I don't know if I'd say a lot of math, but it can get confusing. There are a few different ways to use a planetary. Coming from a drill I'm sure they use max reduction, which is holding the ring gear, spinning the sun (pinion), and the carrier for the planets is the output.
I "THINK" I have this right.....
You need to know the number of teeth of the pinion and the ring. The number of teeth of the planets doesn't matter.
Calculate the gear ratio from those 2 numbers. Then add 1.
Example... 12 tooth sun, 24 tooth ring, is 2:1, add 1 and it's 3:1.
Now if you were to hold the sun and spin the ring, using the planets as output still, it's different.... 12/24 = 0.5:1, add one = 1.5:1 (I THINK?)
Holding the planet carrier and spinning the sun, ring as ouput, it's just 24/12 or 2:1 but spinning backward.
Holding planets, spinning ring, sun as output, it's 0.5:1 also spinning backward.
I believe an automatic 3 speed tranny has a single planetary gear set for everything.... I'd have to look to verify it. First gear uses that 3:1 example, second gear uses 1.5:1, 3rd gear is direct drive straight through. Reverse is the 2:1 spinning backward setup. 4 speed auto's I know use 2 sets of planetaries, but I just can't remember on the 3 speeds.... can someone else help out?