3-RPS并联平台机构的位置正解与奇异构形分析的数值-符号解  

Positional forward solution and numeric-symbolic solution of singular configuration analysis for 3-RPS parallel platform mechanism

作　　者：王进戈[1] 范丽华[1] 徐礼钜[2] 

机构地区：[1]西华大学机械工程与自动化学院,四川成都610039 [2]四川大学,四川成都610065

出　　处：《机械设计》2005年第5期15-19,共5页Journal of Machine Design

基　　金：国家自然科学基金资助项目(50375104);四川省应用基础研究资助项目(0322129);四川省重点学科资助项目(SZD425231)

摘　　要：基于Groebner基法和计算机符号处理技术,对3-RSP并联平台机构的位置正解问题进行了符号求解。该法通过对变量排序、建立多项式对的集合、求SP多项式和约简等运算,将一组非线性方程组化简为等价的三角化方程组,得到了封闭形式的解析解。推导了雅可比矩阵和数字-符号表示的奇异位形判别的解析表达式,对该并联机构的可操作性和奇异性进行了分析。同时给出了具体数值实例。The symbolic solution was carried out upon the positional forward solution issues of 3-RPS parallel platform mechanism based on Groebner base method and computer symbolic manipulating technique. By means of the calculation of ordering on variables, establishing set of polynomial pairs, finding SP polynomial and its reduction, this method let a set of nonlinear equation set be simplified into an equivalent triangularization equation set, thus obtained the close formed analytical solution. The Jacobin matrix and the analytical expressions for the discrimination of singular configuration signified by numerals-symbols were derived, and an analysis was carried out on the operability and singularity of this parallel mechanism. At the same time, concrete numerical living examples were presented.

关 键 词：GROEBNER基 并联机构 位置分析 可操作性 奇异位形 

分 类 号：TH112[机械工程—机械设计及理论]