Planetary gear trains (PGT) with the aim of achieving multiple speed ratios are widely used in automatic transmission (AT). A fast configuration analysis method is of significance for improving the efficiency of AT design, and it is essential to study the automatic configuration analysis method for AT. For this purpose, the AT configuration is represented by a matrix model, which includes the structural matrix of PGT and shifting elements (SEs) matrix. Based on the proposed matrix representation, the speed relation and torque relation matrices of AT are automatically derived to analyze the kinematics and dynamics. Five performance indexes of AT configuration, specifically transmission ratio, rotation speed of components, torque transmitted by SEs, power flow, and transmission efficiency, are automatically calculated through the analysis result. The entire analysis process can be completed in 1 s on the computer. The proposed matrix model offers a unified representation for the configuration of AT derived from different synthesis algorithms. It facilitates rapid automated configuration analysis and performance evaluation, thereby positively influencing the design of automatic transmissions. Furthermore, the matrix model can be applied to the configuration synthesis of AT.
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