Dynamic Analysis of a Motion Transformer Mimicking a Hula Hoop

Hula-hoop motion refers to the spinning of a ring around a human body; it is made possible by the interactive force between the moving ring and the body. Inspired by the generic concept of hula-hoop motion, this study proposes a novel motion transformer design that consists of a main mass sprung in one translational direction and a free-moving mass attached at one end of a rod, the other end of which is hinged onto the center of the main mass. It is expected that the transformer is capable of transforming linear reciprocating motion into rotational motion. In addition, the transformer could be integrated with coils, magnets, and electric circuits to form a portable energy scavenging device. A thorough dynamic analysis of the proposed transformer system is conducted in this study in order to characterize the relationships between the varied system parameters and the chance of hula-hoop motion occurrence. The governing equations are first derived with Lagrange’s method, which is followed by the search for steady-state solutions and the corresponding stability analysis via the homotopy perturbation method and the Floquet theory. Direct numerical simulation is simultaneously performed to verify the correctness of the approximate analysis. In this manner, the feasibility of the proposed design and the occurrence criteria of hula-hoop motion are assessed.