One of my favorite parts of Feynman's brilliant talk about the limits of minaturizing mechanical devices, "There's plenty of room at the bottom":
"""If, for instance, having made a small lathe with a pantograph, we find its lead screw irregular – more irregular than the large-scale one – we could lap the lead screw against breakable nuts that you can reverse in the usual way back and forth until this lead screw is, at its scale, as accurate as our original lead screws, at our scale.
We can make flats by rubbing unflat surfaces in triplicates together – in three pairs – and the flats then become flatter than the thing you started with. Thus, it is not impossible to improve precision on a small scale by the correct operations. So, when we build this stuff, it is necessary at each step to improve the accuracy of the equipment by working for awhile down there, making accurate lead screws, Johansen blocks, and all the other materials which we use in accurate machine work at the higher level. We have to stop at each level and manufacture all the stuff to go to the next level – a very long and very difficult program. Perhaps you can figure a better way than that to get down to small scale more rapidly."""
Many ideas contributed to the modern process of 5nm lithography, but having flat surface plates whose precision is determined by the correct application of operations rather than an external standard has turned out to be one of the most profound.
Now, of course, you can buy a granite surface place with accuracy exceeding almost anything available 100 years ago, for $30. And there are youtube videos of flat surface aficinados who scrape their own.
Making a precision lead screw is an important step. Maudslay invented the modern metal lathe. His original, from around 1800, is in the Science Museum, London, and it has most of the features of a metal lathe of 1900. Or today.
A screw cutting lathe requires a good lead screw as its reference. Maudslay invented a "screw origination machine"[1], a clever special-purpose device for making a more accurate screw than the one you have. It only cuts soft metal, so the screw it makes is used in a second lathe to make one in hard steel. This is another of the key steps in bootstrapping to precision.
Early precision work was limited to flat things and round things. Take a look at a steam locomotive from around 1900. Every surface that has to be held to a tight tolerance is flat or round. That's because the precision tools of the era were the planer, lathe, and drill. The general purpose milling machine came later.
Incidentally, this is the real reason manholes were round. In the great era of city sewer-building, you could make round metal manhole covers easily, by casting and a quick lathe pass. The ring into which they fit could also be easily finished on a lathe. Making an iron rectangular frame and a lid to fit it would have been a much harder and more expensive job.
Some of this is covered in One Good Turn: The Natural History of the Screwdriver and the Screw, which I enjoyed more than The Perfectionists.
https://www.amazon.com/gp/product/B00CVR143M/
Circa mid-1960s, this defined precision: https://www.amazon.com/Foundations-mechanical-accuracy-Wayne... (at this level of precision, you need a room-within-a-room climate control, because thermal expansion of objects). That leads down the rathole of "jig borers" for making precisely located holes of precise radius and diamond turning machines which are nice for cutting optics.
> Incidentally, this is the real reason manholes were round.
This doesn't pass the sniff test to me. A manhole lid fits loosely in its frame, and is simply cast. The round shape is used ecause that way the lid cannot fall into the hole (frame is a slightly narrower diameter than the lid is in any orientation)
There's a lovely article from 1886, written by Henry Rowland, who made the first decent diffraction gratings. He wrote about his process of lapping the screw threads to take out minor local errors. His screw didn't have to do a lot of work, but it had to be damn uniform.
Interestingly, even after that work, they ended up having to debug a really tricky problem. They sent their gratings to the premier astronomer at Harvard, who reported they weren't "perfect. Eventually this was debugged to a situation where a cam advanced the cutting tool after completing a cutting row, but only occurred when the cable connecting the motor to the tool had a slight bulge due to how the cable was cut and joined.
If you are interested in the history of precision engineering. I can highly recommend the book titled "The Perfectionists: How Precision Engineers Created the Modern World".[1]
It does into detail on how precision manufacturing was created from the beginnings of the industrial revolution until today. The book has some funny anocdotes from history, and despite being quite long i found it easy to read.
If you're going to go down such a rabbit hole, you'll be well served by checking out the ostensible bible on the subject as well, "Foundations of Mechanical Accuracy" by Moore.
This book astounds me. The depths they went to achieve millionth of inch accuracy was crazy. That book is quite expensive and rare it seems. I have a copy but it was 100$+ dollars.
There are a couple guys on YouTube doing very nice demonstrations of high-accuracy operations. One is Ox Tool Company. Interesting grinding operations etc.
Really smart stuff. These machinists of the 1930 1940 1950s were just as clever as John Carmack or whoever your modern nerd heroes are.
Why are people so obsessed with "the real reason" for round manhole covers?
Manholes are round, or were, so that they wouldn't cave in. Everything in a Victorian sewer is round. The passages are too.
You have a round hole in the ground. You need to put a cover on it. Why would you put a square cover? It's going to be smaller than the hole and restrict access or larger than the hole and waste materials.
That's plenty of reason. There doesn't have to be some aspect of machining or a brain-teaser about square covers falling in when on edge or anything else.
We put square covers on round ducts and vice versa for a bunch of reasons in HVAC today. Aesthetics, ease of making dampers, flow... it's a pain in the neck, but we do it, because something is forcing us to. You need a reason to put a square cover on a round hole.
The reason people are obsessed, is that it was published in a book about software interviews, but the stated answers aren't always "right". For example, there are square manhole covers and the world doesn't fall apart. The reason isn't necessarily "because the geometry dictates this answer" but at times was probably expedient.
Even today modern precision work is cheaper for round things than other shapes. This is why you will not see internal combustion engines with square pistons / cylinders.
Something I've discovered by accident is that the lathe sits idle in most machine shops these days. If you can design something that can be made on the lathe, you can often get it done with virtually no waiting time.
I got into machine rebuilding after buying a reasonable 1950's machine shop worth of equipment a few years ago when I started in the auto industry after my master's degree. I happened onto a Craigslist ad of a machine rebuilder going out of business near the office and I picked up basically the whole kit -- cast iron surface plates, power and hand scrapers, bluing medium, etc etc. It took another 6 months before I ran into a guy who was willing to teach me to use all that equipment, up near Flint. He spent a whole career doing fitting and repair for a CNC dealer traveling all over the state and a piece of the rest of the midwest. He was just about the nicest guy I've ever done business with, and he supplies equipment and advice to a huge percentage of the Youtube machinist crowd, plus he saved me the couple grand it would have cost to go take one of Rich King's classes.
All in all, this is a great skill that will persist for a long time, longer than you might think, even if modern machines use replaceable linear rails rather than scraped ways. If you feel like taking it up, watch one of the many Youtube videos from Stefan Gotteswinter or Keith Rucker. Look into the equipment, but think about building your own carbide sharpener, scraper and handle.
I assume he is talking about Richard King. I don't think he has his own channel. but as mentioned Stefan Gotteswinter and Keith Rucker both have videos of the scraping skills they learned from him. (Rucker has actually hosted several of King's classes in his workshop)
edit: I clearly misread the end of OP's post. Definitely not talking about Richard King.
He did years of scraping before he met Rich, but he did take a Rich King class to learn power scraping. Made it easier to justify skipping the expensive class for me.
He doesn't have one, but Solid Rock Machine did a tour of his shop a while ago. He mostly supplies advice and equipment through the grapevine and Practical Machinist.
I remember one of the "ancient aliens" TV shows back in the 70s which claimed that the precision with which Inca masons fitted stones together was impossible without alien technology.
Then an archaeologist showed how fit two stones together with the same precision in about a half hour, using no tools at all. Just rubbing and banging them together.
I asked my mom once how the Egyptians could have possibly made the pyramids straight. She replied pull a long string tight, that's the reference. Figuring I had her this time, I asked how they could have leveled the pyramid foundation. She said dig a trench and fill it with water. The water level forms the reference.
I remember an interview with an archeologist that studied the Nazca Lines. She said one year she had a grad student who was a farm boy. He showed her how to draw a long straight line by setting up a stick a 1000 feet away and then just walking towards it while dragging a another stick behind him. It was perfectly straight.
It's basically the same as the old draftsman's trick for drawing a straight line.
It’s quite accurate, somewhat hard to believe until you try it a few times. Good enough for many layout tasks if you’re drawing a reference line to cut to, for example.
Also works for cutting straight lines with an exacto knife.
I remember a theory (and I’ve no idea if it’s archaeologically verified) that the level for the pyramids was formed by building a wall around the general area. You then flood this with water and wait for it to evaporate / leak out. As the water recedes, every time a piece of land emerges get a squad of slaves to dig it down and level it out. Eventually you end up with a flat plain.
People also made TV shows proving that the Egyptians had discovered pi because pi was in the ratio between the base and the height, or more likely space aliens built it because pi was improbable for the Egyptians.
Then some wit torpedoed it by pointing out that if you used a measuring wheel of 1 cubit in diameter, and measured out the base using so many rotations of the wheel, and measured out the height in cubits, pi is in the ratio without needing to discover it.
A cubit is the distance from a (standardized) man's elbow to his middle fingertip, from Latin "cubitum" = "elbow". Perhaps a more convenient reference than the foot when measuring things that aren't on the ground.
Skilled hand scrapers... can generate plane surfaces accurate to 40 millionts per foot. The same method applied to lapping of glass can generate flats to 1/2 millionth per foot... The average guy working in an open shop careful of cleanliness and uncontrolled heat input to the work will find 0.0005 per foot readily achievable and 0.0002" per foot with a little more care and effort.
Folks who enjoyed this may appreciate Simon Winchester's recent book The Perfectionists, where he covers this method amongst other things. Core to the idea of perfection are machine tools, what we in software often refer to as a toolchain. The way the toolchain revolution allowed us to go from intricate one off clockwork to reliable longitude measurement, better locks, and industrialized machinery parallels compilers, operation systems, etc.
I thought he went rather quickly from some of the earliest processes (boring, for instance) to stuff that's so abstract as to be removed from anybody's practical experience (disregarding metrologists, of course) and then goes farther into philosophical matters than I found interesting.
I would have much more a book that stayed in the realm of machine tools for about half the content, covering the process of bootstrapping precision in the pre-electronic era.
An interesting third quarter could discuss the limits of precision in practical mass manufacturing and the ways we work within tolerances that are economical. The engine block and head of an internal combustion engine have a large and irregularly-shaped mating surface that's subjected to repeated heating and cooling cycles. How flat do they have to be for a gasket to seal them effectively?
The last quarter of the book could cover developments in the era of CNC, and talked about the interplay between electrical components (e.g. stepper motors) and mechanical components (e.g. lead screws, timing belts, etc) and what we gain and lose in using those type of processes. Boring a hole for example, remains more accurate than CNC'ing it on a mill because good control when one x or y approaches zero becomes difficult both mechanically and mathematically.
Anybody interested in this sort of thing might enjoy "How Round is your Circle", by the way.
Have three planes with curvatures c1, c2 and c3. Scraping 1 against 2 results in curvatures: c1' = (c1-c2)/2 and c2'=(c2-c1)/2 (proof is left as an exercise to the reader). The calculation is similar for scraping 1 against 3 and 2 against three. The three scraping operations define three linear transformations on the curvature vector c=(c1, c2, c3): A, B and C.
The article describes a cyclic permutations of these operations, so the final curvature is (A.B.C)^n*c. The absolute value of the largest eigenvalue of A.B.C determines the efficiency of this procedure, it's 1/sqrt(8). It means that by each cycle the slowest mode decays to its 1/sqrt(8) multiple. By each step it decays by (1/sqrt(8))^(1/3) = 1/sqrt(2) on average.
I've been doing woodworking with handtools, and it's amazing what 90 year old tools can do. I bought an old stanley plane in good condition, and was able to start pulling cuttings that are 4/1000" easily. My modern lee valley plane is even easier to set, and I just did a 1/1000" shaving. That means you can surface a piece of wood to 1/1000th of an inch.
This is the kind of accuracy you typically associate with modern CNC machining.
Wood is an interesting medium - it's always in motion so it's in some ways more challenging than working with steel. You can't just machine and glue wood together if you want to make something that'll last for centuries, like old furniture used to. The art is still alive, and I encourage people to check it out!
I think most people would say, although you might observe such sizes when cutting wood, temperature and humidity will swamp out those precisions within a day or two.
The YouTube channel oxtoolco has a video showing lapping of surface plates. Not the same as hand scraping, but the principle of using a reference surface is similar, and the master plate looks like the illustrations in this 100-year old document. Plus I think with modern synthetic diamond abrasives, you can directly lap the plates against each other.
I am no machinist, but I like the glimpse into the hobby/profession shown on channels like this and others that comments have mentioned. In the video, the channel owner hires a company to service his stone regency plates, so there is an expert who comes and uses specialized tools to measure and then flatten the plates (and certify them too). You can see and experience the expertise that the guy has with these physical systems, yet it’s just one niche job in a huge engineering tool chain. It really made me think a lot about metal machining and fabrication, and how those rely on fundamental measurements and properties such as flatness.
While I was studying engineering I worked in a machine shop. In that time I hand scraped or lapped a good few bearings and surfaces. Fast forward six years, researching optical sensing, and I've had to pull those old tricks out of the bag recently. For some reason, of all the skills and techniques I've learned, manual or academic, making a properly flat surface remains the most satisfying.
Today, large telescope mirrors are finished using ion figuring: neutral atoms are shot at the surface of the mirror blank, for a precision ablation of a few angstroms. This works especially well for hexagonal mirror segments, because you can control the surface shape right to the edge of the mirror. Mechanical figuring (using ceramic or glass blanks) has troubles near the edge.
About 25? years ago I bought the book How to make a Telescope and two six-inch blanks and grinding materials and set off to grind my own mirror. I never finished (it was super boring and really humid in the basement of my rented apartment) and I have no idea where the "blanks" are anymore but now I live in an area well outside of town where I can see the Milky Way with the naked eye if my neighbors turn their lights off so it might not be a bad project to restart.
Bonus: I have the room to build a grinding machine so I don't have to do it all by hand.
Hand grinding telescope lenses (well, usually mirrors) is a fairly accessible hobby; you need patience more than anything else. It’s amazing how little technology you need to attain sub-micrometer precision.
I like this video from John Dobson about handmade telescopes, where he builds a complete telescope including hand grinding the mirrors. https://www.youtube.com/watch?v=snz7JJlSZvw
From what I understand, hand-grinding small mirrors is down to process as much as skill. Solid grinding compounds, once they start to wear, end up wearing themselves too. If you keep the pieces moving just so, you can eyeball a rough radius with the grinding material, and it will smooth itself out while smoothing the glass until they mate up.
Basically once you have a wheel with a high precision axle, you can make lots of curves or straight lines.
I'm familiar the the bubble, Morty. I also dabble in precicion, and if you think you can even approach it with your sad, naked, caveman eyeball and a bubble of f* air, you're the reason this species is a failure, and it makes mis angry!
People wanting a full treatise on hand scraping should look into Machine Tool Reconditioning by Connelly, available on the used market and the usual other sources. A close runner up for books is Foundations of Mechanical Accuracy by Moore. If you can get a physical copy of the latter, and can afford it, you should - the photographs are magnificent.
Thanks for submission, a really interesting read! I'm into restoring old woodworking machinery, and hand scraping is one of the methods for truing lathe ways that I've read about. Could possibly be required for the Walker-Turner lathe I'm working on. :)
Also a woodworker here. I have to ask: how bad are the ways on this lathe and how could they get worn? Moving the banjo and tailstock on a wood lathe shouldn't wear the ways the way the routine use of a metal lathe wears the ways.
I haven't gotten to measuring wear on the ways yet, don't think I'll need to scrape them but that's a possibility. This is a pet project of mine, a barn find that was in a pretty bad shape when I got it: rusty, crusty, with missing parts and undesirable modifications by previous owners. Specifically the ways are pitted from rust; worse in places that were exposed to the elements. I'll have to try and measure the effect of this pitting on tailstock positioning. I don't think banjo positioning is going to be affected, the ways are not that bad. But then there's always the obsession with perfection, so who knows. :)
I have a soft spot for pre-1950 Walker-Turner machinery, their aestetics are off the charts; I'm trying to restore this lathe to its former glory, or even better. Not quite a classic car showroom condition but as close to it as I can get without spending a fortune in time and money. :)
The current stage is painting; turned out it's pretty tricky to spray glossy enamel so it would level out smooth! Especially in our cool and humid coastal climate, paint takes a while to dry and even longer to fully cure so the process is quite challenging. Not to mention the countless hours it took to grind out casting imperfections, apply bondo filler, sand it, etc etc.
I thought I was getting into woodworking but found that restoring machinery is lots of fun in its own right, and nothing compares to the satisfaction of using a well made and beautifully restored vintage tool. Especially when I'm the one who did the restoration. :)
Ah, I hadn't thought of rust. Good call. My experience with the tops of my table saw and band saw is that as long as they were ground pretty smooth originally, they don't really pit and I can scrape the superficial rust off and have a pretty good surface. They were, however, stored inside-ish. I could see a barn find in bad shape suffering a lot more than that.
I love the look of the old W-T stuff too, but I've somehow become a Delta man for the stationary tools, probably because of the ubiquity of their old stuff. None of mine is old enough to have the really nice castings. My Unisaw is from '78, and it has the sheet metal base rather than the old cast one. My 14" band saw is (I think) pre-war, but the original buyer didn't spring for the cast art-deco base :-(
Do you have pictures or a build thread on this project? I'd love to see it. And kudos to you for doing the paint and cosmetic stuff. There is nothing I hate more than doing paint.
My Unisaw is covered in years of (somebody else's) overspray. I've stripped it off the chromed fence rails because it was interfering with it working, but the cabinet? Screw it. I can live with it. My 14" drill press, however was flaking off (somebody else's) 3 or more poorly applied coats onto me and anything I drilled. I stripped and repainted that, but that's how bad it has to be for me to entertain painting. The paint job is not what anybody would call flawless, but at least it isn't coming off :-D
> I could see a barn find in bad shape suffering a lot more than that.
Yeah well, in between being a bottom feeder and looking for fun, machines usually come to me as project pieces rather than usable tools. :) I'd never opted to restore any of these rust buckets if I'd depend on them to do woodworking for a living; that said, the purpose of a hobby is to occupy my mind and give me a challenge that is rarely encountered in my day job anymore. So, the rustier, the better. :)
> I've somehow become a Delta man for the stationary tools, probably because of the ubiquity of their old stuff.
I can definitely relate to that, W-T makes a minority of my resto projects. Most of them are Delta as well, as I'm looking to build myself a fully equipped vintage woodworking shop. I'm almost there in fact, as several projects are nearing the assembly stage: a '64 Unisaw, a '52 HD Shaper (going in tandem with the Unisaw), a '54 14" bandsaw, a '60 combo sander, a mid-50s LD shaper, and a '42 6" jointer that I got for free in a total rust-bucket condition. That one was a challenge in itself, especially the motor.
It's just Walker-Turner machines are so beautiful, they're special. Next up after the lathe is a 1939 16" bandsaw, the final quest machine that I acquired last fall. I'll have to fight scope creep real hard on that one...
> My 14" band saw is (I think) pre-war, but the original buyer didn't spring for the cast art-deco base :-(
Ye shall seek and ye shall find, if you want to. :) Besides trawling your local Craigslist (that's where I find my projects), sign up on http://www.owwm.org and post an ad in BOYD forum. Cast iron bases do come up for sale somewhat regularly. Beware that even looking at that website is very dangerous, slippery slope ahoy. ;)
> Do you have pictures or a build thread on this project? I'd love to see it.
I don't usually take pics of the resto projects... I guess I'm just lazy. If you're into vintage tool porn, check out the OWWM community I linked above, and its sister site http://vintagemachinery.org. Lots of drool inducing pics there, I really cannot add anything that hasn't been done already. :)
> The paint job is not what anybody would call flawless, but at least it isn't coming off :-D
That's usually enough for many cases... If a machine doesn't have a sentimental value, why, just refurbing it to acceptable mechanical condition is par for the course. That's what I did with my current set of machines; no offense to Grizzly but their utilitarian cabinet saw aestetics do not really justify the amount of work that goes into stripping and repainting. A vintage Unisaw, on the other hand... I had to learn how to do cabinet scale electrolysis derusting, some basic metalworking, spray painting techniques, not to mention mechanical and electrical challenges. Heaps of fun! :)
Checked out your website... Wow. I have a long, long way ahead to that kind of woodworking projects. ;)
Oh dear, another OWWM'er on HN :-) I lurk, but I mostly try to avoid that rabbit hole unless I'm trying to solve a specific problem. Turns out, I waste enough time on the internet already without drooling over the work people do there restoring old machines to better-than-new condition. Seriously, some of those folks are nuts (as you well know).
It sounds like you've got a nice shop going. I'm a little jealous. My stationary tools are actually stashed in a literal barn right now because I no longer have a basement to put a shop in. I work out of a makerspace, but that's closed due to present conditions, so I moved my bench into my living room. I gave in and fetched my band saw, and it's now sitting on my covered porch. And I have no blades for it at the moment. I'm getting a lot of exercise milling lumber entirely by hand. Honestly, my arms are going to fall off (or get huge) if the lockdown continues much longer.
I'm with you on the modern tools, by the way. On the vintage stuff, a lot of companies really took pride in their industrial design (as you well know). And even the totally utilitarian stuff has stylistic variation between manufacturers. The only difference between Grizzly and current Powermatic tools is the color of the paint. I remain hopeful that Festool having proved that there's a market for higher-priced tools means that somebody will start making nice stationary tools again.
That's probably a lot to hope for, though I recently discovered that Northfield is still chugging along and so is Tannewitz. They're out of my price range for the time being, but I hope they survive long enough for my price range to intersect their prices! It's a real pity that Oliver is now yet another nameplate on the same castings from overseas. The school I went to has a vintage 166 jointer and a 399 planer that I'm in love with.
> Checked out your website... Wow. I have a long, long way ahead to that kind of woodworking projects. ;)
Thanks! I'm a long way from making actual money at this. I'm lucky to be married to somebody very supportive. We'll see how the economy does. I have a couple of paid projects that appear to be holding, and we'll see where things go from there. I guess there's always software to go back to?
The worst thing is neglect, rust, and accidental damage. In low volume use, e.g. proto shop or home shop, the ways should be virtually eternal. Keep them covered, clean and oiled.
If I'm on a desert island, I know how to make a flat plane via ABC grinding. How do I make a right angle? Do I decide on a measure, grind 12 gauge blocks to the same height and make a 3-4-5 triangle?
First, you make a surface gauge. A heavy weighted base with a pointer you can vary in height and distance from the base. You scrape/grind the base flat using a surface plate as reference.
You take something you think is roughly square (a long rectangular prism is good), scrape/grind one face flat with one of your surface plates. We'll call this face 1. Then scrape/grind the opposite face flat, and using the surface gauge to check height (position the box with face 1 down on a surface plate. Position the gauge next to it, with the point touching face 2 somewhere. Slide the gauge back and forth: if it gets pushed up face 2 is tilted up in that direction with respect to face 1. If a gap forms under the tip, it's tilted down.) and thereby get it parallel with face 1.
Then scrape/grind two faces which are adjacent to each the first and opposite each other flat. You now have a shape like \_/ or |_/ or such, though with a top parallel to the bottom.
You stick your surface gauge along one side, touching at the base and at some point near the top of that side with the indicating point. You then turn the WIP straight edge box 180 degrees, and see if the other side touches the indicating tip or the base first. The distance from touching both at once tells you how far out of parallel that side is from the first. You then proceed to scrape them both to be a bit more flat and parallel. Then you turn the box onto its top (face 2) and repeat that. Using 180 degree rotations in two dimensions will get you a good square.
Another thing that can be used as a check (if you can draw) is to build a compass and a straightedge. Side 1 of your box is a good straightedge! You can then use basic geometric construction to make a right angle, and can compare any finished box to that angle.
Practically, the fastest and easiest way would be to turn a good cylinder and measure the diameter at several points (or roll on a surface plane) to make sure it's not tapered, because the face will sit square to the sides even if the axis cutting the face is concave.
More fundamentally though, you can use a similar method -- start with a surface plate, and make three almost-90-degree right angles. Label them A, B, and C.
Scrape A and B so they perfectly mate with each other while they sit flat on the surface plate. They might be something like 89 degrees and 91 degrees, so scrape C to be a copy of B, and then mate it with B. From that you can tell if they're both acute or obtuse, do the correction, and repeat.
Same method essentially. You need three roughly square pieces that are checked for bearing against each other repeatedly, but this time you also have intermediate steps of checking each face for flatness against the master.
While I find random publications--such as this page from _Audels machinists and tool makers handy book_, page 245 Fig 10 & 11 'Method of shifting belt of a counter shaft drive lathe while running...' [1]--about industrial processes utterly fascinating, this one on the Truly Flat Plane is abstruse.
I am reminded of a problem faced by geometers in antiquity of building straightedges; how do you draw a straight line when you have no existing straight line to copy from?
I've done this myself recently, and it's a worthwhile experience if you have the patience for it.
If the short treatise in the OP interests you, I would suggest the book 'Foundations of Mechanical Accuracy', PDF easily available though I won't link here. I can also recommend the bible of hand scraping, 'Machine Tool Reconditioning and Applications of Hand Scraping' otherwise known as the Connelley Book.
When I was in high school, it was popular among some of the students to make telescope mirrors. The technique of hand-grinding them to incredible perfection was both simple and astounding.
It's interesting to get more precise and accurate machines out of the ones came before.
These days, if you want to get milling and grinding down to 1 micron without lapping using only your own expertise and some parts from eBay (air bearings and precision-ground slabs):
It wasn't nearly so easy. Dan hand-scraped in several surfaces on the lathe; for example the headstock, to get the axis parallel to the ways, and so on.
I read this on a whim and now I'm amazed: I never considered algorithms as part of mechanical engineering. Very clever. And in a pedantic reading of Richard Dawkins, this is the kind of "meme" he was talking about.
I never considered algorithms as part of mechanical engineering.
Oh, yes. Metal work is all about calculating. The classic book is "Machinery's Handbook", published for 105 years. Machinist's toolboxes often have a built-in space for it.
The "bible" though, is "Foundations of Mechanical Accuracy" by Moore. Machinery's Handbook is more of a practical reference used in the shop (like when you want to know what a certain spline or thread profile should look like), whereas Foundations is more theoretical.
Is there a good book for sheet metal bending? There are lots of things I'd like to make, but when I think through it, the bends always run into each other (at least in my head). Which is why I haven't bought a break yet. Would love to learn the basics about tools, marking, cutting. (My cuts always drift, and deform the metal, would like to learn how to NOT do that.)
"""If, for instance, having made a small lathe with a pantograph, we find its lead screw irregular – more irregular than the large-scale one – we could lap the lead screw against breakable nuts that you can reverse in the usual way back and forth until this lead screw is, at its scale, as accurate as our original lead screws, at our scale.
We can make flats by rubbing unflat surfaces in triplicates together – in three pairs – and the flats then become flatter than the thing you started with. Thus, it is not impossible to improve precision on a small scale by the correct operations. So, when we build this stuff, it is necessary at each step to improve the accuracy of the equipment by working for awhile down there, making accurate lead screws, Johansen blocks, and all the other materials which we use in accurate machine work at the higher level. We have to stop at each level and manufacture all the stuff to go to the next level – a very long and very difficult program. Perhaps you can figure a better way than that to get down to small scale more rapidly."""
Many ideas contributed to the modern process of 5nm lithography, but having flat surface plates whose precision is determined by the correct application of operations rather than an external standard has turned out to be one of the most profound.
Now, of course, you can buy a granite surface place with accuracy exceeding almost anything available 100 years ago, for $30. And there are youtube videos of flat surface aficinados who scrape their own.