The gear train of a Bulova pocketwatch

Many years ago, Bulova sold mechanical pocketwatches like this one:

It's a Bulova 1937 Chesterfield and I've taken the case-back off so you can see the movement is a 17AE. The dial looks something like this one from mybulova.com. You can see various gears, held in place by a screw and/or an odd-shaped metal plate (called a bridge). So you can understand the terms, here's a photo from a parts catalogue:

The center rod of the gear is called the "arbor". The small gear attached to the arbor is called a "pinion" and its cogs are called "leaves". The outer gear attached to the arbor is sometimes called a "wheel" and its cogs are called "teeth". None of the catalogues I can access list the size of each gear nor the number of teeth/leaves. All this data was guessed at using AI (chatGPT or Gemini, usually) using photos I could find online.

The mainspring powers the watch, causing the hands to move around the dial in a complicated mechanical process. You wind the watch, which tightens a spring wound around the arbor of a hollowed out gear called the "barrel" (these barrels are very small and flat, unlike a typical barrel you might see at a winery or a western movie). Inside the hollowed space of the barrel is the mainspring, a very thin flat piece of alloy metal coiled up like a snake. As the spring unwinds, it slowly turns the barrel. To speed up this turn, the clever idea of a "gear train" is used. The teeth of the barrel mesh with the leaves of the pinion for the center wheel, which turn the teeth of the center wheel a bit faster than the teeth of the barrel. To speed this up further, the teeth of the center wheel mesh with the leaves of the pinion for the third wheel, which turn the teeth of the third wheel a bit faster than the teeth of the center. Adding a fourth wheel to this "train" gets the rotation up to the speed needed for a watch. You get the idea, but better is to use an animation.

Using AI, I created a manim Python module to animate this process.

This animation is a simplified mathematical model of the gear train of a Bulova 17AE mechanical watch movement, showing the barrel wheel, center wheel and pinion, third wheel and pinion, and fourth wheel and pinion rotating in mesh. The mainspring (unshown) inside the barrel is slowly unwinding and that energy turns the pinion of the center wheel, which turns the third wheel pinion, and so on.

The large wheels are partially transparent so that overlapping components on different mechanical planes remain visible, and each large wheel has a white reference tooth to make its rotation easier to follow. Over the main 224-second animation, the barrel wheel turns only about one-quarter revolution, while the gear ratios progressively increase the rotational speed through the train. With the tooth counts used in this model, the fourth wheel rotates 450 times as fast as the barrel, completing about 105 revolutions during the 3:49 animation.