Optimal design of the isotropy performance of a six-dimensional force sensor based on a generalized Gough-Stewart structure lying on a pair of circular hyperboloids

For a six-dimensional force sensor, a key issue in its structural design is to realize low coupling and high precision. A standard Gough-Stewart structure based six-dimensional force sensor is able to achieve the best force isotropy with a value of 0.707, and its intrinsic isotropy performance directly affects the measuring accuracy of a sensor. In this paper, a generalized Gough-Stewart structure is used to design a six-dimensional force sensor. The concept of a pair of circular hyperboloids is introduced to define a generalized Gough-Stewart structure with minimal and independent description parameters, and to achieve the optimal design of a six-dimensional force sensor with isotropy. The optimal design routine is built by deriving the closed-form and analytic formulation. Full force isotropy is proven accessible. An performed routine is proposed to design the Gough-Stewart structure with force isotropy for a six-dimensional force sensor, which could meet the position requirement of the force measure point. The research shows that the proposed routine is a novel method to generate a class of six-dimensional force sensors with best isotropy based on generalized Gough-Stewart structures, and also is a new synthesis method of parallel mechanisms.