engineering fundamentals Gears: Epicyclic Train Example
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Epicyclic Train Example

We use the method introduced in Epicyclic Ratio Calculation for determining the final gear ratio of an epicyclic gear train. This method is extremely methodical, which is appropriate since use of intuition is quite futile with an epicyclic gear train such as the following example.


A plan view of the epicyclic gear train arrangement


A 3D view of the epicyclic gear train arrangement

Unlike the previous section, however, we begin by giving the ARM one positive turn (instead of the entire assembly one positive turn). The technique is to choose an arbitrary rotation in which gear movements are intuitively obvious. Some iteration may be required to determine an appropriate set of gear movements to obtain the overall gear ratio.

STEP 1 Set up the following table after having thought about a set of movements which are obvious to visualize:

Action Arm A B C D E
Gears locked, arm given one positive turn.            
Arm locked in vertical position, C turns CW (negatively) once.            
Add the above two columns to obtain the RESULTANT TURNS            

STEP 2 Mentally perform the first row action on the gear train and list the turns, which are obviously all +1 (CCW).

Action Arm A B C D E
Gears locked, arm given one positive turn. +1 +1 +1 +1 +1 +1
Arm locked in vertical position, C turns CW (negatively) once.            
Add the above two columns to obtain the RESULTANT TURNS            

We now must calculate the effects of the second row action. The rotation response of the gears to giving C one negative (CW) turn is determined as follows:

The ARM is stationary:   

Gear A turns are calculated as follows. The negative sign is a result of A and B being external gears.

Gear B turns are calculated as follows.

Gear D turns are the same as those for Gear B.

Gear E turns are calculated as follows.

STEP 3 Now, inputting into the table:

Action Arm A B C D E
Gears locked, arm given one positive turn. +1 +1 +1 +1 +1 +1
Arm locked in vertical position, C turns CW (negatively) once. 0 6.7 -2.3 -1 -2.3 -.78
Add the above two columns to obtain the RESULTANT TURNS            

STEP 4 Now, utilizing superposition to add the two rows:

Action Arm A B C D E
Gears locked, arm given one positive turn. +1 +1 +1 +1 +1 +1
Arm locked in vertical position, C turns CW (negatively) once. 0 6.7 -2.3 -1 -2.3 -.78
Add the above two columns to obtain the RESULTANT TURNS 1 7.7 -1.3 0 -1.3 .22

The overall ratio of the epicyclic gear train can be derived from the last row, as with the previous example.

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