On Wed, 25 Nov 2009 13:39:35 -0000, "invalid"
wrote:

In the explanations (W.O.Davis, T.C.F.Stott) for constant angular velocity,
appeal is made to a smooth belt coming off the base circle of one gear
wheel and being pulled onto the base circle of the second gear wheel,
and it is then said that provided the line of action between two mating
teeth
follows the path of the imaginary belt, then constant angular velocity will
be
imparted from one gear wheel to the other.

I have no dispute with that. It is a concise explanation of what is
happening.

My question is this. The explanation given suggests that the velocity ratio
between the two gears would be determined by the ratio of the diameters
of the base circles taken with the imagined belt, but it is not, it is
determined
by the ratio of diameters of the pitch circles, which are bigger.

Can anybody out there solve this quandary?

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.