Kinematic Investigation of the Deployable Bennett Loop

[+] Author and Article Information
J. Eddie Baker

School of Information Technologies, The University of Sydney, NSW 2006, Australiajebaker@it.usyd.edu.au

J. Mech. Des 129(6), 602-610 (Jun 14, 2006) (9 pages) doi:10.1115/1.2717229 History: Received March 01, 2006; Revised June 14, 2006

Despite the many studies devoted to it and its value as a learning tool, the Bennett linkage has never been employed as a working mechanism. It has recently found favor, however, among structural analysts as a possible unit in deployable networks owing to the potential for true spatial displacement without flexure. Although the loop can be analyzed in this application by means of purely geometrical methods, a wealth of kinematic examinations is available for more efficient treatment. The particular form that the chain must adopt as a deployable object and the special case of the linkage demanded by the purpose constitute the subject of the present exposition, which takes full advantage of prior analyses of the chain’s kinematic characteristics.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

The Bennett linkage in outline with reference frame defined

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Figure 2

The linkage’s line of symmetry in relation to opposing joint axes

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Figure 3

The two reguli of the Bennett chain’s J-hyperboloid, one of them containing the loop’s joint axes; also in evidence a typical “eccentric angle” ψ

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Figure 4

Positioning of the Bennett loop on its L-hyperboloid and identification of the link lines with both sets of generators, the inset detailing the conventional definition of joint angles

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Figure 5

The frames of reference of the loop’s J-hyperboloid and L-hyperboloid in relation to each other

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Figure 6

The frames of reference of the chain’s J-hyperboloid and double helix in relation to each other

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Figure 7

An alternative set of links for the Bennett isogram

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Figure 8

Dispositions of hinge lines of the equilateral loop with respect to its line of symmetry




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