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The question of minimax loop-size in planar homogeneous kinematic chains

Dibakar, Sen and TS, Mruthyunjaya (1996) The question of minimax loop-size in planar homogeneous kinematic chains. In: Mechanism and Machine Theory, 31 (6). 821-829 .

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A homogeneous planar kinematic chain (KC) is a KC having all its constituting smallest independent circuits (fundamental circuits) of the same size. Davies [J. Mech.3, 87–100 (1968)] established, using graph theory, that a planar KC (homogeneous) of mobility M cannot have all fundamental circuits of size greater than M + 4. In the present paper many counterexamples to Davies's statement are presented and it is indicated that the maximum size of the circuits depends not only on the mobility of the mechanism but also on the number of links. The counterexamples given consist of, primarily, single degree of freedom (DOF) planar homogeneous KCs of loop sizes 6, 7 and 8; some zero DOF and tw DOF chains are also included. The causes for the failure of Davie's theorem have been analysed in detail to show that it is valid only in the domain of planar KCs with planar graphs.

Item Type: Journal Article
Publication: Mechanism and Machine Theory
Publisher: Elsevier
Additional Information: Copyright of this article belongs to Elsevier.
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 23 Apr 2007
Last Modified: 19 Sep 2010 04:37
URI: http://eprints.iisc.ac.in/id/eprint/10719

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