Single-layer (SL) non-overlapping windings are applied to flux reversal permanent magnet (FPRM) machines, to extend the family of stator-PM machines. The machine topology and operating principle are introduced, and the general rules of symmetrical phase flux-linkages in machines with various slot/pole number combinations are found. The even order coil flux-linkage harmonics can be cancelled in the resultant phase waveforms due to opposite polarities of either magnets or coils. Moreover, based on finite element (FE) analysis, the FRPM machines with different rotor pole numbers, equipped with SL or double-layer (DL) windings, are comprehensively compared. The results reveal that compared to their DL counterparts, the FRPM machines with SL windings (FRPM-SL) exhibit similar torques and iron losses, as well as enhanced flux-weakening and fault-tolerant capabilities due to higher self-inductances but lower mutual-inductances. A pair of FRPM-SL prototype machines are manufactured and tested to validate the predictions.