Stability analysis of a waveboard multibody model with toroidal wheels

This paper analyses the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. In this paper, the system is described using a multibody model with nonholonomic constraints. To study the stability of the forward upright motion with constant speed, the equations of motion are linearized with respect to a reference motion. The employed numerical linearization procedure is valid for general multibody systems with holonomic and nonholonomic constraints. In practice, the employed approach makes use of the Jacobian matrix, which is expressed in terms of any of the main design parameters of the waveboard. This paper introduces a sensitivity analysis of the eigenvalues with respect to the forward speed, the casters' inclination angle, the torsional stiffness of the torsion bar, the aspect ratio of the toroidal wheels and the mass of the human rider. Lastly, a summary with the influence of these design parameters on the external actuations exerted by the rider in the waveboard maneuvering is shown.