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The Application of Geometric Constraint Programming to the Design of Stephenson III Dwell Linkages

[+] Author Affiliations
John A. Mirth

Rose-Hulman Institute of Technology, Terre Haute, IN

Paper No. DETC2016-59083, pp. V05BT07A082; 6 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


Stephenson III linkages provide a means to create an approximate dwell mechanism without the use of cams. The dwell cycle is created by first choosing or designing a four-bar linkage that contains a coupler path with a near circular segment. An external dyad is attached to the coupler point such that the center of the floating link of the dyad coincides with the center of the circular portion of the coupler curve. This connection produces a dwell in the external dyad as the four-bar linkage traverses the circular portion of the coupler curve. This paper demonstrates how the necessary conditions for a dwell linkage can be obtained with the use of Geometric Constraint Programming (GCP). The construction process is initiated by using GCP techniques to develop a four-bar linkage with a minimum of four path points that lie on a prescribed arc. This part of the problem also uses GCP to apply additional constraints to the four-bar linkage. These include the application of appropriate link dimensions to achieve a Grashof linkage with a crank input, and the specification of the required crank rotation angle during the dwell cycle of the mechanism. Once the four-bar is defined, an external dyad is attached to the coupler link of the four-bar to produce the specified dwell characteristics. The dwell dyad may include for its output either a rotational link whose range of angular travel is defined, or a sliding link whose range of linear motion is defined. GCP techniques are used to enforce a specified range of motion for the output dyad through the use of an instant center construction to define the limits of travel of the four-bar coupler curve relative to the dwell ground pivot. If the dwell dyad is designed for angular displacements, the construction is completed by using GCP to define the desired angular displacement of the dwell link, resulting in the specification of the link length and ground pivot location. If the dwell dyad is a linear (slider) output, the final part of the GCP construction is used to define the desired length of linear travel, which results in the complete specification of the slider path and angle. The GCP techniques are presented with the development of an example, with sample results presented for a dwell mechanism with a rotational dwell cycle, and also for a dwell mechanism with a linear (slider) dwell output. The example demonstrates the ability of GCP methods to use standard solid-modeling software to obtain Stephenson III linkages with dwells that deviate from the dwell position by less than 0.1% of total motion.

Copyright © 2016 by ASME



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