In NBN and likely in Turning Point, Linear Punchers were an effective method of shooting a ball in a fairly consistent, near-linear path. The name of the mechanism comes from it's linear actuation and the forceful impact on the ball that sends it flying.
A couple of things to note about the design:
The shooting is powered by rubber bands (not shown, but connected from the standoff on the back of the rack c-channel to the front of the assembly)
The puncher is drawn as the rack and pinion set moves the rack away from the ball, and then when the shaved section of the pinion gear reaches the rack, the rack is released and shoots forward
The rack shown in the photo is stopped from exiting the assembly by the horizontal bolts with black spacers. This will cause metal fatigue over time, and is not recommended. Instead, use nylon rope tied between the rack and the bottom of the assembly.