This paper brings an identified model for a 6 degrees of freedom (dof) industrial robot, the Denso VP-6242G robot, first without payload, then with a payload. This last is composed of a force sensor fixed between a spherical handle and the robot end-effector. This equipped end-effector is intended to experiments in the field of Physical Human-Robot Interactions (PHRI), for co-manipulation purposes. The control algorithms that are necessary to achieve a good PHRI, require a good knowledge of the robot dynamical model, especially the inertia matrix which should be positive definite whatever the configuration of the robot. However, most of industrial robots are supplied without any datasheet containing the inertial parameters nor Computer-Aided-Design (CAD) model. Hence, we propose to apply an identification procedure to experimental data, based on the Inverse Dynamic model Identification Method (IDIM). To ensure the positive definiteness of the inertia matrix, the used optimization step addresses the problem of nonlinear Weighted Least Squares (WLS), derived from the mathematical formulation of the identification problem, under a set of nonlinear constraints in the parameters.