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    Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages

    Source: Journal of Mechanical Design:;1992:;volume( 114 ):;issue: 001::page 153
    Author:
    C. W. Wampler
    ,
    A. J. Sommese
    ,
    A. P. Morgan
    DOI: 10.1115/1.2916909
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The problem of finding all four-bar linkages whose coupler curve passes through nine prescribed points has been a longstanding unsolved problem in kinematics. Using a combination of classical elimination, multihomogeneous variables, and numerical polynomial continuation, we show that there are generically 1442 nondegenerate solution along with their Roberts cognates, for a total of 4326 distinct solutions. Moreover, a computer algorithm that computes all solutions for any given nine points has been developed.
    keyword(s): Kinematics , Algorithms , Computers AND Polynomials ,
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      Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages

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    http://yetl.yabesh.ir/yetl1/handle/yetl/110666
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    contributor authorC. W. Wampler
    contributor authorA. J. Sommese
    contributor authorA. P. Morgan
    date accessioned2017-05-08T23:39:12Z
    date available2017-05-08T23:39:12Z
    date copyrightMarch, 1992
    date issued1992
    identifier issn1050-0472
    identifier otherJMDEDB-27594#153_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/110666
    description abstractThe problem of finding all four-bar linkages whose coupler curve passes through nine prescribed points has been a longstanding unsolved problem in kinematics. Using a combination of classical elimination, multihomogeneous variables, and numerical polynomial continuation, we show that there are generically 1442 nondegenerate solution along with their Roberts cognates, for a total of 4326 distinct solutions. Moreover, a computer algorithm that computes all solutions for any given nine points has been developed.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleComplete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages
    typeJournal Paper
    journal volume114
    journal issue1
    journal titleJournal of Mechanical Design
    identifier doi10.1115/1.2916909
    journal fristpage153
    journal lastpage159
    identifier eissn1528-9001
    keywordsKinematics
    keywordsAlgorithms
    keywordsComputers AND Polynomials
    treeJournal of Mechanical Design:;1992:;volume( 114 ):;issue: 001
    contenttypeFulltext
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