<p>In order to calculate the torque of a slotted-type eddy-current coupler (ECC) precisely, a new three-dimensional (3-D) analytical model using the 3-D magnetic vector potential method is proposed. The conductor layer in the slotted-type ECC incorporates two distinct materials of copper and back iron, and they are alternately arranged. To define the spatial relationships of these materials, two different 3-D Cartesian coordinate systems corresponding to permanent magnetic (PM) field and induced magnetic field are established, respectively. And the precise formulation of the torque is derived by the 3-D magnetic vector potential method, which is composed of the electromagnetic torque of the copper layer, the slots, and the back iron of the copper layer. The air gap magnetic field and the torque are simulated by finite element analysis. The results calculated by the proposed model are very consistent with those obtained by simulation and experiment, which errors are only below 10% even under high-slip conditions. This model fills the research gap in the 3-D analytical model of slotted-type ECCs considering multi-medium effects, reduces the theoretical calculation error, and provides a reliable basis for the design and optimization of slotted-type ECC. All of these provide a valuable design method for the slotted-type ECCs.</p>