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In my opinion, centre-crank-driven wheels are not really suited for production spinning due to the stop-and-start procedure already mentioned in depth. On old illustrations, these smaller spindle-equipped wheels are often found in the context of weaving workshops - there might also be some spinning shown in these pictures, but the presence of looms makes it pretty clear to me that we have winding wheels in action here.
Small wheels, centre-crank-driven and equipped with a flyer, however, are a different beast altogether, and they were definitely used for spinning, as lots and lots of pictures show.
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The game-changer here is the flyer, though, as it eliminates the need to stop and start the drive wheel by conveniently twisting and winding the spun yarn at the same time. So once you've brought your wheel up to convenient speed, you can happily crank on to keep that speed and spin with your free hand.
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Rijksmuseum NL, see the original file here.
So - centre-crank driven wheel with spindle - winding wheel, centre-crank driven wheel with flyer - spinning wheel; though this is not a Great Wheel, then, obviously.
Also obviously, turning the crank requires one hand, leaving only one hand free for drafting. This means these wheels are always shown with an attached or accompanying distaff to hold the fibre and provide some resistance for drafting. Since the speed that you can build up turning the crank on the small wheel and the ratio between the wheel and the flyer pulley is not going to be very high, these wheels will not give you a yarn with particularly high twist, and the bobbins do not look large enough to accommodate sensible quantities of really thick yarn, which would be nicely stable with relatively little twist. So my personal opinion is that these spinning tools were predominantly used for flax/hemp/nettle, long fibres that do not need a large amount of twist and that can be drafted quite easily with one hand only.