On the Impulsive Dynamics of M-blocks

    2014, Volume 19, Number 2, pp.  214-225

    Author(s): Ivanov A. P.

    This paper is concerned with the motion of a cubic rigid body (cube) with a rotor, caused by a sudden brake of the rotor, which imparts its angular momentum to the body. This produces an impulsive reaction of the support, leading to a jump or rolling from one face to another. Such dynamics was demonstrated by researchers from Massachusetts Institute of Technology at the IEEE/RSJ International Conference on Intelligent Robots and Systems in Tokio in November 2013. The robot, called by them M-block, is 4 cm in size and uses an internal flywheel mechanism rotating at 20 000 rev/min. Initially the cube rests on a horizontal plane. When the brake is set, the relative rotation slows down, and its energy is imparted to the case. The subsequent motion is illustrated in a clip [13]. Here the general approach to the analysis of dynamics of M-cube is proposed, including equations of impulsive motion and methods of their solution. Some particular cases are studied in details.
    Keywords: gyrostat, impulsive dynamics, friction, robotic dynamics
    Citation: Ivanov A. P., On the Impulsive Dynamics of M-blocks, Regular and Chaotic Dynamics, 2014, Volume 19, Number 2, pp. 214-225

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