为获得Stewart台体并联机器人位置正解的解析解,使用分次字典序Groeb-ner基和Sylvester结式相结合的代数方法对该问题进行研究.利用计算代数中的分次字典序Groebner基算法,计算该机器人位置正解封闭数学模型的分次字典序Groebner基;从得出的51个基中选取20个基,构造20阶Sylvester结式,分析符号形式方程组的变量次数,可以直接得出该机器人位置正解一元高次方程的次数为40且最多有40组解的结论,其结果与前人的完全一致,但结式的尺寸却小得多.为了对结果进行验证,使用同伦连续法对同一个数字算例进行计算,两种方法得到结果一致.为并联机构位置正解的研究提供了一种新的有效算法. In order to obtain the analytic solution of the positive solution of the parallel manipulator in Stewart platform, the problem is studied by using the algebraic method of subdividing dictionary-based Groeb-ner basis and Sylvester knot combination.In this paper, We calculate the graded dictionary order Groebner basis of the mathematical model of the robotic position positive unblocking; choose 20 bases from the 51 bases, construct the 20th order Sylvester knot, and analyze the number of times of the symbol form equations, The result of the robot position exact solution of the unary high-order equation is 40 and the maximum is 40, the result is consistent with the previous one, but the size of the knot is much smaller. To verify the result, Calculating the same numerical example, the results of the two methods are consistent, which provides a new effective algorithm for the research of the positive solution of the parallel mechanism.