There was a superb video on the complete reconstruction of the Antikythera device where it explained why and how the different teeth count on the wheels came into play.
I did post this video on 13 Dec 2021... At that time it was a very recent video on YouTube.
https://elakiri.com/threads/decoding-the-antikythera-mechanism.2022379/
Sadly this video is no longer available. If I remember right it was about Michael Wright, the British Mechanical engineer who first reconstructed the working prototype of the mechanism.
Here's a short video showing a virtual reconstruction.
Also there are several episodes on "The Antikythera Mechanism" in the Clickspring channel.
