The term I was seeking was a "roulette" curve. http://en.wikipedia.org/wiki/Roulette_%28curve%29 E.g., the focus of a rolling parabola is a catenary. But the main question is: what is the class of curves that can be roulettes on a horizontal line? I.e., What is the class {K | there exists a convex curve C s.t. C rolling (rouletting?) on a line generates K}. At 10:05 AM 11/26/2012, Fred lunnon wrote:

On 11/26/12, Henry Baker <hbaker1@pipeline.com> wrote:

...

A cycloid is produced by a point on a circle as the circle rotates without slipping on a surface.

I think this may have been intended to read something like:

"A cycloid is the curve described by a point on a circle as the circle moves rigidly in the plane, while maintaining contact with a fixed line without slipping."

...

What if we turn the problem around ?

What curves can be produced by another curve rotating without slipping on a surface ?

E.g., a semicircle is produced by a line segment "rotating without slipping" on a surface.

But I'm afraid I still can't decipher this description ... WFL