Abstract
The direct three-dimensional (3-D) method represents the mathematical assembly of the magnetic field of separate cuboidal magnets and the vectors of the coil current density of a linear moving coil actuator within the global space. The mathematical description allows the variation of the design parameters of the actuator and the position of the coils with respect to the magnet array. The presented method describes a complete analytical derivation of the 3-D magnetic field and coil current. A numerical integration is applied to obtain the forces and torques appearing in a six degrees-of-freedom actuator as functions of the relative position of the coils with respect to the magnets in the 3-D space. The method and its governing equations are implemented as a rapid-design computational tool in Mathcad, and the simulation results are experimentally verified.
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