An epicyclic gear train consists of two gears mounted so that the center of one gear rotates about the center of the other. A carrier connects the centers of the two gears and rotates to carry one gear, called the planet gear, around the other, called the sun gear. The planet and the sun gears mesh so that their pitch circles roll without slip. A point in the circle of the planetary gear traces an epicycloid curve. In this simplified case, the planetary gear is fixed and the planetary gears rotate around the planetary gear.
An epicyclic gear train can be mounted so that the planetary gear rolls within the passing circle of a fixed, external gear ring or ring gear, sometimes called an annular gear. In this case, the curve drawn by a point on the planet's pitch circle is a hypocycloid. The combination of epicyclic gear trains with a planet that engages both a solar gear and a crown is called a planetary train. In this case, the ring gear is usually fixed and the solar gear is driven.
The epicyclic gears get their name from their earliest application, which was the modeling of the movements of the planets in the heavens. Believing that the planets, like everything in the heavens, were perfect, could only travel in perfect circles, but their movements seen from Earth could not be reconciled with circular motion. Around 500 BC, the Greeks invented the idea of epicycles, of circles traveling over circular orbits. With this theory, Claudius Ptolemy at Almagest in AD 148 was able to predict planetary orbital paths. The Antikythera Mechanism, circa 80 BC, had a gear that was able to approach the elliptical path of the Moon through the heavens, and even to correct the nine-year precession of that path. (Of course, the Greeks would have seen it not elliptical, but rather epicyclic, movement).