非线性方程组求解的等概率混沌序列与滑块机构函数综合

Synthesis of equal pro-bability chaos sequence and function of slider mechanism solved with nonlinear equation set

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。研究了Logistic映射的概率特性,通过变换转化为等概率混沌序列,首次提出了等概率混沌序列的非线性方程组求解新方法,并对曲柄-滑块机构进行了研究,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 problems in natural science and engineering could all be transformed into problems of solving the nonlinear equation set. The Newton iteration method is an important one dimension and multi-dimension iteration technique, its iteration itself is very sensitive to the initial point. This paper studied the probability property of Logistic mapping, and was translated into equal probability chaos sequence by means of transformation and the new method of solving the nonlinear equation set of the equal probability chaos sequence was put forward for the first time. A research has been carried out on the crank-slider mechanism and a calculation example was presented. This method is simple and practical; it offered multiple selection schemes for the design of practical mechanism and provided brand-new method for the design of mechanism.