A matrix-based method for synthesizing planetary gear trains to facilitate the creation of transmission systems

Abstract

The structural synthesis of planetary gear trains (PGTs) lays an important foundation for creating new mechanisms of transmission systems. Most existing studies focused on the synthesis of single degree-of-freedom (DOF) PGTs, while the synthesis of multi-DOF PGTs is very limited. This paper presents a matrix-based method for the automatic synthesis of non-fractionated PGTs with both single and multiple DOFs. First, the concept of a modified dual graph is proposed, based on which a new and simple method is presented to efficiently detect fractionated graphs. Then, the concepts of vertex adjacency index and moment matrix are defined, and a reliable algorithm is proposed to detect isomorphic graphs. Finally, a matrix-based method for the automatic synthesis of non-fractionated PGTs is presented, and the complete databases of non-fractionated PGTs with 3–9 links and 1–3 DOFs are generated for the first time. The creative design of mechanisms of 6-speed automatic transmission (AT) is taken for instance to illustrate how to design new transmission systems based on our databases.