OPTION 2: ORBITING GEAR CENTRES
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.
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 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
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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.
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VARIATION 1: Carrier (C) as Driving Gear; Stationary Sun (S); Driven Annulus (A)
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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.
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Step 1: Add Gear-Pair 1
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See 'How to Add a Gear-Pair with an Orbiting Centre'
| 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 |
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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 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 |
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Add a Part
| STEP 2: | Join the new Part to the Sun |
| 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'.
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The Select Element dialog-box opens. When the Select Element dialog-box opens, you must select ALL of the elements again.
Because we selected the 'Free' Point first.
| • | The Free- Point is at the top of the list. |
| • | 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)
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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 |
| 3. | key up |
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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 |
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MechDesigner adds the second Gear-Pair with the default options:
| • | Module and Number-of-Teeth to agree with the existing length of the Line-of-centres. |
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| • | 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
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VARIATION 2: Carrier (C) as Driving Gear Stationary Annulus (A); Driven Sun (S)
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This is a video of the model after I have added Profiles and Extrusions to the Gear-Pairs.
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Step 1: Add Gear-Pair 1
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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 |
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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
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 |
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| STEP 1: | Add a Part |
| STEP 2: | Join it with a Pin-Joint to centre of the Sun Gear |
| 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.
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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.
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, Points and |
| 3. | key up |
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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 |
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MechDesigner adds Gear-Pair 2 with the options:
| • | Module and Number-of-Teeth to agree with the length of the Line-of-centres. |
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| • | 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
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VARIATION 3: Sun (S) as Driving Gear; Stationary Carrier (C); Driven Annulus (A)
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This is a video of the model after I have added Profiles and Extrusions to the Gear-Pairs
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Step 1: Add Gear-Pair 1
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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 |
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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 |
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| STEP 1: | Add a Part |
| STEP 2: | Join it with a Pin-Joint to centre of the Sun Gear |
| 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
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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 |
| 3. | key down |
|
|
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 |
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The Gear-Pair 2 is added with the default options:
| • | Module and Number-of-Teeth to agree with the length of the Line-of-centres. |
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| • | 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
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