Spirograph

Spirograph

This collection of templates represents a comprehensive set of spirographs useful for drawing curves of all kinds.

What is a spirograph and how does it work?

A spirograph is an instrument used to draw curves called hypotrochoids. It is based on a simple concept: a circumference that rotates in a bigger circumference in a specified ratio. In fact what is important to understand how it works is to know the number of teeth of the bigger wheel, which we call R and the number of teeth of the smaller wheel, which we call r. The nominator of fraction reduced to its lowest terms between R and r tells us the number of petals that our hypotrochoids will have while the denominator, the number of revolutions the smaller wheel will do in the bigger one. The higher the numerator and denominator, the denser hypotrochoids will be, this is likely to happen when the denominator is high and a prime number since it will not be possible to reduce the fraction.

How to draw?

To draw, you must select and position the large circle (the one with teeth facing inward) in the center of the sheet. Then, choose a small circle (the one with teeth facing outward) and place it inside the large circle so that the teeth mesh. Finally, insert the pen into the desired hole and begin making elliptical movements, trying to follow the path of the small circle while ensuring it never separates from the large one.

How to print the model?

Each print profile features a wheel R—named after the profile itself—along with smaller wheels r designed to produce a particularly interesting result when combined with that R wheel.
You can therefore print the large wheel and any or all of the small wheels included in the print profile.
There is nothing to stop you from using small wheels "r" from other print profiles to achieve endless variations.

Documentation

Before printing, you can view a preview of the designs that can be created using various combinations of large wheels (R) and small wheels (r).
 

This is an example of what you will find in the preview; this way, you can identify a design you like and know exactly which wheel size and which wheel hole to use.