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


The areas of one of the inner lenses, heart-shaped half-region, and entire enclosed region (which resembles a lemniscate are


If a=c, then C is a circle of radius b with a figure of eight inside it.

See also

Heart Curve, Nephroid, Watt's Parallelogram

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Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, p. 162, 1967.MacTutor History of Mathematics Archive. "Watt's Curve."

Referenced on Wolfram|Alpha

Watt's Curve

Cite this as:

Weisstein, Eric W. "Watt's Curve." From MathWorld--A Wolfram Web Resource.

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