Kinematic and Elastodynamic Design Optimisation of the 3-DOF 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 Gantry-Tau improves this ratio by allowing a change of assembly mode without internal link collisions or collisions between the links and the moving TCP platform. However, the optimal kinematic, elastostatic and elastodynamic design parameters of the machine are still difficult to calculate and this paper introduces an optimisation scheme based on the geometric approach for the workspace area and the functional dependencies of the elements of the static matrix and the Laplace transform to define the first resonance frequency. The method to calculate the first resonance stiffness assumes that each link and universal joint can be described by a mass-springdamper model and calculates the transfer function from a Cartesian force or torque to Cartesian position or orientation. These approaches are significantly faster than analytical methods based on the inverse kinematics or the general Finite Elements Method (FEM). Kinematic design obtained by optimisation according to this paper gives a workspace/footprint ratio of more than 2.7 and the first resonance frequency of more than 50 Hz with components of an existing lab prototype at the University of Agder.