What is a Harmonograph?

A Harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are *Lissajous curves, or related drawings of greater complexity. The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890s, cannot be conclusively attributed to a single person, though Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor.

A simple, so-called 'lateral' harmonograph uses two pendulums to control the movement of a pen relative to a drawing surface. One pendulum moves the pen back and forth along one axis and the other pendulum moves the drawing surface back and forth along a perpendicular axis.

By varying the frequency of the pendulums relative to one another (and phase) different patterns are created. Even a simple harmonograph as described can create ellipses, spirals, figure eights and other Lissajous figures. Inputing sound into the device can also vary the frequency and produce interesting results. More complex harmonographs, such as ‘Harmony’, incorporate three or more pendulums , or involve rotary motion in which one or more pendulums is mounted on gimbals to allow movement in any direction.

*Lissajous curve
In mathematics, a Lissajous curve is a graph which describes a complex harmonic motion such as a heartbeat depicted on an Oscilloscope.

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Fig. I
Lateral, two-pendulum, harmonograph
(note the perpendicular direction of the pendulums)


Fig. II
Rotary, three-pendulum, harmonograph
(third pendulum has a rotary ‘gimbal’ allowing movement in any direction)


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