Starting civilization over

A question that came up in conversation had to do with rebuilding civilization from the ground up.

What machine or tool would you want in order to rebuild the other machinery you want and/or need? One thing you need is the ability to measure parts very precisely.

Clayton Cramer's answer to obtaining precise measurements is, quite literally, screw it.

It turns out that most precision machine tools rely on the turn of a screw. The photograph here is of a 1/4-20 machine screw (of which there must be several hundred million sitting around above ground). What is that, exactly? It is a screw that fits in a 1/4" threaded hole, and that has 20 threads per inch (20 tpi). Twenty revolutions will move the screw one inch--and using a micrometer shows that this is really and truly the case--or pretty darn close. That means that moving the screw one revolution (and thus pushing a part against that screw) should move it 1/20th of an inch--and when I measure it, it seems to be .0532", which is about 6% from 1/20th of an inch--and most likely the discrepancy is because the last revolution was a bit more than one turn. Okay, one revolution this gets us to five hundredths of an inch--good, but not good enough to rebuild our machine tool civilization. Notice that nut with the numbers at the base? Hexagonal nuts have six sides--and I have used Liquid Paper and a pen to mark each side with the numbers 0 through 5. If I turn the screw, depending on which number is upright, I can get down one-sixth of five hundredths of an inch--or .0083" of precision. With a little more care--perhaps marking the left and right side of each of those six faces of the nut--we can get down to .00415" precision--or four thousandths of an inch.

And there are other ways you can build in more precision: Mount a large washer on the head of the screw and divide it into sections. Any power of two is easy – the ancient Greeks knew how to bisect any angle. Dividing the circle into six parts is also easy. If you want fifths and tenths, you can, with a little more knowledge, construct a regular pentagon and bisect that. After that, you can use vernier techniques and the mathematics of beats. A washer divided into fifths turning next to a washer divided into sixths will let you measure down to a thirtieth of a turn – down to 1/600 of an inch, probably well below where the slop in how well the screw fits into the nut begins to matter.

Overcome that using a lever. Mount a lever on the end of a screw, and mount your measuring device a tenth of a way out from the fulcrum. Every inch of movement at the end of the lever translates to a tenth of an inch at your measuring point. A twentieth of an inch of movement at the end gives you a two-hundredth of an inch at your measure point.

I saw this a month ago, but it's worth bringing up again.