类Exechon并联模块弹性静力学建模与分析
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摘要
针对Exechon并联模块动平台摆角范围较小的问题,提出了一种拓扑构型为2RPU&1RPS的类Exechon并联模块.在前期完成的概念设计基础上,对类Exechon并联模块进行了自由度计算及运动学逆解分析.采用子结构综合法,建立了计及关节弹性变形和支链体柔性的类Exechon并联模块弹性静力学模型.依托所建模型,计算了该类并联模块极限位姿下动平台的弹性位移和关节约束反力(力矩),并进一步给出了两者在工作空间内的映射.研究表明,模块自重对类Exechon并联模块动平台的弹性位移和关节约束反力(力矩)具有重要影响,其静力学特性在工作空间内随位姿变化明显,且在沿z向的工作截面上呈对称性映射.
A novel Exe-variant PKM with a topological arrangement of 2RPU&1RPS was proposed by the authors to achieve a better platform rotational ability over the Exechon parallel kinematic machine(PKM).After introducing the concept design,the mobility analysis and inverse kinematics of the proposed Exe-variant PKM are conducted.With the substructure synthesis techniques,a kinetostatic model that includes joint deflections and limb flexibilites is developed to investigate the kinetostatic characteristics of the Exevariant PKM.The platform's elastic displacements and joint reaction forces/moments of the Exe-variant PKM at the extreme position are analyzed.Furthermore,their mappings over any work plane are evaluated throughout the entire workspace.The results reveal that the gravity-caused elastic displacements of the platform and joint force/moment reactions are noticeable.The mappings of platform's elastic displacements and joint forces/moments reactions in the entire workspace are position-dependant and demonstrate a symmetry over any given work plane.
A novel Exe-variant PKM with a topological arrangement of 2RPU&1RPS was proposed by the authors to achieve a better platform rotational ability over the Exechon parallel kinematic machine(PKM).After introducing the concept design,the mobility analysis and inverse kinematics of the proposed Exe-variant PKM are conducted.With the substructure synthesis techniques,a kinetostatic model that includes joint deflections and limb flexibilites is developed to investigate the kinetostatic characteristics of the Exevariant PKM.The platform's elastic displacements and joint reaction forces/moments of the Exe-variant PKM at the extreme position are analyzed.Furthermore,their mappings over any work plane are evaluated throughout the entire workspace.The results reveal that the gravity-caused elastic displacements of the platform and joint force/moment reactions are noticeable.The mappings of platform's elastic displacements and joint forces/moments reactions in the entire workspace are position-dependant and demonstrate a symmetry over any given work plane.
引文
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[2]XIE F,LIU X J,LI T.Type synthesis and typical application of 1T2R-type parallel robotic mechanisms[J].Mathematical Problems in Engineering,2013(9):497-504.
[3]ZHANG D,GOSSELIN C M.Kinetostatic analysis and design optimization of the tricept machine tool family[J].Journal of Manufacturing Science and Engineering,2002,124(3):725-733.
[4]HENNES N.Ecospeed-an innovative machinery concept for high performance 5-axis machining of large structural components in aircraft engineering[C]//3rd Chemnitz Parallel Kinematic Seminar.Zwickau:Verlag Wissenschaftliche Scripten,2002:763-774.
[5]LI Y G,LIU H T,ZHAO X M,et al.Design of a3-DOF PKM module for large structural component machining[J].Mechanism and Machine Theory,2010,45(6):941-954.
[6]NEUMANN K E.Exechon concept[J].Parallel Kinematic Machines in Research and Practice,2006,33:787-802.
[7]李彬,黄田,刘海涛,等.Exechon混联机器人的三自由度并联机构模块位置分析[J].中国机械工程,2010(23):2785-2789.LI Bin,HUANG Tian,LIU Haitao,et al.Position analysis of a 3-DOF PKM module for a 5-DOF hybrid robot Exechon[J].Chinese Journal of Mechanical Engineering,2010(23):2785-2789.
[8]ZHANG J,ZHAO Y Q,JIN Y.Kinetostatic-modelbased stiffness analysis of Exechon PKM[J].Robotics and Computer-Integrated Manufacturing,2015,37(C):208-220
[9]ZHANG J,ZHAO Y Q,JIN Y.Elastodynamic Modeling and analysis for an Exechon parallel kinematic machine[J].Journal of Manufacturing Science and Engineering,2016,138(3):031011.
[10]BI Z M,KANG B.An inverse dynamic model of over-constrained parallel kinematic machine based on Newton-Euler formulation[J].Journal of Dynamic Systems,Measurement,and Control,2014,136(4):041001.
[11]BI Z M,JIN Y.Kinematic modeling of Exechon parallel kinematic machine[J].Robotics and ComputerIntegrated Manufacturing,2011,27(1):186-193.
[12]TANG T F,ZHAO Y Q,ZHANG J,et al.Conceptual design and workspace analysis of an Exechon-inspired parallel kinematic machine[C]//Advances in Reconfigurable Mechanisms and Robots II.Switzerland:Springer International Publishing,2016:445-453.
[13]付红栓,赵恒华,杨辉.3-TPT型并联机床静力学及刚度研究[J].组合机床与自动化加工技术,2013(1):42-44.FU Hongshuan,ZHAO Henghua,YANG Hui.Study on the statics and stiffness of 3-TPT parallel machine tool[J].Modular Machine Tool&Automatic Manufacturing Technique,2013(1):42-44.
[14]PIRAS G,CLEGHORN W L,MILLS J K.Dynamic finite-element analysis of a planar high-speed,highprecision parallel manipulator with flexible links[J].Mechanism&Machine Theory,2005,40(7):849-862.
[15]KLIMCHIK A,CHABLAT D,PASHKEVICH A.Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings[J].Mechanism and Machine Theory,2014,79:1-28.
[16]落海伟,张俊,王辉,等.3-RPS并联机构静刚度建模方法[J].天津大学学报(自然科学与工程技术版),2015,48(09):797-803.LUO Haiwei,ZHANG Jun,WANG Hui,et al.Static stiffness modeling method of 3-RPS PKM[J].Journal of Tianjin University(Science and Technology),2015,48(09):797-803.
[17]黄真.高等空间机构学[M].北京:高等教育出版社,2006.
[18]MAJOU F,GOSSELIN C,WENGER P,et al.Parametric stiffness analysis of the Orthoglide[J].Mechanism and Machine Theory,2007,42(3):296-311.