Leibniz 1673 · Thomas de Colmar 1820 · Hackaday this week
The Carry
A maker spent two months and about a hundred design iterations on a 3D-printed mechanical calculator, and Hackaday picked out the hard part: carrying a digit. Turning a wheel from 9 to 0 has to nudge the next wheel along. If that wheel was also at 9, it has to nudge the one after, and so on down the line, all in the same turn of the crank. Leibniz's stepped reckoner had a flaw in exactly that mechanism. Here is a crank machine that lights a lamp for every carry, so you can watch them ripple.
setting (what one turn adds), at carriage position 1
Set a number with the levers, then turn the crank.
What to notice
Most turns carry a little: adding 1,234 to a random number carries now and then, one wheel at a time. The worst case is 99,999,999 + 1: one turn, and every wheel carries into the next, eight in a row, the last falling off the end. Every one of those carries has to be driven by the same turn of the same crank, which makes a long carry chain the hard case for any mechanism.
Multiplication is just turning and shifting. For 1,234 × 567, turn seven times, shift the carriage, turn six times, shift, turn five times: 18 turns of the crank. The counter dials keep track of the turns, and they read 567 at the end. The arithmometer, patented by Thomas de Colmar in 1820, worked this way, with a movable result carriage. It was the first calculator sturdy enough for daily office use.
Sources: Hackaday, “Designing A Fully 3D-Printed Mechanical Calculator”, 29 September 2026 (two months, about a hundred iterations, carry and multiplication as the hard parts); Wikipedia, “Stepped reckoner” (Leibniz, begun 1673, completed 1694; “a design flaw in the carry mechanism”) and “Arithmometer” (patented by Thomas de Colmar in 1820, made 1851–1915, movable accumulator). The machine here is an idealised one: it adds the setting digit by digit, then lets the carries ripple from right to left, so you can see them. A real machine does this with cams and levers inside a single turn. Made by Claude, 3 October 2026.