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Simultaneous Topological and Dimensional Synthesis of Planar Morphing Mechanisms

[+] Author Affiliations
Lawrence Funke, James P. Schmiedeler

University of Notre Dame, Notre Dame, IN

Paper No. DETC2016-59618, pp. V05BT07A037; 12 pages
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5B: 40th Mechanisms and Robotics Conference
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5016-9
  • Copyright © 2016 by ASME


This paper presents a general method to perform simultaneous topological and dimensional synthesis for planar rigid-body morphing mechanisms. The synthesis is framed as a multi-objective optimization problem for which the first objective is to minimize the error in matching the desired shapes. The second objective is typically to minimize the actuating force/moment required to move the mechanism, but different applications may require a different choice. The paper shows how all possible topologies can be enumerated for morphing mechanism designs with a specified number of degrees of freedom and how infeasible topologies can be removed from the search space. A multi-objective genetic algorithm is then used to perform the optimization since it can handle both the discrete nature of the topological optimization and the continuous nature of the dimensional optimization. In this way, candidate solutions from any of the feasible topologies enumerated can be evaluated and compared simultaneously. The method also allows for the straightforward incorporation of specific design constraints, such as size limitations and joint location bounds. Ultimately, it yields a sizable population of viable solutions, often of different topologies, so that the designer can manage engineering tradeoffs (beyond those associated with the two objectives) in selecting the best mechanism for the specified application. Two examples are presented to illustrate the strengths of this method. The first examines the advantages gained by considering and optimizing across all topologies simultaneously instead of individual topologies one at a time. The second demonstrates the versatility of the method by incorporating prismatic joints into the morphing chain to allow for morphing between shapes that have significant changes in both shape and arc length.

Copyright © 2016 by ASME



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