Optimal variable transmission ratio and trajectory for an inertial load with respect to servo motor size

This paper addresses the selection of the optimal trajectory and transmissi on 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 an swer the following questions. What is the gain in terms of required motor t orque by optimising the trajectory for minimal motor torque given a require d smoothness? What is the corresponding optimal trajectory? What is the gai n in terms of required motor torque by inserting a mechanism (variable tran smission) between the motor and the load? What is this optimised variable t ransmission ratio? The final example shows how a realistic mechanism can ap proximate this theoretically optimised variable transmission ratio and, hen ce, the corresponding reduction in required motor torque.