Integrated design of topology and characteristic parameters for Planetary Gear Trains (PGTs) is critical for automatic transmissions (AT) because they are closely related to clutching sequences and gear ratios. A systematic method consisting of four steps for the synthesis of multi-speed ATs is proposed based on four-row Ravigneaux-based PGTs. First, the digraph model and adjacency matrix are employed to enumerate all the non-isomorphic four-degree-of-freedom (four-DOF) and three-DOF topologies. Second, the rules for configuration of gear shift elements are summarized to eliminate their infeasible combinations, and the speed matrix equations are established to obtain all potential gear ratios with given number of brakes and clutches. Third, Monte Carlo simulations based on the Latin hypercube sampling-Chi square (chi(2)) test method is adopted to classify all the gears into four groups to significantly reduce the number of gear permutations. Finally, the characteristic parameters are optimized by the internal penalty function method. The method is verified by synthesizing eight-speed and nine-speed Ravigneaux ATs.
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