# Patent Analysis and Structural Synthesis of Epicyclic Gear Trains Used in Automatic Transmissions
###### Abstract  
A patent survey is conducted to investigate the application status of epicyclic gear trains (EGTs) used in automatic transmissions (ATs). In this regard, 673 AT patents are investigated firstly, and 274 different EGTs are obtained after the patent processing. EGTs are presented by corresponding double bicolor graphs (DBGs) and they are sorted into 13 groups in accordance with the degree of freedom (DOF) of DBGs and the degree of hollow vertices. Then, structural characteristics of obtained EGTs, which are used to detect whether the EGTs obtained in the future can be used in ATs, are analyzed and summarized. Finally, a new approach is proposed to obtain new configurations of the EGTs with one main shaft based on the transformation relation between DBG and the basic graph. Several examples are presented to illustrate the validity of the proposed approach. epicyclic gear trains; automatic transmission; characteristic analysis; synthesis approach 2020 10 82019 120 2020 2019  
freedom (DOF) and up to eight links. [PERSON] [3] classified planetary mechanisms in detail and defined the simple planetary gear train (PGT) consisting of two central gears, one or more planet gears and one arm. [PERSON] and [PERSON] [4], and [PERSON] [5] introduced the graph theory into the synthesis process of geared kinematic chains (GKCs) and obtained epicyclic gear chains with up to five links. [PERSON] and [PERSON] [6] applied the graph and the matrix theories to synthesize GKCs and obtained all one-DOF EGTs with up to four fundamental loops. Furthermore, [PERSON] [7] computed the characteristic polynomial of EGTs for the isomorphism detection and synthesized non-isomorphic EGTs with up to six links using the genetic graph approach. Moreover, [PERSON] and [PERSON] [8] synthesized non-fractionated two-DOF EGTs based on the proposed method. Then, [PERSON] and [PERSON] [9] synthesized EGTs with up to seven links based on a recursive method, which proved the validity of [PERSON]'s achievements. [PERSON] [10,11] presented a new graph representation, namely, an acyclic graph representation of PGTs with Lam. Then he proposed a synthesis method for GKCs based on the proposed graph representation [12]. [PERSON] and [PERSON] [13,14] presented the canonical graph representation of GKCs to solve the pseudo-isomorphic problem, and synthesized EGTs with one-, two- and three-DOF up to eight links. [PERSON] [15] presented a synthesis method regarding the planets and carriers and 1-DOF EGTs up to nine links were synthesized. [PERSON] et al. [16, 17, 18] presented unified topological representation models for planar kinematic chains and synthesized EGTs with up to nine links. Moreover, [PERSON] [19] proposed an approach in accordance with the hamming number and generated EGTs with up to seven links. [PERSON] [20] utilized the vertex incidence polynomial, proposed a synthesis method and listed one-DOF non-isomorphic EGTs up to 6 links. [PERSON] et al. [21,22] synthesized the one-DOF EGTs with up to seven links using the concept of building of kinematic units and performed symmetry analysis of EGTs. Many synthesis methods for EGTs have been proposed so far and subsequently different configurations have been obtained, which are helpful for the innovation of ATs. Up to now, a wide variety of ATs have been proposed, analyzed and produced. In 1939, the Hydra-Matic was invented through the combination of a hydraulic coupling with a three-row EGT, and it was installed on GM Oldsmobile cars [23]. The Hydra-Matic could achieve four forward gears and one reverse gear so that it was considered as the symbol of ATs at that era. Since then, the ATs have rapidly developed. In 1950, Ford company developed a three-gear AT equipped with the torque converter, representing that the AT technology enters the maturity stage. In 1965, AP company produced the first AT installed on the front engine and front drive (FF) vehicles, which promoted the miniaturization of ATs [24].