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This paper investigates the performance analysis and mathematical modeling of a staggered-tooth transverse-flux permanent magnet linear synchronous machine (STTF-PMLSM), which is characterized by simple structure and low flux leakage. Firstly, the structure advantages and operation principle of the STTF-PMLSM are introduced, and a simplified one phase model is established to investigate the performance of the machine in order to save the computation time. Then, the electromagnetic characteristics, including no-load flux linkage, electromotive force (EMF), inductance, detent force and thrust force, are simulated and analyzed in detail. After that, the theoretical analysis of the detent force, thrust force, and power factor are carried out. And the theoretical analysis results are validated with 3-D finite-element method (FEM). Finally, an improved mathematical model of the machine based on d-q rotating coordinate system is proposed, in which inductance harmonics and coupling between d- and q-axis inductance is considered. The results from the proposed mathematical model are in accordance with the results from 3-D FEM, which proves the validity and effectiveness of the proposed mathematical model. This provides a powerful foundation for the control of the machine. [ABSTRACT FROM AUTHOR]