Designing a Planetary Gearbox to increase speed?

[IKE]

Originally Posted by Tom Ore

Ns * Ss + Nr * Sr = (Ns+Nr) * Sc

where N is number of teeth and S is speed, s, r, and c are sun, ring, and carrier.

If the speed of the Ring (Sr) is zero then:

Ns * Ss = (Ns + Nr) * Sc

or

Sc= Ns / (Ns + Nr) * Ss

(This is for a simple planetary)

As Tom is showing, technically, all 3 can spin at a given rate. One of the more recent and famous versions of this is the drivetrain of a Prius:
http://en.wikipedia.org/wiki/Hybrid_Synergy_Drive

In your scenario, you are used to seeing a PSR or Planetary speed reducer. This is usually because you have a high speed source (like an electric motor) and want high torque to do some useful work.

Windmills are the opposite and have PSI or planetary speed increasers as they blades produce a lot of torque, but the generator wants higher speeds.