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Topological Synthesis of All 2D Mechanisms Through Assur Graphs

[+] Author Affiliations
Offer Shai

Tel Aviv University, Tel Aviv, Israel

Paper No. DETC2010-28926, pp. 1727-1738; 12 pages
doi:10.1115/DETC2010-28926
From:
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4410-6 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME

abstract

It is well known that every planar kinematical linkage can be decomposed into basic topological structures referred as Assur Groups. A new reformulation of Assur Group concept into the terminology of rigidity theory, as Assur Graphs, has yielded the development of new theorems and methods. The paper reports on an algorithm for systematic construction of Assur Graph classes, termed fundamental Assur Graphs. From each fundamental Assur Graph it is possible to derive an infinite set of different Assur Graphs. This mapping algorithm is proved to be complete and sound, i.e., all the Assur Graphs appear in the map and each graph in the map is an Assur Graph. Once we possess the mapping of all the Assur Graphs, all valid kinematical linkage topologies can be constructed through various Assur Graph compositions.

Copyright © 2010 by ASME

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