>>63946225
Archimedean screws are actually part of the flintlock, not just to attach the metal to the wood but the important breech plug. While the screws themselves were not "eyeballed", the tools needed to make them were and everything had to be carefully calculated to fit.

When the Qing attempted to copy British artillery during the unprovoked Chinese aggression against innocent British merchants wars they could not reproduce the elevation screw, apparently unaware of the device, with their artisans casting a similar shaped piece of metal sticking out of the gun with no utility in raising or lowering the gun.

As far as I know the Chinese never had the screw until Europeans brought it to them and even then they were slow to adopt it, certainly the use of precise metal screws and metal nuts. I found this source claiming it was introduced, but jesuits to upper class academics who apparently did not transmit this information to their workers.

https://www.jstor.org/stable/43150795

this is also pretty interesting

https://www.youtube.com/watch?v=X_O1-chxAdk