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Epitrochoid Evolute

\begin{figure}\begin{center}\BoxedEPSF{EpitrochoidEvolute.epsf scaled 800}\end{center}\end{figure}

The parametric equations of the Evolute of an Epitrochoid specified by circle radii $a$ and $b$ with offset $h$ are

$\displaystyle x$ $\textstyle =$ $\displaystyle {ah(a+b)c_1(t)\cos t+bc_2(t)\cos\left[{(a+b)t\over b}\right]\over b^3+(a+b)h^2-b(a+2b)h\cos\left({at\over b}\right)}$  
$\displaystyle y$ $\textstyle =$ $\displaystyle {ah(a+b)c_1(t)\sin t+bc_2(t)\sin\left[{(a+b)t\over b}\right]\over b^3+(a+b)h^2-b(a+2b)h\cos\left({at\over b}\right)},$  

where $c_1(t)\equiv h-b\cos(at/b)$ and $c_2(t)\equiv b-h\cos(at/b)$.




© 1996-9 Eric W. Weisstein
1999-05-25