﻿ Epictrochoid: Epicycloid, Contracted and Protracted

# Epictrochoid: Epicycloid, Contracted and Protracted

### OPTION 2: ORBITING GEAR CENTRES

#### Epicycloid and Epitrochoid Curves

 Epicyclic Gears are arranged so that a gear rolls around the outside of a fixed gear. You can show a Trace-Point of a Point on the rolling gear. The curve is called an Epicycloid if the point is on the pitch-circle of the rolling gear. The curve is called an Epitrochoid if the point is not on the pitch-circle of the rolling gear. If the point is inside of the Pitch-Circle, it is called 'Contracted [also 'Curtate'], and if outside the pitch-circle 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, even if the gear ratio is a ratio of two prime numbers, for example. Equal Number of Gear Teeth. This curve is called a Limaҫon. If the Point is on the Pitch-Circle it is called a Cardioid. The image shows four curves. Epicycloid One curve is given by a point on the pitch-circle of the orbiting gear - it is the Epicycloid Epitrochoid Two Prolate Epitrochoid curves  are given by points outside the pitch-circle. One Curtate Epitrochoid curves is given by a point inside the pitch-circle. 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 pitch-circle - it is the Epicycloid Epitrochoid Two curves are given by points outside the pitch-circle One curve is given by a point inside the pitch-circle The Gear ratio is 8: 1 There are four curves: 3 outside, one on the pitch-circle Gear Ratio is 13:11 There is ONE curve. Use a Gearing FB to rotate the carrier 11 times to complete the Epicycloid Path. Gear Ratio 2:3 There is ONE Curve. Use a Gearing FB to rotate the carrier 3 times to complete the Epicycloid Path. Gear Ratio 24:6 There is ONE Curve. This is because the ratio reduces to 4:1 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

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