I've dabbled with a few illustrations of the object and its origin in my show The Astro Time Machine. Since creating this show, I've worked a little on my animation of how this device was thought to portray the motion of the moon's elliptical orbit.
The journal Nature published a description of the use of a pin and slot mechanism to create elliptical motion. I've created an animated version of the pin and slot mechanism on my website (Pin and Slot):
And using four gears would have allowed the modeling of additional motions, such as the change in axis of the moon's orbit.
I don't claim to accurately show the arrangement of gears used in the Antikythera device. My animation is meant only to show how two wheels with a pin and slot produce the motion of an elliptical orbit. My animated model could easily be replicated with real wheels for a classroom project. Gears could be replaced with wheels connected by belts of elastic cord. With the correct tools, I think it would be easier to build a real elliptical motion mechanism than to program a model, at least for me.