泛灰数学在平面刚体导引连杆机构综合中的应用

Application of Universal Grey Number to Synthesis of Plane Rigid Guidance

对刚体导引四杆机构综合问题中产生的非线性方程的求解问题进行了研究。在概述泛灰数的概念及其运算规则的基础上 ,介绍了泛灰数与区间数的转化 ,利用泛灰数的可扩展性对区间进行分析。根据对求解区间的泛灰函数性质 (如果在区间上有解 ,则 0∈F(X) )进行判定是否有解 ,剔除无解区间 ,细化有解区间 ,从而求解非线性方程的全部解。泛灰数不仅具有区间分析的功能 ,而且能解决区间分析所不能解决的问题。基于泛灰数的性质而提出了求解非线性方程组的一种新求解方法。

This paper focuses on the method of solving the non-linear equation arising form the synthesis of plane rigid guidance. Based on the concept of universal Grey number and the rules of four algebraic operation of universal Grey number,it is introduced that universal Grey number is changed into interval Grey number ,then gives interval analysis with extensible characteristic of universal Grey number. According to the characteristic of universal Grey function,namely, if there has solution in the universal Grey interval, it must be 0∈F(X),confirming whether it has solution and removing non-solution interval and decomposing interval that has some solutions, finally finding all solutions of non-linear equation. Universal Grey function can deal with some problems that Grey number or interval analysis can't. Based on the characteristic of universal Grey function,a new method has been proposed. At last an example is given.