Planetary gear trains (PGTs) are used in automatic transmission to achieve any desired speed ratios. At present, the study on the relationship between speed ratio and topology is not significant. Therefore, this paper focuses on studying the speed ratio based on topology. For this purpose, the graph theory is used to represent PGTs, and a concept of the speed topological graph is introduced. Based on the proposed graph representation, the relationship between the speed ratio and topology is studied. Three types of topological graphs are analyzed, which includes path, tree, and unicyclic graph, and necessary results are presented. The results reveal the relationship between speed ratio and topology, which helps in understanding the PGTs further. The result can help engineers to arrange the clutches and brakes to achieve desired speed ratio during the conceptual design phase, which can greatly improve the design efficiency of PGTs. The presented kinematics analysis method can be extended to analyze multi-input and multi-output planetary transmission.

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