We were thinking of using a kicker design with elastics providing most of the power and a motor to wind the lever back. We’re not quite sure how much space, power and whether the motor would be able to wind back in time for the next kick.
So, figure out how many Watts of energy it takes to move X distance with Y force in Z seconds… and see if your motor can deliver that power. (Be conservative - if you need 100 watts, look for 150 or 200. Friction and other losses need to be considered)
Stability of the linear motion also effects this (elaborating on loss of power): twisting of mechanism’s frame, etc… Note any type of friction of the linear bearings you plan on using as well, if you can find the CoF of the bearing, that is. (Assuming something similar to 1114’s punch in 2008).