Jerome said:
the problem is that you are talking about today's tech and building new plant. And the 32mm system was established just after the war when existing tech and machines had to be used. The reason was because of the huge need due to the destruction caused by the war together with the lack of money and resources to build new plant. And that tech was capable of reliably and economically spacing no closer than 32mm QED
Gears haven't just been around for several decades. They have been around for many centuries. If 32 mm was a minimum achievable pre-WWII size, then that would make for a rather bulky pocket watch. Wouldn't it? [big grin]
The module of a gear is what dictates the geometry of the teeth. Two gears of different diameter will mate as long as they have the same module. That is not a 20th century invention, nor are the mathematics anything new.
So the only difference between a 30mm gear and a 32mm gear, when both have a module of 1 (or even 2), is the number of teeth cut. Each tooth has the same shape, and that is why they will mesh. But one gear would be rotated 1/32 of a revolution per tooth (for a module of 1) while the other would be rotated 1/30 of a revolution per tooth, and of course the net diameter of the gear would be 32mm versus 30mm.
So the very same equipment that could make a 32 mm gear with a specific module (assume 1) with 32 teeth, would also make a 30 mm gear with 30 teeth (or even a 12 mm gear with 12 teeth). As long as the module of the gear stays the same, the geometry of the teeth stays the same, and the only thing that varies is the diameter and number of teeth. The ratio of those two parameters is in fact the module of the gear. That is why it is such a critical parameter in gear design.
Edit: If you look at the image below, you will see that the size, shape, and spacing of the teeth are the same. The only thing that varies is the diameter and number of teeth.