n. the curve described by a point on (or rigidly connected to) the circumference of a circle as it rolls without slipping on a straight line. The cycloid is extended if the point is outside the circle, and contracted if the point is inside. If the term is used without qualification, usually the common cycloid is intended; the terms trochoid and roulette are sometimes used for the more general concept, and prolate and curtate trochoids are extended and contracted cycloids (or vice versa: there is no consistency about which is which). A cycloid has parametric equations
x = r (θ - sin θ); y = r (1 - cos θ).
Compare epicycloid, hypocycloid. diagram of a cycloid. pg. 134, fig. 108.