A methodology for designing a parallel, passiveassist device to augment an active system using energy minimization based on a known maneuver is presented. Implementation of the passive-assist device can result in an improvement in system performance with respect to efficiency, reliability, and/or utility. In previous work we demonstrated this concept experimentally on a single link robot arm augmented with a torsional spring. Here we show that the concept can effectively be applied to other machines performing known periodic motions by simulating a reciprocating single axis machining table and an X-Y table performing a slot milling operation. The addition of optimized springs results in a decrease in energy consumption of 79% and significantly outperforms springs based on a state-of-the-art force-displacement curvefitting approach. Finally, we show that a significant increase in performance can be realized if the maneuver is redesigned considering that a passive-assist device will be added to the system.