Determination of the largest collision-free and singularity-free workspaces for spatially isotropic Stewart platforms

Based on the same direction vectors of the six links that can achieve spatial isotropy, a lot of spatially isotropic Stewart platforms can be designed, which means some physical parameters do not affect the Cartesian stiffness. However, these physical parameters will affect the collision-free and the singularity-free workspace of the spatially isotropic Stewart platform. In order to find the combinations of the physical parameters that do not affect the Cartesian stiffness matrix but can determine the largest collision-free and singularity-free workspace, this paper proposes several algorithms to optimise the spatially isotropic Stewart platforms based on the position of the TCP expressed in spherical coordinates and the orientation of the moving platform expressed by a unit quaternion with angle-axis. By this way, the symmetric constant-position workspace and constant-orientation workspace are dependent only on the rotation angle in the angle-axis representation and the sphere radius, respectively. At the same time, the singularity locus and collision-free workspace can be clearly illustrated and optimised.