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Comment by bschne | Hacker News Reader

Extremely naive question, but I always wonder how you can "bootstrap" this kind of precision — intuitively for something to be this precise, the tools and equipment that "create" it should also have to be more or less equally precise.

Or is it a matter of manufacturing it, testing it, and rejecting some percentage of things that don't fit your requirements due to imprecisions?

Are there any good background resources on how some of these things are done?

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Take three somewhat flat stones to start out. Alternate rubbing the surfaces together in a random fashion. As you continue the high spots of the stones will be ground down and the surfaces will become flatter and flatter. In the end you can get very precise flat surfaces.

Two stones is not enough, you can then end up with two spherical surfaces. With three this isn't possible (imagine two of them are convex, when you rub them together they will grind eachother down and become less convex).

With images: https://ericweinhoffer.com/blog/2017/7/30/the-whitworth-thre...

That is, one plate remains stationary while the other is lapped against it, and then the opposite is performed

Is it a strict requirement that one plate remains stationary?

In relative terms, one of the two plates remains stationary even if both are moving.

Obligatory machine thinking: https://www.youtube.com/watch?v=gNRnrn5DE58

Altough, I disagree with the "random fashion". Alternating the pairs AB -> BC -> CA seems more logical to me.

It is necessary to grind in a random fashion (OP is talking about the method of grinding, not the order), or you will end up with imperfections. Lots of info about this if you look in to grinding mirrors for telescopes.

Also, the order being random wouldn't effect the end result.

If it's a machine doing the grinding, what is the source of randomness?

function setPostion(float x=random(), float y=random()){}

I imagine the PRNG they use for this is a rather thorough implementation. Unless perhaps it is even necessary to used a cryptographic chip to generate true randomness.

pseudocode my man, pseudocode. ignite the imagination, and let the reader run wild.

however, now my imagination is now running, and thinking about how overkill "true" random might be for this application. something "random" like an orbital sander would probably be enough. you're just trying to get away from side-to-side, left-circle, right-circle, up/down patterns. you're doing this to 3 different surfaces, so they would grind out any slight patterns which is the point. seems like a try crypto random would be as "effecient" as my roomba appears not to be.

I suppose I went a bit overboard (no pun intended). 1 KB implementation should be more than enough for their precision.

Maybe some code then, instead: https://www.dwitter.net/d/20446

input

When grinding the concave plate why didn't that make then other flat plate convex again?

It did – but less so than the original was concave. By rubbing them together, you're effectively “averaging out” the convex / concavenesses.

As the sibling comment explains, it does make the other flat plate convex, but by a smaller amount. Their shapes sort of average out.

I'll add that this depends on the materials having similar properties, so when ground together, they are grinding each other. This means whatever residual shape you have in one of them, it won't be transferred completely to the other.

If the materials had very different hardnesses, one of them would dominate over the other when they're ground together.

or a long-form textbook on the foundations of mechanical accuracy. Someone linked to this a year ago and I found it a fascinating deep dive:

https://pearl-hifi.com/06_Lit_Archive/15_Mfrs_Publications/M...

From what I've seen as an amateur that is yet fascinated by mechanical engineering: iteratively work up to the precision limits with your current methods then try to find/research a (slightly) better way of measuring and/or manufacturing. Since humanity has worked up to this point over centuries/millenia, you wouldn't need to "bootstrap" it from the beginning anymore, just choose the appropriate level of (manufacturing/measuring) precision for your usecase. Otherwise start with a surface plate.

Nice summary:

https://www.youtube.com/watch?v=gNRnrn5DE58 ("Origins of Precision" by "Machine Thinking")

This is a beautiful video!

On a very high level, a good place to start is on Metrology — the science of measurement [0].

Test, measurement and calibration equipment for new technologies (think 5G/UWB, mmWave, even up to CERN LHC) can be right on the cutting edge of technology. Companies who specialize in these areas tend to have large budgets on research and commercialization.

[0] https://en.m.wikipedia.org/wiki/Metrology

> Are there any good background resources on how some of these things are done?

For a cultural history of precision see The Perfectionists: How Precision Engineers Created the Modern World by Simon Winchester:

* https://www.goodreads.com/book/show/35068671-the-perfectioni...

* https://www.youtube.com/watch?v=RvOEcyYsiHc

Yup, seconded. I was going to recommend that book.

You might enjoy this video, 'Origins of Precision'. https://youtu.be/gNRnrn5DE58

> intuitively for something to be this precise, the tools and equipment that "create" it should also have to be more or less equally precise.

Very reasonable assumption that I used to have too. (Un?)fortunately it's also wrong, or at best, incomplete. :-) e.g., maybe you don't have the technology to make precisely straight lines, but if you can make a flat surface (like paper), then you can fold it in half and get a straight line. Then fold that in half and get a pretty-close-to-90-degree angle.

I also vaguely recall that feedback can increase precision in a system... like you can get 2% accuracy with a circuit that has only 5%-accurate resistors by using feedback (or something along those lines). Unfortunately I no longer recall how this is done. I just remember my mind was blown when I learned it.

Look at the «Whitworth three plate method». As far as I understand, it should allow a «gain» in precision.

You mention it already - bootstrapping. Always optimising, always correcting for yet another flaw in materials, processing, environmental conditions, quality control and usage procedures. Usually, it is helpful that there are multiple ways to do a particular thing that can be used to calibrate each other. Also, there are physical processes that can produce high-quality surface finishes that can be used for calibration tasks, for example by splitting crystals. The resulting shapes are dependent on the crystal lattice, and improvements in material purity reduce any irregularities.

A more general approach is to understand measurement as a process where a minute signal has to be amplified to be more easily evaluated. There are many such methods.

In the case of surface metrology, Coherence scanning interferometry is such a method which uses the properties of interfering light waves to directly visualize surface anomalies as bands of lights. Another, more direct method is to drag a stylus across the surface and to amplify variations in position. Sort of like a turntable does.

On a related note, there's the powerful technique of doing things in a way where the factor(s) that are difficult to measure or control cancel out.

Examples of this is the device[1] used for the redefined kilogram[2], LIGO[3] and many others.

[1]: https://www.nist.gov/si-redefinition/kilogram-kibble-balance

[2]: https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_ba...

[3]: https://www.ligo.caltech.edu/LA/page/faq (first question)

Simon Winchester's book "The Perfectionists" [1] is a good popular level intro to Maudsley, Whitworth et al.

[1] https://www.amazon.com/Exactly-Precision-Engineers-Created-M...

NB: I guess he changed the title to Exactly for the paperback release.

>Extremely naive question, but I always wonder how you can "bootstrap" this kind of precision — intuitively for something to be this precise, the tools and equipment that "create" it should also have to be more or less equally precise.

You can build a machine like that and most machines are built like that because simply reproducing the precision that is already in the machine is cheaper than building a complex intelligent system that knows how to compensate for flaws in precision. Think about how many 3d printers do auto leveling in software rather than simply make the bed perpendicular to the print head by hand. Those old manual milling machines and lathes didn't have all that fancy software so they simply reproduced their own flaws.

Well, given a smart enough human he can compensate for the flaws in the tools and get to a higher degree of precision.

> Extremely naive question, but I always wonder how you can "bootstrap" this kind of precision

Scraping https://www.toyoda.com/news-events/rpd-blog-the-importance-o...

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