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 and with offset 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 $c_2(t)\equiv b-h\cos(at/b)$ .