The Curve of Striction of the Bennett Loop’s Fixed Axode

[+] Author and Article Information
J. Eddie Baker

Honorary Research Associate, School of Information Technologies, The University of Sydney, New South Wales 2006, Australiajebaker@it.usyd.edu.au

J. Mech. Des 127(4), 607-611 (Sep 08, 2004) (5 pages) doi:10.1115/1.1897746 History: Received May 22, 2004; Revised September 08, 2004

In previous work, the algebraic representation of a fixed axode of the Bennett linkage has been revealed as extraordinarily cumbersome. In this sequel we use properties of the ruled surface to determine the central point of a typical generator of the axode and hence its curve of striction as the intersection of two comparatively simple surfaces. Because of its special significance in this case, we also obtain the equation to the central tangent surface. A feature of the investigation is the direct employment of screw vectors in dual format rather than unit line vectors.

Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

The Bennett linkage in schematic outline with frame defined.

Grahic Jump Location
Figure 2

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

Grahic Jump Location
Figure 3

The central tangent to the fixed axode’s generator as the common normal between it and an infinitesimally close neighbouring generator, also defining the central point Ψ(X,Y,Z) and the central normal.




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