Friday, 19 March 2010

Divisumma Diary - It Works!

The Divisumma has been sitting on a corner of my desk in full working order for a couple of weeks now. There's a picture of it at the bottom, complete with case and very attentive full-time Divisumma Operator.

Progress since the last posting involved several more variations on the Battle of the Springs, and a lot of lubrication. The problem with springs is that they age, losing some of their strength. Replacing them with new springs is a risky business, because in many cases the exact strength of the spring is important.

I mentioned before the problem that multiplication sometimes gave the wrong answer. At the same time, I noticed that the key that allows you to transfer the result of a multiplication to the multiplier register - for example when computing powers or strings of products like 123 x 456 x 789 - no longer worked.

The Divisumma uses a clever trick to speed up multiplication. If it needs to multiply by 4 or less, it uses repeated addition. For 5 or more, it instead adds an extra one to the next digit, then subtracts. So to multiply by 9, it subtracts once, then adds an extra one to the next digit. If you multiply by 99999, it only performs two actual arithmetic operations, effectively multiplying by 100000 and subtracting 1. The effect is to halve the time to multiply, on average. As you can imagine, the mechanism to do all this, purely mechanically, is frighteningly complex. As ever, I'm lost in admiration for the designer of the machine, Natale Capellaro.

The error in the multiplication could be explained if in certain cases, a value was added instead of being subtracted. To cut a long story short, the problem turned out to be where I had replaced a spring, the long spring 277 from the Battle of the Springs, by a stronger one. It completely solved the problem there, but unfortunately the static end of the spring is not really static, it's a little hook on the end of something that moves. The stronger spring was holding it a fraction of a millimetre away from its correct resting position, and that was enough to block two pieces of the machine: the lever that decides whether to add or subtract, and the lever that causes the multiplication result to be transferred.

So I had to revert to the original spring, and solve my Battle of the Springs problem another way. The service manual says that in certain cases, to get things to work, you should "act upon" various cam followers and the like. So indeed I "acted upon" the little lug 150a, until it stayed out of the way of lug 286n when it was supposed to. It's now twisted quite a lot, I'm sure more than the spirit of "acting upon" would demand, but the machine now works.

Another spring problem caused an equally odd problem. Sometimes, an add or subtract would trigger a total operation, wiping out the value just entered. Curiously, this was related to the length of the number just added. If it had just one digit, the problem didn't happen. If it had 12 digits, it always happened.

The immediate cause of the problem is the mechanism for printing the result of a multiplication or division. This uses the total machinery, and it does it by pulling down the total key at the end of the cycle. It's almost as if a big arm reached out of the machine and pressed the button down. The arrangement for triggering this is amazingly complex, with flimsy levers that run the whole length of the machine. It turned out that the mechanical shock to the machine when the digit carriage was restored, was just enough to trigger one of the pieces of this.

The mechanical stresses in the machine are pretty high. There is very little time to restore the digit carriage within the overall quarter second or so main cycle - maybe 50 milliseconds, to move something quite heavy through 5 centimetres or so. So when it hits the stop, it is moving fast and there is a lot to absorb. Designing these machines to work reliably, considering everything that was going on, was a lot harder than just getting one to work on a bench in the lab.

Anyway, the fix in this case was just to use a new, stronger spring. Problem solved.

Then it was time to put the machine back in its case. The first step was to replace it on the steel base. It hadn't been too hard to get it off - there are just five bolts that hold them together. But getting the holes lined up again was nearly impossible - they have to be correct to within less than a tenth of a millimetre or the bolts just don't engage with the nuts. And two of these bolts are completely inaccessible. Luckily I had just bought these bolt-handling tweezers from Micromark, which were exactly what it took to weave the bolt through the levers and get it to the right place. Even so, for one of them I had to hand-turn the machine to a certain point in a division cycle, to move a lever out of the way and give me access. I can't imagine how they did this assembly in the factory, there must be a trick that I missed.

After that it was just a matter of putting the case back on, cleaning things up, replacing the ribbon, and now I have a perfect piece of retro-computing sitting on my desk. I even use it occasionally, instead of firing up the Windows calculator.

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