基于Groebner基的平面五杆机构位置分析符号解

Symbolic Approach for Displacement Analysis of Planar Five-bar Linkages Based on Groebner Base Method

基于Groebner基法和计算机符号处理技术 ,对各种结构型式的平面两自由度五杆机构位置分析问题进行了符号求解。该法通过对变量的排序 ,建立多项式对的集合 ,求S -多项式 ,约简等运算 ,将一组多项式方程化简为一个同价的三角化方程组 ,得到了封闭形式的解析解。本文研制的软件可以适用于各种结构形式的平面两自由度五杆机构位置分析进行符号求解 ,导出的三角化的Groebner基不仅可以用于研究输入参数对输出构件位置的影响 ,也可以研究调节构件几何参数对输出构件位置的影响规律。

Symbolic solutions to displacement analysis for various types of planar two-DOF five-bar linkages are proposed based on Groebner base method and computer symbolic manipulating technique in this paper. A set of nonlinear polynomial equations are transformed into a set of equivalent triangularization equations by using the following operations: ordering of variables, forming all pairs of polynomials, finding S-polynomial, reduction etc. The analytical solutions in the closed form are obtained. Corresponding software is developed which can be used to find the symbolic solutions to displacement analysis for various types of planar two-DOF five-bar linkages. The triangularization Groebner base derived not only can be used for the research of the effects of input parameters on output link positions, but also can be used for the research of the effects of geometric parameters on output link positions.