The emerging polarization states from a linearly polarized monochromatic light passing through a rotating linear quarter-wave plate have been characterized as the intersection curve of a cylinder and the Poincaré sphere. But in the cases where the input polarization states are in general elliptical or circular and pass through a rotating linear retarder, the emerging polarization states produce trajectories that do not correspond to the intersection of a sphere with one cylinder. Hence, in this work, we present a full characterization of the trajectories on the Poincaré sphere for monochromatic input beams with an arbitrary polarization state passing through a rotating linear retarder as the intersection curve of the Poincaré sphere with a cone. Moreover, it is shown that these trajectories are characterized by their projection on the equator plane, having the form of limaçon of Pascal (Pascal's snails).