Jerk distribution of a 6–3 Gough-Stewart platform

This paper is devoted to forward and inverse jerk analyses, by means of screw theory, of a Gough-Stewart platform with special topology, namely type 6–3. Given a set of generalized coordinates, and their time derivatives, the reduced jerk state or, for brevity, the jerkor of the moving platform, with respect to the fixed platform, is easily obtained by taking advantage of the properties of the Klein form, a bilinear symmetric form of the Lie algebra, e(3). Finally, the joint rate jerks of the parallel manipulator are found, expressing in screw form the jerkor of the moving platform with respect to the fixed platform. A numerical example is provided.