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• A coupling mechanism model of an FSDB unit is developed and verified. • Mathematical analysis is explored to reveal the coupling mechanism of an FSDB system. • Rigid and elastic motions of disk and cyclic blades induce diagonal and cross-coupling terms. • The motion patterns of cyclic blades are classified and clarified. • Effects of motion patterns of cyclic blades on NFs and CSs are applied to interpret and validate the dynamic coupling. This paper focuses on the influence mechanism of cyclic blades on the dynamic coupling of a flexible shaft-disk-blade (FSDB) system through mathematical analysis and numerical simulation. Firstly, a coupling mechanism model of an FSDB unit is developed through a Lagrange method and the assumed mode method (AMM), after considering the coupling behavior among shaft bending, shaft torsion, disk vibration, and blade bending. The modal comparison results between the proposed model and FEM affirm the validity of the model. Then the analytical interpretation is explored by decomposing and discussing the diagonal coupling and cross-coupling matrices of the FSDB system. The mechanism discussion reveals that the coupling matrices originate from the rigid and elastic motions of flexible disk and cyclic blades, indicating that the motions of cyclic blades play an important role in dynamic coupling. Therefore, the motions of cyclic blades are classified and analyzed, and their effects on natural frequencies (NFs) and critical speeds (CSs) are applied to further interpret and validate the dynamic coupling through numerical simulation. The numerical results indicate that motions of cyclic blades can increase, decrease, and eliminate the magnitude of dynamic coupling significantly. [ABSTRACT FROM AUTHOR]