Some mopeds had internally geared hubs.

I am in the middle of researching this and info is scarce but I do know that the Piaggio Ciao has something crazy going on in it.
After reading and looking around it seems it was just used a gear reduction with some models having the rear clutch of a torque converter internal to the wheel.
 
The Caios are Sweet bikes!
Mine and probably 90% of them had a fixed belt and pulley setup with the gear reduction being a separate unit from the moped. Its either a 2 gear or a 5-gear reduction setup that was cast into the wheel, basically just a bigger hub to account for that space.
Vespa-transmissions.jpg


Single-speed Europe and Ohio you got the 14:1 gear ratio to limit the top speed to around 20-25mph. then you got the 7:1 for the higher top end (basically everywhere else)
the variated versions were about 11-12:1 with the only difference being a different shaft for the variated models.
 
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