The ingenious Ifach adder

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The ingenious Ifach adder
A carry mechanism with no gears!

I’ve seen many dial adders, like this, or this, or this, where you enter the numbers to be added with a stylus into a round dial disc with holes. The disc goes around, and its position indicates the sum -- until it comes full circle, when some mechanism effects the tens carry, incrementing the next disc one position. This normally involves some gear mechanism, usually a “mutilated gear wheel” with a single tooth. Simple enough.
And then, there is the Sumadora Ifach, or Ifach Adder.

Click photo to enlarge

This adder has the dial disc, it has the stylus, and it has the second disc for the tens (and hundreds) below the first one; the tens digit is visible through the small readout hole in the top disc. But it has no gears! In fact, it has only two moving parts, which are those two discs, fixed to a wooden base (sized 11.5x12 cm) with a central screw; and that’s all. You can see in the photo below how that’s all there is. So where is the carry mechanism?

Disassembled adder. Note the two “stop” holes in the wood
Click photo to enlarge

Well, the carry function is executed, almost magically, by the structure of the two discs. You can see that the top disc has 20 holes in it, while the bottom disc has 21 holes, which are visible through the top holes. But because there are 21, these are a bit closer to each other; you can see the growing misalignment between top and bottom holes as you move away from the red zero position in the photo below.

Click a photo to enlarge

To understand why this matters, consider the steps you'd use to execute an addition of a sequence of (single digit) numbers. Refer to the diagram above to identify the parts.

Clear the adder by sticking the stylus in the small reset hole in the top disc and rotating the disc counterclockwise until it stops. The stylus will at some point fall into a hole in the lower disc and drag it along for the ride; the stop happens when the stylus lands in a small hole in the wooden base, located at the 3 o’clock position in the photo. At this point both arrows point to zero, and the lower disc shows a blank in the “tens” readout hole.
Now dial in the first number to be summed: stick the stylus in the hole next to it in the input scale (the black numbers on the left side of the device), and turn counterclockwise until it stops (due to another small hole in the base at 6 o’clock). Note that the stylus will also engage and drag the bottom disc.
Repeat step 2 for each number to be added.
Read and note the units digit of the result, pointed at by the arrow on the red units readout scale to the right.
Insert the stylus at the hole next to the other arrow on the black scale to the left; turn it counterclockwise to the stop at 6 o’clock (again, the stylus will also engage and drag the bottom disc).
Now read the tens digit(s) of the result (a value from 0 to 40) in the tens readout hole.

    And now, here is the magic: when you move the top disc by one unit (say, from 1 to zero), it turns 18 degrees (360/20). Meanwhile the bottom disc only advances 17.14 degrees (360/21), because the stylus drags the top hole a bit before it engages the edge of the misaligned bottom hole. By the time the top disc has moved 10 units -- 180 degrees -- the bottom one moves 171.4 degrees. The missing 8.6 degrees mean that the bit of lower disc visible through the tens display window has shifted -- and just enough to expose the next tens value. 8.6 is about 360/42, and there are 42 numbered positions on the bottom disc (including the blank position before zero); the math all works out!
    This trick with the misaligned holes is ingenious, but it has one issue: as numbers are dialed in, the tens readout changes gradually, not in one jump as in a mutilated gear setup; so for much of the cycle the front portion of the next number coexists in the tens readout hole with the back portion of the previous one. That would never do, which is why step 5 was thrown in, along with the blank position of the tens that is exposed when the adder is reset. Adding the number at the “other” arrow brings the units to zero, and increments the half-exposed tens readout to the next integer. Problem solved!
    I received with this device a photocopy of the tiny instruction booklet, 9 x 6.5 cm in size, and I've scanned it, converted it to Spanish text, then translated it to English text. The instructions assume use of the adder to add multi-digit numbers column by column, as in a ledger, with the carry within a column handled automatically and the carry between columns entered manually after resetting the adder as one moves to the next column.
    The Sumadora Ifach was invented by Genaro Calatayud Sanjuán, a pharmacist from Calpe, Alicante, Spain; Ifach is the name of a prominent landmark in Calpe. He patented his invention in 1943 and produced it locally in the small workshop of Matías Pastor Ivars (whose company seems to still exist today!). Calatayud also invented the Hogar typewriter, also made by Pastor. The antiquary who sold me the adder pointed out that at the time Spain was recovering from its horrible civil war, and experiencing shortages and poverty; both the adder and the typewriter were designed to be made from readily available or recycled materials. The Ifach adder is, indeed, very frugal -- yet it makes up in ingenuity what it lacks in advanced mechanics.

Exhibit provenance:
eBay, from an antiques store in Spain.

More info:

Here are the scan, the Spanish text, and the English translation of the instructions manual.
A small adder utilizing the same idea of misaligned holes (but a different solution to the gradual change of the tens display) was patented in 1921 by the German Josef Funke. See Stephan Weiss’s article in the Journal of the Oughtred Society.

The ingenious Ifach adder

A carry mechanism with no gears!