A point on the pitchcircle of a gear that rolls around the outside of a stationary gear gives a curve called an Epicycloid. If the point is not on the pitchcircle of the rolling gear, it has a generic name of Epitrochoid. If the point is inside or outside the pitchcircle: Curtate and Prolate Epitrochoid Curves are traced by a Point that is on a gear that rolls (orbits) around the outside of a fixed internal gear. The shape of the curve depends on the ratio of the teeth. The ratio of the teeth is always a rational number. Therefore, the curve repeats, 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 given by a point on the pitchcircle of the orbiting gear  it is the Epicycloid Epitrochoid Two Protracted Epitrochoid curves are given by points outside the pitchcircle. One Contracted Epitrochoid curves is given by a point inside the pitchcircle. 

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

The Gear ratio is 8: 1 
Gear Ratio is 13:11 
Gear Ratio 2:3 
Gear Ratio 24:6 
Epicycloid and the Hypocycloid Curves that give StraightLines
One of the most basic Epicycloid and Hypocycloid Curves that the GearPairs can give is a perfect Straight Line. Please see YouTube video to show designs. 

Straight Line Curve with Hypocycloid Gears  Internal Mesh The Video shows the TracePoint follows a perfectly straight line. You can see that the smaller gear has half the teeth of the other. This is the standard StraightLine Epicyclic GearPair configuration. 

Straight Line Curve with Epicycloid Gears  External Mesh  1  the Easy Way There are two ways to assemble this mechanism in MechDesigner The not easy, and the easy way. This is the Easy Way 

Straight Line Curve with Epicycloid Gears  External Mesh  2  the Not Easy Way
Spot the difference.
