Drawing Machines


Exploring the physics and geometry of mechanical drawing machines, I built a simulation of a harmonograph with three rotating pendulums and turned it into this online interactive.

Harmonograph 2

For the 2017 Festival of Numbers at the Science Centre Singapore, we built what was called ‘Probably the World’s Largest Harmonograph’ (PWLH) – a horizontal beam suspended from just below the ceiling of the exhibition hall on two long steel wires.

Kids around the PWLH drawing table

This kind of harmonograph can be modelled as a single pendulum with both a swinging and a twisting motion. The weights on the horizontal beam of the PWLH could be adjusted and re-positioned along the beam to change the oscillations of the swing and the twist.

While planning the PWLH, I had built another online interactive, to simulate this kind of harmonograph as well.

The ultimate test of this simulation was to try and recreate some drawings produced by the real harmonograph, which I think we passed:

Harmonograph drawings recreated
HarmoCycloDraw image gallery 1

Moving away from pendulums, I decided to simulate a drawing machine that utilises a combination of three rotating disks and a series of articulated arms that control the location of a pen drawing on a rotating table… With so many variable components, there is a lot more potential for interesting outcomes.

HarmoCycloDraw image gallery 2

There are even more variables to play with in the digital simulation, achieving effects that would not be possible with the physical machine. For example, the simulation actually draws straight lines between (usually closely spaced) points along the computed path of the pen. Increasing the step size between these points then results in some interesting drawings.