<< Click to Display Table of Contents >> Navigation: Getting Started Tutorials  MechDesigner > Tutorial 14: GearPairs / RackPinions > B: Orbiting Gear Centres > Hypotrochoid: Hypocycloid, Contracted and Protracted 
Hypotrochoid Curves are produced by a Point an GearPair, with an Internal Mesh. The Gear that Orbits can be Inside or Outside the Stationary Gear.
•Orbiting Inside: The standard Hypocycloid Gears  see below •Orbiting Outside The Peritrochoid Gears  See Peritrochoid Curves The shape of the Hypotrochoid curve depends on the ratio of the gearteeth. With gears, the ratio is a rational number. Therefore, the curve will repeat eventually, even if the gear ratio is a ratio of two prime numbers. 

Inside The Orbiting Gear is half the diameter of the fixed gear: 1 : 2 Curve is the Hypocycloid It is of the Point on the pitchcircle of the Orbiting Gear  . It is straight line. Hypotrochoid Curves The Hypotrochoid Curves are ellipses. Curves are of Point on the outside the pitchcircle . Curve is of a Point on inside of the pitchcircle. 

The revolving gear inside has 36T: the outside gear has 48T Hypocycloid The image shows one trace point that is on the pitchcircle It is the Hypocycloid. Hypotrochoid The image shows two curves of points outside the pitchcircle. You can see the curve is near to a square. You can use the EulerSavary Equation to calculate the best distance from the center of the orbiting gear to give a curve with the best straightline curve.


Hypocycloid One curve that is given by a point on the pitchcircle  it is the Hypocycloid The Gear Ratio is 48:18 

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 Hypocycloid StraightLine Epicyclic GearPair configuration. 