Putting all the mathematical modelling aside, I think team 1726 has demonstrated that the ball can be launched with pneumatic cylinders, and without springs or other energy storage:
2014 FRC 1726 Shooter Test 1 NERDS Pneumatic Catapault
Here's what I see:
- This is a "rolling release" catapult. An improvement over cup type ball holder.
- The linkage starts with a reverse leverage (better term ??) where the mechanical advantage decreases with rotation; as the piston extends, the moment applied by the rod decreases.
- The small initial moment with the inertia of the ball/catapult-arm, allows the pressure to build in the cylinder.
Nice work N.E.R.D.S. !