一种零耦合度三平移并联机构的设计及运动学

摘要/Abstract

摘要： 根据基于方位特征方程的并联机构拓扑设计理论和方法，设计出一种零耦合度且运动解耦的非对称三平移输出的并联机构(RPa‖3R)2R+RPa，分析了该并联机构的方位特征、自由度、耦合度κ等主要拓扑特性。由于该机构耦合度κ=0，因此直接导出其解析式位置正解。通过位置反解，分析计算了机构的工作空间及奇异性特性。由Jacobian矩阵导出了机构动平台质心的速度与加速度计算公式，并给出了其仿真曲线。

关键词: 并联机构, 运动学, 耦合度, 工作空间, 奇异性

Abstract: According to the topology design theory based on position and orientation characteristic（POC）equations, a new asymmetric 3T PM (RPa‖3R)2R+RPa with zero coupling degree and decoupled motions was designed. The main topological characteristics such as POC, degree of freedom, and coupling degree were calculated. Workspace and singularity of the PM were analyzed based on inverse position solutions of the PM. Velocity and acceleration of the center of mass of the PM were obtained by Jacobian matrix, and simulation curves of velocity and acceleration was put forword.

Key words: parallel mechanism(PM), kinematics, coupling degree, workspace, singularity

中图分类号:

TH12

沈惠平;吴成琦;许可;赵迎春;杨廷力. 一种零耦合度三平移并联机构的设计及运动学[J]. 中国机械工程.

SHEN Huiping;WU Chengqi;XU Ke;ZHAO Yingchun;YANG Tingli. Design and Kinematics of 3-translation Parallel Mechanisms with Zero Coupling Degree[J]. China Mechanical Engineering.

参考文献

[1]刘辛军, 汪劲松, 李剑锋,等. 一种新型空间3自由度并联机构的正反解及工作空间分析[J]. 机械工程学报, 2001, 37(10):36-39.
LIU Xinjun, WANG Jinsong, LI Jianfeng, et al. Positive andNegative Solutions and Workspace Analysis of a Novel 3-DOF Spatial Parallel Mechanism[J]. Journal of Mechanical Engineering, 2001, 37(10): 36-39.
[2]VISCHER P, CLAVEL R . Kinematic Calibration of the Parallel Delta Robot[J]. Robotica, 1998, 16(2):207-218.
[3]STOCK M, MILLER K. Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot[J]. Journal of Mechanical Design, 2003, 125(2):292-301.
[4]BOURI M, CLAVEL R . The Linear Delta: Developments and Applications[C]//2010 41st International Symposium on and 2010 6th German Conference on Robotics. Munich, 2010: 978-3-8007-3273-9.
[5]KELAIAIA R, COMPANY O, ZAATRI A. Multiobjective Optimization of a Linear Delta Parallel Robot[J]. Mechanism & Machine Theory, 2012, 50(2):159-178.
[6]TSAI L W, WALSH G C, STAMPER R E. Kinematics of a Novel Three DOF Translational Platform[J]. 1996, 4(4): 3446-3451.
[7]李仕华，黄真. 一种特殊3-UPU并联平台机构瞬时运动特性[J].中国机械工程，2005，16（18）：1641-1646.
LI Shihua, HUANG Zhen. Kinematic Characteristics of a Special 3-UPU Parallel Platform Manipulator[J]. China Mechanical Engineering, 2005，16（18）：1641-1646.
[8]LI S, HUANG Z, ZUO R. Kinematics of a Special 3-DOF 3-UPU Parallel Manipulator[C]//ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Montreal, 2002: 1035-1040.
[9]赵铁石, 黄真. 一种三维移动并联平台机构的运动学分析[J]. 中国机械工程, 2001, 12(6):612-616.
ZHAO Tieshi, HUANG Zhen. Kinematics Analysis of a Three-dimensional Mobile Parallel Platform Mechanism[J]. China Mechanical Engineering, 2001, 12 (6): 612-616.
[10]尹小琴, 马履中. 三平移并联机构3-RRC的工作空间分析[J]. 中国机械工程, 2003, 14(18):1531-1533.
YIN Xiaoqin, MA Lüzhong. Workspace Analysis of 3-RRC Parallel Mechanism with Three Translations[J]. China Mechanical Engineering, 2003, 14 (18): 1531-1533.
[11]ZHAO Y. Dimensional Synthesis of a Three Translational Degrees of Freedom Parallel Robot while Considering Kinematic Anisotropic Property[J]. Robotics and Computer-integrated Manufacturing, 2013, 29(1):169-179.
[12]ZENG Qiang, EHMANN K, CAO Jian. Tri-pyramid Robot: Design and Kinematic Analysis of a 3-DOF Translational Parallel Manipulator[J]. Robotics & Computer-integrated Manufacturing, 2014, 30(6):648-657.
[13] ZENG Qiang, EHMANN K, CAO Jian. Tri-pyramid Robot: Stiffness Modeling of a 3-DOF Translational Parallel Manipulator[J]. Robotica, 2016, 34(2):383-402.
[14]LEE S, ZENG Q, EHMANN K F. Error Modeling for Sensitivity Analysis and Calibration of the Tri-pyramid Parallel Robot[J]. International Journal of Advanced Manufacturing Technology, 2017(5):1-14.
[15]BHUTANI G, DWARAKANATH T A. Novel Design Solution to High Precision 3 Axes Translational Parallel Mechanism[J]. Mechanism & Machine Theory, 2014, 75(5): 118-130.
[16]LI W, GAO F, ZHANG J. A Three-DOF Translational Manipulator with Decoupled Geometry[M]. Cambridge, UK: Cambridge University Press, 2005.
[17]沈惠平, 熊坤, 孟庆梅,等. 并联机构运动解耦设计方法与应用研究[J]. 农业机械学报, 2016, 47(6):348-356.
SHEN Huiping, XIONG Kun, MENG Qingmei, et al. Design Method and Application of Motion Decoupling for Parallel Mechanisms[J]. Journal of Agricultural Machinery, 2016, 47 (6): 348-356.
[18]杨廷力,刘安心，罗玉峰,等. 机器人机构拓扑结构设计[M]. 北京：科学出版社, 2012.
YANG Tingli，LIU Anxin, LUO Yufeng, et al. Topological Structure Design of Robot Mechanisms[M]. Beijing: Science Press, 2012.
[19]黄真, 孔令富, 方跃法. 并联机器人机构学理论及控制[M]. 北京：机械工业出版社, 1997.
HUANG Zhen, KONG Lingfu, FANG Yuefa. Theory and Control of Parallel Robot Mechanism[M]. Beijing: Machinery Industry Press, 1997.