What simple machines have an ability to make a part that is more precise than any available part within a machine?

This is partly related to history about how early machine parts improved in precision. But modern science might have discovered shorter paths to it, those answers are also of interest.

Simple geometries like a ball, screw rod, cylinder, are likely to be the easiest to bootstrap in precision. If you think other shapes like a flat plate or rectangle bar are important, you can describe a path to improve them too.

For example, assuming the first screw is made crudely, by hand. Then screw cutting machine may use this screw to cut another screw, but because screw in the machine may be flipped or shifted, errors of the crude crew will be averaged out, while general structure, the thread, will still be applied. New screw will have higher precision than the initial screw. If you have examples of a simple chain of machines fulfilling the same job, those are also of interest.

https://en.m.wikipedia.org/wiki/Pantograph is often mentioned in discussion on this topic, but I dont think it is quite helpful, because it cant make parts well as big but more precise, or its own parts, such as straight rods or bearing. Or if it can, help me understand how.

My main interest is scale-less geometry precision, so that if error was 1% surface roughness to max length, new version is to have 0.1% surface roughness to max length, regardless if it is bigger or smaller. Exact size match, like making a ball exactly 3cm dia is of interest too, but less so.

TLDR: how would you recreate more precise geometry for a ball, screw, cylinder, if you have only crudely made machines at hand?

  • $\begingroup$ Compass, dividers and even set squares are easily made from crude materials but the results can be very accurate. $\endgroup$
    – Solar Mike
    Feb 6 at 7:14
  • $\begingroup$ I've thought about this question myself, but I think mike basically nailed it. There are processes where precision is created "from nothing", where a precision result can be obtained even if the process components are not themselves precise. For example lapping can create flat surfaces without a flat reference surface. $\endgroup$
    – Drew
    Feb 8 at 21:32

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