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Epitrochoid Evolute


EpitrochoidEvolute

The parametric equations of the evolute of an epitrochoid specified by circle radii a and b with offset h are

x=(ah(a+b)c_1(t)cost+bc_2(t)cos[((a+b)t)/b])/(b^3+(a+b)h^2-b(a+2b)hcos((at)/b))
(1)
y=(ah(a+b)c_1(t)sint+bc_2(t)sin[((a+b)t)/b])/(b^3+(a+b)h^2-b(a+2b)hcos((at)/b)),
(2)

where

c_1(t)=h-bcos((at)/b)
(3)
c_2(t)=b-hcos((at)/b).
(4)

See also

Epitrochoid, Evolute

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Cite this as:

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

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