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The reason is alignment. And with that said, flat or cogged belts on stub shafts (bearing on one side of pully/sprocket only) will run away from the bearing. As the load increases and engine, bearings, and chassis flex, the movement will be greatest on the unsupported side of the shaft. This is 1935 FFA stuff.
If you look at an old flat belt drive on a tractor, the stub shaft support always protrudes more than halfway through the pully. This helps to minimize the tendency of the belt to run off of the pully. They also used pulleys that were tapered so as to be slightly smaller in the center of the drive surface. Harley just lets the belt move, and uses fences to keep it on the sprocket.
And Alan is correct about which way they move on different scooters.
If you look at an old flat belt drive on a tractor, the stub shaft support always protrudes more than halfway through the pully. This helps to minimize the tendency of the belt to run off of the pully. They also used pulleys that were tapered so as to be slightly smaller in the center of the drive surface. Harley just lets the belt move, and uses fences to keep it on the sprocket.
And Alan is correct about which way they move on different scooters.