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A closed-form solution for the position analysis of a novel fully spherical parallel manipulator

SUMMARY In this paper, a novel 3(RPSP)-S fully spherical parallel manipulator (SPM) is introduced. Also, an innovative method based on the geometry of the manipulator is presented for solving the forward position problem of the manipulator. The presented method provides a framework for the future research to solve the forward position problem of the other fully spherical PMs (for examples 3(UPS)-S and 3(RSS)-S). In the proposed method, two coupled trigonometric equations are obtained by utilizing the geometry of the manipulator and Rodrigues' rotation formula. Using Bezout's elimination technique, the two coupled equations lead to a polynomial of degree eight. We show that the polynomial is minimal and optimal. Furthermore, the other method is proposed for selecting an admissible solution of the forward position problem. This algorithm is required to control modeling and dynamic simulations.