Dynamic Isotropy in 3-DOF Gantry Tau Robots - an Analytical Study

3-DOF Gantry Tau is a type of parallel robot, consisting of six struts configured in three clusters, which provides three translational DOFs. It has increasing industrial use in applications where large workspace and high stiffness are required. In fact, the concept of dynamic isotropy, where all the natural frequencies of a system are equal, can be employed in order to effectively optimize the geometry of robots. However, no study on dynamic isotropy of Gantry Tau robots has yet been reported in the literature. In this paper, the problem of dynamic isotropy in 3-DOF Gantry Tau robots is analytically addressed. Firstly, the kinematics is established based on a general approach with 36 geometric variables. Jacobian and stiffness matrices are also investigated where the struts are considered to be axially flexible. Subsequently, analytical solutions to obtain both a decoupled stiffness matrix and a complete dynamic isotropy are presented. Finally, as an example, dynamically isotropic geometries of a Gantry Tau robot are calculated, for a reference platform, using the developed analytical method.