Planetary gear train for robotics

A recursive matrix model concerning the geometric analysis, kinematics and dynamics of a Bendix wrist planetary bevel-gear train for robotics is established in this paper. The prototype of this mechanism is a three-degree-of-freedom system with seven links and four bevel gear pairs. Controlled by electric motors, three active elements of the robot have three independent rotations. Supposing that the position and the rotational motion of the platform are known, an inverse dynamic problem is developed using the virtual power approach. Finally, some recursive matrix relations and some graphs for the torques of the actuators are determined.