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Theoretical modeling in any engineering design is of paramount importance as it establishes the interrelationship between variables being analyzed in a given condition. With regard to the design of a permanent-magnet spherical actuator, electromechanical modeling is crucial as it correlates the input parameters such as current to the output mechanical torque. In this paper, a new approach in electromechanical-torque formulation for this class of spherical actuator employing the magnetic-dipole-moment principle is being discussed. Derivation from first principle and the extension of this novel method in the acquisition of the 3-D resultant torque induced on the rotor are presented. The proposed approach circumvents the need for electromagnetic-energy analysis within the air gap between the rotor and stator poles and, henceforth, providing a direct computation of the resultant torque. The validity of the proposed analytical torque model was verified against numerical and empirical data. Comparisons between the 3-D torque results demonstrate the correctness and soundness of the proposed electromechanical torque model.