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    A Mobility Determination Method for Parallel Platforms Based on the Lie Algebra of SE(3) and Its Subspaces

    Source: Journal of Mechanisms and Robotics:;2021:;volume( 013 ):;issue: 003::page 031113-1
    Author:
    Sánchez-García, A. J.
    ,
    Rico, J. M.
    ,
    Cervantes-Sánchez, J. J.
    ,
    López-Custodio, P. C.
    DOI: 10.1115/1.4050096
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: This contribution presents a screw theory-based method for determining the mobility of fully parallel platforms. The method is based on the application of three stages. The first stage involves the application of the intersection of subalgebras of Lie algebra, se(3), of the special Euclidean group, SE(3), associated with the legs of the platform. The second stage analyzes the possibility of the legs of the platform generating a sum or direct sum of two subalgebras of the Lie algebra, se(3). The last stage, if necessary, considers the possibility of the kinematic pairs of the legs satisfying certain velocity conditions; these conditions reduce the platform’s mobility analysis to one that can be solved using one of the two previous stages. Several examples are illustrated.
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      A Mobility Determination Method for Parallel Platforms Based on the Lie Algebra of SE(3) and Its Subspaces

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4276092
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    • Journal of Mechanisms and Robotics

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    contributor authorSánchez-García, A. J.
    contributor authorRico, J. M.
    contributor authorCervantes-Sánchez, J. J.
    contributor authorLópez-Custodio, P. C.
    date accessioned2022-02-05T21:39:56Z
    date available2022-02-05T21:39:56Z
    date copyright3/15/2021 12:00:00 AM
    date issued2021
    identifier issn1942-4302
    identifier otherjmr_13_3_031113.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4276092
    description abstractThis contribution presents a screw theory-based method for determining the mobility of fully parallel platforms. The method is based on the application of three stages. The first stage involves the application of the intersection of subalgebras of Lie algebra, se(3), of the special Euclidean group, SE(3), associated with the legs of the platform. The second stage analyzes the possibility of the legs of the platform generating a sum or direct sum of two subalgebras of the Lie algebra, se(3). The last stage, if necessary, considers the possibility of the kinematic pairs of the legs satisfying certain velocity conditions; these conditions reduce the platform’s mobility analysis to one that can be solved using one of the two previous stages. Several examples are illustrated.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleA Mobility Determination Method for Parallel Platforms Based on the Lie Algebra of SE(3) and Its Subspaces
    typeJournal Paper
    journal volume13
    journal issue3
    journal titleJournal of Mechanisms and Robotics
    identifier doi10.1115/1.4050096
    journal fristpage031113-1
    journal lastpage031113-11
    page11
    treeJournal of Mechanisms and Robotics:;2021:;volume( 013 ):;issue: 003
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
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