Evaluation and Representation of the Orientation Workspace of the Gough-Stewart Platform

Abstract

The evaluation and representation of the orientation workspace of robotic manipulators is a challenging task. This work focuses on the determination of the orientation workspace of the Gough-Stewart platform with given leg length ranges [ρimin, ρimax]. By use of the Roll–Pitch–Yaw angles (φ, θ, ψ), the orientation workspace at a prescribed position can be defined by 12 workspace surfaces. The obtained orientation workspace is a region in the 3D Cartesian orientation space O φ θ ψ. As all rotations R(x, φ), R(y, θ) and R(z, ψ) take place with respect to the fixed frame, any point of the orientation workspace provides a clear measure for the platform to respectively rotate in order around the (x, y, z) axes of the fixed frame. Also, as the shape of the 3D orientation workspace is very complex, a numerical algorithm is presented to compute its volume.