Usually, the joint transmission friction model for robots is composed of a viscous friction force and of a constant dry friction force. However, according to the Coulomb law, the dry friction force depends linearly on the load driven by the transmission. It follows that this effect must be taken into account for robots working with large variation of the payload or inertial and gravity forces, and actuated with transmissions as speed reducer, screw-nut or worm gear. This paper proposes a new inverse dynamic identification model for n degrees of freedom (dof) serial robot, where the dry friction force is a linear function of both the dynamic and the external forces. A new identification procedure groups all the joint data collected while the robot is tracking planned trajectories with different payloads to get a global least squares estimation, in one step, of inertial and new friction parameters. An experimental validation is carried out with a 1 dof prismatic joint composed of a Star high precision ball screw drive positioning unit, which allows large and easy variations of the inertial and gravity forces.