Invented in the 1940s, this is an entirely mechanical multiplication device. To operate it, you set the sliders on the side to the first number, and then turn the crank on top an appropriate number of times to multiply by the second number. Because of it’s obvious resemblance, this is affectionately known as the pepper-grinder calculator.
In the video, the narrator takes his Curta apart and explains a bit of the inner-workings of the device.
If they don’t have one already, the Calculator Museum should definitely make acquiring a Curta a top priority!
Thanks to Ivan for showing me this!