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This paper presents the rotor design optimization for a reaction sphere (RS) actuator. The RS is a permanent-magnet synchronous spherical actuator whose rotor is magnetically levitated and can be accelerated about any desired axis. The RS is composed of an 8-pole permanent-magnet (PM) spherical rotor and of a 20-coil stator. Due to the highly complex geometry of the spherical rotor, consisting of...