Graph theory is a powerful tool in structural synthesis and analysis of planetary gear trains (PGTs). In this paper, a new algorithm has been developed for detecting degenerate structure in planetary gear trains. The proposed algorithm is based on the concept of fundamental circuits' rotation graphs. Detection of degeneracy is entirely based on finding one key element. The key element or link that makes planetary gear train into two groups is found in this work. The main advantage of the proposed method lies in the drastic reduction in the required combinatorial analysis compared to other methods available.

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