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Centerless cylindrical lapping is a technique used to create a smooth and round cylinder through the use of microscopic abrasive compounds.

My question is a chicken and egg problem, because it seems to me that one would require perfectly round and smooth cylinders to begin with. Is there a requirement of a perfect cylinder to make a perfect cylinder?

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    $\begingroup$ Isn't this a version of the three plane lapping method for flat surfaces? There there's no requirement for perfect initial planes; basically convergence follows due to one of the fixed point theorems. Maybe the same applies here? $\endgroup$ Mar 26, 2022 at 0:28

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I was curious about this question as well. Answer is no. Let me explain.

For achieving precision from nothing you need to somehow provide measurment from one area of an object to all other areas of that object.

Three plate method ahieves thay with plate being in contact with all the area there is, of both other plates. And bumps are measured against all of this surfaces.

With cylinder you can roll it - and get a perfect ring. But for cylinder entirety you need to also move the item by the axis of rotation. And you only can move one on top and only so far before you realise grinding it at the edges ruins the edges. This also doesnt help to do the messurment between two lower cylinders. left part of a one of the lower cylinder never meets right part of the another lower cylinder. Therefore they never make this error go away if it is present.

But there is a similar object that can in fact be made to a higher precision than it was before. It is a screw. Because a screw passes through its entire length along another screw - they can make measurments on the whole screw against every point of another screw. Among all the things that allow to achieve precision from nothing, this is the most significant one I think. More so than three plate method, because screw cutting can be automated much more easily. And once you have a screw of a good precision, you can work your way up to all of mankinds cool machines. Even if you dont have any good machinery to begin with.

Hope this helps with your quest, even if I cant give you a good way to make cylinders. Other than making a good screw first, and then use it to make a cylinder.

https://en.m.wikipedia.org/wiki/Screw-cutting_lathe - history section, modern

https://en.m.wikipedia.org/wiki/Surface_plate - history section

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