Trochoid

The curve described by a point at a distance $b$ from the center of a rolling Circle of Radius $a$.

$$x = a\phi-b\sin\phi$$

$$y = a-b\cos\phi.$$

If $b<a$, the curve is a Curtate Cycloid. If $b=a$, the curve is a Cycloid. If $b>a$, the curve is a Prolate Cycloid.

See also Curtate Cycloid, Cycloid, Prolate Cycloid

References

Lee, X. ``Trochoid.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/Trochoid_dir/trochoid.html.

Wagon, S. Mathematica in Action. New York: W. H. Freeman, pp. 46-50, 1991.

Yates, R. C. ``Trochoids.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 233-236, 1952.