# How to calculate gear tooth position while assembling a planet gear?

A stepped planet series gear looks like this:

Given that:

• Planet gears are evenly distributed (with 120°)
• Sun-gear-1 and Sun-gear-2 is lined up.
• Sun gear tooth counts: nS1, nS2
• Planet gear tooth counts: nFGS (first gear step), nSGS (second gear step)
• Ring gear tooth count: nR1
• Ring gear belongs to Sun-gear-1 and FGS
• One tooth of FGS and one tooth of SGS is lined up (on the same line to the center) and marked with M.
• FGS of Planet-gear-1 is touching the Ring at Mth tooth.

In order to assemble this gearbox:

• Make M point of first-gear-step of Planet-gear-1 touch the Ring at Ring-tooth-0.
• Make M point of first-gear-step of Planet-gear-2 touch the Ring at Ring-tooth-x.
• Make M point of first-gear-step of Planet-gear-3 touch the Ring at Ring-tooth-y.
• Roll the Planet-gear-2 to R1/3th tooth of the Ring.
• Roll the Planet-gear-3 to R1*2/3th tooth of the Ring.

In this procedure, how do we calculate x and y values?

# Example Case

Taken from http://tricolour.net/rohloff.html

I realized I needed to turn each index tooth by 2/3 of a tooth to get it to mesh.

Index tooth (M point) of the gears are marked with a black dot in the picture.

• Maybe something is being lost in translation, but shouldn't x and y just be R1/3 and 2*R1/3 since the planets are equally spaced?
– jko
Sep 9 '20 at 11:38
• @jko No. I added the example case, please see my edit. Sep 10 '20 at 5:21