In this paper, one-dimensional self-alignment of a rigid object via stick-slip vibrations is studied. The object is situated on a table, which has a prescribed periodic motion. Friction is exploited as the mechanism to move the object in a desired direction and to stop and self-align the mass at a desired end position with the smallest possible positioning error. In the modeling and analysis of the system, theory of discontinuous dynamical systems is used. Analytic solutions can be derived for a model based on Coulomb friction and an intuitively chosen table acceleration profile, which allows for a classification of different possible types of motion. Local stability and convergence is proven for the solutions of the system, if a constant Coulomb friction coefficient is used. Next, near the desired end position, the Coulomb friction coefficient is increased (e.g. by changing the roughness of the table surface) in order to stop the object. In the transition region from low frictionto high friction coe cient, it is shown that, under certain conditions, accumulation of the object to a unique end position occurs. This behavior can be studied analytically and a mapping is given for subsequent stick positions.


    Access

    Download


    Export, share and cite



    Title :

    Vibrational self-alignment of a rigid object exploiting friction


    Contributors:

    Publication date :

    2011-01-01


    Remarks:

    Hunnekens , B G B , Fey , R H B , Shukla , A & Nijmeijer , H 2011 , ' Vibrational self-alignment of a rigid object exploiting friction ' , Nonlinear Dynamics , vol. 65 , no. 1-2 , pp. 109-129 . https://doi.org/10.1007/s11071-010-9878-0



    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English


    Classification :

    DDC:    629



    Weight/shape structural optimization exploiting rigid movement

    Morris, A.J. / Ponzi, S. | Tema Archive | 1993


    Exploiting Friction Anisotropy for Soft Robot Locomotion

    Asawalertsak, Naris / Gorb, Stanislav N. / Kovalev, Alexander et al. | Springer Verlag | 2022


    Exploiting Friction Anisotropy for Soft Robot Locomotion

    Asawalertsak, Naris / Gorb, Stanislav N. / Kovalev, Alexander et al. | TIBKAT | 2023


    Global Non-rigid Alignment of Surface Sequences

    Budd, C. / Huang, P. / Klaudiny, M. et al. | British Library Online Contents | 2013


    Inverse dynamics with rigid contact and friction

    Zapolsky, S. | British Library Online Contents | 2017