Watt,s Curve
المؤلف:
Lockwood, E. H
المصدر:
A Book of Curves. Cambridge, England: Cambridge University Press
الجزء والصفحة:
...
16-10-2021
1725
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
 |
(1)
|
The areas of one of the inner lenses, heart-shaped half-region, and entire enclosed region (which resembles a lemniscate are
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.
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