Planetary gear trains are widely used in many fields, such as aerospace, industrial facilities, medical devices. In this paper, the design theories and free vibration characteristics of a type of planetary gear trains, that is, linkage planetary gear trains, are studied. The kinematic principles of coaxial, non-coaxial transmission and structural symmetry of linkage planetary gear trains are studied. Compound structures based on linkage planetary gear trains are extended and the calculation method of the reduction ratio of the extended structures is also carried out. Parallel planetary gear trains, one of the most advantageous types of linkage planetary gear trains, are further investigated. By considering translational vibration, torsional vibration, and gyroscopic effect, a dynamic model of a typical linkage planetary gear train is established to investigate its free vibration characteristics. The natural frequencies and vibration modes of the structure are obtained by solving the governing equations. Based on the properties of the modal vector, the vibration modes are classified into six types, namely carrier vibration mode, sun gear vibration mode, planetary gear vibration mode, translational vibration mode, torsional vibration mode, and all-components vibration mode. The influences of the gyroscopic effect, the bearing position, and meshing stiffness on the natural frequencies and vibration modes are also investigated.
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