<P> An epicyclic gear train consists of two gears mounted so that the center of one gear revolves around 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 sun gears mesh so that their pitch circles roll without slip . A point on the pitch circle of the planet gear traces an epicycloid curve . In this simplified case, the sun gear is fixed and the planetary gear (s) roll around the sun gear . </P> <P> An epicyclic gear train can be assembled so the planet gear rolls on the inside of the pitch circle of a fixed, outer gear ring, or ring gear, sometimes called an annular gear . In this case, the curve traced by a point on the pitch circle of the planet is a hypocycloid . </P> <P> The combination of epicycle gear trains with a planet engaging both a sun gear and a ring gear is called a planetary gear train . In this case, the ring gear is usually fixed and the sun gear is driven . </P> <P> Epicyclic gears get their name from their earliest application, which was the modeling of the movements of the planets in the heavens . Believing the planets, as everything in the heavens, to be perfect, they could only travel in perfect circles, but their motions as viewed from Earth could not be reconciled with circular motion . At around 500 BC, the Greeks invented the idea of epicycles, of circles traveling on the circular orbits . With this theory Claudius Ptolemy in the Almagest in 148 AD was able to predict planetary orbital paths . The Antikythera Mechanism, circa 80 BC, had gearing which was able to approximate the moon's elliptical path through the heavens, and even to correct for the nine - year precession of that path . (Of course, the Greeks would have seen it not as elliptical, but rather as epicyclic motion .) </P>

How many gear ratios can be achieved through a planetary gear set