Direct Position Kinematics of a Three Revolute- Prismatic-spherical Parallel Manipulator

In this work, the direct position kinematics of a 3 degree-of-freedom parallel manipulator with three identical limbs, type revolute-prismatic-spherical (RPS), is analyzed. In contrast to the previous studies on this class of manipulators, the revolute joints of the proposed manipulator are actuated rather than the prismatic joints. Direct position kinematics of the manipulator leads to a system of three nonlinear equations in three unknowns that are reduced to a univariate polynomial of degree eight and two quadratic equations in sequence using Sylvester dialytic elimination method. In addition, to show the efficiency of the presented method a numerical example is provided.