Equivalent Kinematic Chains of Three Degree-of-Freedom Tripod Mechanisms With Planar-Spherical Bonds

Abstract

The paper aims to analyze the equivalent kinematic chains of a family of three-degree-of-freedom (3-DOF) tripod mechanisms with planar-spherical bonds in order to determine the platform motions generated by the mechanisms, and then to develop a prototype of a 3-DOF 3-RPS type parallel mechanism, which can be used as a wrist robotic device. After a short introduction to mechanical generators of Lie subgroups of displacement, the mobility formula of a general 3-DOF tripod mechanism based on the modified Grüebler’s criterion is given. Using displacement group theory theorems, the analyzed closed-loop system becomes finally equivalent to three contacts between a rigid assembly of three moving spheres onto three fixed planes. As an application of the above method, a prototype mechanism is designed and fabricated based on the kinematics analysis, the force capability and the simplicity.