Floating offshore wind turbines experience periodical platform motions due to waves and currents, which intensify vibrations in wind turbine gearboxes. In these gearboxes, the gear mesh characteristics of the planetary gear train system (PGTS) are vulnerable to vibrations caused by platform motions. However, many PGTS models lack attention to gear mesh characteristics affected by platform motions. This study introduces a novel instantaneous multi-teeth contact model that integrates a loaded tooth contact analysis model with dynamic displacements. A rigid-flexible coupling dynamic model of PGTS that accounts for platform motions is established, and then the model is validated using the Finite Element Method, and gear mesh characteristics of PGTS are thoroughly analyzed. Simulation results show that platform motions disturb contact force distribution, increase peak forces and fluctuations, and pose a risk of tooth disengagement.