<< Click to Display Table of Contents >> Navigation: Getting Started Tutorials  MechDesigner > Tutorial 14: GearPairs / RackPinions > B: Orbiting Gear Centres > Epictrochoid: Epicycloid, Contracted and Protracted 
Epicyclic Gears are arranged so that a gear rolls around the outside of a fixed gear. You can show a TracePoint of a Point on the rolling gear. The curve is called an Epicycloid if the point is on the pitchcircle of the rolling gear. The curve is called an Epitrochoid if the point is not on the pitchcircle of the rolling gear. If the point is inside of the PitchCircle, it is called Contracted (also Curtate), and if outside the pitchcircle it is called Protracted (also Prolate). Epitrochoid Curves are traced by a Point on a gear that rolls (orbits) around the outside of the fixed internal gear. The shape of the curve depends on the ratio of the teeth. With gears, the ratio of the teeth is always a rational number. Therefore, the curve will always repeat, eventually, even if the gear ratio is a ratio of two prime numbers. 

Equal Number of Gear Teeth. This curve is called a Limaҫon. If the Point is on the PitchCircle it is called a Cardioid. The image shows four curves. Epicycloid One curve is by a Point on the pitchcircle of the orbiting gear  it is the Epicycloid Epitrochoid Prolate Epitrochoid curves are by points outside the pitchcircle. Curtate Epitrochoid curves is given by a point inside the pitchcircle. 

The External Gear is half the diameter of the fixed gear. The image shows four curves. Epicycloid One curve is given by a point on the pitchcircle  it is the Epicycloid Epitrochoid Two curves are by points outside the pitchcircle . One curve is by a point inside the pitchcircle. 

The Gear ratio is 8: 1 There are three curves. 
