Perhaps the most ingenious part of the Antikythera Mechanism is a rather small unassuming gear pair. But despite its simplicity, the K1/K2 gears very closely model the eccentricity of the moons orbit.

The is very clearly a missing module to the Antikythera Mechanism and it is widely believed to be a geocentric planetarium. Without fragments there is no way to recreate it, but it does allow us to step into the shoes of our ancestors and figure out what should be there to match observations and theories of the time.

The historical device uses an approximation, but it is fairly straightforward to modify to a very accurate mechanism with an added gear and whippletree

A comprehensive explanation of the workings and construction of the recreation.