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I'm talking a very basic robot using breadboards, icecream sticks, motors, an adruino or something like that, and making it move the arm in preconfigured motions, like circle or square, etc. Nothing fancy.
It might be a good idea to look at a pantograph for something like this, you could probably build a simple linkage out of popsicle sticks and use a couple of servos to control it. It would take some trigonometry to get it right but it's probably the easiest to build with those materials
Potentially you could even make two "arms" one with potentiometers to measure the angles at different points on the linkage and a second with servos set to reproduce those angles. So a person can trace out an object or drawing on the first one, then the second one shadows/reproduces it. It would simplify any code substantially and would probably be more impressive to the judges