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PULLEY WHEELS came in different diameters for different speeds. Factories ran on water power or steam power which turned a long axle with take-offs for different types of machinery. This is just one possibility. They were also used on steam powered equipment. Your wheels are smooth, or were smooth before they got rusty. The belts hung loose on the main axle. A long stick hooked the belt and a quick twist put it in place. Removing a moving belt the stick was quickly inserted at an angle which caused the belt to ride up the stick and off the pulley. They are not wheels or handles.
In the OP's second picture I can see an elongated area on the hub at 5:00 which could be where the set screw goes. At this point I think they are pulleys, but they could be wheels.
If you can't see set screws/slots what holds your "wheel" on the axle?
washer and cotter pin like the engine cart photo i attached