A novel method for the solution of the forward displacement problem of spherical parallel manipulators

In this paper, a novel method that solves the Forward displacement problem (FDP) of several common spherical parallel manipulators (SPMs) is presented. The method uses the quaternion algebra to express the FDP as a system of equations and the Dixon determinant procedure to construct univariate polynomials whose roots can be found either numerically or analytically. A case study is solved for a specific SPM, which satisfies certain geometric conditions, having 3 - R(E)R architecture, with R denoting a revolute joint, E a planar motion generator and underlines indicating the actuated joint. In this case, the solutions of the system are obtained analytically by a symbolic method exploiting symmetries.