Abstract This paper studies the forward motion of the Waveboard, a variant of the Skateboard that consists of two platforms and two caster wheels. This system exhibits a very interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms, without touching the ground. Because of the complex nature of the Waveboard dynamics, a three-dimensional multibody model is proposed, modeling the wheels as two rings first and as tori later on. Some holonomic constraints arise at the contact of the wheels with the ground, while some non-holonomic constraints appear from the assumption of rolling without slipping. The equations of motion of the system are derived and a kinematic and inverse dynamics simulation of a realistic meandering trajectory is carried out, in order to understand the necessary forces and torques to obtain the desired motion. Moreover, an analysis of the influence of the design parameters on the external actions exerted by the rider is made. Finally, the multibody model is enhanced by modeling the wheels as two tori, performing a comparison between the ring and toroidal models.

中文翻译：

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波板三维多体模型前向运动的逆动力学研究

摘要 本文研究了 Waveboard 的向前运动，它是滑板的一种变体，由两个平台和两个脚轮组成。该系统展示了一种非常有趣的推进机制，因为骑手可以通过平台的摆动横向运动实现向前运动，而无需接触地面。由于波板动力学的复杂性，提出了一个三维多体模型，先将车轮建模为两个环，然后再建模为圆环。一些完整的约束出现在车轮与地面的接触处，而一些非完整的约束出现在滚动不打滑的假设中。推导出系统的运动方程，并对真实的曲折轨迹进行运动学和逆动力学模拟，以了解获得所需运动所需的力和扭矩。此外，还分析了设计参数对骑手施加的外部动作的影响。最后，通过将车轮建模为两个圆环来增强多体模型，在环形模型和环形模型之间进行比较。