An Application of Modified Path Matrix Approach for Detection of Isomorphism Among Epicyclic Gear Trains

Abstract

The identification of isomorphism in epicyclic gear trains has been found a lot of attention by researchers for the last few years. Various methods have been suggested by different authors for the detection of isomorphism in planer kinematic chains and epicyclic gear trains (EGTs), but everyone has found some difficulties to address new issues. In this paper, a modified path matrix approach was presented in order to compare all the distinct geared kinematic mechanisms. A new method based on the matrix approach and corresponding train values is required to identify isomorphism among epicyclic gear trains and their mechanisms. The proposed method was examined on the basis of various examples from four-link, five-link, six-link, and eight-link one-degree-of-freedom EGTs and six-link two-degree-of-freedom EGTs. All the examples have been found satisfactory results with existing literature.

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Correspondence to Jiyaul Mustafa.

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Mustafa, J., Hasan, A. & Khan, R.A. An Application of Modified Path Matrix Approach for Detection of Isomorphism Among Epicyclic Gear Trains. J. Inst. Eng. India Ser. C 101, 463–472 (2020). https://doi.org/10.1007/s40032-020-00556-9

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Keywords

  • Epicyclic gear trains
  • Modified path matrix
  • Isomorphism
  • Pair value
  • Train value