Off-line robot dynamic identification methods are based on the use of the Inverse Dynamic Identification Model (IDIM), which calculates the joint forces/torques (estimated as the product of the known control signal-the input reference of the motor current loop-with the joint drive gains) that are linear in relation to the dynamic parameters, and on the use of linear least squares technique to calculate the parameters (IDIM-LS technique). Most of the papers dealing with the dynamic parameters identification of parallel robots are based on simple models, which take only the dynamics of the moving platform into account. However, for advanced applications such as output force control in which the robot interaction force with the environment are estimated from the values of the input reference, both identifications of the full robot model and joint drive gains are required to obtain the best results. In this paper a systematic way to derive the full dynamic identification model of parallel robots is proposed in combination with a method that allows the identification of both robot inertial parameters and drive gains. The method is based on the total least squares solution of an over-determined linear system obtained with the inverse dynamic model. This model is calculated with available input reference of the motor current loop and joint position sampled data while the robot is tracking some reference trajectories without load on the robot and some trajectories with a known payload fixed on the robot. The method is experimentally validated on a prototype of parallel robot, the Orthoglide.