Flux-switching permanent magnet (FSPM) machines are gaining in popularity due to their robustness, wide speed range, high torque, and high power density. However, their strong cogging torque can lead to vibration and noise due to the double-saliency structure. This paper investigates the effects of the short permanent magnet (PM) and stator flux bridge (FB) on the cogging torque reduction of three-phase 12/10-pole FSPM machines. Four different FSPM machines, including an inner-inner topology, an inner-outer topology, an outer-inner topology, and an outer-outer topology, are developed and analyzed with both short PM and stator FB. The configurations are obtained by placing the FB at inner/outer stator lamination and reducing the PM towards inner/outer directions. The cogging torque, average output torque, and PM utilization ratio of different topologies are extensively studied and compared by the finite element method (FEM). Finally, prototype machines are manufactured and tested. The experimental results have validated the numerical models and the effectiveness of the developed machine in reducing the cogging torque. The results also suggest that the outer-inner topology is more effective to reduce the cogging torque, which not only reduces the utilization of the PM materials, but also mitigates the cogging torque at only slight cost of torque performance.