Dynamic parameters are crucial for the definition of high-fidelity models of industrial manipulators. However, since they are often partially unknown, a mathematical model able to identify them is discussed and validated with the UR3 and the UR5 collaborative robots from Universal Robots. According to the acquired experimental data, this procedure allows for reducing the error on the estimated joint torques of about 90% with respect to the one obtained using only the information provided by the manufacturer. The present research also highlights how changes in the robot operating conditions affect its dynamic behavior. In particular, the identification process has been applied to a data set obtained commanding the same trajectory multiple times to both robots under rising joints temperatures. Average reductions of the viscous friction coefficients of about 20% and 17% for the UR3 and the UR5 robots, respectively, have been observed. Moreover, it is shown how the manipulator mounting configuration affects the number of the base dynamic parameters necessary to properly estimate the robots’ joints torques. The ability of the proposed model to take into account different mounting configurations is then verified by performing the identification procedure on a data set generated through a digital twin of a UR5 robot mounted on the ceiling.