How A Mechanical Calculator Works

The fundamental requirement of a mechanical calculator is to perform the carry opperation. When a number dial has passes above 9, it must return back to 0 and add 1 to the place holder dial abover it. This must also happen in reverse. When a number dial passes bellow 0, it must return to 9 and subtract 1 from the place holder dial above it. With this in place, we can then do addition, subtraction, multiplication and division. 

This mechanical calculator has 4 dials. One for each place holder. Each dial has the digits 0 to 9. So the returning to 9 to 0 and 0 to 9 is covered simply by the circular dial. How do we perform the carry to the next place holder up? We need a single gear tooth on the dial, so that whenever it passes between 0 and 9, the wheel above is turned by one tenth, thus adding or subtracting 1.

The video below demonstrates addition and subtraction, then read below to learn how to extend this to multiplication and division.

Advanced Operations

What is nice is how the machine makes it intuitive that more advanced opperations are built from the more fundamental operations.

Multiplication

Multiplication is essentially repeated addition.

Example 3 x 7

1) Set the machine to "0".

2) Add 3 repeatedly, counting as you go. 1,2,3...

3) Stop when you reach 7.

4) Read the answer 21

Division

Division is essentially repeated subtraction. 

example 22 / 3

1) Set the dials to show 22.

2) Subtract 3 repeatedly, counting as you go. 1,2,3,4...

3) When you reach a number that is smaller than your diviser then stop. ...5,6,7

4) You should now see "1" on the machine. This is smaller than 3 so stop.

5) Your count equals the answer and the number on the machine is the remainder.  So 22/3 = 7 with a remainder of 1.