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Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms With Prismatic Joints

[+] Author Affiliations
Kai Zhao, James P. Schmiedeler

University of Notre Dame, Notre Dame, IN

Andrew P. Murray

University of Dayton, Dayton, OH

Paper No. DETC2011-48503, pp. 523-533; 11 pages
doi:10.1115/DETC2011-48503
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5483-9
  • Copyright © 2011 by ASME

abstract

This paper presents a procedure to synthesize planar rigid-body mechanisms, containing both prismatic and revolute joints, capable of approximating a shape change defined by a set of morphing curves in different positions. With the introduction of prismatic joints, the existing mechanization process needs to be revisited via a building-block approach. The basic block is the Assur group of class II, and the auxiliary block is a fourbar mechanism, crank slider or binary link. To approximate shape changes defined by both open and closed curves, a single degree-of-freedom (DOF) mechanism is generated by assembling these building blocks. In the case of a large number of morphing curves, a weighted least squares approach is applied to determine center point locations for revolute joints and sliding paths for prismatic joints in individual building blocks. Then, the building blocks are located in an assembly position to regenerate the morphing chain using a numerical optimization method. Because of the additional constraints associated with prismatic joints compared to revolute joints, the size of the solution space is reduced, so random searches of the design space to find solution mechanisms are ineffective. A genetic algorithm is employed here instead to find a group of viable designs within reasonable computational limits. The procedure is demonstrated with synthesis examples of two 1-DOF mechanisms, one approximating five open-curve profiles and the other four closed-curve profiles.

Copyright © 2011 by ASME

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