Sand Spirograph

thingiverse

My math spirograph brings the beach to your school desk. **About the design:** Modeled in Blender with the original Spirograph toy in mind that I used as a kid. I tried to keep the list of printed parts minimal by creating a two-gear system instead of a more complex scissor extension arm. A unique feature of my design is the guide wheel that supports the tracing gear to keep it level and from falling into the sand while still allowing the gear to rotate. **Assembly:** *(same for both large and small designs) See video for visual* 1.) Assemble the tracing gear with the tracing pins at any of the four holes into the top face of the gear. You may use any combination of the pinholes. 2.) Stack the base, guide wheel, and then tracing gear. **How To Use:** *Large math spirograph* 1.) Find dry sand and make a flat surface with it. Sprinkle a thin layer of moist sand on the top for a more contrasting result. 2.) Place the math spirograph on top of the sand surface, then turn the tracing gear by holding the gear's handle and guiding it in a circular pattern. 3.) After making as many revolutions as you like, lift the entire math spirograph off the sand to see your spirograph creation. *Small math spirograph* 1.) Using the blank castle mold and fine dry sand, create a blank puck shaped castle. Sprinkle a thin layer of moist sand on the top for a more contrasting result. 2.) Place the small spirograph assembly over the sand "puck." 3.) Turn the tracing gear by holding the gear's handle and guiding it in a circular pattern. 4.) After making as many revolutions as you like, lift the entire math spirograph off the sand to see your spirograph creation. **Math spirograph background info:** The math spirograph is a toy that produces mathematical roulette curves. My design creates a hypotrochoid roulette curve with the parametric equations: x(θ) = (R - r) cos(θ) + d cos((R - r) / r) y(θ) = (R - r) sin(θ) - d cos((R - r) / r) where r is the radius of the inner tracing gear. R is the radius of the fixed gear on the base of the assembly. d is the distance of the tracing pin from the center of the inner tracing gear. The math spirograph was invented by mathematician Bruno Abakanowicz around 1881 and was used to calculate the area delimited (bounded) by curves. Drawing toys using gears started to become popular around 1908 when the Sears catalog advertised The Marvelous Wondergraph. The Math Spirograph toy brand was started in 1965 by Denys Fisher and named 1967 Toy of the Year. It was a 2014 Toy of the Year finalist.