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Flux-switching permanent-magnet (FSPM) machines have high torque density, high efficiency, and robust rotor structure. In order to achieve a high level of fault-tolerant capability and torque capability simultaneously, a multi-tooth 6-stator pole, 19-rotor pole fault-tolerant FSPM machine with twisted-rotor (MTFTFSPM-TR) is investigated and its design specifications including rotor pole numbers and gap width between the stator tooth and the fault-tolerant tooth are analyzed in this paper. Compared with a 12-stator pole, 14-rotor pole alternate poles wound fault-tolerant FSPM (FTFSPM) machine, the MTFTFSPM-TR shows higher torque density, better capability to inhibit short-circuit current, and lower cogging torque. Moreover, the twisted-rotor structure can achieve a symmetric and high sinusoidal back-electromotive force in each armature coil without the value reduction. Electromagnetic performance of the MTFTFSPM-TR has been verified experimentally on a prototype machine.