混沌映射牛顿迭代法与平面并联机构正解研究

The Research of Newton Iterative Method Based on Chaos Mapping and its Application to Forward Solutions of the 3-RPR Planar Parallel Mechanism

自然科学与工程中的许多问题都可以转化为非线性方程组的求解问题,牛顿迭代法是重要的一维及多维的迭代技术,其迭代本身对初始点非常敏感。运用混沌映射xn+1=cos(2/xn)产生初始点,首次提出了基于混沌映射的牛顿迭代法求解非线性方程组的新方法。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,为机构学设计提供了全新的方法。

Many questions in natural science and engineering canbe transformed into nonlinear equations to be salved, Newton iterative method is an important technique to one-and multi-dimensional variables and iterative process exhibits sensitive dependence on initial guess point. For the first time, a new method to find all solutions based on utilizing chaos mapping xn x＋ 1 = cos （ 2/xn） to obtain locate initial points for finding all solutions of the nonlinear questions is proposed. The problem of the 3-RPR planar parallel mechanism was solved by this method. This provides a simple realization method for mechanism design.