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Vibration caused by torque ripple and radial force harmonics is a concern in many applications of permanent magnet synchronous machines (PMSMs). Alternative methods of machine design and/or stator excitation to minimize torque ripple have received considerable attention in recent years. Comparatively, methods to minimize radial force harmonics have received less attention. In this paper, a field reconstruction (FR) method is derived that provides a designer with the capability to rapidly determine the radial and tangential components of force under arbitrary stator excitation. Using the field reconstruction method, stator current waveforms that minimize the ripple of both torque and radial force are derived subject to the constraint of maintaining a satisfactory level of torque density.Index Terms-Finite element analysis (FEA), force density, permanent magnet machine, torque ripple.