Beyond Inertial Match: Optimal transmission ratio values for a payload subject to additional forces

In high-dynamic mechatronic systems, the inertial match principle is a widespread concept used by engineers to assist with actuator and transmission selection. Inertial match describes the optimal transmission ratio between payload and actuator inertia for minimum peak current and minimum thermal dissipation, where the effective inertia of the payload due to the transmission ratio is equal to the inertia of the actuator. This article presents an extension of the inertial match principle, for applications where the payload is subject to a constant force (such as gravity) or friction. Unlike the classical inertial match case, two different optimal values are now found, one for minimum peak current and one for minimum thermal dissipation.