Building the World's First Computer: Babbage's Analytical Engine

My card reader had been working pretty well. Then I put it in the back seat of my car to take it to show someone, but before the demo it sat  outside, on a hot day, for a couple of hours. As pet owners know, the interior of a car can easily get to 120ºF or more, and it did. The result was serious deformation of some of the printed parts made from PLA -- Polylactic acid -- the most common and easiest to print plastic filament that I've been using for almost everything.  Right angles and straight edges under the least bit of tension became terribly distorted, and of course the card reader stopped working. This permanent bending of PLA-printed parts when exposed to heat was well known to the 3D printing aficionados I sobbed to, who recommended switching from PLA to PETG, Polyethylene Terephthalate Glycol, which is good up to at least 160ºF. Even better would be ASA, Acrylonitrile Styrene Acrylate, but that is more difficult to print. I took the baby step and reprinted the deforme...

Babbage, probably inspired by the control mechanism in Jacquard's fabric looms,  proposed using punched cards in the Analytical Engine for three purposes: Operation cards that hold the "instructions" for the computer Variable cards that specify which locations in the Store (memory) should be read or written Number cards that hold constants needed for the calculation His card reading mechanisms most often used a six-sided cylindrical object he called a "prism" that the cards were wrapped around, draping down below for as many cards as needed. The front-facing side of the prism was advanced against a serial of pins or rods, which would either be pushed by the card or not, depending on whether there was a hole in that position. The movement of those rods would control other mechanisms in the machine. (Remember: you can click to get larger versions of all the images.) The rods shown here (drawing A/094 from August 14, 1841) are in pairs, linked so that when one goes...

Starting from the very early plans in the mid 1830s, Babbage realized that if each individual operation needed to bring operands in from the Store and return the result to the Store, sequential operations on many operands would be very slow. So he allowed any number of additions and subtractions to be chained together in an arbitrary sequence, with intermediate results retained in the Mill and only written back at the end.  The numbers were, of course, signed integers. In all his mature Plans, the Store holds them in sign-magnitude representation: one decimal wheel on top indicates, by being odd or even, whether the number is positive or negative. The rest of the wheels represent the absolute value of the number. This makes the numbers easy for a human to read on the column, and also simplifies multiplication and division.  For addition and subtraction in the Mill, he uses 10's complement representation: a negative d-digit number N is stored as 10 d -N. For example, a four-dig...

 I've expanded the prototype to have 4 digits plus a sign wheel in the Store, and gotten it to be somewhat more reliable. Here's a video of four cycles in quick succession: write from Mill register to Store location restore the rack read from Store location to Mill register restore the rack This is running at the "Babbage speed" of 157 milliseconds per digit, which is the fastest he thought the engine should ever be run. Tim Robinson points out that an alternative Babbage design for restoring the racks is to use two vertical bars that come in from either side and "trap" the racks in the center regardless of what position they are currently in.  I'm looking into doing that, in part because it makes initial setup a lot easier.  As it is there are dozens of mechanisms that have to be adjusted exactly right for initial conditions, including the rack-restoring wheels. Half the time when things go wrong during a test, it's because one of them was slightly ...

In my last blog I said "I need to work on a better, softer detent mechanism". Here it is: It's assembled from five parts of which only the pusher tip is 3D printed. The screw is drilled and bored on my mini-Lathe to create a shoulder that retains the head of the pusher, then tapped for the screw that retains the low-k spring made of 0.2mm wire. Four of them look like this when installed in the anticipating carriage. That sufficiently reduces the torque needed to rotate the carriage digit wheels when all four carry warning arms are triggered simultaneously. Hopefully it also will work for a stack of 20 or 30 wheels!

 As far as I know, Babbage never discussed how much torque he expected would be needed to rotate the various shafts with gears. My prototype mill section wasn't functioning well because the answer for me was "too much". Consider giving off a number from the A register digit stack to the anticipating carriage. The gear train goes from the digit wheel, to the long pinion connector, to the fixed long pinion, perhaps to the reversing gear (depending on whether it is for addition or subtraction), to the carriage connector, and finally to the anticipating carriage digit wheel. So there are either 5 or 6 gears in series.  The torque required to turn the A register stack finger shaft is a combination of: rotational friction of all the vertical shafts friction from meshing of the gear teeth at all the interfaces spring tension holding the the weak locks on the anticipating carriage friction at the interface between the carriage wheel point and the carry warning arms rotational fri...

I'm finally back to building prototypes. The target is eventually to build a simplified version of Babbage's Plan 27, which has three pairs of "register" digit wheels in the Mill that have a linear rack interface to the Store, three long pinion shifters, and two reversible anticipating carriages. A lot of the design parameters since the previous Fibonacci-computing prototype have changed, including new gear parameters and reducing the cage height from 2.3" to 2". In order to check those changes out, I've built a smaller prototype that has a Store with one pair of numbers plus the rack restorer, and a Mill with one pair of register numbers, one set of long pinion shifters, and one anticipating carriage. It also has prototypes of the sign wheel, and the counters that will be needed for multiplication and division. front view Store view Mill view  I continue to be plagued by sloppy 3D printed parts, and even sloppier supporting structures fabricated poorly ...

 It turns out that there is another gear loop in the Plan 27 design that needs to carefully designed to mesh correctly. The long pinion is connected to the anticipating carriage (which does addition and subtraction) by an intermediate transfer pinion. But sometimes during complex operations like division, an additional reversing gear needs to be inserted into the chain. Babbage does that by vertical motion of the transfer and reversing pinions, with the reversing pinion being double height. Here are the two configurations: non-reversing reversing Although clearly all three gears are never meshed as shown  in the plan view, the teeth need to be aligned in order for the vertical movements to happen without tooth conflicts.  There are far fewer degrees of freedom for axis positions here than for the 5-gear mesh described in the earlier posting. Given the constraints on locations of the gears to avoid interference, the first attempt failed to produce any solutions.  But ...

The gear loop mesh analysis program is now expanded to work on all three Mill groups in the Plan 27 layout: Babbage drawing A/093 from July 28, 1841 Each group contains a figure wheel stack (A), fixed and movable long pinions to effect shifts (L and S, respectively), and the necessary connecting pinions (G, J, C, and J). There are two anticipating carriages (F), which mesh to the fixed long pinions of the middle and right groups. The moveable long pinions are meshed with additional pinions (O) meshed to the rack that connects to the Store. You can see quite a few other wheel stacks in the drawing, which are there to implement multi-precision arithmetic and many other complex features. My simplified version omits them, and includes only the 22 stacks described above. Still, precisely positioning all the axle centers so that the various loops of gears mesh correctly is a challenge. Babbage's drawings and notes are not clear on whether he had gotten to do that yet. Each group has a le...

 My design is based on a simplification of Babbage's Plan 27 from 1841. There are, like for all of his plans, many details unspecified, and many hidden subtleties.  One such subtlety relates to the ability of loops of gears to mesh correctly. Consider the following section of the Mill, from drawing A/093 dated 28 July 1841: The circles represent the pitch circles of the gears and are tangent in the drawing to enforce the required separation between the axle centers. ''A and 'A are stacks of 8" diameter figure wheels with 80 teeth. Two occupy one "cage" at each decimal position, so each stack holds two interleaved independent numbers. ''L are fixed long pinions, and ''S are movable long pinions, which together serve as shifters to multiply or divide numbers by 10. They are made of concentric locked gears of different pitch. ''G, ''J, 'G, and 'J are linking pinions that can be moved into place vertically to link the l...

I've given a half-hour slideshow talk about this project a few times. The last time it was done over Zoom, so we recorded it. If you're interested, I uploaded it to YouTube here: https://youtu.be/HRmGAhwOo0s

In most of Babbage's designs, he calls for horizontal framing plates to separate each digit position in the stacks of digit wheels and pinions. Here's an example drawing from Plan 27. In this design each digit position is composed of a "cage" with digits from two interleaved numbers on the same stack. There are two primary motivations for the framing plates:  To provide a bearing surface for the wheels and pinions of a shaft so they don't bear on the ones below them. to constrain, using close holes through the plates, the lateral motion of the shafts, to the extent that they might have a tendency to bend or were not manufactured sufficiently straight. After all, for designs with 30 digits the shafts might be 9 or 10 feet long. But there are some significant drawbacks: The massive weight of all those thick iron plates. Obscuring the view of the mechanisms during operation. Making detection and repair of problems difficult because parts can't easily be accessed....

I've mostly adopted Babbage's Plan 27 arrangement for the Mill, including the use of independent columns of pinions for the various meshing: the rack with digit wheels, digit wheels with long pinions, and long pinions with the anticipating carriage. But is is appealing for the Store to use a simplification that he introduced in Plan 28: to engage the digit wheels by lifting, rather than with separate columns of pinions. That not only eliminates one of the lifting motions, but also two rotating motions for locking the digit wheels, since their vertical motion can lock them to fixed fingers on the frame.  The store wheels are duplicated many times, so having only two independent motions -- lift for meshing, and finger rotation for giving-off -- instead of five is a huge advantage. It is unfortunately not possible to do this in the Plan 27 Mill because both digit wheels in a "cage" (a pair of wheels representing the same decimal position of two different numbers) are som...