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The multiple coupled circuit model of a three-phase cage induction machine and the uses of a modified winding function theory to calculate the time-dependent inductances of the motor with a general eccentricity fault, including static, dynamic and mixed eccentricities, in a unified manner are considered. By defining the inverse air gap function of the eccentric machine, determining its indefinite integral and assuming step variations for the turn functions at the centres of the slots, precise analytic equations are obtained for the inductances. Differentiating these analytic equations against the rotor angular position also gives precise analytic equations to calculate the derivatives of the inductances, which may be used to determine the electromagnetic torque. Consequently, dynamic simulations of an induction machine with any eccentricity type and degree as well as a healthy one is made possible in the frame of a single Simulink program. At the beginning of the simulation process, the eccentricity components' degree and position are introduced and the program is then executed accordingly. A simple technique was used to make an industrial induction motor temporarily eccentric, with varying degrees, and experiments were conducted on it. By defining and applying effective air gap length and effective eccentricity components' degrees, good agreements are achieved between the simulated and the experimental results, which implies that the whole unified simulation program is effective.