An Update on M- and K-Circle Theory for Planar Dyads and Triads

[+] Author and Article Information
John R. Mlinar

 3M Company, 900 Bush Avenue, St. Paul, MN 55144 jrmlinar@mmm.com

Arthur G. Erdman

Department of Mechanical Engineering University of Minnesota, Minneapolis, MN 55112

J. Mech. Des 127(3), 464-468 (Jul 05, 2004) (5 pages) doi:10.1115/1.1864113 History: Received August 01, 2003; Revised July 05, 2004

M and K circles are solution loci for three design positions of a dyad when one design angle is varied. This paper updates M- and K-circle theory through a geometric explanation of why regions without solutions, known as forbidden regions, exist for the case of path generation with prescribed timing and not for the case of motion generation. The extension of M-K circle theory to the linear solution of triads is also presented. This work presents the finding of circular solution curves for the linear solution of triads along with the conditions for forbidden regions.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 5

Triad with grounded first vector

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Figure 4

Sketch of the locus of K circle centers for path generation with prescribed timing

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Figure 3

K circle and both forbidden regions

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Figure 1

M and K circles for path generation with prescribed timing along with the first forbidden region

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Figure 8

Forbidden regions for triads

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Figure 7

Circular solution loci for triads (M, V, and K circles)

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Figure 6

Triad in two design positions



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