A novel modular arc-linear flux-switching permanent-magnet motor (MAL-FSPM) used for scanning system instead of reduction gearboxes and kinematic mechanisms is proposed and researched in this paper by the finite element method (FEM). The MAL-FSPM combines characteristics of flux-switching permanent-magnet motor and linear motor and can realize the direct driving and limited angular movement. Structure and operation principle of the MAL-FSPM are analyzed. Cogging torque model of the MAL-FSPM is established. The characteristics of cogging torque and torque ripple are investigated for: (1) distance (dend) between left end of rotor and left end of stator is more than two rotor tooth pitch (τp); and (2) dend is less than two rotor tooth pitch. Cogging torque is an important component of torque ripple and the period ratio of the cogging torque to the back electromotive force (EMF) equals one for the MAL-FSPM before optimization. In order to reduce the torque ripple as much as possible and affect the back EMF as little as possible, influence of period ratio of cogging torque to back EMF on rotor step skewing is investigated. Rotor tooth width and stator slot open width are optimized to increase the period ratio of cogging torque to back EMF. After the optimization, torque ripple is decreased by 79.8% for dend > τp and torque ripple is decreased by 49.7% for dend < τp. Finally, 3D FEM model is established to verify the 2D results.