Workspace Analysis of the 4RRR Planar Parallel Manipulator with Actuation Redundancy

In order to overcome the drawbacks of 3RRR non-redundant parallel manipulators,a redundantly actuated planar parallel manipulator,the 4RRR manipulator,was examined.In the current study,three types of workspace were analyzed.In the analysis of the reachable workspace,the shape of the workspace of 4RRR PMs was illustrated,and the relationship between the parameters of parallel mechanisms（PMs） and this kind of workspace was discussed.In the analysis of the m-orientation workspace,a procedure for calculating this type of workspace was presented,and the relationship between this type of workspace and the requirement of rotational displacement was revealed.In the analysis of the nonsingular workspace,the singularity of 4RRR PMs was discussed,the boundary of the singularity was illustrated,and a scheme to maximize the nonsingular workspace was presented.Depicting the properties of 4RRR PMs from different perspectives,the analyses of these three kinds of workspace can serve as helpful references for the structure design and mechanism control of 4RRR PMs.