NGP并联机构运动学正解的高效通用解析方法

An efficient general analytical approach to forward kinematic analysis of NGP parallel mechanism

研究了NGP(nearly general stewart-gough platform)并联机构动平台位置与姿态变量之间的耦合关系,将9个变量中的6个用其余的3个表达出来,从而实现了位置变量和姿态变量的解耦.运用Gr bner基算法,得到了15个只含有其余3个变量的4次相容方程.在此基础上,采用变量代换的方法消去其中的高次项,最终将NGP并联机构的运动学正解问题简化为求解一个一元20次的代数方程;这个方程是通过计算一个10阶行列式得出的,并且通过一个具体的算例验证了该方法的正确性.该方法适用于所有的NGP并联机构.

The coupling relationship between the position and orientation variables of the NGP′s moving platform was studied.Six in nine variables are expressed by the three remainder variables,so the position and orientation variables are decoupled.By applying Grbner basis algorithm,fifteen four order compatible algebraic equations containing three remainder variables are obtained.By eliminating higher terms and introducing substitution variables,the problem of the forward kinematic analysis of NGP parallel mechanism can be expressed as a twenty-order algebraic equation in the end.This equation is obtained by calculating a tenth-order determinant.An example is introduced to verify the result.This method suits for all NGP parallel mechanisms.