The motions of a hula hoop are commonly regarded as the circular oscillations where a ring undergoes around a moving human body. Based on fundamental dynamic concepts, the hula loop motions are made possible by the interactive forces between the moving ring and human body. Inspired by the generic concept of the hula hoop motion, this study proposes a novel design of a motion transformer that consists of mainly 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 main mass. It is expected that the transformer is capable of transforming linear reciprocating motions to rotary ones based on the concepts similar to the hula hoop motions. In this way, the proposed transformer could be integrated with coils, magnets, and electric circuits to form a portable power generator. To ensure the aforementioned performance of the proposed transformer, a thorough dynamic analysis on the proposed transformer dynamic system is conducted in this study to understand relation between the varied system parameters and the chance of occurrence of a hula-loop motion. The governing equations are first formulated based on dynamic principles, which is followed by the search for steady-state solutions and corresponding stability analysis via the methods of harmonic balance and Floquet theory, respectively. Based on the obtained results, the design guidelines for determining transformer parameters to ensure the occurrence of hula-loop motions are distilled.