On what kind of surface would a square wheel function the same as a round wheel?

Let's start this from the beginning. We will assume we are trying to achieve smooth (as in not bumpy) motion with a square wheel.

This means that the motion of the center of the wheel should be in the X direction only, described by "X=V*T", and its Y coordinate should remain constant.

We can reverse the roles, and picture the surface moving beneath a wheel that rotates in one spot at a uniform rate.

Assume our "wheel" is some length "L" floobles (:) to the side (it's a square, remember?) This means that when it's resting "upright" - or on the midpoint of its side - the surface is L/2 floobles away.

When the "wheel" is in a "diagonal" position, the surface is (√2) * (L/2) floobles away from the center.

hrmph... the next step eludes me for now

Posted by levik on 2002-11-21 09:46:43