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Hypocycloid Evolute

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HypocycloidEvolute

For x(0)=a,

x=a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)]
(1)
y=a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)].
(2)

If a/b=n, then

x=1/(n-2)[(n-1)cosphi-cos[(n-1)phi]a
(3)
y=1/(n-2)[(n-1)sinphi+sin[(n-1)phi]a.
(4)

This is just the original hypocycloid scaled by the factor (n-2)/n and rotated by 1/(2n) of a turn.

See also

Hypocycloid, Hypocycloid Involute, Involute

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Cite this as:

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

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