Spinning Machine is actually called a picker....

The spindle table and the spinning wheel are basically correct, but the spinning machine is what we (wool/fiber spinners) call a "picker". This is used to pull apart fiber and lets 'vegetable matter' (hay and weeds) that is trapped in the fiber fall out so the fiber is easier to process. I know this seems like a small thing, but it seems to me that you would want to have it correct.