A graph-based approach for detection degenerate structures in multi-planet gear trains

Abstract

A locked chain is an immovable sub-chain within a kinematic chain. The detection of immovable sub-chains is a critical step in the structural synthesis of planetary gear trains (PGTs). This paper presents a simplified method for the identification of locked chains in PGTs based on the vertex-edge mobility criterion. The vertex-edge mobility criterion is formulated, and the detection method is proposed. A connectivity matrix is developed for the analytical determination of locked chains in multi-planet gear trains. The algorithm is suitable for planetary gear trains with any degree of freedom (DOF). For the automatic identification of locked chains, a MATLAB program is developed. The only input to the program is the adjacency matrix. The result of this work is beneficial for the automation of the structural synthesis of planetary gear trains.