Direct and Inverse Position Kinematics of 3-UPS Parallel Manipulators

Abstract

In this paper, the equations for the inverse and direct kinematics problems of a 3-UPS spatial parallel mechanism (universal-prismatic-spherical) of six degrees of freedom with two actuated joints and four passive joints in each of three parallel branches have been studied.
The number of solutions to the inverse kinematics problem is shown to be not more than 64, and the solution of the direct kinematics problem has been shown to be reducible to an 8th order polynomial. This implies that for a given set of actuated angles, this 3-UPS parallel mechanism can be assembled in at most 8 different configurations. Further numerical computations were performed to check the algebra and numerical examples were solved to demonstrate the procedure