A Mathematical Jamboree

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By Brian Bolt (1995)

("A Mathematical Jamboree" is an updated version of Brian Bolt's "More Mathematical Activities, a Resource Book for Teachers" [1985], but intended for a wider audience.)   

This is not an in-depth guide, but a brief overview of a few different Hamonograph designs. 

The Slab Pendulum is very simple in design and easy to build, but limited in the families of curve it can produce.  These drawing machines characteristically exhibit motion similar to a Blackburn’s Pendulum (a bob suspended from a Y).  It is also difficult to harmonically tune the different motions.  

The Lissajous figure Drawing Machine, one of two usual configurations.  (If the two pendulums were provided with a conical gimbals, then this apparatus would be the much more capable Two Pendulum Harmonograph!  

 The “Meccano” (British variation of an American “Erector Set” toy) Twin-elliptic Pendulum, classic “Top Hamper” version.

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I believe that the middle harmonogram drawing was accomplished by manipulating the pendulums and changing their motion half way through the drawing, or maybe it was a serendipitous accident such as somebody kicking it by mistake. It is an interesting effect.

Slab Pendulums; very simple design, build it large or small.

Lissajous Figure Drawing Machine

The "Meccano" Twin-elliptic Pendulum Harmonograph