# Calculus-performing mechanical calculator

A clip from the Discovery Channel's Dirty Jobs program on tanneries demonstrates the workings of a calculus-performing mechanical calculator that measures the surface-area of irregularly shaped hides with a fascinating and clever set of gears, calipers and ratchets.

Dirty Jobs - Tannery Mechanical Surface Integrator
(*Thanks, Dad!*)

Cool. . . but how the hell. . . ?

Does each arm measure a strip?

That’s what i’m guessing. Measures from when arm goes up, to when arm goes down, then adds it all up for the dial.

Amazing, but it looks like it would rip your arm off as soon as look at you

“Amazing, BECAUSE it looks like it would rip your arm off as soon as look at you”

FIFY. :-)

A planimeter, of which I have a couple, is a mechanical device that does more or less the same thing–more slowly and requiring more operator skill. It traces the outside of an irregular shape and computes the area through a hardware–as in wheels, gears, and arms–implementation of Green’s Theorem, an algorithm for computing the double integral of a surface by a path integral of its boundary. Newer planimeters are electronic and not nearly as much fun, or as good to look at. The instruction booklet that came with my K+E planimeter, bought on eBay, actually explains the math of how it works.

I used one of these in a physics lab once:

http://en.wikipedia.org/wiki/Planimeter

Pretty clever gizmo.

I am enjoying how much the mechanism reminds me of piano keys/hammer/frames.

This machine looks really ingenious and very accurate, but I don’t think it’s performing calculus, at least not what we commonly consider calculus. It’s measuring discrete strips of area and mechanically adding them together as a sum on the main dial. This machine could probably be used to demonstrate the fundamentals of calculus though. That planimeter described above seems like an implementation of calculus.

What you described is calculus.

It’s just not infinitesimal calculus. Finitesimal?

Discrete! As opposed to the indiscreet kind.

Or Simpson’s Rule.

Nope, trap rule. Simpson’s uses parabolas doesn’t it?

Yes, but I was thinking the parts where you divide the area under the curve into strips. The Trapezium Rule is closer to what the machine is doing, but Simpson’s Rule also uses the same trick.

I’ve always heard it called the

trapezoidalrule, myself. First thing I learned in calculus, only thing I ever needed… just program your computer to start at one and increment the number of trapezoids until the result suddenly goes loony tunes – that’s where you’ve reached the limit of precision of your device, so take the last result before the meltdown and that’s the area under your curve, or close enough for any real-world physical need. You can do this with Simpson’s rule too, I suppose.No, what the other guy described (the planimeter) is performing calculus. This machine seems to use the ‘Method Of Exhaustion’ to approximate the area of the shape in rectangular strips of discrete width and possibly of discrete increments of height. This makes it a mechanical brute-force computer of area. As someone else pointed out, and as I pointed out in my comment, this machine demonstrates how calculus works, but doesn’t perform it. It doesn’t derive from the curve what the area is.

the planimeter is more elegant and much more precise, but they are both “just measuring” approximations to an integral. operator error and mechanical tolerances are never exact and if you want to get ridiculously pedantic, there is always the planck length…

the method displayed above is much more practical for directly measuring solid objects rather than just closed plane curves.

It’s measuring discrete strips of area and mechanically adding them together as a sum on the main dial.Take the limit of that function as the number of strips approaches infinity, and you will have invented the integral. Calculus!

Indeed it does. But it isn’t actually performing calculus. It’s just measuring.

it’s calculating Riemann sums

Now play it back with blades and cut later things into the approximate shape of the first thing.

but play it back 10% bigger. And hide it in this machine, so every time you put a hide in, a larger one comes out.

That’s enough, you two.

The machine in the background on the freeze-frame that is displayed before you play the video looks like a mutant Dalek.

It’s called an air compressor.

very cool. y’all might also want to check out this post from Mark last year about cams:

http://boingboing.net/2011/03/09/using-cams-to-solve.html

I *think* this might be the patent for this machine….. (from back when a patent actual was for something novel and was required to actually do something)

http://www.freepatentsonline.com/2021218.html

78 years ago, some disgruntled engineers were grumbling to each other after work about how this device is trivial, and back in their educations/apprenticeships they did

basicallythe same thing with stuff lying around the lab, and if you want to see a real patent, just look at James Watt’s steam engine but man of course he got screwed out of the money, just like everyrealinnovator, and…Pretty clever machine. I’ve always enjoyed Dirty Jobs, so am still kind of bummed out that Discovery has cancelled it.

:-( I’ll take a good educational program over faked drama any day.

Mike Rowe is awesome.

Is he allowed to wear a shirt? Isn’t partial nudity in his contract?

Workplace safety regulations. They’ll send in hired goons, make no mistake.

The first computers available for (wealthy) home use were analog – very suitable for implementing algorithms of calculus.

See: http://www.heathkit-museum.com/computers/hvmec-1.shtml

“It’s pre-metric…”

Well, maybe, the metric system was invented in 1799 according to wikipedia, so unlikely

“It’s pre-roman numerals”

No.