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Gravity-Based Kinetostatic Modeling of Parallel Manipulators Using screw theory

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Chinese Journal of Mechanical Engineering 2023年第6期36卷 73-86页

作者： Chao Yang Fengli Huang Wei Ye Qiaohong Chen College of Mechanical and Electrical Engineering Jiaxing UniversityJiaxing 314001China National and Local Joint Engineering Research Center of Reliability Analysis and Testing for Mechanical and Electrical Products Zhejiang Sci-Tech UniversityHangzhou 310018China School of Computer Science and Technology Zhejiang Sci-Tech UniversityHangzhou 310018China

The pose accuracy of parallel manipulators(PMs)is a key index to measure their performance.Establishing the grav-ity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement.In this paper,a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs.First,the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches.Sec-ond,the gravity model of the mechanism is established based on the screw theory and the principle of virtual work.Finally,the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained,and the influences of the external load,platform gravity,and rod gravity on the stiffness of the mechanism are decoupled.The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method.This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity.

关键词： Parallel manipulator Kinetostatic model Gravity screw theory

Type Synthesis of Self-Alignment Parallel Ankle Rehabilitation Robot with Suitable Passive Degrees of Freedom

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Chinese Journal of Mechanical Engineering 2024年第1期37卷 160-175页

作者： Ya Liu Wenjuan Lu Dabao Fan Weijian Tan Bo Hu Daxing Zeng School of Mechanical Engineering Yanshan UniversityQinhuangdao 066004China School of Mechanical Engineering Dongguan University of TechnologyDongguan 523808China Dongguan Engineering Technology Research Center for Parallel Robot Dongguan 523808China The DGUT Innovation Center of Robotics and Intelligent Equipment Dongguan 523808China

The current parallel ankle rehabilitation robot(ARR)suffers from the problem of difficult real-time alignment of the human-robot joint center of rotation,which may lead to secondary injuries to the patient.This study investigates type synthesis of a parallel self-alignment ankle rehabilitation robot(PSAARR)based on the kinematic characteristics of ankle joint rotation center drift from the perspective of introducing"suitable passive degrees of freedom(DOF)"with a suitable number and form.First,the self-alignment principle of parallel ARR was proposed by deriving conditions for transforming a human-robot closed chain(HRCC)formed by an ARR and human body into a kinematic suitable constrained system and introducing conditions of"decoupled"and"less limb".Second,the relationship between the self-alignment principle and actuation wrenches(twists)of PSAARR was analyzed with the velocity Jacobian matrix as a"bridge".Subsequently,the type synthesis conditions of PSAARR were proposed.Third,a PSAARR synthesis method was proposed based on the screw theory and type of PSAARR synthesis conducted.Finally,an HRCC kinematic model was established to verify the self-alignment capability of the PSAARR.In this study,93 types of PSAARR limb structures were synthesized and the self-alignment capability of a human-robot joint axis was verified through kinematic analysis,which provides a theoretical basis for the design of such an ARR.

关键词： Ankle rehabilitation robot Self-alignment Parallel mechanism Type synthesis screw theory

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 process.However,the traditional representations cannot achieve this because of the absence of coordinate invariance.Therefore,the coordinate invariant method is an important research issue.First,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is explained.Based 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 deduced.Further,Newton-Euler＇s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is obtained.The formulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived.An index of dynamical coupling based on dynamics Hessian matrix is presented.In the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae.The 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

Generalized Kinematics Analysis of Hybrid Mechanisms Based on screw theory and Lie Groups Lie Algebras

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Chinese Journal of Mechanical Engineering 2021年第5期34卷 171-184页

作者： Peng Sun Yanbiao Li Ke Chen Wentao Zhu Qi Zhong Bo Chen College of Mechanical Engineering Zhejiang University of TechnologyHangzhou 310023China State Key Laboratory of Fluid Power and Mechatronic Systems Zhejiang University Hangzhou 310027China

Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms,and the generalized analysis method and concise kinematics transfer matrix are obtained.In this study,first,according to the kinematics analysis of serial mechanisms,the basic principles of Lie groups and Lie algebras are briefly explained in dealing with the spatial switching and differential operations of screw vectors.Then,based on the standard ideas of Lie operations,the method for kinematics analysis of parallel mechanisms is derived,and Jacobian matrix and Hessian matrix are formulated recursively and in a closed form.Then,according to the mapping relationship between the parallel joints and corresponding equivalent series joints,a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are examined.A case study is performed to verify the calculated matrices wherein a humanoid hybrid robotic arm with a parallel-series-parallel configuration is considered as an example.The results of a simulation experiment indicate that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practically feasible.

关键词： Hybrid mechanism screw theory Lie groups Lie algebras Kinematics analysis Humanoid robotic arm

Actuation Spaces Synthesis of Lower-Mobility Parallel Mechanisms Based on screw theory

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Chinese Journal of Mechanical Engineering 2021年第1期34卷 280-291页

作者： Shihua Li Yanxia Shan Jingjun Yu Yaxiong Ke Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic Systems Yanshan UniversityQinhuangdao 066004China School of Mechanical Engineering Yanshan UniversityQinhuangdao 066004China School of Liren Yanshan UniversityQinhuangdao 066004China Robotics Institute Beihang UniversityBeijing 100191China

The lower-mobility parallel mechanism has been widely used in the engineering field due to its numerous excellent characteristics.However,little work has been devoted to the actuator selection and placement that best satisfy the system's functional requirements during concept design.In this study,a unified approach for synthesizing the actuation spaces of both rigid and flexure parallel mechanisms has been presented,and all possible combinations of inputs could be obtained,laying a theoretical foundation for the subsequent optimization of inputs.According to the linear independence of actuation space and constraint space of the lower-mobility parallel mechanism,a general expression of actuation spaces in the format of screw systems is deduced,a unified synthesis process for the lower-mobility parallel mechanism is derived,and the efficiency of the method is validated with two selective examples based on screw theory.This study presents a theoretical framework for the input selection problems of parallel mechanisms,aiming to help designers select and place actuators in a correct and even optimal way after the configuration design.

关键词： Lower-mobility parallel mechanism screw theory Actuation space Actuator placement Input selection

Mobility Analysis of the Deployable Structure of SLE Based on screw theory

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Chinese Journal of Mechanical Engineering 2013年第4期26卷 793-800页

作者： SUN Yuantao WANG Sanmin LI Jianfeng ZHI Changjian School of Mechanical Engineering Northwestern Polytechnical University

Scissor-like element has a number of applications in deployable structures such as planar deployable structure (PDS) and ring deployable structure(RDS). However, the mobility analysis of the multi-loop deployable structures is made more difficulty by the traditional mobility formula, because the deployable structure is a very complex structure with multi-loop. Therefore, On the basis of screw theory, the calculation method of mobility of deployable structures of SLE is thoroughly discussed. In order to investigate the mobility, decomposing and composing structures(DCS) are developed, and the basic units are able to be obtained. On the basis of the deployable structures’ geometrical characteristics, there exists a closed-loop quadrilateral structure and some non-closed-loop quadrilateral structures in PDS. Also, a six legs parallel structure is present in RDS. The basic units’ mobility can be solved by both the methods of screw theory and topology constraint graphs. Then, composing the related basic units, the formula of planar deployable structures’ mobility can be built and solves the mobility of ring deployable structure. The analysis method solves the mobility analysis of the multi-loop deployable structures which is difficulty by the traditional method, and plays an important role in further research about the mobility of other complex deployable structures.

关键词： Scissor-like element(SLE) screw theory decomposing and composing structures (DCS) mobility

Kinematics and Dynamics of Deployable Structures with Scissor-Like-Elements Based on screw theory

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Chinese Journal of Mechanical Engineering 2014年第4期27卷 655-662页

作者： SUN Yuantao WANG Sanmin MILLS James K ZHI Changjian School of Mechanical Engineering Northwestern Polytechnical University Department of Mechanical and Industrial Engineering University of Toronto5 King's College Rd.Toronto OntarioCanada

Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.

关键词： scissor-like-element screw theory kinematics dynamics the principle of virtual work

ANALYSIS OF SPATIAL COMPLIANCE BEHAVIOR OF COILED SPRINGS VIA screw theory

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Chinese Journal of Mechanical Engineering 2002年第4期15卷 293-297,318页

作者： Ding XilunRobotics Research Institute, Beijing University of Aeronautics and Astronautics,Beijing 100083, ChinaSelig J M South Bank University, UK Robotics Research Institute Beijing University of Aeronautics and Astronautics 北京 100083 South Bank University 英国

A new method is presented to describe and analyze the spatial compliance ofcoiled springs using screw theory. After an abbreviated description for the deformation of a beamelement using screw theory, the spatial compliance density for a beam element is derived based onthe fundamental material theory and reasonable assumptions, and the spatial compliance of the beamwith finite length is obtained by integral. The spatial compliance of coiled springs is furtheranalyzed using the spatial compliance density of the beam element. By calculating theeigencompliance and Ball's principle screws for the whole compliance of system, the complianceproperties varying with the basic physical parameters of the system are illustrated in detail. Thebasic ideas can be used for the design and application of the coiled springs and the other compliantmechanisms with spatial compliant beam element.

关键词： eigencompliance coiled springs screw theory mechanisms

INVESTIGATION ON KANE DYNAMIC EQUATIONSBASED ON screw theory FOR OPEN-CHAIN MANIPULATORS

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Applied Mathematics and Mechanics(English Edition) 2005年第5期26卷 627-635页

作者：刘武发龚振邦汪勤悫 College of Mechanical Engineering Zhengzhou UniversityZhengzhou 450002 P.R.China School of Electromechanical Engineering and Automation Shanghai UniversityShanghai 200072 P.R.China

First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and generalized inertial force according to screw theory.After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.

关键词： screw theory partial velocity twist open-chain manipulator Kane dynamic equation