Hypocycloid Evolute

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HypocycloidEvolute

For x(0)=a,

x = [画像:a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)]]

(1)

y = [画像:a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)].]

(2)

If a/b=n, then

x = [画像:1/(n-2)[(n-1)cosphi-cos[(n-1)phi]]a]

(3)

y = [画像: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 Resource. https://mathworld.wolfram.com/HypocycloidEvolute.html

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