机构综合的新型同伦算法研究

The Research of New Homology Continuation Algorithm to Mechanism Synthesis

机构学问题的数学模型常可化为多元非线性方程组,一般求解多元非线性方程组需要初始值,而初始值的选择是相当困难的,同伦方法不需初始值就能求出全部解,为求解决这一问题提供了可行的方法,但需要编写专用的程序.通过构造新型同伦函数并结合Maple高级程序设计语言的通用工具箱,提出了同伦算法的原理与实现方法.运用该算法编写了MAPLE程序对3-RPR平面并联机构综合问题进行了研究,求出了全部解,为实际机构的设计提供了多种选择方案,为同伦方法提供了简便的实现方法.

The mathematical model of mechanism problems can be translated a multi - variables non-linear equations, and, it is a difficult problem to give the initial value for the no-linear equations. The homology continuation algorithm has resolved this difficult problem without given initial value and can find all solution, but a special programming is compiled at the same time. A numerical solution of new general homology function and homology continuation algorithm was put forward and programming with Maple10.0 toolbox. The problem of 3-RPR planar parallel mechanism was solved by this method, and all solutions were obtained. This provides a simple realization method for homology continuation method.