The mathematical theory of linkages was once found beautiful, but is now comparatively unknown.

One of its highlights was what Florian Cajori (1859–1930) called the ‘beautiful discovery’ of the Peaucellier–Lipkin linkage (found independently in 1864 and 1871), a simple mechanism that transforms circular motion into linear motion (see attached image).

The importance of such a mechanism is that it can produce straight-line motion without using guide-rails and thus reducing friction. Previous linkages such as James Watt's (1736–1819) only *approximated* straight-line motion.

J.J. Sylvester, (1814–97) (who characterized his mathematical work as ‘the worship of the True & Beautiful’) admired a pump based on the linkage for ‘[i]ts elegance, and the frictionless ease with which it can be worked (beauty as usual the stamp and seal of perfection)’.

When the physicist William Thomson (later Baron Kelvin; 1824–1907) was able to work a model of the linkage, he was reluctant to hand it back, saying: ‘No! I have not had nearly enough of it — it is the most beautiful thing I have seen in my life’.

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