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Cycloid Evolute

CycloidEvolute

The evolute of the cycloid

x(t)=a(t-sint)
(1)
y(t)=a(1-cost)
(2)

is given by

x(t)=a(t+sint)
(3)
y(t)=a(cost-1).
(4)

As can be seen in the above figure, the evolute is simply a shifted copy of the original cycloid, so the cycloid is its own evolute.

See also

Cycloid, Cycloid Involute, Evolute

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Cite this as:

Weisstein, Eric W. "Cycloid Evolute." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CycloidEvolute.html

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