Inverse dynamics of a planetary gear train for robotics

Recursive matrix relations concerning the geometric analysis, kinematics and dynamics of a Bendix wrist planetary bevel-gear train for robotics are established in the paper. The prototype of this mechanism is a 3-DOF system with seven links and four bevel gear pairs controlled by electric motors. Supposing that the rotational motion of the platform is known, an inverse dynamic problem is developed using the principle of virtual powers. Some relations and graphs for torques and powers of three actuators are determined.