Parallelism in Planar Manipulators: A Measure

[+] Author and Article Information
A. C. Rao

 QIS College of Engineering & Technology, Vengamukkapalem, Ongole, A.P. Pin: 523 272, Indiaqiscet@hotmail.com

J. Mech. Des 128(1), 66-68 (Jan 18, 2005) (3 pages) doi:10.1115/1.1992512 History: Received October 25, 2004; Revised January 18, 2005

Parallelism can be associated with every closed kinematic chain or its representative graph. Parallelism throws light on work space, rigidity, speed ratios (mechanical advantage), etc., and is of great help in selecting multi degree-of-freedom (dof) chains for robotic applications. Numerous distinct chains with the same number of links and dof exist. The extent of parallelism differs from chain to chain and hence a numerical measure is necessary to quantify the same so that the designer gains insight simply based on the structure without having to actually design all the distinct chains before selecting the best chain for the specified task. To the author’s knowledge, no measure is available in graph theory to quantify the extent of parallelism and the present work is an attempt in this direction.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 2

(a) Links 1 and 2 joined, (b) vertices 1 and 2 connected by an edge

Grahic Jump Location
Figure 3

(a) Links 1 and 2 connected by two joints, (b) vertices 1 and 2 are joined by two edges

Grahic Jump Location
Figure 4

(a) Four-bar chain, (b) graph of four-bar chain

Grahic Jump Location
Figure 1

(a) Two independent links, (b) two independent vertices

Grahic Jump Location
Figure 5

Links 1 and 2 having two paths between them

Grahic Jump Location
Figure 6

(a) Form-bar chain, (b) group of 4‐bar chain

Grahic Jump Location
Figure 7

(a) Stephenson chain, (b) Watt chain

Grahic Jump Location
Figure 8

(a, b, c) 7-link, two dof chains



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