A cam with a  translating flat-face follower is desired to have the follower motion
$$y\left ( \theta \right )=4\left [ 2\pi \theta -\theta ^{2} \right ],\:\:\:0\leq \theta \leq 2\pi .$$ Contact stress considerations dictate that the radius of curvature of the cam profile should not be less than $40\:mm$ anywhere. The minimum permissible base circle radius is _________$mm$ (round off to one decimal place).