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The gyroscopic exercise tool to train the hand muscle, which utilizes the gyroscopic effect caused by the whirling motion of the high speed rotating body is considered. This tool shows the contact phenomenon between the rotor and the case. When the input motion with several Hz is added to the case, the rotor spins in thousands rpm whirling with the slow precession motion. Conventional studies on this tool have assumed the continuous rolling motion of the rotor on the track in the case. This paper does not set this assumption, and develops the dynamical model of this tool considering the contact/separation conditions and the slide between the rotor and the case. Two kinds of motions are observed in the numerical simulation, one is the uniform precession synchronous to the input case motion which was observed in the conventional studies. The other is the periodically reverse precession asynchronous to the input motion, which was not observed in the conventional studies. These two motions are physically explained, their stabilities are clarified by the energy analysis. These motions are also observed in the experiment.

Dynamical Modeling and Stability Analysis of a Gyroscopic Exercise Tool Considering Contact/Separation and Slide between the Rotor and the Case