A Linear Relaxation Method for Computing Workspace Slices of the Stewart Platform

The workspace of a Stewart platform is a complex six-dimensional volume embedded in the Cartesian space defined by six pose parameters. Because of its large dimension and complex shape, this volume is difficult to compute and represent, and comprehension on its structure is being gained by studying its three-dimensional slices. While successful methods have been given to determine the constant-orientation slice, the computation and appropriate visualization of the constant-position slice (also known as the orientation workspace) has proved to be a challenging task. This paper presents a unified method for computing both of such slices, and any other ones defined by fixing three pose parameters, on general Stewart platforms possibly involving mechanical limits on the active and passive joints. Advantages over existing methods include, in addition to the previous, the ability to determine all connected components of the workspace, and any motion barriers present in its interior.