This paper gives the detailed derivation of a parameterized cage induction machine dynamic model in the natural frame of reference. The model is suitable for the analysis of the impact of a different number of rotor bars on machine transients as well as steady state performances. After the initial induction machine design process, for a predetermined number of stator slots and rotor bars, the parameterized model means that any different number of rotor bars could be chosen, resulting in different machine parameters. During this process, the stator winding scheme as well as the rated power of the machine is invariant. The model of the machine is derived by means of winding functions. Thus, in the way described, a very powerful model is obtained that enables the analysis of a dozen of the different number of rotor bars in an hour. The advantage of this is self-evident compared with models based on the finite element method. The power of the model is illustrated by an analysis of a specific machine with three different numbers of rotor bars.