This paper proposes a novel linear–rotary permanent-magnet actuator (LRPMA) with interlaced poles, which has the merit of using only 50% of the neodymium–iron–boron permanent magnets when compared with those used in traditional Halbach structure. By assuming the stator is slotless, the magnetic field distribution of the LRPMA is initially analyzed using the magnetic scalar potential in the Cartesian coordinate system. A method for calculating the relative permeance by Schwarz–Christoffel transformation (SCT) is subsequently deduced to analyze the magnetic field in detail and predict the cogging force/torque of LRPMA very accurately. The analytical linear cogging force and rotary cogging torque are derived and verified for the design optimization of the actuator. The 3-D finite-element method is used to verify the correctness and effectiveness of the proposed SCT.