基于几何约束方程的2-RPC/2-SPC并联机构位置正解分析

Forward Position Analysis of 2-RPC /2-SPC Parallel Mechanism Based on Geometric Constraint Equation

以四自由度2-RPC/2-SPC并联机构为研究对象,列出了该机构的正解方程;通过分析动平台位姿变量之间的耦合关系,建立了几何约束方程,作为辅助方程联立正解方程,最终经过化简得到关于q的一元八次方程,求解了机构的全部位置正解。该解法使复杂的非线性正解方程组变得简单易解,提高了求解速度,并通过实例验证了该方法的正确性。

By the study object of 4-DOF 2-RPC/2-SPC parallel mechanism,the forward solution equation of the mechanism was listed.Through analyzing the coupling relationships among the position and orientation variables of the moving platform,geometric con-straint equations were obtained.By combining the equations as auxiliary and the forward solution equation,finally through the reduc-tion,an eighth order equation about q was obtained,and all of the forward solutions for position of mechanism were solved.This meth-od makes the non-linear forward equations easier and simple with fast solution speed.Moreover a specific example is introduced to veri-fy the validity of method.