The original Spirograph

During a recent trip to the Science Museum I happily found myself distracted from the 8 foot by 8 foot calculator in the Mathematics exhibition, by this:

Harmonograph at the Science Museum, London

...and it reminded me of an early blog post of mine about the maths of the spirograph. I had assumed that the spirograph was designed for the sole purpose of entertaining under 5s on rainy days and testing children’s patience with numerous snapped pencil leads. But no, it seems there was a scientific use at the beginning of it’s ancestral line...

Introducing, the harmonograph (ps. before we go any further i am not saying that the Spirograph is defs a direct descendent of the harmonograph, this is purely ill-informed speculation). 

The harmonograph was invented in the 1870s to analyse vibrations and was used in the study of sound. However, predictably, by the 1900s it was already regarded as a scientific toy for creating pretty patterns!

copyright Conor Lawless

The harmonograph works by utilising the swinging motion of two pendulums - one mounted to a pen and one to a drawing table - which swing at right angles to each other with the pen tracing out the resulting combinations of movement onto paper.

Weights can be added or moved up and down the pendulums to vary the speed that they swing at, creating varied patterns.

The Science Museum has a number of curve-drawing machines on show, like Stanley’s and George Adam’s geometric pens which arguably were the first spirographs, but with fancier cogs.

George Adams' Geometric pen at Science Museum, London

Stanley's geometric pen at Science Museum, London

There was also a surprisingly elaborate contraption on display masking as a tool for ornamental turning used on lathes - the geometric chuck.

Geometric chuck at Science Museum, London

This example, at the Science Museum, is the only known example of a 4-stage chuck for use on paper...and boy does it do good things to paper.

The chuck works by drawing the epicycloidal motion of each tier (determined by different sizes of cog) onto the paper at the top of the chuck. The motion of each tier can be superimposed upon another, or other tiers can be fixed so that the motion of only one tier is drawn.

So there we have it, an introductory tour of curve-drawing machines with very little science or maths and a lot of “it makes pretty things”. That’s what I like. But...if you do want some maths - the old Spirograph post has a bit to whet your appetite or you can go all-out with this article - which has some amazing examples and a bit of science behind their construction.

The Science Museum Mathematics exhibition is on the Second floor and is a permanent fixture (for now).