Previously, I have tried to find “theoretically” the tooth counts of the Nexus-7 internal gear hub. Some nice numbers were obtained, but there were some suspects (you may think yourself what **can** be wrong with the numbers given in the link). Soon after, I disassembled the real hub and counted the teeth of all rings. Here are **the real numbers**. This is how the hub works:

- The hub has two
**gear systems**, each with own planet carrier. Call “first” the one which is closer to the sprocket. - The
**axle**is immobile. - Each gear system has:
- Two suns. Either can be immobilized by attaching to the axle with the pawls, activated by the shifter.
- Two gears on the planet carrier, each meshing with own sun. The
**smaller**gear on the planet carrier meshes with the ring. - One ring gear. The ring gear meshes with the
**smaller gear**of the planets.

- In lower gears 1 and 2, power input from the sprocket applies to the
**ring**of the first gear system. This carrier lowers down the transmission ratio. Depending on which sun is locked to the axle by a pawl, two step-down ratios are obtained. The second gear system is not involved. - In higher gears 6 and 7, the first carrier is not involved. Power input from the sprocket applies to the
**planet carrier**of the second gear system. Depending on which sun is locked to the axle by a pawl, two step-up ratios are obtained. The first gear system is not involved. - In middle gears 3, 4 and 5, both gear systems are involved, so that the first lowers the ration, the second raises it.

The table explains which exactly rings are engaged, and gives teeth numbers:

Gear | Power transmission |
Sun | Planet meshed with the sun |
Planet meshed with the ring |
Ring | Exact ratio |
Documented ratio |

1 | Ring1->Planets1 | 42 | 14 | 14 | 72 | 12/19 | 0.632 |

2 | Ring1->Planets1 | 36 | 20 | 20/27 | 0.741 | ||

3 | Gears 1 and 6 together | 0.843 | |||||

4 | Gears 2 and 6 together | 0.989 | |||||

5 | Gears 2 and 7 together | 1.145 | |||||

6 | Planets2->Ring2 | 30 | 19 | 14 | 66 | 279/209 | 1.335 |

7 | Planets2->Ring2 | 36 | 14 | 17/11 | 1.545 |

Note that in the step-up ring (Ring2), 30+19+14=63, while the ring has 66 teeth. I do not understand how so big difference (3 teeth) makes a working combination.