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    Rational Motion Interpolation Under Kinematic Constraints of Spherical 6R Closed Chains

    Source: Journal of Mechanical Design:;2008:;volume( 130 ):;issue: 006::page 62301
    Author:
    Anurag Purwar
    ,
    Zhe Jin
    ,
    Q. J. Ge
    DOI: 10.1115/1.2898879
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The work reported in this paper brings together the kinematics of spherical closed chains and the recently developed free-form rational motions to study the problem of synthesizing rational interpolating motions under the kinematic constraints of spherical 6R closed chains. The results presented in this paper are an extension of our previous work on the synthesis of piecewise rational spherical motions for spherical open chains. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of spherical closed chains in the Cartesian space. Quaternions are used to represent spherical displacements. The problem of synthesizing smooth piecewise rational motions is converted into that of designing smooth piecewise rational curves in the space of quaternions. The kinematic constraints are transformed into geometric constraints for the design of quaternion curves. An iterative algorithm for constrained motion interpolation is presented. It detects the violation of the kinematic constraints by searching for those extreme points of the quaternion curve that do not satisfy the constraints. Such extreme points are modified so that the constraints are satisfied, and the resulting new points are added to the ordered set of the initial positions to be interpolated. An example is presented to show how this algorithm produces smooth spherical rational spline motions that satisfy the kinematic constraints of a spherical 6R closed chain. The algorithm can also be used for the synthesis of rational interpolating motions that approximate the kinematic constraints of spherical 5R and 4R closed chains within a user-defined tolerance.
    keyword(s): Motion , Chain AND Interpolation ,
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      Rational Motion Interpolation Under Kinematic Constraints of Spherical 6R Closed Chains

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    contributor authorAnurag Purwar
    contributor authorZhe Jin
    contributor authorQ. J. Ge
    date accessioned2017-05-09T00:29:44Z
    date available2017-05-09T00:29:44Z
    date copyrightJune, 2008
    date issued2008
    identifier issn1050-0472
    identifier otherJMDEDB-27875#062301_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/138885
    description abstractThe work reported in this paper brings together the kinematics of spherical closed chains and the recently developed free-form rational motions to study the problem of synthesizing rational interpolating motions under the kinematic constraints of spherical 6R closed chains. The results presented in this paper are an extension of our previous work on the synthesis of piecewise rational spherical motions for spherical open chains. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of spherical closed chains in the Cartesian space. Quaternions are used to represent spherical displacements. The problem of synthesizing smooth piecewise rational motions is converted into that of designing smooth piecewise rational curves in the space of quaternions. The kinematic constraints are transformed into geometric constraints for the design of quaternion curves. An iterative algorithm for constrained motion interpolation is presented. It detects the violation of the kinematic constraints by searching for those extreme points of the quaternion curve that do not satisfy the constraints. Such extreme points are modified so that the constraints are satisfied, and the resulting new points are added to the ordered set of the initial positions to be interpolated. An example is presented to show how this algorithm produces smooth spherical rational spline motions that satisfy the kinematic constraints of a spherical 6R closed chain. The algorithm can also be used for the synthesis of rational interpolating motions that approximate the kinematic constraints of spherical 5R and 4R closed chains within a user-defined tolerance.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleRational Motion Interpolation Under Kinematic Constraints of Spherical 6R Closed Chains
    typeJournal Paper
    journal volume130
    journal issue6
    journal titleJournal of Mechanical Design
    identifier doi10.1115/1.2898879
    journal fristpage62301
    identifier eissn1528-9001
    keywordsMotion
    keywordsChain AND Interpolation
    treeJournal of Mechanical Design:;2008:;volume( 130 ):;issue: 006
    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