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Turbo and Kerry give spot on answers... I think of it a little differently, but it just helps me wrap what braincells I have left around the concept:

Maximum Sprocket = what shimano says is the biggest cog I can put back there. In reality there are times when I might be able to get away with a tooth or two more.

Total Capacity = how much chain the pulley cage is designed for... just how much can it take up the slack? The bigger values are the long cage types, usually mean't for triple chainrings, while the smaller values are for doubles.

Drone 5200 said:
What's the difference between "maximum sprocket" and "total capacity" for a derailleur?

Shimano's website says the RD-7700 and RD-7800 have a max sprocket of 27T and a total capacity of 29T. While the RD-7703 has a max sprocket of 27T and a total capacity of 38T.

What is "total capacity"?
 

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I haven't done it myself, but I have seen it done. The one bike I saw it on worked fine.

Drone 5200 said:
WOW! I'm impressed. You are a knowledgeable crowd. Thanks for sharing the wisdom. And so fast, too.

One follow-up: Is that 27T max for real? Anyone with experience using a 29T on the RD-7800?
 
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