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Mixed Exact and Approximate Position Design of Planar Linkages via Geometric Constraint Programming (GCP) Techniques

[+] Author Affiliations
John A. Mirth

Rose-Hulman Institute of Technology, Terre Haute, IN

Paper No. DETC2015-46116, pp. V05BT08A063; 6 pages
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5B: 39th Mechanisms and Robotics Conference
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5713-7
  • Copyright © 2015 by ASME


The synthesis of mechanisms to reach multiple positions can often be satisfied by the specification of a combination of exact and approximate positions. Geometric Constraint Programming (GCP) uses industry standard parametric modeling software to obtain solutions to planar synthesis problems. This paper demonstrates the capability of GCP to solve problems that contain a combination of exact and approximate positions. The approximate positions are added to existing GCP design approaches by the application of geometric constraints to locate moving points on a mechanism within specified circular target zones. The target zones are used to guide the coupler point of a linkage along an approximate path between critical precision positions. The approach applies to the synthesis of both four-bar and complex linkages. In complex linkages, the target zones can be applied to multiple points on the linkage to better coordinate the motion of one or more floating links with the overall mechanism motion. The methods presented in the paper focus on the use of 2 exact positions plus 2–3 approximate positions. Examples are provided for the solution of rigid-body guidance problems for both four-bar and six-bar linkages. As with many GCP solutions, the graphical solutions presented are well within the capabilities and understanding of both undergraduate students and the practicing engineer.

Copyright © 2015 by ASME



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