Workspace analysis and singularity representation of three-legged parallel manipulators

This paper presents a numerical algorithm for the analysis of reachable workspace and singularity representation of three-legged parallel manipulators. After finding out the approximate maximum workspace, a radial and equal area discretization is done. Then, a multitasking search is performed to determine the exact workspace boundary. The volume of the workspace is determined easily by a numerical integration method. Any void inside the workspace is found out. information about its position and stretch is determined and singularity curves inside the workspace is also drawn. A three-legged modular parallel manipulator is considered to demonstrate the effectiveness of the algorithm and found to work quite satisfactorily. The model is based on Product-of-Exponential scheme of formulation and, hence, the algorithm is uniformly applicable to any combinations of revolute and prismatic joints in the configuration of the leg.