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.

Epicycloid-Limacon

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 curve2s is given by a point on the pitch-circle of the orbiting gear - it is the Epicycloid

Epitrochoid

Two Prolate Epitrochoid curves3s4s are given by points outside the pitch-circle.

One Curtate Epitrochoid curves1s-red is given by a point inside the pitch-circle.

Epicycloid-Nephroid

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

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 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 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

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

 

Tutorial and Reference Help Files for MechDesigner and MotionDesigner 13.2 + © Machine, Mechanism, Motion and Cam Design Software by PSMotion Ltd