Differential Gear-Trains

Differential Schematic

Differential Schematic

These are more complex to model because they have two degrees-of-freedom.

Differential Gears use two independent input drives to rotate a single output shaft.


There are two standard variations:

1.Sun and the Carrier are Driving Gears. The Annulus is the Output Gear.
2.Annulus and the Carrier are Driving Gears. The Sun is the Output Gear.

If you take one as the input and one as the output, the effective gear ratio between them depends on the speed of the third gear.


Differential Gears are frequently used:

to shift the phase of the output shaft relative to the input shaft
to modulate the output speed
where you need a wide gear ratio

QST14-5-1A

tog_minusVARIATION 1: Carrier (C) and Sun (S) as Drivings; Driven Annulus (A)

For information: this is the model after completion of this step.

Profile Elements also added.

QST14-7-1

STEP 1: Add two PartsRed-14-1bRed-14-2
STEP 2: Join PartRed-14-1b with a Pin-JointRed-14-3 to a Point at the end of LineRed-14-4 in the Base-Part

Steps 1 and 2 are complete.

 

Both Gear-Pairs use the CAD-Line along the centre of PartRed-14-1b as the Line-of-centres.

QST14-7-2

STEP 3: Join PartRed-14-2 with a Pin-Joint to the Point in PartRed-14-1b

 

Step 3 is not complete...

The PointRed-14-3 at the end of PartRed-14-2 is selected (it is red) and

The Pin-JointRed-14-5, with two Points, is about to be clicked.

QST14-7-3

The Select Element dialog-box opens.

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

This is why we select a 'Free' Point first. PointRed-14-3 is not ambiguous.

The second Point in the Pin-JointRed-14-5 is ambiguous.

Which Point do we select in the Select Elements dialog-box to complete Add Pin-Joint?

We must select the Point7 in PartRed-14-1b because LineRed-14-4 is in PartRed-14-1b and is the Line-of-centres.

QST14-7-4

To select the elements in the Select Elements dialog-box:

1.Ctrlb down
2.Select all Elements you need to complete the command.

QST14-7-5

Step 3 is complete

QST14-7-6

STEP 4: Add two Rocker Motion-Dimension FBs to the two Parts
A Rocker Motion-Dimension FB between the CAD-Line in PartRed-14-1b and the LineRed-14-4 in the Base-Part.
See Motion-DimensionRed-14-5 (Remember: A Rocker Motion-Dimension needs a Kinematically Defined Line and a 'Free' Line. Only, the Pin-Joint1 satisfies this requirement.)
The Second Motion-Dimension FB is between the CAD-Line in PartRed-14-1b and the CAD-Line in PartRed-14-2.
See Motion-DimensionRed-14-6 (Remember: Only, the Pin-Joint2 is available for the Rocker as Pin-Joint 1 is used.)

Step 4 is complete

Qst14-7-7

STEP 5: Add a new Part to the end of the Part Red-14-1b
STEP 6: Add a Gear-Pair

Select the Cad-Lines in PartsRed-14-1bRed-14-2Red-14-3. Note: New Numbers in the image for Elements

Step 5 complete.

Step 6 not complete.

QST14-7-8

Step 6 complete.

qst14-7-9

STEP 7: Edit the Gear-Pair

 

Edit: Number-of-Teeth and Module:

Gear 1 Red-14-1b = 60
Gear 2 Red-14-2 = 30
Module =3

QST14-7-10

We must now add a second Gear-Pair.

Use the same CAD-Line as the Line-of-centres
Use Gear 2 as the Drive Gear for Gear-Pair 2
Add a new Part as Gear 2 for Gear-Pair 2
STEP 8: Add a new Part Red-14-1b
STEP 9: Add a Pin-Joint

Step 9 is not complete...

PointRed-14-2 at the end of PartRed-14-1b is selected (it is red) and the Point at the Pin-JointRed-14-3 is clicked.

QST14-7-11

The Select Element dialog-box opens.

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

This is why we select a 'Free' Point first. PointRed-14-2 is not ambiguous.

The second Point in the Pin-JointRed-14-3 is ambiguous.

Which Point do we select in the Select Elements dialog-box to complete Add Pin-Joint?

We must select the Point7 in PartRed-14-1b (again) because it is the Line-of-centres.

QST14-7-12

To select the elements in the Select Elements dialog-box:

1.Ctrlb down
2.Select all Elements to complete the command.
3.Click OK

QST14-7-13

Step 9 is complete.

 

STEP 10: Add a Gear-Pair

With reference to the image:

Select the CAD-Lines in PartsRed-14-1bRed-14-2Red-14-3

QST14-7-14

Step 10 is complete.

 

STEP 11: Edit the Gear-Pair

Remember: Double-click the Gear in the graphic-area.

Edit: Number-of-Teeth Module and Mesh

Gear 1Red-14-1b = 30 (the planet gear) same as Gear 2 in the Gear-Pair 1
Gear 2Red-14-2 = 120
Module =3
Internal Mesh for Gear 2

QST14-7-15

Step 11 is complete.

QST14-7-16

STEP 11: Add a Linear-Motion FB
STEP 12: Add two Gearing FBs
STEP 13: Connect the Linear-Motion FB to the Gearing FBs and a Gearing FB to each Motion-Dimension FB
STEP 14: Cycle the Gear-Pairs

Steps 11,12,13 are complete

Edit the Gear Ratio on the Gearing FBs

Motion-Dimension 1 controls the speed of the Carrier

Motion-Dimension 2 controls the speed of the Sun - see note

(Note: Motion-Dimension 2 is relative to Motion-Dimension 1. Hence, a Gear Ratio of 0 given to Motion-Dimension 2 means the Sun rotates at the same speed as Motion-Dimension 1 not necessarily 0.

To stop the rotation of the Sun, you must apply the negative Gear Ratio in the Gearing FBs.

For example,1 and -1 in the Gearing FBs will make the Sun stationary.

Tutorials and Reference Help Files for MechDesigner and MotionDesigner 14.2 + © Machine, Cam, Mechanism, and Motion Design Software by PSMotion Ltd