Previous works on parallel robots have shown that their visual servoing using the observation of their leg directions was possible. There were however found two main results for which no answer was given. These results were that (i) the observed robot which is composed of n legs could be controlled in most cases using the observation of only m leg directions (m < n), and that (ii) in some cases, the robot did not converge to the desired end-effector pose, even if the observed leg directions did (i.e. there was not a global diffeomorphism between the observation space and the robot space). Recently, it was shown that the visual servoing of the leg directions of the Gough-Stewart platform and the Adept Quattro was equivalent to controlling other virtual robots that have assembly modes and singular configurations different from those of the real ones. These hidden robot models are tangible visualizations of the mapping between the observation space and the real robots Cartesian space. Thanks to this concept, all the aforementioned points pertaining to the studied robots were answered. In this paper, the concept of the hidden robot model is generalized for any type of parallel robots controlled using visual servos based on the observation of elements other than the end-effector, such as the robot legs into motion. It is shown that the concept of the hidden robot model is a powerful tool that gives useful insights about the visual servoing of robots and that it helps define the necessary features to observe in order to ensure the controllability of the robot in its whole workspace. All theoretical concepts are validated through simulations with an Adams mockup linked to Simulink.