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Structural Synthesis and Enumeration of Epicyclic Gear Mechanisms Up to 12-Links Using Acyclic Graph Method

[+] Author Affiliations
M. S. El-Gayyar, H. M. El-Eashy, M. Zaki

Mansoura University, Mansoura, Egypt

Paper No. GT2006-91136, pp. 711-717; 7 pages
  • ASME Turbo Expo 2006: Power for Land, Sea, and Air
  • Volume 5: Marine; Microturbines and Small Turbomachinery; Oil and Gas Applications; Structures and Dynamics, Parts A and B
  • Barcelona, Spain, May 8–11, 2006
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 0-7918-4240-1 | eISBN: 0-7918-3774-2
  • Copyright © 2006 by ASME


In this paper, a new approach for graphical enumeration of epicyclic gear mechanisms is presented using the concept of acyclic graph. A new graphical code has been introduced to specify the priorities of all vertices of associated displacement graph. This graphical code is used to identify open graph, redundant links and isomorphic graphs. A computer program has been developed for automatic enumeration of displacement graphs as well as automatic detection of isomorphic graphs and open graphs and graphs with a redundant link without using adjacency matrices. This simplified methodology has been applied for the enumeration of epicyclic gear mechanisms with up to 12-links having up to 9 coaxial links. An atlas for 11 and 12-link mechanisms has been constructed using the proposed methodology.

Copyright © 2006 by ASME



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