Geometric isotropy indices for workspace analysis of parallel manipulators

This paper addresses the isotropy of a workspace in terms of its geometric shape. Workspace isotropy analysis plays a crucial role in improving the quality of workspace for parallel manipulators. When a parallel manipulator is installed on a moving platform (e.g., satellites, aircrafts, ships, etc.), the geometry of its workspace is critical to achieve the planned tasks. This paper proposes three novel workspace isotropy indices, namely, translational workspace isotropy index (TWII), rotational workspace isotropy index (RWII), and entire workspace isotropy index (EWII), for workspace isotropy analysis in terms of the geometric shape of the workspace. All three indices are mathematically defined. TWII and RWII can be applied to both planar and spatial parallel manipulators with movable bases while EWII can work for planar parallel manipulators with movable bases. Random rotational disturbances are applied to the movable bases of multiple parallel manipulators in simulation. Simulation results show that the proposed workspace isotropy indices are effective in evaluating how isotropic the geometric shape of a workspace is. They are good at reflecting the robustness of a parallel manipulator to rotational disturbances to its movable base. The proposed indices can also be used as guidelines for the optimal design of parallel manipulators.