一种求解一般Stewart台体型机构位置正解的算法

An Algorithm for the Forward Position Kinematics of General Stewart Platform Mechanism

提出了一种新的求解一般Stewart台体型并联机构位置正解的代数求解方法。首先根据一般Stewart台体型的几何结构建立20个含9变量的原始方程,然后采用分次逆字典序对原始方程求Groebner基,从中可选择29个基并压缩合适的变量构造Sylvester结式,利用结式为0可获得40次一元高次方程,采用回代法求出其他对应该变量的全部40组解。通过数字实例验证了该方法的有效性,并且该方法也适用于其它型式并联机器人机构的位置正解分析问题。

A new algebra algorithm for the forward position kinematics of general Stewart platform（ GSP）is presented. First of all,the 20 original equations containing 9 variables are built according to the geometric construction of GSP. Then,the Groebner basis under the degree reverse lexicographic term ordering for the 20 equations is solved,and the 29 Groebner basis can be selected from it and compressing proper variable,the 2929 Sylvester matrix is constructed. A 40 th degree univariate equation is achieved from the determinate of the matrix. Finally,the total 40 solutions of the corresponding other variables can be obtained by back substitution method. A numerical example is deployed to verify the algorithm. The algorithm is also suitable for the forward position kinematics analysis of the other type of parallel- mechanism.