Dynamic isotropic design of a class of Gough-Stewart parallel manipulators lying on a circular hyperboloid of one sheet

This paper proposes an optimal design method based on dynamic isotropy conditions of a generalized natural frequency matrix in task space for a standard Gough-Stewart parallel manipulator (GSPM). Firstly, the dynamic isotropy conditions are discussed and presented. Next, it is proved that standard GSPMs lie on a circular hyperboloid of one sheet. Further, we present a method to use a circular hyperboloid to construct 3-3-, 6-3- and 6-6-type standard GSPMs. Moreover, such novel definition is used to examine various dynamic isotropy conditions as functions of the coefficients of a hyperboloid. An optimal design method is also proposed accordingly. Finally, a numerical example is given to illustrate the design procedures. The results are very close to the complete dynamic isotropy.