New methodology for the forward kinematics of 6-DOF parallel manipulators using tetrahedron configurations

This paper presents a new methodology of using tetrahedron configurations to determine the forward kinematics of 6-DOF parallel manipulators. The approach is introduced in a form of the tetrahedron proposition and theorem using the special characteristics tetrahedral geometry which are then applied to obtaining the kinematic solutions of two 6-DOF parallel manipulators such as those previously introduced by Hunt-Primrose (1993) and by the authors (2000). The proposed methodology has the advantage in greatly reducing the complexity of formulation and computational burden required by conventional methods for solving the forward kinematics. As a result, the methodology allows a significant simplification in the formulations and provides an easier means of obtaining the solution.