Kinematics and Dynamics of a 3-CRU Spherical Parallel Robot

This paper describes the kinematics and dynamics of a spherical parallel wrist called 3-CRU after the topology of its legs. After a mobility analysis showing the geometrical conditions that yield motions of pure rotation, its kinematics is worked out in closed-form for both position and velocity problems. Then inverse and direct dynamics models are developed and the latter is investigated by the use of the multibody NOC method. Seven bodies are considered by the models: two links for each one of the three legs and the moving platform, while inertial joints parameters have been neglected. Finally, numerical simulations are presented to validate the model. This architecture adopts kinematic pairs that make it suitable for being realized at a mini- or microscale. The Authors are presently developing the design of a robot based on such a concept.