Recently, the interest in consequent-pole flux-switching permanent magnet (CP-FSPM) machines has been increasing because of the flux-focusing PM arrangements and the removal of the flux-barrier effect. A simple and rigid outer-rotor salient pole rotor structure can be adopted in CP-FSPM machines, making them applicable for in-wheel direct-drive applications. In this study, three CP-FSPM machines with II-shaped (II-PM), V-shaped (V-PM), and straight U-shaped PM (SU-PM) arrays are analyzed and compared. Moreover, a CP-FSPM machine with inclined U-shaped PM (IU-PM) arrays is proposed to improve the flux-focusing effect and stator slot utilization. The working principles of CP-FSPM machines are analyzed by adopting a semi-analytical model. Combining the finite element analysis (FEA) results of air gap flux density and the analytical model of phase back electromotive force (EMF), the contributions of multiple working harmonics to the back EMF are quantitatively analyzed. Additionally, 6/16 and 6/17 CP-FSPM machines with different PM arrangements are globally optimized. Both the no-load and on-load performance of the optimized machines are included in the performance comparison. The results illustrate that the 6/16 and 6/17 machines exhibit their respective merits, and the IU-PM machine shows the best torque production ability in these CP-FSPM machines with the same design criteria.