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Analytical expressions for the no-load magnetic field distribution of slotless brushless permanent-magnet (PM) machines with static, dynamic, and mixed rotor eccentricities are presented. The proposed analytical expressions can be used for slotless brushless PM machines with any radius-independent magnetization pattern. The analytical expressions and the results for six different magnetization patterns are presented. Based on the analytical magnetic field distribution, the line and phase back-electromotive force waveforms, local traction components and unbalanced magnetic forces are obtained. The analytical results are compared with those from finite-element analyses to validate the derived expressions.