-386页

作者： Sen Wang Shihua Li Xueyan Han Jiahao Wei Xueyuan Gao Hongyu Xu Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic Systems Yanshan UniversityQinhuangdao 066004China School of Mechanical Engineering Yanshan UniversityQinhuangdao 066004China

Pointing mechanism is widely used in aerospace field,and its pointing accuracy and stability have high *** pointing mechanism will be affected by external interference when it *** order to eliminate the impact of interference forces on the output accuracy of the mechanism,firstly,this paper proposes a design method for highprecision pointing mechanisms based on interference separation,aiming at the high-precision pointing requirements of pointing *** on the screw theory,a synthesis method for inner compensation mechanisms has been *** a new type of double-layer parallel mechanism has been designed to compensate for interference ***,the kinematics and dynamics of the mechanism are carried *** evaluation index for compensating external interference forces is *** interference compensation analysis is conducted for the pointing *** correctness of the proposed interference force compensation coefficient is ***,in order to find the optimal solution for the workspace and interference force compensation coefficient of the pointing mechanism,multi-objective optimization design of the structural parameters of the mechanism was carried out based on the particle swarm optimization *** provides a theoretical basis for the prototype design of the subsequent double-layer parallel *** double-layer parallel mechanism combines the advantages of large load-bearing capacity,large workspace,and high output *** can be better applied in the aerospace field where high-precision pointing and force interference compensation are integrated.

关键词： Pointing mechanism Interference separation Double-layer parallel mechanism Force compensation coefficient Multi-objective optimization

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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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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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An Untethered Soft-Swallowing robot with Enhanced Heat Resistance,Damage Tolerance,and Impact Mitigation

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Chinese Journal of Mechanical Engineering 2024年第6期37卷 456-465页

作者： Haili Li Xingzhi Li Pan Zhou Jiantao Yao Zhejiang Provincial Key Laboratory of Part Rolling Technology School of Mechanical Engineering and MechanicsNingbo UniversityNingbo 315211China Parallel Robot and Mechatronic System Laboratory of Hebei Province Yanshan UniversityQinhuangdao 066004China

Soft robotics focuses on addressing the locomotion problem in unstructured environments and the manipulation problem of non-cooperative objects,which inevitably leads to soft robots encountering multiple uncertainties and ***,improving the robustness of soft robots in hostile environmental conditions has always been a *** methods usually improve this robustness through damage isolation,material elasticity,and self-healing *** contrast to existing methods,this paper proposes a method to improve the robustness of an untethered soft-swallowing robot based on the physical properties of fluids,such as the high specific heat capacity of water,the viscosity of soft glue,and the shear thickening of non-Newtonian *** on this method,we developed a soft-swallowing robot with enhanced heat resistance,damage tolerance,and impact mitigation capability by only replacing its fluid working *** show that the developed soft-swallowing robot can withstand high temperatures above 600°C,maintain high performance even after enduring hundreds of damages,and protect grasped object from more than 90%of external *** principle extends beyond the three fluids used in this *** fluids,such as magnetic fluid,can increase adhesion to metal materials,whereas oily fluids can reduce frictional resistance between soft ***,other solid materials with elasticity and compliance can serve as alternative working mediums for the soft-swallowing *** work contributes an effective method for fluid-dependent soft robotic systems to resist the damage from uncertain factors in harsh environments.

关键词： Soft gripper Untethered design Heat resistance Damage tolerance Impact mitigation

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A 0.5-meter-scale,high-load,soft-enclosed gripper capable of grasping the human body

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Science China(Technological Sciences) 2023年第2期66卷 501-511页

作者： LI HaiLi ZHANG Shuai ZHANG XuanHao ZHAO WuMian YAO JianTao Zhejiang Provincial Key Laboratory of Part Rolling Technology Faculty of Mechanical Engineering&MechanicsNingbo UniversityNingbo 315211China Parallel Robot and Mechatronic System Laboratory of Hebei Province Yanshan UniversityQinhuangdao 066004China

Developing large,soft grippers with high omnidirectional load(above 40 kg)has always been *** address this challenge by developing a powerful soft gripper that can grasp the human body based on a soft-enclosed grasping structure and a soft-rigid coupling *** envelope size of the proposed soft gripper is 611.6 mm×559 mm×490.7 mm,the maximum grasping size is 417 mm,and the payload on the human body is more than 90 kg,which has exceeded most existing soft ***,the grasping force prediction of the gripper is achieved through theoretical *** primary contribution of this work is to overcome the size and payload limits of current soft grippers and implement a human-grasping experiment based on the soft-grasping method.

关键词： soft gripper large size high-load soft-enclosed grasping

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