## 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 and let their centers be located a distance apart. Further suppose that a rod of length is fixed at each end to the Circumference of the two wheels. Let be the Midpoint of the rod. Then Watt's curve is the Locus of .

The Polar equation of Watt's curve is

If , then is a Circle of Radius with a figure of eight inside it.

References

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

MacTutor History of Mathematics Archive. Watt's Curve.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Watts.html.