混沌最小二乘法及其在机构近似综合中的应用  

Chaos Least Square Algorithm for Finding Solution of Non-linear Equations and Its Application to Mechanism Approximate Synthesis

作　　者：文会军[1] 幸理[2] 

机构地区：[1]湖南文理学院,湖南常德415000 [2]武汉工业学院工商学院,湖北武汉430065

出　　处：《机械设计与研究》2007年第2期40-42,共3页Machine Design And Research

基　　金：湖南省"十一五"重点建设学科(湘教通[2006]180号)

摘　　要：结合MATLAB6.5.1高级程序设计语言采用简单的最小二乘法迭代,并将非线性方程视为非线性的动力学系统,利用使系统产生混沌的Julia集的点求解方程的全实数解,而Julia集的点集用二周期逆像函数求得,再在其邻域内求解即可。运用该算法编写了MATLAB程序,对平面四杆机构近似综合问题进行了研究,从而找到了实现最大精确点时该问题的全部的解,为实际机构的设计提供了多种选择方案,为机构学设计提供了全新的方法。The mathematical models of mechanism problems can be converted into mulivariable nonlinear equations. To select an initial value for the nonlinear equations is really a difficult problem, The homology continuation algorithm has resolved this difficult problem without initial value and can find all the solutions. However it needs to write special program and the calculating workload is quite large. In order to solve the problem, the iteration of least square algorithm is used and the nonlinear equation is considered as a nonlinear dynamic system in which Julia set leads to Chaos. The points of Julia set are found by constructing repulsion two-cycle point function and using the inverse-image iterative methods. Then in the adjacent region of Julia point all the solutions of nonlinear equations can be achieved. The problem of approximate synthesis for planar four-link mechanism is solved by this method, and thus all solutions for this problem with maximum precision positions are obtained. Therefore, a pretty new and method is provided for mechanics design.

关 键 词：机构尺度综合 混沌算法 最小二乘法 MATLAB程序设计语言 

分 类 号：TH112[机械工程—机械设计及理论]