3-RPR平面并联机构正解的混沌方法  

Forward Solutions of the 3-RPR Planar Parallel Mechanism with Chaos Solution Method

作　　者：罗佑新[1] 

机构地区：[1]湖南文理学院机械工程系,常德415003

出　　处：《机械科学与技术》2004年第8期916-918,共3页Mechanical Science and Technology for Aerospace Engineering

基　　金：教育部重点科研项目 ( 0 2 10 8);湖南省教育厅青年项目( 0 2B0 3 6)资助

摘　　要：采用简单的牛顿迭代法迭代 ,并将非线性方程视为非线性的动力学系统 ,利用使得系统产生混沌的Julia集的点求解方程的全实数解 ,而Julia集的点在Jocobi矩阵行列式的值 (记为 |J|)为零的解集的邻域内。因给设定矩阵的行列式中一些变量为已知 ,仅只有一个变量未知 ,把 |J|=0转化为一元非线性方程 ,进而求出其全部解。再确定未给定变量的搜索范围 ,运用粗、精迭代在其邻域内求解即可。对 3 RPR平面并联机构正解问题进行了研究 ,给出了算例。该方法简单、实用 ,为实际机构的设计提供了多种选择方案 。A numerical method was found, taking the iteration of Newton method as a nonlinear dynamic system in which Julia sets leads to Chaos. Those points of Julia set was in the neighborhood of those points which belong to the determinant of Jacobian matrix equal to zero. Jacobian matrix equation was changed to a non-linear equation with one variable by giving the other variable′s value and the variable scope of non-given variable. Then all solutions were found by iteration method. The problem of the 3-RPR planar parallel mechanism was solved by this method. This provides a simple realization method for mechanism design.

关 键 词：并联机构 6R-Ⅲ级组 混沌算法 牛顿迭代法 JULIA集 

分 类 号：TH112[机械工程—机械设计及理论] TH133