Here’s a CAD rendering of the mechanical design of FRC Team 980’s 2014 robot:
The catapult is driven by two sets of compression springs housed in the green tubes. A van door motor drives the catapult winch, which is engaged/released by an idler gear driven by a pneumatic piston. The ball pick-up roller is shown in red (design inspired by Team 16’s 2008 robot). The electronics, battery and pneumatics (not shown) are housed in a “belly pan” mounted to the chassis frame below the ball. The robot has a very low center-of-gravity and has plenty of weight margin (and provisions for mounting ballast below the chassis frame).