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This paper presents a method for analytically analyzing the magnetic field and predicting the cogging force and torque of a linear and rotary permanent magnet actuator (LRPMA). The tubular mover of the LRPMA is transferred into a planar one by using a proposed magnetic field curvature factor and a relative permeance function for the stator slotting so as to simplify the magnetic field calculation. Magnetic field distributions of the LRPMA when the stator slotting is neglected are analytically analyzed using the magnetic scalar potential, and validated by 3-D finite-element method. The linear cogging force and rotary cogging torque of slotted LRPMA are subsequently predicted by the Maxwell stress tensor method and verified by the experimental results on the prototype.