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.
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March 2014
Technical Briefs
Kinematic Synthesis for Infinitesimally and Multiply Separated Positions Using Geometric Constraint Programming
James P. Schmiedeler,
James P. Schmiedeler
Fellow ASME
Department of Aerospace and Mechanical Engineering,
e-mail: schmiedeler.4@nd.edu
Department of Aerospace and Mechanical Engineering,
University of Notre Dame
,Notre Dame, IN 46556
e-mail: schmiedeler.4@nd.edu
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Barrett C. Clark,
Barrett C. Clark
Department of Mechanical and Aerospace Engineering,
e-mail: clark.1872@osu.edu
The Ohio State University
,Columbus, OH 43210
e-mail: clark.1872@osu.edu
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Edward C. Kinzel,
Edward C. Kinzel
Department of Mechanical and Aerospace Engineering,
e-mail: kinzele@mst.edu
Missouri University of Science and Technology
,Rolla, MO 65409
e-mail: kinzele@mst.edu
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Gordon R. Pennock
Gordon R. Pennock
Fellow ASME
School of Mechanical Engineering,
e-mail: pennock@ecn.purdue.edu
School of Mechanical Engineering,
Purdue University
,West Lafayette, IN 47907
e-mail: pennock@ecn.purdue.edu
Search for other works by this author on:
James P. Schmiedeler
Fellow ASME
Department of Aerospace and Mechanical Engineering,
e-mail: schmiedeler.4@nd.edu
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,
e-mail: clark.1872@osu.edu
The Ohio State University
,Columbus, OH 43210
e-mail: clark.1872@osu.edu
Edward C. Kinzel
Department of Mechanical and Aerospace Engineering,
e-mail: kinzele@mst.edu
Missouri University of Science and Technology
,Rolla, MO 65409
e-mail: kinzele@mst.edu
Gordon R. Pennock
Fellow ASME
School of Mechanical Engineering,
e-mail: pennock@ecn.purdue.edu
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. Mar 2014, 136(3): 034503 (7 pages)
Published Online: January 10, 2014
Article history
Received:
August 15, 2013
Revision Received:
November 29, 2013
Citation
Schmiedeler, J. P., Clark, B. C., Kinzel, E. C., and Pennock, G. R. (January 10, 2014). "Kinematic Synthesis for Infinitesimally and Multiply Separated Positions Using Geometric Constraint Programming." ASME. J. Mech. Des. March 2014; 136(3): 034503. https://doi.org/10.1115/1.4026152
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