基于Groebner平面两自由度七杆机构位置分析的符号解

Symbolic Solution to the Displacement Analysis of Planar Two-DOF Seven-Bar Linkages Mechanism Based on Groebner Method

借助Groebner基法和计算机符号处理技术,对平面两自由度七杆机构位置分析问题进行了符号求解。该法通过对变量排序,建立多项式对的集合,求SP多项式,约简等运算,将一组非线性方程组化简为等价的三角化方程组,导出了单变量的8次代数方程,得到了封闭形式的解析解,并给出了具体数值实例。

A method for displacement analysis of planar two-DOF （degree of freedom） seven-bar linkages is proposed based on Groebne Method and computer symbolic manipulating technique in this paper. A set of equivalent triangularization equations are obtained by using the following operations： ordering of variables, forming all pairs of polynomials, finding S-polynomial, reduction etc. An eighth order algebraic equation with single variable is derived for the closed form solutions of displacement analysis of planar two-DOF seven-link mechanisms. A numerical example is given to demonstrate the efficiency and advantages of the method.