In this paper, cogging torque characteristics in both single-phase and three-phase flux switching transverse flux permanent magnet machines (FS-TFPMM) are analyzed by 3-D finite element method (FEM). It is found that the cogging torque of the FS-TFPMM is significantly influenced by the ratios of stator and rotor core circumferential widths to pole pitch, ks and kr. When kr > 1-ks, the cogging torque waveform has additional two zero-crossing points, whilst its amplitude is significantly reduced. The optimal ratios of ks and kr are selected to reduce the cogging torque and to maximize the permanent magnet flux linkage. A 380 W three-phase prototype is designed, manufactured, and tested to verify the optimization.