Function Generation With Finitely Separated Precision Points Using Geometric Constraint Programming

[+] Author and Article Information
Edward C. Kinzel, Gordon R. Pennock

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

James P. Schmiedeler

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210

J. Mech. Des 129(11), 1185-1190 (Nov 22, 2006) (6 pages) doi:10.1115/1.2771575 History: Received February 16, 2006; Revised November 22, 2006

This paper extends geometric constraint programming (GCP) to function generation problems involving large numbers of finitely separated precision points and complex mechanisms. In parametric design software, GCP uses the sketching mode to graphically impose geometric constraints in kinematic diagrams and the numerical solvers to solve the relevant nonlinear equations without the user explicitly formulating them. For function generation, the same approach can be applied to any mechanism, requiring no unique algorithms. Implementation is straightforward, so the designer can quickly generate solutions for a large number of precision points and/or with complex mechanisms to accurately match the function. Examples of function generation with a four-bar linkage, a Stephenson III six-bar linkage, and a seven-bar linkage with a mobility of two are presented.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Four-bar linkage for function generation

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Figure 2

Synthesized four-bar linkage for three precision points

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Figure 3

Error of four-bar function generation

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Figure 4

Synthesized Stephenson III six-bar linkage for 11 precision points

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Figure 5

Error of six-bar function generation

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Figure 6

Synthesized seven-bar linkage for array of nine precision points

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Figure 7

Error distribution showing nine precision points for the seven-bar linkage




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