History of Mechanical Calculators

Long before electronic computers were invented, people have come up with ways to calculate without electricity. For example, the Chinese developed a device called the armillary sphere to simulate the earth’s and moon’s orbit. It can be used to predict the moon phase and relative direction of the sun from earth, which was then used to produce precise calendars.

However, in contrast to a modern computer, all the results are shown by moving parts instead of numeric value. In analogy, it is like an analogue computer. An improved version of this device can be driven automatically by water flow. (Wikipedia, 2018)

Another mechanical computing device called abacus is much more common in ancient times. Although we cannot determine the exact origin of this device, we know that most merchants in China, Russia and Europe used it for accounting. The device acts more like a memory than a computer. People can store digits on the device and manipulate the number to get the desired result. Abacus is quite hard to learn because the device does not do any calculations itself and people need to learn the math rules to operate it. However, because the numbers are stored on a device instead of people’s brain, it is less likely to make errors after people learned it. (Wikipedia, 2019)

A modern variant of the abacus is pocket adders. Its main interface is a set of dialing plates, with each of them representing a digit. There is a pointer on each plate that points to the current number. It works similarly to an abacus. People still need to manually rotate the pointer based on math rules. The advantage is that the interface is less obscure than abacus and it is cheap to produce. (Scherphuis, 2016)

As technology developed, people eventually developed devices that can not only store numbers but also calculate automatically. For example, Hamann Manus R is a cumbersome mechanical calculator that can add numbers without asking the user to remember math rules.

This was the device that caught my interest when I visited one of my professors and inspired me to write on this topic. A photo of this device is shown below:

Source: (Wikipedia, 2008).

It seems that some ideas are brought from abacus: there is a counter at the bottom that records the current number, just like what people do on an abacus. The difference is that there is a huge control panel on top of the counter where the user can dial a second number. The panel is connected to mechanical parts inside, and it will push the counter automatically when the user rolls a handle. The counter will bring a carry to the next digit when a digit exceeds 9. In this way, it can add numbers automatically. To subtract a number, the user can roll the handle in reverse direction so that the counter decreases. It can also calculate multiplication, but the process is quite tricky. If we want to multiply a number by 6, we add the number 6 times! There is another counter that records how many times we have rolled the handle, so we do not need to worry about forgetting it. Here is another trick: we can shift the counter, which is equivalent to shifting the control panel in reverse direction. If we want to calculate 24*36, we can first calculate 24*6 by rolling the handle six times, then shift 24 to 240 and roll the handle three times to add 24*30 to the result! (24*30=240*3; 24*30+24*6=24*36)

Note that we do not need to clear the counter during the process, so there is no need to remember the result of 24*6. We just directly add subsequent numbers to it. Amazingly, a division is also possible. The basic idea is to count how many times we can subtract the denominator from the numerator. We can also use the shifting trick to speed up the process. Sadly, there is no way to multiply or divide automatically on this device.