On Sun, 21 Aug 2005 14:13:11 -0500, Don Foreman
wrote:

We're making this far too complicated.

A point on the periphery of an arbitrarily-shaped must be at the same
angular position after each revolution. If it were not, the periphery
would make net angular progress relative to the axel and "wind up".

If there is no slippage between road and wheel periphery, then the
vehicle must progress one peripheral distance per revolution, whatever
the various radii might be.

If the wheel were a circle this peripheral distance would be
circumference. Call it whatever you like for a non-round wheel.

A tank-tread analogy does not apply because the tread is driven only
where the tread is in contact with the rigid round wheel, where all
points on a tire's periphery are mechanically (albeit elastically)
coupled to the axel by the sidewalls.