Dynamic isotropic design for modified Gough-Stewart platforms lying on a pair of circular hyperboloids

This paper proposes an optimal design method for a Gough-Stewart Platform (GSP) with complete dynamic isotropy at a single point. Generally, dynamic isotropic behavior is associated with the geometric structure, which should be carefully designed to match the payload. However, in this work, we use a pair of circular hyperboloids to describe a modified GSP. Through an investigation of the dynamic isotropy conditions based on an analysis of the natural frequency matrix in the task space, the relationship between the dynamic isotropy and the geometric parameters of the pair of hyperboloids was found. These results allow us to categorize isotropic modified GSPs based on the ratio of the throat radii of the hyperboloids. Classes of complete isotropic GSPs can be constructed systematically using this method. This paper also shows that, for an isotropic modified GSP, one of the inertial constraints imposed upon an SRSPM (Semi-regular Stewart platform manipulator), has been removed.