Differential Analyzer Cranks out Math like a Champ at VCF 2016

Here at VCF, we stumbled across a gigantic contraption that spanned several tables. Rube Goldberg machine this was not. Instead, this device actually does something useful! [Tim Robinson’s] differential analyzer can solve differential equations through several stages of mechanical integrators. The result is a pen-plot graph of the solution to the input equation, input by displacing a rod as a function of time.

Differential analyzers have been around for over a century. [Tim’s] claim to fame is that this particular DA is constructed entirely from Meccano-branded parts. We’re thrilled to see Meccano, over 100 years old at this point, continue to find new uses outside the toy box.

diff_analyzer
The Torque Amplifier

The differential analyzer is riddled with mechanisms that are bound to swing some heads for a double-take. Since the input shaft that transmits the input function f(x), has very little friction, the result can only be carried through the remainder of the machine with some means of torque amplification. To do so, [Tim], and most other DA designers implement a torque analyzer. For [Tim], though, this feat proved to be more difficult (and more triumphant) than other solutions, since he’s using a set of parts that are entirely from Meccano. In fact, this feature took [Tim] through about 20 iterations before he was finally satisfied.

VCF West continues to run through the end of the weekend at the Computer History Museum in Mountain View, CA. If you haven’t already packed your bags for DEF CON, stop by for a few more bewildering brain teasers.

18 thoughts on “Differential Analyzer Cranks out Math like a Champ at VCF 2016

  1. A Meccano Differential Analyser built at Manchester University in 1934 by Douglas Hartree and Arthur Porter made extensive use of Meccano parts, and it proved “accurate enough for the solution of many scientific problems”. A similar machine built by J.B. Bratt at Cambridge University in 1935 is now in the Museum of Transport and Technology (MOTAT) collection in Auckland, New Zealand. It is estimated by Garry Tee of Auckland University that about 15 Meccano model Differential Analysers were built for serious work by scientists and researchers around the world.

      1. A point of interest, I thought, that these machines were in their time not just demonstrations but contributed to real scientific work. It is one thing to build a model, another to build a useful instrument.

    1. Pretty sure there’s one in the science museum in London, along with brilliant analogue / mechanical bomb-aiming computers and whatnot. Well, really _everything_ there is awesome, let’s be honest, the place rocks and HaD should probably write a load of articles about it.

  2. Meccano was a huge part of my childhood. When I settled overseas my mum packed it all up (maybe 100lbs of stuff), shipped it off and it was never seen again. I miss it mightily.

  3. I wonder what would have become of me if I had Meccano as a kid?
    Wonderful stuff with all those moving parts, gears and pulleys. And I assume that just like Lego, you’d never have enough.

    1. Yep, I treasured my meccano and the next big idea was always 2 of everything short. I had about a shoe box full. Come to early teens, I was disrespecting it a bit and using all the handy parts in other projects. So it suffered some attrition, particularly in using it for the frame/chassis of a radio controlled LandRover and snowmobile. Unfortunately the remains passed out of my ken when I had to do a long distance move…

      Fast forward a decade or so… to last year, and I see a cheapo version turn up in the the local dollar stores (Check pound store in UK) and argued with myself about buying it… well.. a couple of months passed, then I was having a heck of a time braining out this fancy hinge mechanism upon which an idea was pivotal (Groan) and I finally broke down and went and got 5 boxes of it, woohooo… then it took me longer to unbox all 5 “kits” than it did to whip up a scale model of the mechanism, which proved it nicely. Weirdly though, despite yearning for meccano all these years I never saw so much as a single nut or bolt of it at yard sales (Think jumble sales and car boots) and flea markets around here, until after I picked up the cheapy, then fell over a couple of small sets, which I also picked up, can’t have enough, ever. Definitely don’t have enough gears or pulleys in what I got so far.

      The advantage over lego is that it’s somewhat easier to interface to the real world as it were, drill a couple of holes and your custom bits bolt up to it.

    1. Hydraulics is just a medium, it doesn’t amplify. You could call the control valve, an amplifier. A cars power steering is like this, it is somewhat similar to a torque amplifier.

      In robotics it’s simpler just to use electronics but it’s very interesting to see what was used in per-computer days.

      Here is a mechanical unit that was used in astronomy. Light phases could be detected with primitive photography and the distance to stars calculated by phase (harmonic) analysis and that was done by this machine.

      In it ‘reverse’ mode it’s best described as Fast Fourier Transformation (FFT). It also has a ‘forward’ mode where it does the exact opposite and that is astonishing to me because of the math that is involved. Not just frequencies but also phases and that is what it is designed specifically to do.

  4. I doubt this can be replicated in LEGO. The amount of torque needed to drive everything would probably twist the main shaft and ruin it. Plastics toy aren’t good for high torque use.

  5. These machines are so old that it is hard to find actual examples of how they were used, however this paper shows how similar work was done using an electronic analog computer. Note how the charts have the lettering done by hand, but the curves are machine generated.

    Stability research on parachutes using digital and analog computers
    by Ludwig, R
    Published November 1, 1966

    https://archive.org/details/nasa_techdoc_19670004467

  6. Fantastic! I’m going to have some fun reading all the links on Tim’s website.

    I knew this sort of thing could be done, but I didn’t know so many had been built. I must find out who has the family Meccano. We have quite a lot of it starting with a No 4a & a No 10 dating from the late 50’s.

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