Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by $t$, lying in the interval $0$ to $2 \pi$, is associated with the maximum translation of the follower during one full rotation of the cam rotating about the center at $(x, y) = (0, 0)$ ?

- $x (t) = \cos t, \: y (t) = \sin t \\$
- $x (t) = \cos t, \: y (t) = 2 \sin t \\$
- $x(t)$= $\dfrac{1}{2} + \cos t, \: y(t)=2 \sin t \\$
- $x(t)$= $\dfrac{1}{2}$+$\cos t$ , $y(t)=\sin t$