﻿ Differential Planetary Gears

# Differential Planetary Gears

## Differential Gear-Trains

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 Driver Gears. The Annulus is the Output Gear.
 2 Annulus and the Carrier are Driver 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

#### VARIATION 1: Carrier (C) and Sun (S) as Drivers; Driven Annulus (A)

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

 STEP 2: Join Part with a Pin-Joint to a Point at the end of Line in the Base-Part

Steps 1 and 2 are complete.

Both Gear-Pairs use the CAD-Line along the centre of Part as the Line-of-centres.

 STEP 3: Join Part with a Pin-Joint to the Point in Part

Step 3 is not complete...

The Point at the end of Part is selected (it is red) and

The Pin-Joint, with two Points, is about to be clicked.

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. Point is not ambiguous.

 • The second Point in the Pin-Joint is ambiguous.

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

We must select the Point7 in Part because Line is in Part and is the Line-of-centres.

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

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

Step 3 is complete

 STEP 4: Add two Rocker Motion-Dimension FBs to the two Parts
 • A Rocker Motion-Dimension FB between the CAD-Line in Part and the Line in the Base-Part.
 • See Motion-Dimension [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 Part and the CAD-Line in Part.
 • See Motion-Dimension [Remember: Only, the Pin-Joint2 is available for the Rocker as Pin-Joint 1 is used.]

Step 4 is complete

 STEP 5: Add a new Part to the end of the Part

Select the Cad-Lines in Parts. Note: New Numbers in the image for Elements

Step 5 complete.

Step 6 not complete.

Step 6 complete.

 STEP 7: Edit the Gear-Pair

Edit: Number-of-Teeth and Module:

 • Gear 1 = 60
 • Gear 2 = 30
 • Module =3

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

Step 9 is not complete...

Point at the end of Part is selected (it is red) and the Point at the Pin-Joint is clicked.

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. Point is not ambiguous.

 • The second Point in the Pin-Joint is ambiguous.

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

We must select the Point7 in Part (again) because it is the Line-of-centres.

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

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

Step 9 is complete.

With reference to the image:

 • Select the CAD-Lines in Parts

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

Step 11 is complete.

 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.

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