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In this paper, the diagnosis of actuator faults is addressed for a class of nonlinear systems applied to electric motors drives. The residuals are synthesized using a model- based strategy by applying a differential geometry perspective. According to the dynamic structure of the systems considered in this work, it is proved that the observability codistribution built for this class of systems can be independent of the state under certain conditions, so that the resulting coordinates transformations in the state and outputs spaces are linear mappings. Lastly, it is deduced that the dynamical properties of this class of systems are preserved by different electrical machines. Simulation results are illustrated for a three-phase induction motor application, where it is shown that in this case, the necessary conditions of geometric nature, results in necessary and sufficient conditions to isolate the studied faults. Moreover, in order to detect the actuator faults, it is suggested a directional residual evaluation to properly identify the fault present in the system.