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Eddy-current devices are promising for the passive and semi-active control of vibrations. From the electromechanical point of view, their behavior is characterized by the torque-to-speed curve and the mechanical impedance. In this paper, we report an investigation of the electromechanical behavior of eddy-current dampers/couplers consisting of permanent magnets and a massive conductor. Our goal was to determine the influence of the main design parameters on the torque-to-speed characteristic and on the mechanical impedance. To this end, we studied the dependence of the electrical pole and static damping coefficient on the design parameters under a given current density distribution within the conductor. This approach is equivalent to the procedure used to characterize the inductance and the torque constant of a standard electrical machine and it allows us to show that the electrical pole is determined by the inductive and resistive nature of the conductive part. Even if the conductor is realized by a solid conductor, the approach allows us to determine its equivalent resistance and inductance as a function of the design parameters, such as the number of pole pairs and the thicknesses of the permanent magnets and the conductor. We validated the analytical expressions of the equivalent lumped parameters, of the electrical pole, and of the static damping coefficient by finite-element analysis. This analysis provides the guidelines to identify the project parameters that can be varied to optimize the performances of the device as a coupler, damper, or brake.