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Here's the situation:

I am trying to build a spreadsheet to solve for planetary gear configurations.

I have done most of the work already, but I am getting stuck when solving for planetarydifferentials.

If you don't know, a planetary gear differential is basically a gear set-up that has three shafts that can be used as inputs or outputs.

Let:

S = Speed (in RPM)

N = Number of teeth on the gear

r = ring gear

c = planet carrier

s = sun gear

The relationship can be described by the following equation:

(Sr-Sc)/(Ss-Sc)=Ns/Nr

There are six different configurations I am trying to solve for.

Unfortunately, Algebra and I have been apart for far too long.

Think maybe you can help?

Configuration 1

Ns: known

Nr: known

Sr: known

Sc: known

Ss: not known

Configuration 2

Ns: known

Nr: known

Sr: known

Sc: not known

Ss: not known

Configuration 3

Ns: known

Nr: known

Sr: known

Sc: not known

Ss: known

Configuration 4

Ns: known

Nr: known

Sr: not known

Sc: known

Ss: not known

Configuration 5

Ns: known

Nr: known

Sr: not known

Sc: known

Ss: known

Configuration 6

Ns: known

Nr: known

Sr: not known

Sc: not known

Ss: known

Any help would be greatly appreciated.

Especially if you show me how you did it.

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# Algebra was far too long ago

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