How I built a Mechanical Calculator

How and why I built a mechanical calculator. Basing it on the Arithmometer, I built this calculator by hand out of mostly plywood. I suspect it is the first of its kind built in over 100 years. Working on and off, it took me 8 years.

The gear templates were generated using Matthias Wandel's gear generator program: https://woodgears.ca/gear/

For more, check out my blog: WhatWillMakes.com

00:00 - Intro
00:34 - Materializing Numbers
08:23 - Constructing the Calculator
21:13 - Demonstrating Its Functions
30:07 - History and Conclusions

Sources:

Arithmeum. Bonn, Germany.

Jones, Matthew L. Reckoning with matter: Calculating Machines, innovation, and thinking about thinking from Pascal to Babbage. Chicago, Illinois: The University of Chicago Press, 2017.

MechanicalComputing. “How the Arithmometer Works.”    • How the Arithmometer Works  .

Monnier, Valéry. “www.Arithmometre.Org.” https://arithmometre.org/.

Morar, Florin-Stefan. “Reinventing Machines: The Transmission History of the Leibniz Calculator.” The British Journal for the History of Science 48, no. 1 (2015): 123–46. https://doi.org/10.1017/S000708741400....

Puhle, Jens. “Wilhelm Schickard - Inventor of the Mechanical Calculator.”    • Wilhelm Schickard - Inventor of the mechan...  .

Endnotes:

1 - The Pascaline was not strictly base 10. Furthermore, its method of carrying differs from my model, though the effect, for my purpose, is similar enough. Pascal’s “sautoir” mechanism avoided the “Sufficient Force” issue that Schickard’s device would have had, but I felt this would be too much detail to go into in this video. For more, see this video:    • How the Pascaline Works  

2 - If you're wondering why we would not be able to use the same carrying mechanism in the full calculator as the one I demonstrated in the model at the beginning, it's due to what Jones calls the "Sufficient Force" problem. The issue with that way of doing it that I showed at the beginning (similar to Schickard's calculator), is that when a multi-digit carry happens, such as when adding 1 to 999999, all those carries would happen in basically the same moment. The machine would require way too much force to make all that happen in the same moment, so we needed a way to have carries ripple and each column be essentially isolated (from the perspective of force-needed) from its neighbor.

3 - Fairly sure I should have said "quotient" at 26:17 instead of "divisor."

If you're interested in more videos about mechanical calculators, I suggest the channels    / @chrisstaecker   and    / @jaapsch2  

Image credits:

Pascal: Blaise Pascal, oil painting by an anonymous artist, c. 1650; in the Musée Carnavalet, Histoire de Paris (P1800), Paris Musées

Schickard: Portrait of Wilhelm Schickard at Tübingen University, by Conrad Melperger, 1632

Pascaline image, https://artsandculture.google.com/ass...

Schickard’s calculator reconstruction:    • Wilhelm Schickard - Inventor of the mechan...  

Leibniz Portrait: A portrait of Gottfried Wilhelm von Leibniz - Public Library of Hannover (Lower Saxony), 1703, oil on canvas.

Thomas de Colmar portrait: https://commons.wikimedia.org/wiki/Fi...

Videos in the Arithmeum were taken by me.

L'Académie des Sciences et des Beaux-Arts, Sébastien Leclerc I, 1698
https://www.metmuseum.org/art/collect...

Établissement de l'Académie des sciences et fondation de l'Observatoire, 1666, Henri Testelin
https://collections.chateauversailles...

Drawing of Thomas de Colmar scanned from the 100th anniversary book of the company "Le Soleil" published in 1929: https://commons.wikimedia.org/wiki/Fi...

19th century mechanical calculator production chart from wikipedia:https://commons.wikimedia.org/wiki/Fi...

Music:
"Music is the pleasure the human mind experiences from counting without being aware that it is counting" - Leibniz
Gigue by J.S. Bach, BWV 1009, Cello Suite no. 3 in C major, Netherlands Bach Society:    • Bach - Cello Suite no. 3 in C major BWV 10...  
[2nd] Gigue by J.S. Bach, BWV 1007, Cello Suite no. 1 in G major, Netherlands Bach Society:    • Bach - Cello Suite no. 1 in G major BWV 10...