The curvature function is
$\kappa(s)=\frac{1/b-1/a}{\sqrt{2}(1-\cos(s/b-s/a))^{1/2}}$ where $a<b$ are constant, and $s$ is the arc length of the curve.
I know that the process in order to find the parametrization of the plane curve is to solve the system of Frenet Formulas for the curve (system of differential equations) but it seems to be a difficult task. Is there any other way to solve this ? Maybe any software...