A very nice video with an accompanying paper: A Model of the Cosmos in the ancient Greek Antikythera Mechanism
Using our identified period relations for all the planets, we have devised new theoretical planetary mechanisms expressing the epicyclic theories, which fit the physical evidence. For the inferior planets, previous 2-gear mechanisms are inadequate for more complex period relations because the gears would be too large. Two-stage compound trains with idler gears are necessary, leading to new 5-gear mechanisms with pin-and-slotted followers for the variable motions (Fig. 3c). For the superior planets, earlier models used direct mechanisms, directly reflecting epicyclic theories with pin-and-slotted followers. Here we propose novel 7-gear indirect mechanisms with pin-and-slot devices for variable motions (Fig. 3d), analogous to the subtle mechanism that drives the lunar anomaly. Compared to direct mechanisms, these are more economical; a better match for the evidence; and incorporate period relations exactly for higher accuracy. The crucial advantages of indirect mechanisms are expanded in Supplementary Discussion S4. Without these compact systems that can all be mounted on the same plate, it would have been impossible to fit the gearing into the available spaces. Proofs that the mechanisms in Fig. 3 correctly calculate the ancient Greek epicyclic theories are included in Supplementary Discussion S4.
I'm not sure how much of this is actually science, it strikes me more as some sort of historical-fiction-done-by-astronomy-loving-nerds.
But it's still quite interesting, and it's got some fun number theory.