Kinematics, singularity and workspace of planar 5R symmetrical parallel mechanisms

This paper treats the problems of kinematics, singularity and workspace analysis of the 5R symmetrical parallel mechanism. In the design process, the theoretical workspace cannot be used directly due to the inside singularity. The inverse and forward kinematic solutions determine the working and assembly modes of a mechanism. With different modes, a mechanism will have different singular loci and workspaces. In this paper, the singularity and usable workspace without singularity inside will be determined for the mechanism with a specified mode. A concept, the maximal inscribed workspace (MIW) that is bounded by the maximal inscribed circle (MIC), is defined to characterize the workspace performance. A non-dimensional design space is established to investigate the singular loci and workspace shape of the mechanisms, systematically. The atlas of the MIC radius is presented. Based on the obtained distribution charts of the singularity and workspace shape and the atlas, one can know the singularity and workspace performances of any one of the 5R symmetrical parallel mechanisms. The result, especially that of the MIW, of this paper is very useful for the optimum design of the mechanism.