Flux reversal permanent magnet (PM) (FRPM) machines are popular for the high torque density and low PM usage, as well as the robustness. In order to further improve the torque while mitigate the torque ripple, both sinusoidal arc PMs and sinusoidal superimposed by 3 rd harmonics arc PMs are evaluated on FRPM machines in this paper. By employing finite element (FE) tool, the impacts on PM dimensions and 3 rd harmonic ratio are analyzed for the two shaped PMs. Moreover, three FRPM machines employing conventional arc-shaped PMs, sinusoidal arc PMs, and sinusoidal superimposed by3rd harmonics arc PMs, are comprehensively compared, with particular reference to their flux distributions, back electromotive force waveforms, cogging torques, average torques, and torque ripples. It is revealed that the sinusoidal superimposed by 3 rd harmonics arc PMs contribute to 7.2% higher torques whilst 24% lower torque ripples compared with conventional arc-shaped PMs.