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为获得一般6-6型台体并联机构位置正解的解析解,使用分次字典序Groebner-Sylvester法的代数方法对该问题进行了研究.利用计算代数系统计算该机构位置封闭方程的分次字典序Groebner基,从得出的65个基中选取18个基,构造18阶Sylvester结式.通过分析符号形式方程组的变量次数,得出位置正解的一元高次方程的次数为40且该机构位置正解最多有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.研究结果表明,该计算方法简洁,求解速度快,并从理论上阐明了存在多个不同的结式可以获得该机构的位置正解.最后,从给出的数字实例中,验证了所有解均满足原始方程且无增根,从而为并联机构位置正解的研究提供了一种有效算法.
In order to obtain the analytic solution of the general position solution of the parallel mechanism of Type 6-6 platform, the problem of the algebraic method of the hierarchical dictionary order Groebner-Sylvester method is studied.Using the computational algebraic system, Order Groebner base, from the 65 bases of the selected 18 base, structured 18-order Sylvester knot.By analyzing the number of variables in the system of symbolic form, The result of positive position solution is the same as that of the predecessor, but the size of the knot is much smaller.The results show that the method is simple, A series of different knots can obtain the positive position solution of this mechanism.Finally, from the given numerical examples, it is verified that all the solutions satisfy the original equation and have no rooting, thus providing an effective algorithm for the study of the positive solution of the parallel mechanism .