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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 algebraic solving method for solving the positve solution of general Stewart platform type parallel mechanism is proposed. First of all, based on the geometry of the general Stewart bench body, twenty original equations with nine variables are established. Then, the Groebner basis of the original equation is obtained by the sub-inverse lexical sequence. From this, 29 bases can be selected and the appropriate variables can be compressed to construct the Sylvester knot. The knot is 0 to obtain 40 unary higher order equations, and the rest 40 generations of solutions corresponding to this variable are obtained by the method of substitution. The numerical example shows the effectiveness of the proposed method and the method is also applicable to the positive position analysis of other parallel robot mechanisms.