Optimal Variable Transmission Ratio and Trajectory for an Inertial Load With Respect to Servo Motor Size

Abstract

This paper addresses the selection of the optimal trajectory and transmission ratio for a servo motor driving a purely inertial load. Both aspects are studied with respect to the required motor torque and are formulated in a dimensionless fashion. Consequently, the results are generally valid and answer the following questions. What is the gain in terms of required motor torque by optimising the trajectory for minimal motor torque given a required smoothness? What is the corresponding optimal trajectory? What is the gain in terms of required motor torque by inserting a mechanism (variable transmission) between the motor and the load? What is this optimised variable transmission ratio? The final example shows how a realistic mechanism can approximate this theoretically optimised variable transmission ratio and, hence, the corresponding reduction in required motor torque.