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Watt's Curve


A curve named after James Watt (1736-1819), the Scottish engineer who developed the steam engine (MacTutor Archive). The curve is produced by a Linkage of rods connecting two wheels of equal diameter. Let the two wheels have Radius $b$ and let their centers be located a distance $2a$ apart. Further suppose that a rod of length $2c$ is fixed at each end to the Circumference of the two wheels. Let $P$ be the Midpoint of the rod. Then Watt's curve $C$ is the Locus of $P$.

The Polar equation of Watt's curve is


If $a = c$, then $C$ is a Circle of Radius $b$ with a figure of eight inside it.


Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, p. 162, 1967.

MacTutor History of Mathematics Archive. ``Watt's Curve.''

© 1996-9 Eric W. Weisstein