# Locklin on science

## Ruling engines and lapping the ultimate screw

Posted in Design, metalshop, Progress by Scott Locklin on April 16, 2022

The story of the ruling engine is one of those bizarro incredibly important things that has slipped into obscurity, only really known by people still directly involved in this sort of thing. I was briefly involved in this area working at LBNL’s Advanced Light Source, measuring diffraction gratings, their efficiencies, and attempting to estimate how well they’d work in presence of error. I promptly forgot almost all of it in favor of learning how to pants goth girls or whatever I repurposed that set of brain cells for, but it’s still in there rattling around somewhere.

Diffraction gratings are those little rainbow thingees on your credit card. Or if you’re old, you remember the rainbow patterns on CDs, those were sort of ad-hoc diffraction gratings. Ultimately it is a set of very precise lines across a mirror substrate. There are all kinds of profiles and shapes of diffraction gratings for different purposes, but they all work roughly the same way. Different wavelengths of light are reflected into different angles via constructive interference. The simple grating equation is $\sin(\theta_m)=\sin(\theta) + m \frac{\lambda}{\Lambda}$ where $m$ is the diffracted order, $\theta_m$ is the angle of the diffracted order, $\Lambda$ is the periodicity of the grating, and $\lambda$ is the wavelength of the light diffracted.

This is a long winded way of saying if you reflect light on a grating, it will make a nice rainbow pattern. If you make a slit out of razorblades (this is basically what people use) perpendicular to the first order diffraction angle, you get a monochromator or spectrograph, depending on how you use it. This means you can resolve narrow lines in the spectra of whatever it is you’re looking at. Of course, nothing is perfect, least of all diffraction gratings. There’s a figure of merit in spectroscopy called resolving power; $R = \frac{\lambda}{\Delta \lambda}$ where $\lambda$ is the approximate wavelength of interest and $\Delta \lambda$ is the narrowness of line you want to resolve. It’s easy to show that R is proportional to the number of coherently illuminated perfect grating lines, and that any error in grating line shape or tracking will cause R to be smaller. So  if you want to discover quantum mechanics, you need to make some nice lines otherwise you’re wasting your time. Oh yeah, and obviously if you want to resolve smaller wavelengths of light, say, in the UV, you need to rule your gratings with smaller lines.

Over complex representation of a monochromator or spectrograph

Now a days we have a number of ways of making gratings, but the first way (still important and used) is using a ruling engine, which is a very fine machine tool which mechanically draws lines on a substrate using a diamond anvil. The first important such tool was Rowland’s mentioned several times now; literally the machine that launched American physics and made quantum mechanics possible. There were gratings made before, but Rowland’s was the first to make useful gratings repeatedly. For decades it was the only one capable of making decent gratings; like a machine made by super intelligent alien beings that nobody else can figure out. For decades after this, all the subsequent ruling engines that worked were Rowland designs. The first successful ruling engine which wasn’t a Rowland design is the topic of the rest of this blog; that invented by the underappreciated experimental physicist John Donovan Strong (I’ve definitely been in the same room as him early in my career, but I can’t say I remember anything about him –his book is amazing BTW). This is the type of ruling engine still used today, more or less, with some additional complications of using feedback mechanisms made possible by electronics over the years. I’m following Strong’s article from 1951 as well as a couple of  Scientific American articles.

The original Rowland machine was a sort of overgrown and ultra precise metal shaper (or for a more familiar example; a grocery store meat slicer). Strong took his design cues from the much more uncommon metal planer. The difference, Rowland’s machine advanced the relatively heavy grating blank using the precision screw, making the screw subject to mechanical deformation and stick slip, while moving the diamond using ways that could wear out.  Remember, this thing is making long, straight lines, very precisely on the order of 1000/2000 lines per millimeter; a perfect line every 500-1000 nanometers. Real nanotechnology; not the imaginary kind done with Schroedinger’s equation and pixie dust. For contrast, an atom is around a tenth of a nanometer. While they call the latest semiconductor technology 14nm, it’s really more like 100nm, and diffraction gratings built with screws were doing that, over much larger areas than a defect free wafer more than 140 years ago using doodads such as these very precise screws. There were seven major sources of error with this design in absence of mechanical or manufacturing defects, to give an idea of the type of thing involved here; they were referred to as the “seven demons.”

1. Stick slip/lubrication forces of the various moving parts caused large irregularities.
2. Wear in the various parts of the engine were also hugely important; the carriage might travel miles in ruling a grating and the Rowland carriage was a big beefy object.
3. The metal parts also contain locked-up stresses from creation from raw ore to machining; as the machine ages, the stresses relieve and the perfect surfaces deform.
4. Creep also takes place from external forces; sag, motion, weight support.
5. Any vibration may cause bad gratings to be made; one worker correlated his grating defects to the swaying of trees outside the building (this is huge with optics in general, especially in current year with all kinds of machinery around and driving by).
6. Dust of course is a big problem; get dust under the diamond cutter or in the screw/nut interface and you’re, well, screwed.
7. Finally, the heat radiated by a human body can cause sufficient creep in the engine to ruin a grating.

Strong’s gizmo obviated the stick slip problem by moving the diamond rather than the grating blank, removing the ways for moving the diamond, and improving both the lubrication of the screwing mechanisms, and the alignment techniques.  His thing used two precision screws to advance the diamond, and as they’re pointing in opposite directions, they can cancel out pressure and sag errors as well as angular “fanning” errors in the grating ruling (Rowland’s machine had microradian misalignments that borked the resolving power via this fanning effect; a microradian across a few inches is easily a wavelength of green light). Downside; you need two nice screws instead of just one.

Strong’s exposition was fascinating. He points out that precision in his day was entirely “primitive methods.” Aka geometry, averaging and lapping compounds. The dividing heads on the screws for making microscopic motions were self lapped in place on an oil bath. Instead of a kinematic mounting system for moving the grating, he overconstrained it with multiple ways which averaged out to a nice straight line.

Strong was a great scientist who understood machinery and tooling in great detail. He also had a couple of helpers he credited with his success. One of them was Wilbur Perry, an engineer trained at WPI. Before he went to school he made a bunch of telescopes, and was a proud member of the Springfield Vermont telescope makers society, which still maintains a clubhouse. Let me emphasize the implications of this: a tiny town of a few thousand people had a telescope makers society at the turn of the century, when telescopes were still high technology, and they endowed it well enough it is still physically there. That’s sort of like a small town of a few thousand people having its own privately owned MEMS fab in the 1990s when this became a more common technology. Social capital is highly underappreciated and they had lots of it in those days. Strong himself got many of his ideas for the ruling engine from hanging out in a club he founded with John Anderson (the previous John Hopkins Rowland engine driver); the “100-to-1 shot club.” Some nice oral history before it fades away: an interview with Henry Victor Neher:

NEHER: This was a small group that was formed at Caltech in about 1934 or ’35. The
way it originated was this. John Anderson, who was at the Mount Wilson Observatory, had an office at Caltech when he was working on the 200-inch telescope, back in the thirties. One of the members of the staff was a young fellow by the name of John Strong [professor of physics and astrophysics, 1937-1942], who had his experimental equipment in the same room in Bridge as I did. John Strong was over talking to John Anderson one day. John Strong was always interested in ideas of one sort or another. He was an inventor if there ever was one. John thought that there ought to be a group that considered far-out ideas of one sort or another.

INTERVIEWER: For example.

NEHER: Primarily ideas connected with something scientific or mechanical, or something of that sort. And John Anderson said, “Well, what you are suggesting is to discuss things that have one chance in a hundred of working.” And so, this is the way the 100-to-1 Shot Club was formed. They got a group together which consisted of John Strong, John Anderson, Russell Porter, Roger Hayward—who did that picture up there above the fireplace—and then some others not connected with the Institute, like Byron Graves. And there were a couple of patent attorneys in the group.
Well, I didn’t get into it right away. I guess it was about 1936 or ’37 before I became associated with it. We met once a month at various members’ homes. It was mostly discussions of ideas in connection with astronomy or with physics. There may have been some mechanical things. One of the members was George Mitchell, who designed and made the Mitchell camera that was used in Hollywood for years. Another was George Beadle [professor of biology 1946-1961], who joined after World War II.

INTERVIEWER: Did anything ever come out of it?

NEHER: No. It wasn’t meant to be that. It was just a place where you could just discuss anything you wanted.

Or as Strong himself put it:

We called it the “100 to 1 Shot Club.” We met at various member’s houses at Palomar; in the Mohave Desert; etc. — about 6 or 7 times a year. It was called by the name mentioned to indicate that our considerations (like: Does the water spin in a contrary way in the Southern hemisphere when it runs out of the bath tub? — etc.) were restricted to topics that were fantastic by a factor of 100:1 over scientific. The dozen members included: Trim Barkelov — patent council for Paramount Pictures Roger Hayward — artist and architect Victor Neher laboratory roommate George Mitchell — millionaire manufacturer of the Mitchell camera; a former Hollywood camera man Byron Graves — an amateur astronomer and retired executive from Ford Co. in Detroit John Anderson — my boss Jack McMorris — a chemist (and disappointed concert pianist) George Worrell — successor to Mitchell at the Camera plant Milton Humason — astronomer I mention this because it was a group worthy to go down in history.

The importance of such clubs can’t be overestimated. They’re everywhere in the annals of technological history; from Wernher von Braun and company’s rocket club, to the famous Lunar society, to the X club even the Bohemian Club was responsible for the US nuclear weapons program. Most great human ventures have started in some sort of men’s club. And yes, they were/are men’s clubs, u mad? As my pal BAP put it, only the most depraved ancient Greek tyrants would ban men’s associations:

A brotherhood of men in this form is the foundation of all higher life in general: there is a certain madness, an enthusiasm that exists also in a community of true scientists or artists…. it is totally forbidden in our time…. the dedication, severity, focus and enthusiasm necessary to sustain true scientific enterprise are forbidden because they make women and weaklings uncomfortable.

To remove stress in the screw blanks, he had two garbage cans with inner cells, one for heat the other for dry ice,  so he could stress relieve the screws before the finish cuts. He dipped them in what he called “tincture of skunk cabbage” (overheated Mazola corn oil at 400F, 100F) and “hobo cocktails” (dry ice and alcohol at 10, -60 and -100F). He did this stress relief cycle 50 times per screw.

When he moved on to lapping, he rigged up a tape recorder which kept a record of the torque  of the screw being lapped in its giant split nut. This way he could keep track of progress on the lapping process and the recorder would tell him when there was a burr or requirement for more lapping compound. Mind you this is a 1940s era tape recorder, so in addition to being a great machinist, he must have known a thing or two about electronics back in the vacuum tube era. He also rigged up a motor mechanism and ran the thing on his wall in his basement.

Apparently the whole new ruling engine worked the first time, which is a minor miracle. A hugely successful scientific breakthrough done with a sort of miniature Klein type-1 organization. More of a Klein type-1 A-team;  a common type of group for successful experimental physics ventures. The origins in a couple of men’s clubs and a couple of obscure working class geniuses makes it all the more sweet.

It’s also an object lesson in why current year can’t have nice things. No men’s clubs thanks to various vile and pathetic tyrannies. No working class craftsmen making things in matter. No physicists who understand how a fucking screw works (who worked on the Kansas wheat harvests).  And tens of thousands of nincompoops fiddling around on a computer instead of learning how matter works with the eyes and fingers. The very idea of using such mechanical creativity by talking to other artificers and hammer and tongs precision work is anathema to current year bugmen. I’m pretty sure they’d find a way to call the whole project sexist and racist because they don’t understand how a fucking screw lap works either.

That is the biggest advance in the grating art that I am responsible for. I also made an advance in the lapping of lead screws that is recognized in industry. I developed several techniques which are useful in precision machine tool practice. And that was a consequence of the work on ruling engines. But my work on ruling engines, in a sense, was supernumerary, because now the control of the relative position of the ruling engines components is accomplished by interferometry. Here Harrison was the pioneer.

## From ancient Gears and Screws to Quantum Mechanics

Posted in Design, metalshop, Progress by Scott Locklin on April 10, 2022

The geared mechanical clock, like the pipe organ and the Gothic cathedral is a defining symbol of Western Civilization. Division of the day into mechanically measured hours  unrelated to the movements of the sun is a mechanical symbol of the defeat of the tyranny of nature by human ingenuity and machine culture. The hours of the day used to be something measured locally by the position of the sun. The liturgy of the hours of the Catholic Church caused north-western Europeans to go all spergy and design intricate machines to tell the monks when to say their prayers, rather than using arbitrary times. After all in the sperdo north, it’s often cloudy or dark very early or barely at all: you need something better than the sun to tell the time.

There’s an oldest surviving clock; that of the Salisbury Cathedral (allegedly 1386). It’s an interesting enough looking mechanism, foliot and verge escapement (the first known mechanical escapement for counting the seconds); you can see it running here. These early clocks had the advantage over water clocks in that you didn’t need to haul water up the tower, and they didn’t freeze in the cold northern winter.

One of the interesting mysteries of technological history; nobody knows where gears came from. A gear is sort of like a wheel, or a pulley system, both of which existed long before the gear. There are claims that the Chinese had them before anyone else; the south-facing wagon is a postulated example, though the first document of it was by Yen-Su in the 11th century, long after such mechanisms were in common use in the West.  As with most of early Chinese history, this isn’t well documented and it may have been nonsense. Unless they influenced the Greeks directly, which doesn’t seem to have ever happened otherwise, the Chinese developments weren’t important in a world historical context.

As with most things, the first documented gears are Greek. Aristotle wrote about them in his physics book around 340BC -around the time of Alexander the Great. Ctesibius was first we know of to write about the things (~250BC) being used in interesting ways; his stuff all lost, but written about by later thinkers; he also invented the pipe organ. It has been suggested that water wheels using lantern pinions were the first gears: we learn of them via Vitruvius (probably originally Ctesibius). We know that Heron of Alexandra had well developed gear trains; he described some effectively like the backgears in a lathe. Archimedes invented the worm gear and pinion used in modern clockworks; possibly also the spiral bevel gears used in differentials.

The most shockingly advanced early geared mechanism is the Antikytheria mechanism. It’s one of those things people didn’t for some reason expect, but if you read old astronomy books, I’m virtually certain such mechanisms are much older. The epicyclic theories of Eudoxus (375BC) and Callippus (330 BC) were pretty explicitly gearworks; later expanded by Hipparchus and Claudius Ptolemy, who was contemporary with the Antikytheria mechanism. It’s entirely possible there were no gearworks before Posidonius (maybe) brought us the Antikytheria mechanism. I suppose it’s possible there were no gearworks after. But it seems vastly more likely we didn’t just randomly pick up a unique space alien technology toy off the sea bed, and there are probably more such treasures still buried in other places, perhaps even sitting somewhere in a Museum storage closet.

My pet theory, for which there is exactly zero evidence, is that gears were very ancient and lost with the late Bronze age collapse. Certainly they had brasses and small drills and the ability to fabricate elaborate objects out of much harder materials. Since the Greeks didn’t mention where they got the basic gear idea, I’m assuming it existed before they started making more clever versions of it. I suppose such things could have existed in some other culture (Sumerian, Egyptian, whatever), but it’s my pet theory; feel free to come up with your own.

The Screw might have been an invention of Archimedes as well, though some historians attribute it to a more forgotten artificer called Archytas (my pal Eudoxus‘ teacher from the time of Plato). Screws were used in the Mediterranean region for olive and grape presses. There is a widespread misapprehension that the science of the ancient Greeks was some kind of theoretical construct: not so. The mechanical and scientific ideas of the great ancient philosophers and the Alexandrian Museum were used by ordinary people on a daily basis. From screw presses to waterwheel contraptions, the Hellenistic and Roman world benefited from the applications of Greek thought.

Gears allow one to change the plane of rotary motion, or the angular velocity of the rotary motion. Screws turn rotary motion into linear motion, generally considerably stepped down in velocity. You need both to make something like a modern clock or a mechanical lathe. Screws are commonplace now and used everywhere, but they really are a wonder. An inclined plane wrapped around a cylinder. Early screws were made with tools like hammer and chisel, with taps and dies made in the same way, various kinds of ingenious mechanisms to assist the process.

Making the first set of standardized and precise screws took until around 1800, culminating in Henry Maudslay‘s screw cutting lathe which was one of the most important inventions in human history. The screw cutting lathe required a screw and gears, combined together on a rigid lathe bed. The lathe bed is effectively a plane, allowing for precise motion. You can make these with a chisel and scraper/file out of arbitrary chunks of steel or cast iron; hobbyists still carve and scrape their own lathe beds. The leadscrew allowed the cutter to automatically move along a piece of rotating stock to cut another thread in a piece of rotating stock. Changegears allowed one to cut arbitrary threads from stock, by altering the ratio of screw linear motion to workstock rotation. With all these ingredients you can move a cutter along a piece of rotating screw blank an arbitrary amount, making arbitrary pitch screws. What’s more, you can amplify the accuracy of your leadscrew to a certain extent. There are heroic tales of Maudslay creating his master leadscrew that are in their own way as glorious and Promethean as Benvenuto Cellini casting his Perseus statue.

Maudslay is one of those guys who created a whole center of excellence around himself; he was a blacksmith/locksmith who built a classic Klein type-1 organization. He invented all manner of clever devices we now take for granted, from micrometers to various kinds of steam engine and telescope; he was even involved with the father of Isambard Kingdom Brunel building machines for his various ventures. Maudsley’s students (it wasn’t a school, it was a high technology business) went on to make numerous further innovations and form their own high technology companies. Joseph Whitworth invented all kinds of machine screw standards (BSW still in use today) machine tools and measuring devices, guns and so on and became enormously wealthy. Joseph Clement built the first version of the difference engine.  William Muir manufactured machine tools, Richard Roberts made locomotives and  power looms, and James Nasmyth invented the steam hammer and shaping machine.There aren’t any substantive books written about this amazing group of men, and the one I know about is expensive and out of print, but if done properly it would make an excellent case study of a Klein type-1 organization. All of these guys were giants of invention and industry and they all got stinking rich inventing new technologies and increasing man’s power over nature. There’s a sort of pamphlet about Maudsley available on archive, which is slightly better than nothing.  I assume there were contemporaries who wrote about them, but they’re mostly forgotten today.

Back to screws; using a screw, you can precisely position things on a nanoscale. I’ve done it, using these little buggers called picomotors. You can buy big giant screws made in temperature controlled oil baths which are capable of similar tricks while retaining their accuracy as well. It boggled my mind when I first read about how this is accomplished; basically the same way most mechanical accuracy is achieved; by lapping with abrasives. You can read all about it in the old Wayne Moore book “Foundations of Mechanical Accuracy.”

Which brings me back to Henry Rowland, father of American physics. It was Rowland who invented the techniques for creating the ultra precise nanoscale screw by manually lapping the screw in a giant split nut. He did this to create diffraction gratings using a “ruling engline.” Diffraction gratings are responsible for the origin of modern physics, as scientists needed them to resolve atomic spectra. And of course as I said in the previous blog, Rowland was by his own self largely responsible for American physics activities in general.

The story of the ultra-precise screw and ruling engine is so insanely awesome I’ll dedicate a later blerg or two to the topic.