Dynamically Isotropic Gough-Stewart Platform Design Using a Pair of Triangles

An ideal dynamically isotropic Gough Stewart platform (GSP) has its first six modes of vibration as same, and this enables one to use effectively designed identical dampers to attenuate vibration from a source to a sensitive payload. A modified GSP (MGSP) capable of being dynamically isotropic is considered in this work. For a dynamically isotropic MGSP, the use of a force transformation matrix leads to a set of coupled transcendental equations in terms of design variables. It was observed that all the design variables for an MGSP were related by pairs of triangles. This work develops a general analytical closed-form solution for a dynamically isotropic MGSP using geometrical relations between these triangle pairs. The presented closed-form algebraic solutions can be used directly and supersede the need for any other complex algorithms. Additionally, the design variable in their explicit form offers straightforward solutions, flexible design and can ensure mechanical feasibility. The designs obtained in this work were validated by numerical simulations results done in ANSYS.