Pascaline (Mechanical Calculator)

Boost MeBoosting thi model would really help me to make more :)

It's the year 1645. Blaise Pascal, a brilliant 19-year-old mathematic presents his newly created machine, The Pascaline, also known as Pascal's machine, honoring himself. The machine was a metalic box with some dials to turn and a numeric display. Inside, though, there was an intrincate mechanism of gears that allowed the machine to do simple calculations. It's original purpose was to help Blaise's father with his profession, accountant. Little did he know that his machine would set the first stone towards the computers that we know today -even the one you're reading this through-. Now, it has been 480 years since his invention, and thanks to 3D printing, you can have your own version of it at your home.

 

Here is a model of the Pascaline. Because the original machine was so complicated and big, I have reduced it to only been able tom perform arithmetic operations with 5 digit numbers. Also, keep in mind that the gears 2 and 4 (the tens and thousands/the ones in blue) turn counterclockwise, whilst the others (the yellow ones) turn clockwise. The essence of the machine is perfectly perserved, nontheless. 

 

The concept that this machine uses is the simplest of them all: counting. This is a counting machine. All the gears can be turned independently, but when one of them except the last one passes from 9 to 0, completing a whole cycle, the machine automatically adds one to the next gear. This means that we can count from 0 to 99999 by simply turning the first gear. But we can take advantadge of this to make any addition we want, simply because counting is simply adding 1. To add up two numbers, simply set in the machine the first one, and turn the corresponding gears by the amount of the second number, no need to worry about carrying one to the next digit, the machine's got you covered. For example, to add 1948 + 3726, simply place 1948 in the machine and turn by 6 positions the unit (right-most) gear, 2 for the tens gear, 7 for the hundreds gear and 3 for the thousands gear. The result of the operation is shown in the slots of the top of the machine. 

 

It is imprtant to notice that when the machine arrives at 99999, it switches back to 00000 automatically. So, if the result of any given operation exceeds 99999, the number shown in the machine will be the result of the operation - (100000 x the amount of times you exceeded 99999). This is because this machine works with modular arithmetic, just like analogic clocks, that turn to 1 after passing 12 hours. Here, nubers aren't in a never-ending straight line, but rather in a cycle, where the last and first ones are next to each other. The module of the system is the amount of numbers present in this cycle. For the clock, it's 12, and for the Pascaline, it's 100000. 

 

Maybe now you are wondering: “Ok, it makes sense, but what's up with the top caps with the plus and minus signs…?”. Ok, time to talk about substraction. We already know that the machine is good ad performing additions, but… What about substractions? Well, you can substract one number to another just like you added them, but this time you turn each gear in the opposite direction by the desired amount. But there's a more fancy method for it. It utilizes the compliment to nine. To do 8959 - 657, first put 657 in the machine and flip the top caps, to the “less” position. The resulting number is the 9-compliment of 657, and it's basically 99999-657. With this number in mind, flip again the top caps. Place 8959 in the machine and add the 9-complement of 657. We turned a substraction into an addition. Now, simply add the two numbers, add 1 to the resulting number, and et voilà, the result of the substraction. This works because moving x positions to the right in the cycle is just like moving 99999 - x positions in the opposite direction. We add one because we exceeded 99999 and the machine turned to 00000 automatically. if we want to do a substraction whose result is negative using this method, we'll have to take the 9-complement of the resulting addition, and that'll be the (negative) result of the substraction. 

 

The machine can do more complex calculations, but I'll leave that for you to figure out.

 

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Assembly:

-Start by glueing the numbers onto the cyinders, and the plus and less signs onto the top caps.

-If you are using an A1 Mini, glue the two parts of the box together.

-Pick all the pieces from gear 1 (units). The separators are polygons with more or less sides depending on the gear they have to be placed. The squares are for gear one and the octagons are for gear 5. Glue the pieces of gear one to eachother. Use the axle as a guide, but do not glue it yet. The gears are numerated, and the number should end up facing you. The separators have a number (I or II), it has to be facing up. You should end up with a structure like the shown in the image. Repeat the process with every gear.

-Glue “Turn_Wheel” to “Axle” pieces. Repeat 5x

-Slide the previous assembly in the round holes in the box. Slide gear 1 to five in the corresponding holes and the axle through the hexagonal hole that goes through it. Keep the orientation in mind. Slide the axle to the other side of the box, and glue “End_Cap” to it to fix it in place. It should be able to turn freely. 

-Glue the top wall to the box

-Place the “Top_Cap” pieces in place. They fit without any glue, and with a “clack”. They should be able to turn freely, too.

Glue the numeric display to the front of the assembly, taking account of the direction of each one. 

 

There you have it! Your Pascaline is assembled and ready!

 

Thanks for your support and enjoy it!