0
Technical Brief

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

[+] Author and Article Information
James P. Schmiedeler

Fellow ASME
Department of Aerospace and Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: schmiedeler.4@nd.edu

Barrett C. Clark

Department of Mechanical and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: clark.1872@osu.edu

Edward C. Kinzel

Department of Mechanical and Aerospace Engineering,
Missouri University of Science and Technology,
Rolla, MO 65409
e-mail: kinzele@mst.edu

Gordon R. Pennock

Fellow ASME
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: pennock@ecn.purdue.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 15, 2013; final manuscript received November 29, 2013; published online January 10, 2014. Editor: Shapour Azarm.

J. Mech. Des 136(3), 034503 (Jan 10, 2014) (7 pages) Paper No: MD-13-1354; doi: 10.1115/1.4026152 History: Received August 15, 2013; Revised November 29, 2013

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. By implementing existing, well-known theory, this technical brief 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. For example, four-bar linkages are designed using these techniques with three infinitesimally separated positions and two different combinations of four multiply separated positions. The ease of implementing the techniques may make synthesis for infinitesimally and multiply separated positions more accessible to mechanism designers and undergraduate students.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 2

Second Bobillier construction

Grahic Jump Location
Fig. 3

Final four-bar design for three infinitesimally separated positions

Grahic Jump Location
Fig. 4

Construction of three finitely and one infinitesimally separated positions

Grahic Jump Location
Fig. 5

Final four-bar design for three finitely and one infinitesimally separated positions shown in position 2 of Fig. 4

Grahic Jump Location
Fig. 6

Error in final design for three finitely and one infinitesimally separated positions

Grahic Jump Location
Fig. 7

Construction of two finitely and two infinitesimally separated positions

Grahic Jump Location
Fig. 8

Final four-bar design for two finitely and two infinitesimally separated positions shown in position 1 of Fig. 7

Grahic Jump Location
Fig. 9

Error in final design for two finitely and two infinitesimally separated positions

Grahic Jump Location
Fig. 1

Inflection circle construction

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In