In the field of material manufacturing, torsional vibration has some benefits for cutting or forming processing. In principle, torsional vibration can be caused by the torque ripples of a motor. Flux-switching permanent magnet (FSPM) motors are doubly salient and generate torque ripples, making them an option for manufacturing. However, the amplitude of the torque ripples is related to the motor structure, and frequency has a linear relationship with running speed. The torque ripples cannot be controlled separately from the motor running speed at conventional current excitations. Thus, a novel FSPM machine with an auxiliary rotor (AR-FSPM) is proposed to adjust the torque ripples. The main rotor (m-rotor) outputs the power, and the auxiliary rotor (a-rotor) adjusts the ripple frequency. When the speed difference between two rotors is six times the m-rotor speed, the torque ripple waveforms overlap. In this case, by controlling the phase difference between the two rotors, the amplitudes of the torque ripples can be adjusted. In this study, the principle of this novel machine is introduced, and the relationship between the torque ripple performance and the geometric parameters of the auxiliary rotor is studied. Then, the torque ripple amplitude adjustment method for this machine is discussed. Finally, the prototype of this novel machine is presented to verify its feasibility.