Analytical derivation of singularity-free tubes in the constant-orientation workspace of 6-6 Stewart platform manipulators

Abstract This paper presents the novel concept of a singularity-free tube (SFT) in the constant orientation workspace of a spatial parallel manipulator. The concept is developed and demonstrated in the context of a $6$ - $6$ spatial parallel manipulator, namely, the semi-regular Stewart platform manipulator. Given two points in the said workspace, the SFT is a tubular volume which contains these points and is free of gain-type or forward-kinematic singularities. The purpose of identifying such regions in space is to allow abundant freedom to the path-planner to connect the said points by a path, which can be free of gain-type singularities simply by remaining inside the SFT at all times. To demonstrate the concept, two smooth paths obtained by formulating two different optimisation problems have been presented as examples. The SFT can be of great help in singularity-free path-planning in many similar manipulators.