A harmonograph is a type of drawing machine that creates geometric illustrations. There are a few kinds of harmonographs, we'll be making a type called a pintograph, that employs a pair of motorized rotating hubs to drive an armature with a pen attached to it.

The relative motion of the hubs, which move at slightly different speeds, typically, generates harmonic relationships that drive the curve continually off of the original path, yet bounded by four extreme points. This is in contrast to a roulette drawing machine, such as a Hoot Nanny or Spirograph, which is bounded by a circle and generates petal-like lobes.

If you're interested in learning more about roulette-style drawing machines, check out the incredible Cycloid Drawing Machine by Joe Freedman, and the excellent simulator of it created by Jim Baumgartner https://wheelof.com/sketch/

Here is an excellent online simulator you can use to explore pintographic curves.

This type of curve is called a Lissajous curve, which describe complex harmonic motion as a system of equations.

A terrific resource for learning more about pintographs is this page by Wayne Schmidt.

This guide was first published on Aug 03, 2018. It was last updated on Aug 03, 2018.

This page (Harmonograph Basics) was last updated on Jan 15, 2021.