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I've recently been trying some woodwork. If I want a cube of wood 33 millimetres on a side, I buy a stick of wood hat has been planed down to 33 millimeters on a side with square corners, I set up a mitre saw, I make two pencil marks 33mm apart on the edge of the wood, put the wood on a flat table and extend the marks across the side of the wood using a square resting on the table. I make sure the blade is in the same position relative to the mark each time I cut. I clamp the bar of wood to the back of the saw housing in two places, and I cut twice. If I've been careful the cube is 33mm rather than 34mm.
I believe that a competent metalworker could make a metal cube 33.00 millimeters on a side, I've read about Fabry-Perot etalons which are essentially glass blocks with one dimension precisely 33.0000 millimeters. Where would I look for information at the boringly-detailed level of accuracy that I gave for woodwork of how these extra orders of accuracy are obtained?
I suppose I'm looking for information at a grade that would satisfy a six-year-old's sense of recursive questioning - yes, you measure it with a micrometer, but how did you make the micrometer and ensure it was accurate. I guess this is a one-term module taken in the first year of a mechanical engineering degree, but what's the best textbook for that course?
I believe that a competent metalworker could make a metal cube 33.00 millimeters on a side, I've read about Fabry-Perot etalons which are essentially glass blocks with one dimension precisely 33.0000 millimeters. Where would I look for information at the boringly-detailed level of accuracy that I gave for woodwork of how these extra orders of accuracy are obtained?
I suppose I'm looking for information at a grade that would satisfy a six-year-old's sense of recursive questioning - yes, you measure it with a micrometer, but how did you make the micrometer and ensure it was accurate. I guess this is a one-term module taken in the first year of a mechanical engineering degree, but what's the best textbook for that course?
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Fine-grained hardwoods can be shaped to .3mm or so, and it's not that hard, but I think even hardwoods expand and shrink a bit with humidity, so you'd have to be careful how you used the finished part. In general I would mark, do a test cut so that I could see how much material cutting would lose, cut outside the line, and fine-sand to finish. At that level of precision, an accurate ruler and a magnifying glass is enough, though you might want calipers and a micrometer.
33.00 mm is probably pretty easy in hard metal, but I'm not sure about brass--it might not hold the shape; bronze is harder and might do better. At that level of precision, I believe micrometers and calipers are still used, but I think optical technologies have become more common. Machinists and engineers handbooks give information about cutting precision for various tools--the handbooks will tell you, for instance, how much additional material a particular bit or laser-cutting technique will remove.
At the highest levels of precision, optical interferometry is a typical method of measurement. I think the reasons ceramics are used for high precision is that they're easier to work than metals, they hold shapes slightly better, and they have low coefficients of thermal expansion.