This paper from Tufts describes some of the ways that they approached building models. It includes this link to this diagram of the gearing for the Antikythera Mechanism.
And this site notes that John Gleave, who makes orreries, built his own replica.
Question: has anyone analyzed the isoptic composition of the bronze or brass gear wheels? i’m wondering if the place of production of the machine could be pinned down.
Second; why was there only one machine? One would think that every temple would want sucha useful mechanism. have any ancient greek water clocks survived?
Nature has a good summary article on it, plus the actual paper from the researchers (which requires a subscription to view).
The hypothesis for why it’s the only surviving mechanism is that the metal they are composed of is more valuable than the functional device. So the others have all been melted down. Apparently all surviving Greek bronze statues were also recovered from shipwrecks; all others were destroyed.
It was found with ceramics were made in Rhodes, so it seems the ship had been there. It’s possible the mechanism was produced there as well.
AFAIK, such elaborate orrery-type devices were never common in antiquity (although the surviving example probably wasn’t literally unique). They would have been more on the order of fancy luxury toys than routine scientific tools. If all you want is to calculate planetary positions or eclipses, it would be a lot less expense and trouble just to get a copy of Ptolemy’s Handy Tables and do the computations yourself