Application of incidence matrix to topological structure and kinematic analysis of multi-planet gear trains

Abstract

In this paper, a matrix notation is presented to decompose the structure of any planetary gear train (PGT) into its constituted fundamental geared entities (FGEs). The representation of the PGTs by matrices motivates the need for a method for discretizing PGTs into FGEs. This paper proposes a novel method for the structural decomposition of PGTs with the aim of dividing the structure into several independent substructures with single DOF. This is accomplished by determining the transfer vertices and second level vertices in matrix form. Although there are a large number of existing analysis methods, there is no method yet that entirely performs the kinematic analysis of multi-planet gear trains automatically in the computer in a simple way. Understanding the topological properties of existing PGTs is very useful for benchmark synthesis to explore all possible designs that are based on existing ones. Also, any type of FGEs with any number of links can be investigated without knowing the exact size of gears.

Keywords

• Computer-aided analysis
• Graph theory
• Kinematic analysis
• Planetary gear trains
• Topological structure