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.

本文分析了波板的稳定性，该波板由两个铰接的平台组成，并由扭杆连接并由两个脚轮支撑。挡波板提供了一种有趣的推进机制，因为骑车人可以通过平台的摆动横向运动实现向前运动。在本文中，使用具有非完整约束的多体模型描述了该系统。

为了研究匀速向前直立运动的稳定性，相对于参考运动将运动方程线性化。所采用的数值线性化程序对于具有完整和非完整约束的通用多体系统有效。在实践中，所采用的方法利用了雅可比矩阵，该雅可比矩阵以波板的任何主要设计参数表示。本文介绍了特征值对前进速度，脚轮倾角，扭杆的扭转刚度，环形轮的长宽比和乘员质量的敏感性分析。最后，总结了这些设计参数对骑手在波板操纵中施加的外部驱动力的影响。