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Applying Rigidity Theory Methods for Topological Decomposition and Synthesis of Gear Train Systems

[+] Author Affiliations
Maria Terushkin, Offer Shai

Tel Aviv University, Tel Aviv, Israel

Paper No. DETC2012-70904, pp. 605-614; 10 pages
doi:10.1115/DETC2012-70904
From:
  • ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B
  • Chicago, Illinois, USA, August 12–15, 2012
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4503-5
  • Copyright © 2012 by ASME

abstract

This paper introduces a novel way to augment the knowledge and methods of rigidity theory to the topological decomposition and synthesis of gear train systems. A graph of gear trains, widely reported in the literature of machine theory, is treated as a graph representation from rigidity theory—the Body-Bar graph. Once we have this Body-Bar graph, methods and theorems from rigidity theory can be employed for analysis and synthesis. In this paper we employ the pebble-game algorithm, a computational method which allows determination of the topological mobility of mechanisms and the decomposition of gear trains into basic building blocks—Body-Bar Assur Graphs. Once we gain the ability to decompose any gear train into standalone components (Body-Bar Assur Graphs), this paper suggests inverting the process and applying the same method for synthesis. Relying on rigidity theory operations (Body-Bar extension, in this case), it is possible to construct all of the Body-Bar Assur Graphs, meaning the building blocks of gear trains. Once we have these building blocks at hand, it is possible to recombine them in various ways, providing us with a topological synthesis method for constructing gear trains. This paper also introduces a transformation between the Body-Bar graph and other graph representations used in mechanisms, thus leaving room for the application of the proposed synthesis and decomposition method directly to known graph representations already used in machine theory.

Copyright © 2012 by ASME

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