Involute gear ratios?

That is because the velocity ratio between two gears is not directly determined by the ratio of pitch diameters. It is determined by the number of teeth on each gear. This number is directly proportional to the pitch diameter.

Paul K. Dickman

I thought the base circle reference explained constant angular velocity as the point of contact rolled across the two mating teeth, the same as the involute string unwinding. The base and pitch diameters are in equal proportion so you could also say the tooth tip speeds are equal, which is true but irrelevant.

jsw

Gear teeth engage at the pitch diameters, not at the base diameters. The belt analogy is valid only if a belt of some thickness (like a V belt) runs on base dia, or if a belt of infinitesimal thickness somehow runs on the pitch diameters. In the thick belt case, there is necessarily a thin part running at the pitch diameters; other parts of the belt compress or stretch as the belt goes round a pulley.

Oops.

Should have read the next two pages in the book before posing my question :-)

The base circles are in proportion to the pitch circles by a factor of the cosine of the pressure angle, and thus the two base circles are in the same proportion to each other as are the corresponding pitch circles.

Thanks Jim, as I subsequently found and posted.