A Method for Adjustable Planar and Spherical Four-Bar Linkage Synthesis

[+] Author and Article Information
Boyang Hong

Staff Mechanical Engineer,  Lockheed Martin Maritime Systems and Sensors, P. O. Box 64525, MS U2S26, St. Paul, MN 55164-0525boyang.hong@lmco.com

Arthur G. Erdman

Richard C. Jordan Professor, Morse Alumni Distinguished Teaching Professor,  Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455agerdman@me.umn.edu

J. Mech. Des 127(3), 456-463 (Jul 15, 2004) (8 pages) doi:10.1115/1.1867501 History: Received January 27, 2004; Revised July 15, 2004

This paper describes a new method to synthesize adjustable four-bar linkages, both in planar and spherical form. This method uses fixed ground pivots and an adjustable length for input and output links. A new application of Burmester curves for adjustable linkages is introduced, and a numerical example is discussed. This paper also compares a conventional synthesis method (nonadjustable linkage) to the new method. Nonadjustable four-bar linkages provide limited solutions for five-position synthesis. Adjustable linkages generate one infinity of solution choices. This paper also shows that the nonadjustable solutions are special cases of adjustable solutions. This new method can be extended to six position synthesis, with adjustable ground pivots locations.

Copyright © 2005 by American Society of Mechanical Engineers
Topics: Linkages
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Figure 7

(a) A practical way to produce an adjustable spherical link. (b) Three-plus-two position synthesis. The length of the input and output link Changes: position 4 and 5 are different from 1, 2, 3. The shape of the coupler link remains unchanged.

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Figure 5

A solution for three-plus-two position synthesis for the adjustable planar four-bar. The cross-hatched couplers represent the first three synthesis positions. Positions P4 and P5 are possible after the link length change from L to CL.

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Figure 1

An adjustable planar linkage, from Chuenchom (10)

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Figure 8

Three-plus-three position synthesis. Snapshot of position 1 and 4. The locations of ground pivots change, the shapes of all links remain unchanged.

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Figure 6

The distribution of link length adjustment ratio “C.” For each X1, there can be two corresponding Y1’s. The first pair of X1–Y1 generates “Ca” in Table 1, which is represented by the solid line. The second pair generates “Cb,” which is represented by the dashed line. There are two points with C=1. These are solutions for five-position problem, with no need for link length adjustment.

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Figure 4

Plot of the results from Table 1. One pair of X1–Y1 is plotted as a solid line. The other pair is plotted as a dashed line. Notice that for each point, there is a unique “C.” C=1 indicates that no adjustment is needed.

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Figure 3

A five-position synthesis example from Sandon and Erdman (14).

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Figure 2

A five-position synthesis of adjustable planar dyad. Only positions #1, #2, and #4 are shown.



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