Using cams to solve math problems

[Video Link] Who needs computers when you can simply make grooved cams to solve math equations? (Via Nerdstink)


  1. Cams like that are not really solving equations; one can look at them more as analog lookup tables. These things would be _part_ of an analog computer, equivalent to ROMs.

    1. This is exactly it. You have to already know the answer to build the cam to deliver the answer. The 3-dimensional cam there looks like especially bitchy to produce without 3D design tools and computer controlled lathing. The differential (From the next video in the series) is much more flexible, but as noted is also prone to serious accumulating errors.

      But to answer the original, if only partly-stated, question (“Who needs an [electronic] computer when you can simply make grooved cams to solve math equations?” – “People who don’t want to deal with a large, heavy, expensive, fragile single-function machine that needs silly amounts of maintenance.”

      Mechanical computers silently loose accuracy under changing environmental conditions (warmer and colder), and usually don’t give a clear indication that they’re no longer functioning correctly – until they fail so much the gears bind up of course. If your differential is slipping, you’ll get bad output and will only know once you check your numbers by hand.

      Obviously the simplest ones are more durable, but they can generally be replaced entirely with a slide ruler and a little notebook with interesting values in it – you can TELL your slide ruler is wobbly as all the parts are fully exposed, and it’s not terribly reliant on precision machining, so it’s pretty cheap to replace.

      If you don’t have modern electronic computers, mechanical computers really are awesome if you need results FAST – thus their popularity with artillery crews, and lack of popularity with accountants. If you DO have modern electronic computers… well the difference between a cheap scientific calculator and whatever you’re reading this on is roughly the difference between a couple of hundred pounds of mechanical computer and your computer.

      And even your computer doesn’t need a mechanic on standby to tune it up on a near-constant-basis.

      1. I love this. I’m a machinist, and I know if you want complex machine tool calulations on a machine without CNC or a computer, say if you are designing a custom machine, as DROs (digital readouts) are NOT always correct (they randomly can lose their place, called hysteresis error, I scrapped a piece last night due to this inherent flaw with them) you make custom cams. CNC is only accurate as long as your encoders give consistent feedback.

        Jerril is right about the temperature of the cam material changing it’s accuracy. This is true with all things, all tools. Very accurate tools like gauge blocks (steel blocks, like building blocks, made to an exact size by lapping, usually +or_ 0.000050″, used to set tool measurement to) will expand by that much just by putting your hand over them- the heat from your hand is enough to change their size! People usually counteract this by doing measurement in a temperature controlled “tool room”- set to an international standard of 68 degrees F. This way, thermal expansion error is gone.

        A mechanical cam, properly designed oversize to account for thermal expansion of its material, is more accurate. Steel will expand and contract 0.00005″ sometimes depending on room temperature, which is why you take expansion error into account when making the cam. You make the smallest measurement of any tool you make at least 10x bigger than your greatest sum of known possible error- so if something has thermal expansion of 0.000050″, you make the smallest linear measurements of the cam face to the following stick (using 1st example) no less than 0.0005″ big. Ideally, no less than that, or as much more than than as you can- the bigger the smallest measurement, the less error from thermal expansion matters. This is called the Rule Of Ten in metrology (the science of precision measurement).

        Did I scare anyone with all the technical stuff? The Boing Boing crowd has intelligent people, always. I figure you read that, people here should be able to understand the concepts I work with nicely.

        Why would you want to make a cam for something? What possible use could these have to you? Want to make automata, or fine astronomical instruments- you need to use cams.

        See here:

        Jaquet Droz made the most marvelous automata- exceedingly complex, with lots of cams! The company, not the man, still makes some incredible pieces like those for wealthy customers, and not just watches.

        Finally, old rare astronomical clocks by men like James Ferguson had a cam like the first example, with his stick follower connected to a piece of metal sheet cut out and colored blue like the sea, and the measurements of the tides in England were calculated as it rise and fell on his cam, with the tide piece flanked by decorative rock figures- looking like the sea coast, and the height of the tide scribed on the blue rising sea piece.

        If you are a maker- master making cams by thinking of your measurements on a rotating face. Learn to plot data on graphs, and wrap your outputs around rotary axes. Then you will always be able to make a cam.

        If you understand what they can do, cams are truly wondrous things for a maker. This was an excellent video Mark, well found!

        And finally- Subhan- I think the same way. Mechanical calculation and tools will always work if maintained. They can be repaired after the nuclear apocalypse, PC repair not likely at all. And not affected by EMP or hacking either- precisely why the military has such ballistic calculators using cams and more on all artillery.

  2. @JTMontreal – yeah, and still cool, no matter what.

    Analog computation, with super-speed and awesome precision (if you can measure it!), rocks.

  3. The precision of manageably-sized cams is low, and due to a phenomenon called lash, the imprecision is added or multiplied when the output of one function is the input of another. Analog computers are good at coming to a single close-enough result for a single function.

  4. I love this. For all that I am an aged computer geek and always will be (although the ‘aged’ bit might tend to increase), I often see problems visually and this a very good way of ‘seeing’ what the problem is. I suspect that if I had seen this programme when I was doing Maths at school, I would have understood calculus much more quickly.

    1. right on. visualizing math is the only thing that ever worked for me. flunked algebra (eventually got a B in summer school), aced geometry.

      as I’m following the film: “hey, this is neat.”

      barrel cam: “right on, 3D allows another variable, got it.”

      super-elevation: “never heard of that. [keep watching] Oh. it’s for killing people” :(

  5. Don’t get me wrong, I think mechanical computers are beautiful, elegant solutions to the problems of the time. Lovely bits of engineering, and really really clever.

    But they’re only distantly related to modern computing devices, and for anything other than artistic purposes, I’ll take my $15 casio scientific calculator with the little solar panel. It’s smaller, lighter, more durable, and has a longer working life without maintenance (and I include eventual battery replacement in “maintenace”). I’ve had it for going on 20 years and it STILL works, and it STILL hasn’t needed any maintenance.

  6. Heinlein used cams as trajectory computers in many of his early space stories (also used flywheels!). Interesting to see it here in Boing Boing.

  7. Tagged “kids” when the film is discussing the workings of a naval fire control computer…

  8. Up through the middle of B-52 production (I believe the change-over was between the “D” and “F” models), B-52 bombers used massive mechanical computers.

    The replacement was, IIRC, designed by IBM and built by GE, and used miniaturized tubes in sealed “soup can” circuit packs that were fairly easy to replace quickly.

    Even those electronic computers were rather massive – and not all that smart…

    (I worked on “F” models in the ’60s and never got to see the earlier mechanical computers.)

  9. This is fascinating. But it seems like the math problems are already solved – the cams seem to be more like adjustable tables than what we think of as computers. The great thing about these machines is their infinite adjustability – no rounding by the device, only by the user and the output chart. Obviously the down side is the constant need for calibration, but this appears to be military hardware calibrated for specific weaponry, I’m sure there was a guy whose job it was to make sure the shell hit the right place before the device was put on a ship. One thing the post does not mention is that this was the 1950’s. The first video shows how these things were operated and it seems that digital technology wouldn’t catch up to this accuracy until much later, and that was space technology that could not possibly exist on board a Navy ship. Given the conditions, it seems like these were much like sextants – physical computers made to instantly solve a single problem.

  10. I’d venture a guess that there is still R&D being done on these by the US Military, for the same reasons they still like core memory for some applications – EMP will not phase a mechanical computer in the slightest.

  11. After the example of the 3-dimensional barrel-cam solving the 2-variable problem, I was kind of hoping that the 1950s announcer would continue, “For a 3-variable problem, a tesseract is used as the working surface…”

    1. These aren’t really computers: they’re more like ALUs. You can’t (without re-machining) reprogram them to do something else, but they will do your math instantaneouslyish. And for functions you want to be consistent and unchanging over serious timescales, rather than apple-fashion-trend timescales, mechanical maths is the way to go, I think.

      @Anon: people have been predicting a brick wall for CPUs for a loooong time. No sign of one yet.

      @semiotix: Me too :) But for 3-inputs, I’m guessing you just aggregate multiple 2-input cams. So you’d need one fewer cams than inputs.

      @ackpht: I think the digital/analog thing may be a false dichotomy. Given both time and space allegedly have minimum measures, there are no devices that provide perfectly analog outputs. However, even digital devices can give sufficiently-analog outputs for any desired or imaginable application.

      @BastardNamban: interesting read :)

        1. There’s no such thing as a “universal computer”.
          Stored program electronic digital computers are just one type of computer. Analog computers predate them and are still widely used in analog electronics. Analog mechanical computers can’t match digital ones in any practical metric, but they are cool in their mechanical precision. And they never tried to kill anyone.

  12. And mechanical computers accept continuously changing inputs and produce continuously changing outputs. Digital computers do not. There might be applications out there for which a controller with discrete outputs is less desirable than one with continuous outputs.

  13. To all of you questioning the usefulness of mechanised computation in a modern digital erra,

    CPU’s have kind of hit a brick wall, if you haven’t noticed. The connections within a chip can only get so small before the laws of thermodynamics and electro magnatism totally screw it over. A solution has been postulated that in the near future nano scale mechanical machines and sensors for reading information from them might replace the ALU and other parts of the chips reserved for transistors.

    The whole mechanical computer thing started with Charles Babage and in the end, we’re going back to Charles Babages later works to get better designes for these nano scale mechanisms. So no I don’t think this is completely superfluous and useless. Of course this is rather expensive at the moment so they’re favoring more parallel computational structures.

    If we expect to see more and more powerful computers to come out, don’t expect them to be %100 series computational electronic circuits.

  14. In the Air Force many, many, many, years ago i worked on an analog computer that modeled aircraft so that radar “operators” could practice controlling aircraft. I have mild autism, so i think in pictures while some people think kinetically and others think aurally (words). And at an individual level we each develop our own way of thinking. While it brought back a bit of nostalgia for me, i’m not sure that this really helps children understand arithmetic simply because we all inculcate it differently. Lastly, this reminds me of the work i did in control theory where everything was about aiming weapons and no professor could think of a single peaceful use for control theory – they were wrong, but it is interesting that here is another example of math for war only – definitely don’t want to teach this to children.

  15. When I joined the Army in 1979, our tanks had mechanical fire control computers. We had pushbutton digital laser electronic nothing. Our fire control equipment worked exactly like the WWII systems in warships. The computers worked by using cams, each cam matched to a different type of ammunition. The outer arc of a cam was supposed to be a precise match, in miniature, of the trajectory expected of that type of ammunition. The rangefinder was a coincidence rangefinder about 6 feet long with two imaging mirrors at opposite ends, that worked kind of like binoculars. You changed the focus of the target image in the rangefinder eyepiece until the image was sharp. The range finder then could measure the parallax between the lines of sight from the mirrors, and from that it worked out a rough range. That degree of parallax was transferred to the computer by a mechanical link which caused the cams to rotate an amount that matched the rotation of the rangefinder link. Rollers moved along the cam edges. The position of the roller was transferred to the gun by mechanical linkages; that provided “superelevation,” a sort of rough approximation of the elevation needed to hit the target at the indexed range. The gunner then used the controls to provide fine-tuning of the elevation to get the crosshairs on the target. During gunnery exercises, we averaged first-round hits on targets out to 1800 meters about 72% of the time, which I think was pretty damn good for near-Victorian technology.

  16. Are the cams describing a math function, or do the math functions describe what the cams do?

    How accurate is your calculator at predicting the behavior of the cam machine?

    Another post observed that “digital” computers are still mechanical machines and accumulating errors can still occur.

    Nature is dirty, theoretical math is not. Never the ‘twain shall meet; hence Chaos Theory, which is really trying to tell us what happened when our expensive computers and overly-clean theories fail.

  17. @Anon: when you link to a wiki page to prove your point, you should at least read the page to make sure it does that, and not the opposite:

    “A universal computer is defined as a device with a Turing complete instruction set, infinite memory, and an infinite lifespan. All real-world systems necessarily have finite memory, making the true universal computer a theoretical construct.”

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