When modeling the dynamics of robotic systems containing electric motors, the force generated by the motor is generally considered only as an applied torque or force that is independent of mechanical state variables such as velocity. Due to the electromechanical coupling effects in the motors, this approach leads engineers working on a robotic system to designing faulty controllers. In this paper, we propose a dynamics analysis model in which DC motor dynamics are embedded into a mechanical dynamics model such that the electromechanical coupling effects are included in the overall model. A model for the DC motor is developed based on its equivalent circuit model and incorporated into the generalized recursive dynamics formula previously developed by our group. The resulting dynamic numerical simulation program provides an effective and realistic approach for analyzing the electromechanical dynamics of robotic systems driven by DC motors. The developed numerical simulation tool is evaluated by applying to an industrial robot and a flexible antenna system driven by DC motors for a satellite.