Today’s banner: metalworking layout tools, improvised, on a glass surface plate (also improvised).

We recently overheard an engineering student ask a really good question: where does precision come from? The manufacture of nearly every precision instrument derives that precision, ultimately, from something else that’s even more precise. Think about that. Infinite recursion, ad infinitum, ad nauseum… Where does it end? What’s the base case? It must be a platonic ideal. Perhaps it pulls itself out of its own navel or something. A realization of the Omphalos Hypothesis. It must invent itself.

We tripped over to the local engineering college’s library where we found a copy of Foundations of Mechanical Accuracy by Wayne R. Moore, 1970, The Moore Tool Company. The copy we found was forty years old. During the last forty years, exactly twelve people had read it. This made us sad. We determined to make up for this dearth of readers by reading it several times.

We discovered that, in fact, the base case is the perfect plane. In the 1830s James Whitworth gave us a simple (if arduous and tedious) method for establishing as a flat plane of reference the surface plate. Surface plates are made as large as needed, and since precision instruments are used to build really big things — think “naval engineering” — by large we mean large, heavy, and extremely rigid. Okay, they’re not as large as an aircraft carrier, but you could stretch out and take a nap on one. If you don’t mind a really hard mattress.

The best surface plates are made of cast iron, or ceramic, or even glass, and are flat to within a millionth of an inch. From this plane — as perfectly flat as we can make it — from this plane can be derived the straightedge, the square, and the precision ways of lathes and milling machines.

In Whitworth’s process, surface plates are manufactured in triplets. Each surface plate is repeatedly compared to the other two, mutually proving each other, their surfaces gradually refined by hand, using a scraper, until no imperfections can be detected. How are imperfections found? One way is to paint one surface with a pigment. Try to mate the surfaces of two plates: on the dry surface, any high spots get inked, and any low spots stay dry. When the pigment is uniformly transferred from the wet to the dry surface, we’ve reached the limit of our ability to detect imperfections.

But why make three at a time? It’s a matter of practicality. Surface plates are usually rectangular, so the only easy rotation is 180 degrees. Now image placing a horse’s saddle upside-down atop another saddle. (I know this seems like a totally unrelated tangent, but bear with me.) If the upside-down saddle is rotated ninety degrees, the two saddles will mate well, even though they’re not at all flat. Now rotate that upside-down saddle by 180 degrees. They still mate.

If you do this with a pair of rectangular surface plates with mirrored but matching saddle-shaped deformations, they will appear to mate well. Now suppose the third plate also has a mirrored deformation that mates well with the first plate. Well, it mirrors the first plate, but not the second. The second and third plates won’t mate. So three plates will detect this kind of deformation, allowing the maker to correct the problem.

These days you can’t get much flatter than a good pane of glass. Through an entirely different process, the Pilkington process, so-called “float glass” derives its flatness from gravity. It’s really cool (or rather, very hot): molten glass floats on the surface of molten metal, an alloy chosen to have a low melting point — lower than that of glass. The glass is allowed to cool enough to solidify on the surface of the molten metal. Then you just pluck it out of the pool of molten metal. Not with your bare hands.

As a surface plate in a production line or for large metalwork, a pane of glass would be utterly worthless. But for the hobbyist working on a very small scale, a good, thick pane of glass works great.

We’re going to try using a pane of glass as a surface plate, depending on it to draw really straight lines. We’ll use it derive the centerline of a 2-1/2″ workpiece of 1″x1″ extruded aluminum. (This will only work, by the way, if we know the faces of the workpiece are flat — which we assume but won’t confirm, but could confirm with the pigment trick — and that the faces are parallel. But if it works — if we establish a centerline and can prove it — the parallelism of the workpiece faces will also be confirmed.)

That’s a tube of oil paint from the local art supply store. It’s Prussian blue. Here it’s being smeared onto one face of a small piece of 1″x1″ extruded aluminum. The main reason we’re using it is that scribed lines on bare metal can be hard to see, but a line scribed through a layer of pigment is bright and easy-to-see. We could have used a felt-tipped marker. But we like Prussian blue — it reminds us of finger-painting. Here’s the completed coating:

The scribe is clamped into a dial indicator holder doohickey with a magnetic base, which is stuck to a small piece of flat metal (stolen from an engineer’s metalworking protractor). Here the tip of the scribe has been adjusted to point approximately at the centerline of the workpiece. We intend to find the exact centerline. By simply sliding our scribe-dial-indicator-holder-doohickey-with-a-magnetic-base across the glass surface plate, we scribe a short test line:

We flip the workpiece and try to rescribe the same line, without readjusting the scribe:

When we examine the two test lines, we find that — as expected — they don’t quite align:

Now we adjust the scribe tip. We adjust it to fall between the first two test lines. We then make a new pair of test lines. We repeat the process until the tests lines are as well-aligned as we can make them:

Then, sliding our doohickey, we try scribing a complete centerline. Then we test the centerline: we flip the workpiece, and without adjusting the scribe, we try again, and we check for agreement along the full length:

The scribed lines match, under unaided visual inspection. Just for the heck of it, we added crosshairs. Now comes the fun part: we inspect the line we made:

More detail! We must magnify! We stick the workpiece under a microscope. Here we’ve inkjetted a small millimeter ruler on paper, and we’ve placed it directly below the scribed line, for comparison under the scope:

Our centerline is the single vertical line. Pretty freakin’ spot-on. The parallel scribed lines are our crosshairs. For the heck of it we check the height of the scribe tip:

It lies on the 1/2″ mark, and to the limits of our visual inspection, the alignment is perfect.

Best wishes — stochastic



papercraft keep

Today’s header: an internal dispute in the Wizards’ Keep. Which we made. With paper and glue. (We’re nerds.)

We wanted to give you a complete tour of the keep, and the lake, and the nearby woods, and the surrounding countryside, and — okay, we have more papercraft terrain than can reasonably fit into a single blog post. It’s all the same terrain, part of the same landscape — it’s just really big. Here are two of the five floors of the keep:

The front gate, manned by armed guards:

The entrance to the stables, made of masonry to protect the livestock and the things that we don’t eat but we keep for riding. (Words are hard.) (We’re sure there’s a term for horseys and donkeys and suchlike, but we’re not sure what it is.)

The hayloft is so-situated as to permit dropping bales at the stable’s entrance for easy distribution among the stalls. The page is about to be in trouble for goofing-off.

The keep’s military resources protect a nearby village, and in turn the keep is supported and staffed by the villagers. Here’s one of their cottages:

We’d like to say that a nearby river affords access for commerce, but actually we just wanted a lakeside view. The lake is fed by springs, and in turn drains via an underground river.

As often happens around here, a cat dropped by during photography. Or perhaps it was a catmonster! rampaging through the countryside!

Oh no! The catmonster has invaded the keep, penetrating the defenses as though they were… heh, paper.

Oddly, the catmonster was very careful to not sit on anyone, nor to destroy the walls. Upon reflection, we believe he simply wanted to know whether he would fit in the atrium.

Best wishes,



P.S.: Most of the designs come from Fat Dragon.


lap microlathe

Today’s banner: the Taig MicroLathe. It’s adorable. It’s so small you can hold it in your lap. We’re completely serious:

How cute is that? You could pack it up in a box with some colored paper and take it to a crafting party!

We used it to make the very small collet featured in last week’s post, where we mentioned the need for a tiny slitting saw. Here’s how we did it:

The small silicon-carbide blade is mounted in a Dremel Rotary Tool, mounted to the Taig Lathe milling attachment using parts from a Vanda-Lay Industries Acra Mill Plus. Last week’s collet was parted from the piece of aluminum rod held in the lathe’s four-jawed chuck. Here’s the whole setup:

… One of the cats has made a guest appearance in our brand-new, absurdly-off-the-cuff photo studio. At night we can only see his eyes, which is kind of creepy. We can actually see him today, being as the backdrop is white…

Best — stochastic


Today’s banner: the by-blow of a vacuum vise and a hobby vise, and a squiggly magnetic dial indicator stand, and a dinner plate. And an iPhone.

We made a photo studio!

Read on for component descriptions. First we have the hobbyists’ beloved PanaVise:

A nicely-engineered unbranded dial indicator stand from China — with a really cool mechanical on-off switch for the magnetic base:

A Bessey vacuum vise, which is to say that you can make it stick to things:

And a shiny, unbranded dinner plate. Also from China. We’re not sure why exactly so many Chinese products are unbranded, but we’re pretty happy with the quality.

Below, our new construct is in use to photograph — well, it’s another of our constructs.


Closer still, and it’s clear that we’re still learning about white balance and exposure.

In a subsequent post we’ll showcase the rest of our photo studio, which is also absurdly off-the-cuff, but nicely functional.

Best wishes — stochastic


Today’s banner: inner workings of the Mettler H20 analytical balance, a work of art, a demonstration of stunning artisanship, a 1960s-era substitution balance precise to ten micrograms with a range of 160 grams. It’s analog.

We were shocked. We’d heard of this “analog” before, and we’d encountered the occasional example, but rarely in a device of such complexity.

To be sure, we thought we’d been around. We’ve broken, disassembled, reassembled, repaired and even designed and built a few analog devices in our time (more on this in a future post). But this thing made us humble. More so even than the time we disassembled the 1950s sewing machine (which we did in fact get working again).

Here’s another view of the interior of the Mettler H20. To prevent accumulation of dust we’ve placed a glass pane over the open top.

Notice the variously-sized rings all over the place? They each have a different but very precise mass. There are three sets: combinations of the four large rings total zero to 150 grams in ten-gram steps, shown below. Click for a video; note that the rings count in binary (but — analog?)!

Combinations of the four medium rings total zero to nine grams in one-gram steps. Click for video.

Note that this time the rings don’t count in binary. Only ten combinations of weights were needed — a relaxed constraint which permitted the designers to reduce cumulative error by arranging the weight combinations so that no more than two weights are lifted concurrently. (At least, that’s our best guess. We’re still discussing it.)

Now would be a good time to note that because the rings are concentric, the center of gravity of every ring combination lies on the same axis. This is important (recall how levers work? Yeah, we had to think about it too. We forgot most of grade school. This was on purpose.)

Finally, subsets of the four small rings total zero to 900 milligrams in 100-milligram steps. Click for video. Again, no more than two rings are lifted concurrently, although this time they don’t share the same center of gravity. But note how they’re arranged (from back to front: 200 mg, 300 mg, 600 mg, 100 mg). We’re pretty sure this important, but we’re not sure why…

An optical scale provides one-milligram resolution from zero to 100 milligrams. This raises the question: why doesn’t the range stop at 99 milligrams? The rest of the ranges stop one step short. But they all measure by means of mass-substitution — in other words, they’re independent of gravity fluctuations, and probably very robust to temperature variation, and so on. It’s possible that the milligram range relies on a less-robust mechanism, like spring deflection (which measures weight, not mass — yeah, once again, we had to really think about). This extra step may permit calibration: place a standard 100-milligram calibration mass on the pan, calibrate the scale to read 100 milligrams in the optical scale, and then remove the mass; if all is well, the optical scale should read zero.

A fine-adjustment dial provides ten-microgram resolution from zero to 990 micrograms. When correctly dialed-in, the alignment bar at the right lies exactly between the triangles. This cannot be done when anyone else is awake in the building. This scale measures footsteps two floors away. A cat walking nearby will throw the measurement. Exhalation will throw the measurement. Unless the scale is on a massive slab of marble, or directly on bedrock, both of which were common practice, it’s best to weigh things at 3:00 a.m.

Below is another view of the optical scale, with the lights off. Notice the crispness of the image! The absence of pixel-aliasing! There isn’t even an LCD — it’s completely nondigital, with no electronics whatsoever — and the image is rendered with a tiny projector! Not unlike film, which we’ve also heard of (apparently this is how cameras used to work).

In a subsequent post we’ll provide an explanation of the “substitution” principle in the design of this balance. If we have the time, we’ll also assemble a manual, since they no longer seem to exist. For now, here are three more views as we back-out of this wonderful device:

On your way out, observe the Authentic Lab-Applied Stickers and the thirty-dollar price marking in the next photo. Forty-five years ago this balance cost over a thousand dollars, which is equivalent to perhaps twenty-five thousand dollars today.

From the dusty depths of the local university-surplus store, otherwise known as the Toy Store for Nerds, this balance is another gem.

Best — stochastic

a tiny collet


Today’s banner: a tiny ER 8 collet. For the purpose of improving rigidity for milling operations with a lathe, we tried securing an endmill in a four-jaw lathe chuck:

We wanted to secure the endmill base using an ER 8 collet, but alas, the 3/8″ shank wouldn’t fit in any of our collets. ER 8 collets are absurdly small. But then, so is the Taig lathe. We like tiny things.

In principle we could make a new collet to hold the end of the endmill. Obviously we had to put principle to practice. We often do this, if for no other reason than to see what happens. But making collets is hard. Tiny collets require a tiny slitting saw. We persevered:

Here’s the endmill’s base in the new collet:

And here’s the chucked endmill, capped with the new collet (photographed from the rear of the chuck):

We had fun. To give a sense of size, or lack thereof, here’s the collet next to a thumb and a penny:

Cheers — stochastic

retina pixels


Today’s banner: high-resolution “Retina display” pixels. We found a stereo microscope at the local university surplus store, which is really just a toy store for grownups.

There was an immediate and intense compulsion to put something, anything at all, under the scope. Sadly, none of our cats would fit, and anyway, the illuminator wasn’t working, so we wouldn’t have seen anything.

More casting about and — Voilà! A self-illuminating iPhone 4 with tiny pixels to look at!

We discovered that staring at pixels closeup can make your brain hurt.

Cheers — stochastic

great big ball of tiny magnets


Today’s banner isn’t a stock image. It’s a photo of a thousand tiny magnet spheres that we assembled into a great big surprisingly-well-ordered ball. It was rather heavy.

Of course, we had no choice but to squish it.

Best wishes — stochastic

… added September 29, 2011:

Reader Rose observed:

I have a set of these. Somewhat paranoid about keeping them anywhere near my electronic equipment. Thus, they fail as desk toy.

Yep. The other day one of our laptops began making a sickly thwacking sound — the last resort of a dying hard drive, as it repeatedly homed its read/write heads in an effort to find some data, any data at all, but the data was all gone… it was very sad. There were magnets involved.

But they look great on the refrigerator:

The print on the door, by the way, is Ursula Vernon’s quickie drawing “Morning Dragon”.

Best — stochastic