﻿ Gear-Trains: Planetary and Compound-Planetary

Step 14.5: Planetary Gear-Trains

Planetary Gear-Trains

A Planetary Gear Train.

 • One or more gears (planets) are held in a 'Carrier'. The Carrier rotates gears that themselves may be fixed or rotating with respect to their own axes.
 • The motion of the planet gears consist of a rotation about their own axes and a rotation about the centre axes of the coaxial gears.

Note: Modelling Planetary Gear-Pairs has become more complex because of a new MechDesigner 'Rule'.

The new Rule is 'you cannot use the same Line as the 'Line-of-Centres' for more than one Gear-Pair'.

Before R11: You will see below, the models use one Line as the Line-of-Centres for Gear-Pair 1 and Gear-Pair 2.

R11 and after: To add a second Gear-Pair, you must add a second Line [with a dimension] as the Line of Centres and make Pin-Joints with the new second Line. It becomes coincident with the Line-of-Centres' of the first Gear-Pair. The Point at the centre of the Gear 1 in Gear-Pair 2, must be merged, with the point at the centre of Gear 2 in Gear-Pair 1.

'To model Gear-Pair 2, add a Line, to become coincident with the Line-of-Centres of Gear-Pair 1'.

 Planetary Gear Design Arrangements

P = Pinion; S = Sun; A = Ring/Annulus; C = Carrier

The typical arrangement is shown to the left. It consists of a:

 • Central Sun (S) Gear with External Teeth
 • A Ring (A) Gear with Internal Teeth, with the same centre as the Sun Gear
 • Revolving Planet (P) Gears that engage with the Sun and Ring Gear
 • Planet Carrier (C) in which the Planet Pinions are supported.

Note: The Ring is also called the Annulus. Hence the letter 'A' for 'Annulus' Gear.

The Gear Ratios are a function of the gear - A, S or C - you lock. See YouTube video here: http://youtu.be/hXTzO1UXnLs

There are also possibilities where all three members (A, S or C) rotate. They are called Differential Gears.

Planetary Gears
Schematic of Variation 3

Simple Planetary Gear-Trains

There are six drive variations when we keep one gear stationary.

 • Variation 1: The Carrier (C) is the Input; the Sun (S) is Stationary; the Output is (A). Gear Ratio = [ω(1 +1/ω) input turns : 1 output turn]
 • Variation 2: The Carrier (C), is the Input; the Annulus (A) is Stationary; the Output is (S). Gear Ratio = [1/(1+ω) input turns : 1 output turn]
 • Variation 3: The Sun (S), is the Input; the Carrier is Stationary (C); the Output is (A). Gear Ratio = [-ω input turns : 1 output turn]
 • Variation 4: The Sun (S), is the Input; the Annulus (A) is Stationary; the Output is (C). Gear Ratio = [1+ω input turns : 1 output turn]
 • Variation 5: The Annulus (A), is the Input; the Carrier (C) is Stationary; the Output is (S). Gear Ratio = [-1/ω input turns : 1 output turn]
 • Variation 6: The Annulus (A); is the Input: the Sun is Stationary (S); the Output is (C). Gear Ratio = [(1+ω)/ω input turns : 1 output turn]

ω = Number of Sun-Teeth / Number of Annulus-Teeth

Compound Planetary Gear-Trains.

These gear arrangements give different speed ratio options. They will cost more!

When there are three or more planets, as is the usual case, care must be made to make sure the teeth of both planets can engage.

VARIATION 1: Carrier (C) as Driver; Stationary Sun (S); Driven Annulus (A)

 This is a video of the model after I have added Profiles and Extrusions to the Gear-Pairs. You can also see it on YouTube.

Step 1: Add Gear-Pair 1

 1 Make the Base-Value of the Motion-Dimension = 60º
 2 Number-of-Teeth Gear 1 = 60, Number-of-Teeth Gear 2 =30, External Mesh.

The image shows the:

 • Gear 1: Sun Gear - Stationary
 • Line-of-centres: Carrier - Driver
 • Gear 2: Planet Gear - Rolling around the Sun

Step 2: Add Gear-Pair 2

Gear-Pair 2

Gear 1

The new Planet

The new Planet is in all respects, an identical copy to Planet Gear (Gear 2) of Gear-Pair 1

 • The Planet Gear is a child to a Part that rotates at the same Speed as Gear 2 in Gear-Pair 1

Therefore, when we add Gear-Pair 2, we can select the same Part as Gear 2 in Gear-Pair 1

Line-of-centres

Between the centre of the Planet and the centre of the Annulus

Conveniently, this is the same Part and Line that is the Line-of-centres of Gear-Pair 1

Gear 2

The Annulus

 • It is a new Part. It must have a Line and a Part for the Annulus Gear
 • The Line for the Part must radiate from the centre of the Sun Gear

From the above, we must:

 STEP 1: Add a new Part for the Annulus Gear
 STEP 2: Join it with a Pin-Joint to the centre of the Sun Gear
 STEP 3: Add Gear-Pair 2
 STEP 4: Edit Gear-Pair 2

 STEP 1: Add a Part

 STEP 2: Join the New Part to the Sun
 a. Select Add Pin-Joint
 b. Click the Point at the end of the new Part (the 'Free' Part)
 c. Click the Point at the centre of the Sun Gear

There are two Points at the centre of the Sun Gear

MechDesigner does not know which Point at you want to select - it is 'ambiguous'.

The Select Element dialog-box opens. When the Select Element dialog-box opens, you must select all of the elements again.

 • The first Point you select is always at the top of the list.

This is why we select the 'Free' Point first. It is not ambiguous.

 • The second Point is ambiguous.

Which second Point do we select in the Select Elements dialog-box?

The Point MUST be a child to the Sun Gear (Gear 1 of Gear-Pair 1)

If we join the Part to the Base-Part, we will not join it to the Line-of-centres.

We must join it to the Part that is currently the Sun Gear - Part

To 'CTRL + SELECT' the Points:

 1 key down
 2 Select all Elements you need to complete the command, Point and

 STEP 3: Add Gear-Pair 2

Select these four elements.

 1 The 'Green Line' on Gear Part 1
 2 The 'Blue Line' on Gear Part 2
 3 The 'Green Line' that Joins the Gear centres
 4 The Length Dimension of the Green Line that joins the Gear centre (The Part-Editor opens so you can select the length of Part

MechDesigner adds the second Gear-Pair with the default options:

 • External Mesh
 • Equal number-of-teeth
 • Module and Number-of-Teeth to agree with the existing length of the Line-of-centres.

 STEP 4: Edit Gear-Pair 2
 • Internal Mesh
 • Module = 2 [Same as Gear-Pair 1]
 • Number-of-Teeth: Gear 1 = 30 [Same as Planetary Gear of Gear-Pair 1]
 • Number-of-Teeth: Gear 2 = 120. This is the Annulus.

For information: Gear Ratio: = ω(1 +1/ω)

ω = Ratio of Annulus Teeth / Sun Gear Teeth

VARIATION 2: Carrier (C) as Driver; Stationary Annulus (A); Driven Sun (S)

 This is a video of the model after I have added Profiles and Extrusions to the Gear-Pairs.

Step 1: Add Gear-Pair 1

See Step 14.4. Make the Base-Value of the Motion-Dimension = 60º

 1 Number-of-Teeth Gear 1 = 120, Internal Mesh, Number-of-Teeth Gear 2 =30

The image shows the:

 • Gear 1: Annulus Gear - Stationary
 • Line-of-centres: Carrier - Driver
 • Gear 2: Planet Gear - Rolling inside the Annulus

Step 2: Add Gear-Pair 2

Gear-Pair 2

Gear 1

Is the new Planet (identical copy to original)

 • It must be a child to the Part that rotates at the same Speed as Gear 2 of Gear-Pair 1
 • We can make it the same Part as Gear 2 of Gear-Pair 1

Line-of-centres

New: R12 Edit the Carrier Part and add a Line from its end-Point. Make the Line approximately the same as the length of the Carrier Part and with its end-Point near to the start-Point of the Carrier Part. We we finish this model, the Line will be coincident with the CAD-Line along the centre of the Carrier-Part.

Is between the centre of the Planet and the centre of the Annulus

Conveniently, this is the same Part and Line that is the Line-of-centres of Gear-Pair 1

Gear 2

Is the Sun

 • It is a new Part. It must have a Line and Part for the Sun Gear
 • The new Line must radiate from the centre of the Annulus Gear

From the above, we must:

 STEP 1: Add a new Part for the Sun Gear
 STEP 2: Join it with a Pin-Joint to the centre of the Annulus Gear
 STEP 3: Add Gear-Pair 2
 STEP 4: Edit Gear-Pair 2

 STEP 1:

 STEP 2:

Join it with a Pin-Joint to centre of the Sun Gear

 a. Select Add Pin-Joint
 b. Click the Point at the end of the new Part (the 'Free' Part)
 c. Click the Point at the centre of the Annulus Gear

There are two Points at the centre of the Annulus Gear

MechDesigner does not know which Point at you want to select. It is ambiguous.

The Select Element dialog-box opens.

 • The first Point you select is always at the top of the list.

This is why we select a 'Free' Point first. Point is not ambiguous.

 • The second Point is ambiguous.

Which second Point do we select in the Select Elements dialog-box?

The Point MUST be a child to the Annulus Gear (Gear 1 of Gear-Pair 1)

If we join the Part to the Base-Part, it will not be joined to the Line-of-centres.

We must join it to the Part that is currently the Annulus Gear - Part

To select the Points:

 1 key down
 2 Select all Elements needed for the command, Point and

 STEP 3:

Select these four elements.

 1 The 'Green Line' on Gear Part 1
 2 The 'Blue Line' on Gear Part 2
 3 The 'Green Line' that Joins the Gear centres
 4 The Length Dimension of the Green Line that joins the Gear centres (The Part-Editor opens so you can select the length of Part

MechDesigner adds Gear-Pair 2 with the options:

 • External Mesh
 • Equal number-of-teeth
 • Module and Number-of-Teeth to agree with the length of the Line-of-centres.

 STEP 4:

Edit Gear-Pair 2

 • External Mesh
 • Module = 2 [Same as Gear-Pair 1]
 • Number-of-Teeth: Gear 1 = 30 [Same as Planetary Gear of Gear-Pair 1]
 • Number-of-Teeth: Gear 2 = 60. This is the Annulus.

For information: Gear Ratio: = 1 +1/ω

ω = Ratio of Annulus Teeth / Sun Gear Teeth

VARIATION 3: Sun (S) as Driver; Stationary Carrier (C); Driven Annulus (A)

 This is a video of the model after I have added Profiles and Extrusions to the Gear-Pairs

Step 1: Add Gear-Pair 1

See Step 14.1. Make the Base-Value of the Motion-Dimension = 60º

 1 Number-of-Teeth Gear 1 = 60, Number-of-Teeth Gear 2 =30, External Mesh

The image shows the:

 • Gear 1: Sun Gear - Rotates
 • Line-of-centres: Carrier - Stationary
 • Gear 2: Planet Gear - Turns on its axis as Sun rotates

Step 2: Add Gear-Pair 2

Gear-Pair 2

Gear 1

Is the new Planet (identical copy to original)

 • It must be a child to a Part that rotates at the same Speed as Gear 2 of Gear-Pair 1
 • We can make it the same Part as Gear 2 of Gear-Pair 1

Line-of-centres

Is between the centre of the Planet and the centre of the Annulus

Conveniently, this is the same Part and Line that is the Line-of-centres of Gear-Pair 1

Gear 2

Is the Annulus

 • It is a new Part. It must have a Line and Part for the Annulus Gear
 • The new Line must radiate from the centre of the Sun Gear, and it must be joined to the Base-Part.

From the above, we must:

 STEP 1: Add a new Part for the Annulus Gear
 STEP 2: Join it with a Pin-Joint to the Base-Part at the centre of the Sun
 STEP 3: Add Gear-Pair 2
 STEP 4: Edit Gear-Pair 2

 STEP 1:

 STEP 2:

Join it with a Pin-Joint to centre of the Sun Gear

 a. Select Add Pin-Joint
 b. Click the Point at the end of the new Part (the 'Free' Part)
 c. Click the Point at the centre of the Sun Gear

There are two Points at the centre of the Sun Gear

MechDesigner does not know which Point at you want to select. It is ambiguous.

The Select Element dialog-box opens.

 • The first Point you select is always at the top of the list.

This is why we select a 'Free' Point first. Point is not ambiguous.

 • The second Point is ambiguous.

Which second Point do we select in the Select Elements dialog-box?

The second Point MUST be a child to the Base-Part

If we join the Part to the Sun Gear, it will not be a child to the Line-of-centres.

We must join it to the Base-Part

To select the Points:

 1 key down
 2 Select all Elements needed for the command, Point and

 STEP 3:

Select these four elements.

 1 The 'Green Line' on Gear Part 1
 2 The 'Blue Line' on Gear Part 2
 3 The 'Green Line' that Joins the Gear centres
 4 The Length Dimension of the Green Line that joins the Gear centres (The Part-Editor opens so you can select the length of Part

The Gear-Pair 2 is added with the default options:

 • External Mesh
 • Equal number-of-teeth
 • Module and Number-of-Teeth to agree with the length of the Line-of-centres.

 STEP 4:

Edit Gear-Pair 2

 • Internal Mesh
 • Module = 2 [Same as Gear-Pair 1]
 • Number-of-Teeth: Gear 1 = 30 [Same as Planetary Gear of Gear-Pair 1]
 • Number-of-Teeth: Gear 2 = 120. This is the Annulus.

For information: Gear Ratio: = -ω

ω = Ratio of Annulus Teeth / Sun Gear Teeth

Help Files for MechDesigner and MotionDesigner 11.1 + © Machine, Mechanism, Motion and Cam Design Software by PSMotion Ltd