A Fully Geometric Approach for the Workspace Area of the Gantry-tau Parallel Kinematic Manipulator

One of the main advantages of the Gantry-Tau machine is a large accessible workspace/footprint ratio compared to many other parallel machines. The design presented in this paper achieves a workspace/footprint ratio of more than 2.7 with fixed length links, which is high for a PKM. Typical PKMs, for example the Delta robot, has a ratio less than one. Optimisation schemes are typically used in order to achieve a maximum ratio. In this paper we present a new fully geometric approach for calculating the workspace area of the Gantry-Tau. A fully geometric approach is faster and more accurate than numeric approaches and of significant benefit in kinematic optimisation schemes.