Spiraling Mathematical Drawing Toy

Model Overview & Print Notes

Introduction This Spiraling Mathematical Drawing Toy has mathematical features. It has a pen hole on the tip of a gear tooth which is located at the pitch radius of the virtual circle. All gears fit together in every way. All pen holes are at the same interval. The included source code is a OpenSCAD script. A "sh" file is added to create all the gears and all other shapes with a single command. Spirograph The name "Spirograph" and the Spirograph toy are owned by Hasbro. It is not allowed to sell this design or the 3D models created with it. It is only for personal use. Warning Be careful with small parts and young children. The gears with less than 11 teeth are small. I suggest not to print those when it is used by children. Children might chew on the parts and pieces might break off. Supervision might be needed. How to get started In the folder “Outer Rings”, look for the file "outer_ring_36.stl". That is the best Outer Ring to start with. It is a Outer Ring with 36 teeth.  There are two sets of Gears, for a Fineliner and for a Ballpoint. Select the right folder and select a few gears. The best gears to start with are the gears with 24, 18 and 12 teeth. Print them and check if they fit. When using the gear with 18 teeth and the most outer pen hole, then it should result in a straight line. The XY Size Compensation of the slicer can be used to tune the shape. The Outer Ring can be attached to a paper with tape. From there on, start drawing spirals and make multiple layers of many spirals. Printing I used 0.20 mm layer height with 0.4 mm layer width and 2 walls and 15% Gyroid infill. The compensation for the Elephant foot compensation can be set higher to be sure that the lowest layer is not wider. Mathematics This toy is full of mathematics and it can be used in a different way than other Spirographs. All the gears have pen holes that start at the pitch radius of the virtual circle and all the pen holes are at the same distance and there are markers on the outer rings. The first position on the outer ring has a square. The best result are created with a combination of many layers of spirals. For example, draw the spirals for every pen hole (or every other pen hole), then rotate the gear to the next marker on the Outer Ring and draw all of them again. An other example is to use a large Gear, draw all the spirals for every pen hole, and then do the same with a Gear with half the number of teeth. The number 37 is a prime number. When using a Outer Ring with 37 teeth and a Gear that is also a prime number then the result is different. When I made this design, I learned that there are many things to discover and learn about. For example the Tusi Couple is the straight line with a pen in the most outer hole in a Gear that has half the teeth of the Outer Ring. When using a Gear with one third or a quarter of the amount of teeth, then a Deltoid curve or Astroid can be created. The square marker on the Outer Ring is the start position.   The Source Code In the file "Source Code.zip" is the source code. If you are not familiar with OpenSCAD, then I suggest to start with an other and more simple design. The zip file must be unzipped/unpacked before the source code can be used. The files are: Spiraling Mathematical Drawing Toy.scad (the OpenSCAD script) publicDomainGearV1.5_stone.scad (a script to make gears, Public Domain) Vahika.otf (a font for text on the gears, Public Domain) Vahika_CC0_License.txt (License for the font) make_Spiraling.sh (A sh script to make all the gears and all other shapes) Spiraling_plotting_tests.py (A test to draw spirals, not working very well) Origin of the "publicDomainGearV1.5_stone.scad" file: https://www.thingiverse.com/thing:6596095 Origin of the "Vahika.otf" font: https://www.dafont.com/vahika.font The file "Spiraling_plotting_tests.py" uses the Python Turtle module to calculate spirals and write them to a file. It is a test for myself and the code is not very good. OpenSCAD The Customizer of OpenSCAD can be used. There are three options: Outer Ring Gear Intermediate Ring For larger printers, parts with more gears can be created. When the "Outer Ring" is generated, then the console shows the total size that is needed for the Outer Ring. Instead of using the slicer to tune the shape, the option "tuning" can be used. I suggest not to change the 'tooth_size', 'pressure_angle', 'clearance' and 'backlash'. If they are kept the same, then all the gears will fit with each other. To scale the whole design up or down, the 'tooth_size' can be changed. The "make_Spiraling.sh" file can be changed for your own settings. When using the newest 2024 version of OpenSCAD, then the stl files are created at a high speed.

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