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Kinematic Synthesis for Infinitesimally and Multiply Separated Positions Using Geometric Constraint Programming

[+] Author Affiliations
James P. Schmiedeler

University of Notre Dame, Notre Dame, IN

Barrett C. Clark

The Ohio State University, Columbus, OH

Edward C. Kinzel

University of Central Florida, Orlando, FL

Gordon R. Pennock

Purdue University, West Lafayette, IN

Paper No. DETC2011-48201, pp. 435-443; 9 pages
  • 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


Geometric Constraint Programming (GCP) is an approach to synthesizing planar mechanisms in the sketching mode of commercial parametric computer-aided design software by imposing geometric constraints using the software’s existing graphical user interface. GCP complements the accuracy of analytical methods with the intuition developed from graphical methods. Its applicability to motion generation, function generation, and path generation for finitely separated positions has been previously reported. This paper demonstrates how GCP can be applied to kinematic synthesis for motion generation involving infinitesimally and multiply separated positions. For these cases, the graphically imposed geometric constraints alone will in general not provide a solution, so the designer must parametrically relate dimensions of entities within the graphical construction to achieve designs that automatically update when a defining parameter is altered. For three infinitesimally separated positions, the designer constructs an acceleration polygon to locate the inflection circle defined by the desired motion state. With the inflection circle in place, the designer can rapidly explore the design space using the graphical second Bobillier construction. For multiply separated position problems in which only two infinitesimally separated positions are considered, the designer constrains the instant center of the mechanism to be in the desired location. Example four-bar linkages are designed using these techniques with three infinitesimally separated positions and two different combinations of four multiply separated positions.

Copyright © 2011 by ASME



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