The teeth on wheels in watches may look pretty bog-standard, but they are actually a different type of tooth than the ones you would find on bigger machines that use similar-looking cogs, such as car engines and the like.
If you made the wheels you found in a car engine the size of watch wheels, the teeth would instantly snap off due to the incredible stress on the material. It seems a funny thing to consider – logic might lead you to believe that force is relative to size and that scaling down the wheel, would also scale down the force, but that isn’t the case.
As with the straight and conical pivots, car engine wheels use their form of teeth because, at that size, they can get away with it, but for watchmaking, the teeth need to be a modified EPICYCLODIC curve.
So what’s an epicyclodic curve? Put quite simply, it is the trace of a point on the outside of a circle as that circle rolls around the outside of another circle.
You might hear the following terms, but do not confuse them with EPICYCLODIC.
Cyclodic curve: the trace of a point on the outside of a circle as that circle rolls along a flat and straight line.
Hypocyclodic curve: the trace of a point on the outside of a circle as that circle rolls around the inside of another circle.