France, because of the skew between EN and FR, it won't be easy to find a generic term, I don't think...

The EN emphasizes the function of this 'member', whereas the FR will likely emphaisez its form.

So although something fuzzy like 'élément' (actually no fuzzier than 'member'!) may well suffice, in practice you really need to know exactly what KIND of member it is: a rotary element like a gear wheel, or a shaft, or perhaps even something that slides or reciprocates.

If you can find out any more about how this machine actually operates, maybe get to see a drawing, then you may be able to come up with a more precise term.