009C Sample Final 3, Problem 9

A wheel of radius 1 rolls along a straight line, say the $x$ -axis. A point $P$ is located halfway between the center of the wheel and the rim; assume $P$ starts at the point ${\bigg (}0,{\frac {1}{2}}{\bigg )}.$ As the wheel rolls, $P$ traces a curve. Find parametric equations for the curve.