There was a brief period through the 1960s into the 1970s when the last word in electronics was the calculator. New models sold for hundreds of dollars, and owning one made you very special indeed. Then the price of the integrated circuit at their heart fell to the point at which anyone could afford one, and a new generation of microcomputers stole their novelty for ever. But these machines were by no means the first calculators, and [What Will Makes] shows us in detail the workings of a mechanical calculator.
His machine is beautifully made with gears hand-cut from plywood, and follows a decimal design in which the rotation of a gear with ten teeth represents the numbers 0 to 9. We’re taken through the mechanical processes behind addition, subtraction, multiplication, and division, showing us such intricacies as the carry lever or a sliding display mechanism to implement a decimal equivalent of a bitwise shift multiplication.
We have to admit to be particularly impressed by the quality of the work, more so because these gears are hand made. To get such a complex assembly to work smoothly requires close attention to tolerance, easy with a laser cutter but difficult by hand. We heartily recommend watching the video, which we’ve placed below the break.
We’ve always admired Curta mechanical calculators, and would be very hesitant to dismantle one. But [Janus Cycle] did just that — and succeeded. A friend sent him a Curta Model 2 calculator that was frozen up. Just opening the case involved percussive force to remove a retaining pin, and once inside he discovered the main shaft had been slightly bent. No doubt this calculator had suffered a drop at some point in the past.
I’m sticking to the rule of doing no harm — I’d rather not be able to fix this than do something that causes more problems.
Inside the Curta
But surprisingly, he was able to get it substantially back in working order without completely taking apart all 600+ parts. Most of the issues were shafts whose lubrication had become gummy, and one carry lever was slightly bent. There is still a little more work, but soon this calculator will once again be cranking out results.
Has anyone dismantled a mechanical contraption this complicated before, for example a teletype machine? Let us know in the comments. If you want to brush up on your Curta knowledge, check out the Curta Calculator Page. We also wrote a Retrotechtacular about the Curta before. Thanks to [mister35mm] for sending in this tip.
Last month we carried a piece looking at the development of the 8-bit home computer market through the lens of the British catalogue retailer Argos and their perennial catalogue of dreams. As an aside, we mentioned that the earliest edition from 1975 contained some of the last mechanical calculators on the market, alongside a few early electronic models. This month it’s worth returning to those devices, because though they are largely forgotten now, they were part of the scenery and clutter of a typical office for most of the century.
The Summa’s internals, showing the register on the right and the type wheels on the left.
Somewhere in storage I have one of the models featured in the catalogue, an Olivetti Summa Prima. I happened upon it in a dumpster as a teenager looking for broken TVs to scavenge for parts, cut down a pair of typewriter ribbon reels to fit it, and after playing with it for a while added it to my store of random tech ephemera. It’s a compact and stylish desktop unit from about 1970, on its front is a numerical keypad, top is a printer with a holder for a roll of receipt paper and a typewriter-style rubber roller, while on its side is a spring-loaded handle from which it derives its power. It can do simple addition and subtraction in the old British currency units, and operating it is a simple case of punching in a number, pulling the handle, and watching the result spool out on the paper tape. Its register appears to be a set of rotors advanced or retarded by the handle for either addition or subtraction, and its printing is achieved by a set of print bars sliding up to line the correct number with the inked ribbon. For me in 1987 with my LCD Casio Scientific it was an entertaining mechanical curiosity, but for its operators twenty years earlier it must have represented a significant time saving.
The history of mechanical calculators goes back over several hundred years to Blaise Pascal in the 17th century, and over that time they evolved through a series of inventions into surprisingly sophisticated machines that were capable of handling financial complications surprisingly quickly. The Summa was one of the last machines available in great numbers, and even as it was brought to market in the 1960s its manufacturer was also producing one of the first desktop-sized computers. Its price in that 1975 Argos catalogue is hardly cheap but around the same as an electronic equivalent, itself a minor miracle given how many parts it contains and how complex it must have been to manufacture.
We’ve put two Summa Prima videos below the break. T.the first is a contemporary advert for the machine, and the second is a modern introduction to the machine partially narrated by a Brazilian robot, so consider translated subtitles. In that second video you can see something of its internals as the bare mechanism is cranked over for the camera and some of the mechanical complexity of the device becomes very obvious. It might seem odd to pull a obsolete piece of office machinery from a dumpster and hang onto it for three decades, but I’m very glad indeed that a 1980s teenage me did so. You’re probably unlikely to stumble upon one in 2019, but should you do so it’s a device that’s very much worth adding to your collection.
Earlier this year, [Dan Maloney] went inside mechanical calculators. Being the practical sort, [Dan] jumped right into the Pascaline invented by Blaise Pascal. It couldn’t multiply or divide. He then went into the arithmometer, which is arguably the first commercially successful mechanical calculator with four functions. That was around 1821 or so. But [Dan] mentions it used a Leibniz wheel. I thought, “Leibniz? He’s the calculus guy, right? He died in 1716.” So I knew there had to be at least a century of backstory to get to the arithmometer. Having a rainy day ahead, I decided to find out exactly where the Leibniz wheel came from and what it was doing for 100 years prior to 1821.
If you’ve taken calculus you’ve probably heard of Gottfried Wilhelm Leibniz (who would have been 372 years old on July 1st, by the way). He’s the guy that gave us the notation we use in modern calculus and oddly was one of two people who apparently figured out calculus, the other being Issac Newton. Both men, by the way, accused each other of stealing, although it is more likely they both built on the same prior work. When you are struggling to learn calculus, it is sometimes amazing that not only did someone think it up, but two people thought it up at one time. However, Leibniz also built what might be the first four function calculator in 1694. His “stepped reckoner” used a drum and some cranks and the underlying mechanism found inside of it lived on until the 1970s in other mechanical calculating devices. Oddly, Leibniz didn’t use the term stepped reckoner but called the machine Instrumentum Arithmeticum.
Many of us remember when a four function electronic calculator was a marvel and not even very inexpensive. Nowadays, you’d have to look hard to find one that only had four functions and simple calculators are cheap enough to give away like ink pens. But in 1694, you didn’t have electronics and integrated circuits necessary to pull that off.
It’s funny how creation and understanding interact. Sometimes the urge to create something comes from a new-found deep understanding of a concept, and sometimes the act of creation leads to that understanding. And sometimes creation and understanding are linked together in such a way as to lead in an entirely new direction, which is the story behind this plywood recreation of the Michelson Fourier analysis machine.
For those not familiar with this piece of computing history, it’s worth watching the videos in our article covering [Bill “The Engineer Guy” Hammack]’s discussion of this amazing early 20th-century analog computer. Those videos were shown to [nopvelthuizen] in a math class he took at the outset of degree work in physics education. The beauty of the sinusoids being created by the cam-operated rocker arms and summed to display the output waveforms captured his imagination and lead to an eight-channel copy of the 20-channel original.
Working with plywood and a CNC router, [nopvelthuizen]’s creation is faithful to the original if a bit limited by the smaller number of sinusoids that can be summed. A laser cutter or 3D printer would have allowed for a longer gear train, but we think the replica is great the way it is. What’s more, the real winners are [nopvelthuizen]’s eventual physics students, who will probably look with some awe at their teacher’s skills and enthusiasm.
While necessity is frequently the mother of invention, annoyance often comes into play as well. This was the case with [Blaise Pascal], who as a teenager was tasked with helping his father calculate the taxes owed by the citizens of Rouen, France. [Pascal] tired of moving the beads back and forth on his abacus and was sure that there was some easier way of counting all those livres, sols, and deniers. In the early 1640s, he devised a mechanical calculator that would come to be known by various names: Pascal’s calculator, arithmetic machine, and eventually, Pascaline.
The instrument is made up of input dials that are connected to output drums through a series of gears. Each digit of a number is entered on its own input dial. This is done by inserting a stylus between two spokes and turning the dial clockwise toward a metal stop, a bit like dialing on a rotary phone. The output is shown in a row of small windows across the top of the machine. Pascal made some fifty different prototypes of the Pascaline before he turned his focus toward philosophy. Some have more dials and corresponding output wheels than others, but the operation and mechanics are largely the same throughout the variations.
If you’re into mechanical devices or Fourier series (or both!), you’ve got some serious YouTubing to do.
[The Engineer Guy] has posted up a series of four videos (Introduction, Synthesis, Analysis, and Operation) that demonstrate the operation and theory behind a 100-year-old machine that does Fourier analysis and synthesis with gears, cams, rocker-arms, and springs.
In Synthesis, [The Engineer Guy] explains how the machine creates an arbitrary waveform from its twenty Fourier components. In retrospect, if you’re up on your Fourier synthesis, it’s pretty obvious. Gears turn at precise ratios to each other to create the relative frequencies, and circles turning trace out sine or cosine waves easily enough. But the mechanical spring-weighted summation mechanism blew our mind, and watching the machine do its thing is mesmerizing.
In Analysis everything runs in reverse. [The Engineer Guy] sets some sample points — a square wave — into the machine and it spits out the Fourier coefficients. If you don’t have a good intuitive feel for the duality implied by Fourier analysis and synthesis, go through the video from 1:50 to 2:20 again. For good measure, [The Engineer Guy] then puts the resulting coefficient estimates back into the machine, and you get to watch a bunch of gears and springs churn out a pretty good square wave. Truly amazing.
The fact that the machine was designed by [Albert Michelson], of Michelson-Morley experiment fame, adds some star power. [The Engineer Guy] is selling a book documenting the machine, and his video about the book is probably worth your time as well. And if you still haven’t gotten enough sine-wavey goodness, watch the bonus track where he runs the machine in slow-mo: pure mechano-mathematical hotness!
