一般6-SPS并联机构运动学正解的解析化方法

Analytical Method for Forward Kinematics Analysis of General 6-SPS Parallel Mechanisms

研究了一般6-SPS并联机构动平台位置变量与姿态变量之间的耦合关系,将9个变量中的6个变量用其余的3个变量表达,将位置变量表达为姿态变量的线性组合。运用Grbner基算法,得到了15个只含有剩余3个变量的相容方程;采用正交补方法进行消元,最终将一般6-SPS并联机构的运动学正解问题表达为一元20次代数方程。这样的一元20次代数方程有多个,经过验证,它们都是同解的。

The coupling relationship among the positional and orientational variables of the moving platform of general 6-SPS parallel mechanisms was studied. Six in nine variables were expressed by the three remainder variables, so the position variables were expressed by orientational variables. Applying Grobner basis algorithm, fifteen four order compatible algebraic equations were obtained, which contained the three remainder variables. The orthogonal complement method was used several times to eliminate the redundant variables, by this way the problem of the forward kinematics analysis of the general 6-SPS parallel mechanisms can be simplified as several twenty order algebraic equations in the end. It is verified that these equations have the same solutions.