Cusp points and assembly changing motions in the PRR-PR-PRR planar parallel manipulator  

作　　者：Chengwei SHEN Jingjun YU Xu PEI 

机构地区：[1]School of Mechanical Engineering&Automation,Beihang University,Beijing 100191,China

出　　处：《Frontiers of Mechanical Engineering》2023年第2期177-187,共11页机械工程前沿（英文版）

基　　金：partially supported by the National Natural Science Foundation of China(Grant Nos.U1813221 and 52075015).

摘　　要：Most parallel manipulators have multiple solutions to the direct kinematic problem.The ability to perform assembly changing motions has received the attention of a few researchers.Cusp points play an important role in the kinematic behavior.This study investigates the cusp points and assembly changing motions in a two degrees of freedom planar parallel manipulator.The direct kinematic problem of the manipulator yields a quartic polynomial equation.Each root in the equation determines the assembly configuration,and four solutions are obtained for a given set of actuated joint coordinates.By regarding the discriminant of the repeated roots of the quartic equation as an implicit function of two actuated joint coordinates,the direct kinematic singularity loci in the joint space are determined by the implicit function.Cusp points are then obtained by the intersection of a quadratic curve and a cubic curve.Two assembly changing motions by encircling different cusp points are highlighted,for each pair of solutions with the same sign of the determinants of the direct Jacobian matrices.

关 键 词：planar parallel manipulator assembly changing motions cusp points quartic polynomial discriminant of repeated roots 

分 类 号：TH112[机械工程—机械设计及理论]