To obtain multiple speed ratios, a synthesis methodology of planetary gear trains (PGTs) with multiple operating degrees-of-freedom (DOFs) is proposed based on the variable structure method. Variable structure of PGT is accomplished by changing the fixed interconnection edge. First, PGTs with two operating DOFs are synthesized with a deduction method based on the relationship between the number of planetary gear sets (PGSs) and number of fixed interconnection edges. Next, connection characteristics of fixed interconnection edges are defined as frequency of utilization to construct original speed ratios of the two operating DOFs schemes. The connection characteristics are then obtained based on the power flow analysis. PGT graph model with connection characteristic is built to provide guidance in the design of varying structure. Finally, multispeed PGTs with multiple operating DOFs are synthesized based on the graph model and lever analogy. A design example for three-PGS PGTs is considered to highlight capabilities of the variable structure method.

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