Reddit reviews How Round Is Your Circle?: Where Engineering and Mathematics Meet
We found 6 Reddit comments about How Round Is Your Circle?: Where Engineering and Mathematics Meet. Here are the top ones, ranked by their Reddit score.
Other comments here are spot on.
The simplistic version that underlies all of them is humans are smart so they can identify a problem and approach the desired solution iteratively. This creates a feedback loop.
Before "modern" (the mid to late 1800's onwards) machine tools, you had people making a lot of things custom every time using files to get parts to mate together. There are some exceptions to this with specific measurement and manufacturing tools that were conceived and used but they weren't in wide spread use before the Industrial Revolution and they didn't look as similar to today's machines as everything after. We humans are really good at tweaking stuff slightly until it is far beyond the precision of the individual pieces itself.
Similarly, if I took any old lathe or mill, measured my part to be 0.100" and needed it to be 0.050", I could dial a cut in at 0.05" and take it but depending on the quality and rigidity of the machine, workholding, bearing surfaces and tooling, I would be hard pressed to hit that 0.050" dead on. However, I could take as many passes I wanted while remeasuring until I'm happy with the result. Cut 0.020" off, measure again, I should have 0.030" left but I actually have 0.027" left. Cut again this time at 0.010" and I should have 0.017" left but I have 0.015" left etc.
As others mentioned, the 3 plate method allows you to generate with time and effort, a very precisely flat surface. I could generate that surface, use it as my surface referenced plate and then hand scrape a piece to match it's flatness and squareness to the best of my willingness to work on it. https://en.wikipedia.org/wiki/Hand_scraper if you're unfamiliar. The craftsman inks (blues) up a reference surface, imprints the work piece by rubbing it on that surface. Only the points in contact touch. Using a scraper and some training, you can remove .0002" with a scraper cut. Remove all of the high spots that are blue bringing the high spots closer to the average. Remark and do it again iteratively. Each time you bring your work surface closer to your reference.
The same thing was done with precision lead screws. Hand made screws were cut with primitive methods and put in early lathe like machines to cut more screws. These machines had error compensation methods built in that averaged the thread cutting across the original screw (or sometimes multiple screws) resulting in a screw that was more precise than what you started with.
For calibrating a reference surface for flatness, you can use levels or autocollimators for overall variations. The precision of your level can be increased by increasing the longitudinal radius of your glass bubble dial.
An excerpt from another post I made in /r/cnc:
Some source material to consider:
LINK A great site with collections of documents covering major works in the development of precision tools.
Precision Machine Design - Slocum more of a textbook on precision machine design but has tons of footnotes and talks about some of the developmental history.)
Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance talks about some of the accuracy needed in Oakridge etc to help make the atomic bomb and precision guided missiles before GPS existed even for the military. A number of military interests drove ultra precision development such as this and the large optical diamond turning maching (LODTM)
Rolling Bearings and their contribution to the progress of technology covers the history of bearings that allowed precision machinery.
Machine Tool Reconditioning is an older book and highly technical but is considered the bible for old machine tool rebuilding and goes into the processes of how one would make precision flat surfaces and check all of the geometry on their machines and fix them in a time before lasers and fancy computer controlled equipment.
Foundations of Mechanical Accuracy and the followup book Holes, Contours and Surfaces was written by Moore and his son (I believe, respectively), the first especially is considered a bible on the theory of obtaining super precision tolerances. The authors are part of Moore Tool Company which made amongst other machines Moore Jig Borers.
Mitutoyo has a pdf on the history of gauge blocks
You can further go down that rabbit hole and look at metrology books as one can achieve great tolerances by iteratively approaching a desired value and having proper metrology equipment to check your work as you go. For example, metrology standards
You can also look at old professional telescope building books and newer diy telescope making books as there's a lot of interesting information and techniques to obtain precision optics on the order of wavelengths of light.
As someone else here mentioned: How Round Is Your Circle
I can probably dig up a lot more. I've spent way to much money purchasing old out of print books related to precision machinery, machining and metrology.
From the iterative process of making basic tools, you can then use those tools to make even better tools through iteration. In many ways, it's similar to Moore's law in the electronics world; a exponential curve where we stand on the shoulder of giants and improve upon what already exists. Many have proposed technology as a whole as just that such as Ray Kurzweil in "The Singularity is Near" etc.
Edit: Thanks for the gold!
Here's a really great book that covers this exact topic. Disclaimer: I haven't read it myself, but its on my reading list. It covers some of the history of how precision instruments were first made and the math and engineering behind.
How Round Is Your Circle?: Where Engineering and Mathematics Meet
http://www.amazon.com/dp/0691149925
>How do you draw a straight line? How do you determine if a circle is really round? These may sound like simple or even trivial mathematical problems, but to an engineer the answers can mean the difference between success and failure. How Round Is Your Circle? invites readers to explore many of the same fundamental questions that working engineers deal with every day--it's challenging, hands-on, and fun.
>John Bryant and Chris Sangwin illustrate how physical models are created from abstract mathematical ones. Using elementary geometry and trigonometry, they guide readers through paper-and-pencil reconstructions of mathematical problems and show them how to construct actual physical models themselves--directions included. It's an effective and entertaining way to explain how applied mathematics and engineering work together to solve problems, everything from keeping a piston aligned in its cylinder to ensuring that automotive driveshafts rotate smoothly. Intriguingly, checking the roundness of a manufactured object is trickier than one might think. When does the width of a saw blade affect an engineer's calculations--or, for that matter, the width of a physical line? When does a measurement need to be exact and when will an approximation suffice? Bryant and Sangwin tackle questions like these and enliven their discussions with many fascinating highlights from engineering history. Generously illustrated, How Round Is Your Circle? reveals some of the hidden complexities in everyday things.
Well done!
I think you might enjoy How Round is Your Circle, a book about mechanical approximations (to draw various shapes) and the math behind them.
In addition to Guns, Germs, and Steel:
I recently read this book about circle checking and more. It's quite good but if you're not into math/history/philosophy then I think OP is talking about this.
The problem is you can't do it with a single tool. If we only used a ruler to make a new ruler, which then made a third ruler; each generation is successively worse. By combining a ruler, a level, gauge lengths, etc. you can make more accurate tools down through the generations, which is exactly how we've gotten to the point of creating parts accurate down to tenths of a micrometer.
Theoretically you could 3D print all of the parts needed for a new 3D printer then use traditional manufacturing methods to clean them up - drill, smooth, level, etc. But if you do that you've given up nearly every advantage of 3D printing and made parts unnecessarily expensive. At that point it'd be far cheaper, faster, and easier to just cut the parts out of a hunk of ABS plastic and be done with it.
If you're interested in this, check out How Round is Your Circle and Foundations of Mechanical Accuracy (long out of print but fairly easy to find in libraries). They do a good job of explaining the history of accuracy in mechanical parts.