Let us return back in time to the times when “computers” were not machines but humans. The work of computers improved significantly at the end of 19-th century. At the end of 19-th century the technology was powerful enough to build reliable and mass produced calculators. These calculators were fully mechanical, propelled by a to handle and with successive minor or major innovations remained in use until the 70s of the twentieth century. In the seventies were mechanical machines replaced by cheap Japanese electronic calculators. Suddenly, the mechanical calculators and their human operators – “computers” – became almost overnight unnecessary. But let us return to the beginning of their golden era, to the end of the 19th century. The first commercially successful calculator has been constructed in 1876 by Willgodt Theophil Odhner , a Swedish engineer living permanently in St. Petersburg. His invention became the first mass-produced calculator, which was produced under license in several European factories, especially in Germany. Principle of the calculator consisted in wheels with a varying number of pins. The teeth of the wheel could move and dismiss inside the wheel, depending on the setting of the input register. The quantity corresponding to the number of teeth in action has been added to or subtracted from the result register each time one full rotation of the handle was performed Wheels moved independently with just minor shift between two neighbor wheels which caused that any resistance of the mechanism grew gradually. If a wheel increased in some position the number 9 to a higher number it was necessary to increase the next number by 1. To do this, Odhner used special movable pins. These pins in most cases just missed the wheel of output register and did nothing. If, however, it was necessary to increase the number on the adjacent wheel a special stop moved the pin to the position where this pin added 1 to the adjacent wheel. This operation has been performed gradually from right to the left. A similar process in an opposite direction was used when subtracting. This was a limitation for the size of wheels and in later electric driven models also the speed of wheels. Wheels have to be sufficiently large and could not move too fast. The machine had to be oiled properly. On the other hand, the wheels cannot be overloaded by too much oil. The computer was technical wonder of that time and the owner maintained the calculator at the specialized repairmen. Another register counted the crank revolutions. since the multiplicatoin and division was just repetitive addition and subtraction. There are many videos on the Internet showing basic mathematical operations. Addition, subtraction, multiplication and division. Common are also videos which show how we can use extraction of square root convert into repetitive subtraction. Let us try something different. The output register is long enough for more simultaneous calculations. Since the calculator was designed for businessman let the first example is from the business area. The original price of a good is 745 and the good has been discounted by 12%. We find the discount and the new price. This menas, we find 12 and 88 percent from745. In other words, we have to multiply 745 by the number 0.12 and 0.88 We change the order of multiplication and we will multiply the numbers 0.12 and 0.88 by the number 745. We set 12 on the left end of the input register 88 on the opposite end and will multiply by 745. Let us start on the third position. We add the number 7-times together. which is equivalent to multiplication by 7. After this we shift the register to the second position and add the numbers 4-times to the total. This is equivalent to a multiplicatoin by 74. Now we again shift the register and the previous computation is equivalent to multiplication by 740. Finally we add the numbers 5-times to the total. These operations are equivalent to a multiplication by a factor 745. The results are on the left and right end of the output register. The discount is 89.40 and the new price is 655.60. Another problem is from statistics. When working with data in statistics we often need to sum up numbers and also sum up squares of these numbers. Consider the file of six numbers and we sum up these numbers and at the same time we sum up the squares of these numbers. Like in the previous computation we will use one end of the calculator to sum up numbers and the other end to sum up squares of these numbers. Practically, we set the number to the input register, number 1 on the opposite end and multiply by the number. This gives the desired number and its square in output register. We do the same for all numbers in the file and keep the output register with total sum. Only the counter register is zeroed between calculations. The sum of numbers and its squares accumulates in output register.

Birth of mechanical calculators

One thought on “Birth of mechanical calculators

  • August 2, 2018 at 4:02 pm
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    Skvelé video, veľmi mám rád mechanické kalkulačky a som rád, že sa mi podarilo už nejednu opraviť. Veľmi by ma zaujímalo ako je možné počítať odmocninu, ak by sme mali nejaké video rád by som sa na to pozrel 🙂
    Držím palce! 🙂

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