基于Groebner基法的平面七杆机构位置分析

基于Groebner基法和计算机符号处理技术，对各种结构形式的平面两自由度七杆机构位置分析问题进行了符号求解，该法通过对变量的排序，建立多项式对的集合，求S一多项式，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。给出了机构的装配构形。研制的软件可以适用于各种结构形式的平面两自由度七杆机构位置分析进行符号求解，研究了几何参数和输入参数对机构输出位置的影响，给出几个数字实例。

Displacement Analysis for planar Seven-bar Linkages Based on Groebner Base Method

Symbolic solutions to displacement analysis for various types of palnar two-DOF seven-bar linkages are proposed based on Groebner base method and computer symbolic manipulating technique. 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 ect. The analytical solutions in the closed form are obtained. The assembly configurations for the mechanisms are given. Corredponding software is developed which can be used to find the symbolic solutions to displacement analysis for various types of planar two-DOF seven-bar linkages. The influence of geometric parameters and input parameters on the output positions of the mechanism is investigated.Some numerical examples are given for illustration.