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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。
The problem of solving the nonlinear equation which is produced in the rigid body guidance four-bar mechanism synthesis problem is studied. Based on the concept of pan-gray number and its operation rules, the transformation of pan-gray number and interval number is introduced, and the interval is analyzed by the extensibility of pan-gray number. According to the properties of the pan-graying function (if there is a solution in the interval, 0∈F (X)), it is determined whether there is solution or not, then the solution interval is refined and the solution interval is refined, so as to solve all the solutions of the nonlinear equation . Pan-gray number not only has the function of interval analysis, but also can solve the problem of interval analysis can not be solved. Based on the properties of pan-gray numbers, a new solution to nonlinear equations is proposed.