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    Extension of Graph Theory to the Duality Between Static Systems and Mechanisms

    Source: Journal of Mechanical Design:;2006:;volume( 128 ):;issue: 001::page 179
    Author:
    Offer Shai
    ,
    Gordon R. Pennock
    DOI: 10.1115/1.2120827
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: This paper is a study of the duality between the statics of a variety of structures and the kinematics of mechanisms. To provide insight into this duality, two new graph representations are introduced; namely, the flow line graph representation and the potential line graph representation. The paper also discusses the duality that exists between these two representations. Then the duality between a static pillar system and a planar linkage is investigated by using the flow line graph representation for the pillar system and the potential line graph representation for the linkage. A compound planetary gear train is shown to be dual to the special case of a statically determinate beam and the duality between a serial robot and a platform-type robot, such as the Stewart platform, is explained. To show that the approach presented here can also be applied to more general robotic manipulators, the paper includes a two-platform robot and the dual spatial linkage. The dual transformation is then used to check the stability of a static system and the stationary, or locked, positions of a linkage. The paper shows that two novel platform systems, comprised of concentric spherical platforms inter-connected by rigid rods, are dual to a spherical six-bar linkage. The dual transformation, as presented in this paper, does not require the formulation and solution of the governing equations of the system under investigation. This is an original contribution to the literature and provides an alternative technique to the synthesis of structures and mechanisms. To simplify the design process, the synthesis problem can be transformed from the given system to the dual system in a straightforward manner.
    keyword(s): Robots , Columns (Structural) , Linkages , Mechanisms , Flow (Dynamics) , Force , Kinematics , Trains , Planetary gears AND Statics ,
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      Extension of Graph Theory to the Duality Between Static Systems and Mechanisms

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    contributor authorOffer Shai
    contributor authorGordon R. Pennock
    date accessioned2017-05-09T00:21:10Z
    date available2017-05-09T00:21:10Z
    date copyrightJanuary, 2006
    date issued2006
    identifier issn1050-0472
    identifier otherJMDEDB-27819#179_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/134387
    description abstractThis paper is a study of the duality between the statics of a variety of structures and the kinematics of mechanisms. To provide insight into this duality, two new graph representations are introduced; namely, the flow line graph representation and the potential line graph representation. The paper also discusses the duality that exists between these two representations. Then the duality between a static pillar system and a planar linkage is investigated by using the flow line graph representation for the pillar system and the potential line graph representation for the linkage. A compound planetary gear train is shown to be dual to the special case of a statically determinate beam and the duality between a serial robot and a platform-type robot, such as the Stewart platform, is explained. To show that the approach presented here can also be applied to more general robotic manipulators, the paper includes a two-platform robot and the dual spatial linkage. The dual transformation is then used to check the stability of a static system and the stationary, or locked, positions of a linkage. The paper shows that two novel platform systems, comprised of concentric spherical platforms inter-connected by rigid rods, are dual to a spherical six-bar linkage. The dual transformation, as presented in this paper, does not require the formulation and solution of the governing equations of the system under investigation. This is an original contribution to the literature and provides an alternative technique to the synthesis of structures and mechanisms. To simplify the design process, the synthesis problem can be transformed from the given system to the dual system in a straightforward manner.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleExtension of Graph Theory to the Duality Between Static Systems and Mechanisms
    typeJournal Paper
    journal volume128
    journal issue1
    journal titleJournal of Mechanical Design
    identifier doi10.1115/1.2120827
    journal fristpage179
    journal lastpage191
    identifier eissn1528-9001
    keywordsRobots
    keywordsColumns (Structural)
    keywordsLinkages
    keywordsMechanisms
    keywordsFlow (Dynamics)
    keywordsForce
    keywordsKinematics
    keywordsTrains
    keywordsPlanetary gears AND Statics
    treeJournal of Mechanical Design:;2006:;volume( 128 ):;issue: 001
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
    yabeshDSpacePersian