Here's a picture of our design:
There'll be a spinning wheel with surgical tubing grabbing the balls and shoving them up to a conveyor belt, with the top of the balls squeezed against something rigid. The balls will go up until the rigid part ends and a spinning wheel beings, which grabs the balls, forces them against a hood (that is movable to adjust the angle) and then out of the robot.
Oh, and the top will move somehow. (We are thinking the hood and wheel will be attached separately on a C that goes to the chassis with a lazy susan that is directly underneath the center of where the balls go from the conveyor to the hood, but that's still somewhat rough.)
Now I'm going to go uninstall the painting program I just downloaded