A Comparison of Algebraic and Iterative Procedures for the Generation of the Workspace of Parallel Robots

Computing the workspace of parallel manipulators is critical to characterize their behavior. Usually, workspace is obtained by iterating the robot’s forward kinematics for a discrete range of poses, resulting in a cloud of reachable points. Here we propose an alternative algebraic formulation that is based on a recursive generation of volumes for solids of revolution to evaluate each limb’s workspace. The robot’s workspace is then obtained as the intersection of the limbs’ workspaces. With a practical example on the CaPaMan design and on a 3-UPR architecture, both the numerical and algebraic methods are discussed with their features and limits.