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Design and control of multi-degree-of-freedom (DOF) electromagnetic actuators require a good understanding of the magnetic fields, and involve real-time calculation of magnetic forces. This paper presents a method to derive distributed multipole (DMP) models for characterizing the magnetic field and torque of permanent magnet (PM) based devices. The DMP method, which offers magnetic-field solutions in closed form, inherits many advantages of the dipole model originally conceptualized in the context of physics, but provides an effective means to account for the shape and magnetization of the physical magnet. Three practical applications are given to demonstrate the DMP models for design of PM-based actuators and sensing systems. The magnetic fields and forces calculated using DMP models have been validated by comparing against numerical and experimental results which show excellent agreement.