Determination of the maximal singularity-free orientation workspace for the Gough–Stewart platform

This work addresses the determination of the maximal singularity-free orientation workspace at a prescribed position of the Gough–Stewart platform. Using the Roll–Pitch–Yaw angles (ϕ, θ, ψ), the orientation workspace at a prescribed position can be defined by up to 12 workspace surfaces. A numerical algorithm is developed to determine these 12 workspace surfaces in order to obtain the maximal singularity-free orientation workspace as well as the corresponding leg length ranges. Besides, to compare the maximal singularity-free orientation workspace with the maximal singularity-free sphere, an iterative algorithm for determining the maximal singularity-free sphere is also provided.