[JamesCH95]

In short: make the kicker lighter, it will more efficiently transfer momentum to the soccer ball

I like to look at these sorts of problems holistically. Your motor can only put out a certain force and your kicker can only retract a certain distance, so you have a maximum amount of energy you can store in the springs. EDIT: Lowering the spring rate *might* help if you can work out all the details, i.e. fit a spring on that will get you a greater amount of stored energy, K*x^2. Constant-force springs would be an interesting option to explore, they would allow you to maximize the energy extracted from the motor by keeping it under a higher constant load, rather than a progressive load as shown in Ether's plot.

When considering elastic impacts I found through momentum calculations that for the same amount of applied energy (Force*distance or torque*swept angle) it was beneficial to decrease the mass/inertia of the kicker to improve kicking distance. If you need a 10% increase in range you might need to decrease your kicker's inertia by ~10% but I cannot give you exact numbers without knowing details about your kicker.

This is a good simple paper explaining basic physics behind kicking a soccer ball:

http://www.serioussoccer.net/Documen...csofSoccer.pdf