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    A Polynomial Formulation of Inverse Kinematics of Rolling Contact

    Access Status
    Fulltext not available
    Authors
    Cui, Lei
    Dai, J.
    Date
    2015
    Type
    Journal Article
    
    Metadata
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    Citation
    Cui, L. and Dai, J. 2015. A Polynomial Formulation of Inverse Kinematics of Rolling Contact. Journal of Mechanisms and Robotics. 7 (4): pp. 041003_1-041003_9.
    Source Title
    Journal of Mechanisms and Robotics
    DOI
    10.1115/1.4029498
    ISSN
    1942-4302
    School
    Department of Mechanical Engineering
    URI
    http://hdl.handle.net/20.500.11937/38735
    Collection
    • Curtin Research Publications
    Abstract

    Rolling contact has been used by robotic devices to drive between configurations. The degrees of freedom (DOFs) of rolling contact pairs can be one, two, or three, depending on the geometry of the objects. This paper aimed to derive three kinematic inputs required for the moving object to follow a trajectory described by its velocity profile when the moving object has three rotational DOFs and thus can rotate about any axis through the contact point with respect to the fixed object. We obtained three contact equations in the form of a system of three nonlinear algebraic equations by applying the curvature theory in differential geometry and simplified the three nonlinear algebraic equations to a univariate polynomial of degree six. Differing from the existing solution that requires solving a system of nonlinear ordinary differential equations, this polynomial is suitable for fast and accurate numerical root approximations. The contact equations further revealed the two essential parts of the spin velocity: The induced spin velocity governed by the geometry and the compensatory spin velocity provided externally to realize the desired spin velocity.

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