﻿ Peritrochoid, Epitrochoid, Hypotrochoid

# Hypotrochoid: Hypocycloid, Contracted and Protracted

### OPTION 2: ORBITING GEAR CENTRES

#### Hypocycloid and Hypotrochoid Curves

Hypotrochoid Curves are produced by a Point on a gear that rolls (orbits) around the inside of the fixed gear.

There are two sets of Hypotrochoid Curves.

 • The Stationary Gear has inward facing teeth with the revolving gear orbiting inside.
 • The Stationary Gear has outward facing teeth with the revolving gear orbiting outside. These curves are sometimes called Peritrochoid Curves. See Peritrochoid Curves

This topic shows Hypotrochoid Curves.

The shape of the Hypotrochoid 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, for example. The Revolving Gear is half the diameter of the fixed gear..

The revolving gear is inside, and is half the diameter of the fixed outside gear.

There are four curves

One curve is given by a point on the pitch-circle - it is the Hypocycloid

In this case, when the ratio of teeth is 1:2, it is a straight line.

Hypotrochoid Curves

In this case the three other curves are ellipses.

Two curves  are given by points outside the pitch-circle

One curve is given by a point inside the pitch-circle The revolving gear inside, is 2.3 the diameter of the fixed outside gear.

Hypoycloid

The image shows one trace point that is on the pitch-circle

It is the Hypocycloid.

Hypotrochoid

The image shows two curves of points outside the pitch-circle.

You can see the curve is approximately a square.

You can use the Euler-Savary Equation to calculate the best distance from the centre of the orbiting gear to give a curve with the best 'straight-line' curve. Gear Ratio is 48:18
There is ONE Curve.
You must rotate the carrier 3 times to complete the Hypocycloid Path.

Hypocycloid

One curve that is given by a point on the pitch-circle - it is the Hypocycloid

The Gear Ratio is 48:18. Straight Line Curve with Hypocycloid Gears - Internal Mesh

The Video shows the Trace-Point follows a perfectly straight line.

You can see that the smaller gear has half the teeth of the other.

This is the standard Straight-Line Epicyclic Gear-Pair configuration.

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