Separation of Comprehensive Geometrical Errors of a 3-DOF Parallel Manipulator Based on Jacobian Matrix and Its Sensitivity Analysis with Monte-Carlo Method  

作　　者：SUN Tao SONG Yimin LI Yonggang2 XU Liang 

机构地区：[1]School ofMechanicalEngineering, Tianjin University, Tianjin 300072, China [2]School ofMechanicalEngineering, Tianjin University of Technology andEducation, Tianjin 300022, China

出　　处：《Chinese Journal of Mechanical Engineering》2011年第3期406-413,共8页中国机械工程学报（英文版）

基　　金：supported by Tianjin Research Program of Application Foundation and Advanced Technology of China (Grant No.11JCZDJC22700);National Natural Science Foundation of China (GrantNo. 51075295,Grant No. 50675151);National High-tech Research and Development Program of China (863 Program,Grant No.2007AA042001);PhD Programs Foundation of Ministry of Education of China (Grant No. 20060056018)

摘　　要：Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.

关 键 词：parallel kinematic machines （PKMs） limited-degree-of-freedom （limited-DOF） error separation accuracy analysis Jacobian matrix compensable error non-compensable error sensitivity analysis 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置] TP301.6[自动化与计算机技术—控制科学与工程]