Past research works have proven that the robot end-effector pose of parallel mechanisms can be effectively estimated by vision. For parallel robots, it was previously proposed to directly observe the end-effector. However, this observation may be not possible (e.g. if the robot is milling). Therefore, it has been proposed to use another type of controller based on the observation of the leg directions. Despite interesting results, this controller involves the presence of mapping singularities inside the robot workspace (near which the accuracy is poor). This paper presents a new approach for vision-based control of the end-effector: by observing the mechanism legs, it is possible to extract the Plücker coordinates of their lines and control the end-effector pose. In this paper it is also presented a comparison between the previous approach based on the leg direction and this new approach based on the leg line Plücker coordinates. The new approach can be applied to a family of parallel machines for which the previous approach is not suitable and has also some advantages regarding the workspace of applicability. The simulation results of both the controllers applied on a five-bar mechanism are presented.