The Tricept robot: Inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm

This paper is aimed at presenting a study on the kinematics of the Tricept robot, which comprises a three-degree-offreedom (dof) parallel structure having a radial link of variable length. The robot workspace is characterized and the inverse kinematics equation is obtained by using spherical coordinates. The inverse differential kinematics and statics are derived in terms of both an analytical and a geometric Jacobian, and a manipulability analysis along the various workspace directions is developed using the concept of force and velocity ellipsoids. A Jacobian-based ClosedLoop Direct Kinematics (CLDK) algorithm is presented to solve the direct kinematics problem along a given trajectory. Simulation results are illustrated for an industrial robot of the Tricept family.