Follow me as I attend watchmaking school.
It might be old hat for you but if not I think you'll enjoy this, "Basic Mechanisms In Fire Control Computers". It's a series of 1950s Navy videos explaining how mechanical computation is done.https://www.youtube.com/watch?v=s1i-dnAH9Y4
Thank you, this should prove informative. After all a mechanical watch is nothing more than a simple mechanical computer.