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Shimano rotary-shifting 3-speed[1]              
  Number of gear teeth            
Gear Sun Gear   Pinion to Sun Pinion to Ring Ring gear Path: 1=R to P, 2=Direct, 3=P to R Gear Drive Ratio Stage 1 drive ratio as fraction Total Drive Ratio[2] Total drive ratio as fraction Ratio incre- ment
1 42 14 14 72 1 0.632    12/19   0.632    12/19    
2 36 20 14 72 1 0.741    20/27   0.741    20/27   1.173
3 42 14 14 72 2 1.000 1           1.000 1/1[3] 1.350
[1]
John Allen:
Teeth counted by Konstantin Shemyak.
The disassembly/reassembly instructions for the hub, at www.shimano.com/publish/content/global_cycle/en/us/index/tech_support/tech_tips.download.-Par50lparsys-0022-downloadFile.html include detailed photos and drawings.
[2]
This ratio is the product of those of the first and second stages
[3]
John Allen:
Oddly, Excel gives a 4-digit numerator and denominator.