• L. P. PookEmail author
Part of the History of Mechanism and Machine Science book series (HMMS, volume 12)


Pendulums are an essential part of some structures used for entertainment. Three of these uses are described. These are child’s swings, a child’s rocking horse, and pendulum harmonographs. Child’s swings are ubiquitous in both public playgrounds and private gardens. One of the attractions is that pumping is possible so they can be ridden without external assistance. Details vary widely. One form consists of a horse mounted on two wooden bars. These are suspended by pivoted metal links from a fixed wooden bar, which is at the top of the supporting frame. The attraction of the rocking horse is that it can be pumped by the rider to give an exhilarating ride. The rocking horse is, in essence, a four bar linkage with a coupler. Lissajous figures are plane curves produced when two orthogonal simple harmonic motions are combined. This can be done either theoretically or experimentally. They are named after Jules Antoine Lissajous, who demonstrated them experimentally in 1857. He used an optical method involving mirrors mounted on two tuning forks arranged at right angles. Some authors describe Lissajous figures without saying that this is what they are. They were first described by Nathaniel Bowditch in 1815, and they are sometimes called Bowditch curves. Lissajous figures are sometimes called rectangular curves or rectilinear harmony curves because they are produced by compounding two rectilinear motions. Lissajous figures are aesthetically satisfying, and they are closely related to the mathematics of music. Lissajous figures and some related curves are described. A mechanical device for the production of Lissajous figures and some related curves is called a harmonograph. This term was in use by 1877. There are two main types of harmonograph. A circular harmonograph is based on the rotation of interconnected wheels or gears, and numerous versions have been described. The geometric chuck and lathe described by Bazley in 1875 is, in effect, a circular harmonograph. Pendulum harmonographs are based on the oscillations of pendulums. Curves are close approximations to theoretical ideals provided that pendulum amplitudes are small. Because of friction etc. the amplitude of oscillation decays with time. Hence, the curves produced become progressively smaller. There are many different types of pendulum harmonograph. The earliest pendulum harmonographs were based on the Blackburn pendulum, which was first discussed by James Dean in 1815. It appears to have been re-discovered independently by Blackburn, who first described it in 1844. Twin pendulum harmonographs, which use two pendulums suspended by gimbals so that they are free to swing in any direction, appeared in the 1870s. The first of these was Tilley’s compound pendulum, ca 1873 (for ‘compound’ read ‘twin’). Commercial versions of twin pendulum harmonographs started to become available at about this time. In 1906 Charles Benham introduced his twin-elliptic harmonograph. Both parts of the pendulum of a twin elliptic harmonograph are free to swing in all directions. A harmonograph always has a recording device. This is usually a sheet of paper fastened to a moving table. A pen is mounted on a pivoted pen arm so that it remains in contact with the paper. The figures produced by harmonographs are sometimes called harmonograms. The aesthetic quality of harmonograms produced by pendulum harmonographs became appreciated towards the end of the nineteenth century, and their production was a popular pastime. At about the same time the relationship between Lissajous figures and the theory of music became of interest.


Rest Position Double Pendulum Negative Impulse Private Garden Positive Impulse 
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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.KentUK

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