基于Groebner基的八面体变几何桁架机构位置正解分析

Forward Displacement Analysis of the Octahedron Variable Geometry Truss Based on Groebner Basis

基于Groebner基法对八面体变几何桁架机器人机构进行了位置正解分析 ,得到其位置正解为 16解的结论 ,并给出数值算例。这种基于Groebner基法经过有限步符号消元运算得到三角化方程组的数学机械化方法 ,对涉及非线性代数方程组的机构学问题求解 。

In this paper, the forward displacement analysis of the octahedron variable geometry truss is studied by means of Groebner basis method. The original equations of the problem is changed into triangulated equations in which a single variable polynomial equation has 16th degree. The result shows that octahedron variable geometry truss can have 16 different configurations at most. In the end, a numerical example is studied and all solutions for the example are listed. The presented method provides a new way for solving the other difficult mechanism problems.