同伦算法的常微分方程数值解法及在机构学中的应用

Numerical Solution of General Differential Equations for Homology Continuation Algorithm and Its Application 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,本文结合MATLAB6.1高级程序设计语言的常微分方程数值解法的通用函数,提出了同伦算法的常微分方法数值解法的原理与实现方法。运用该算法编写了MATLAB程序,对平面四杆机构的函数发生器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 equation. 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 general differential equations for homology continuation algorithm is put forward and programming is compiled with Matlab6.1 programming language by use general numerical solution function of general differential equations. The problem of function generation for planar four - link mechanism is solved by this method, and thus all solutions for this problem with maximum precision positions are obtained. This provide a simple realization method for homology continuation method.