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research-article

Nonlinear Dynamical Analysis of the "Power Ball"

[+] Author and Article Information
Tsuyoshi Inoue

Nagoya Univ. Dept. of Mechanical Science and Engineering Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
inoue@nuem.nagoya-u.ac.jp

Kohei Okumura

Nagoya Univ. Dept. of Mechanical Science and Engineering Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
kohei_in_the_u.s@hotmail.co.jp

Kentaro Takagi

Nagoya Univ. Dept. of Mechanical Science and Engineering Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
takagi@nuem.nagoya-u.ac.jp

1Corresponding author.

ASME doi:10.1115/1.4037075 History: Received December 13, 2016; Revised June 01, 2017

Abstract

The gyroscopic exercise tool called the "Power Ball", used to train the antebrachial muscle, is focused on. The basin of attraction of the synchronous rolling motion in the state space of initial condition is investigated. The reduced model governing the synchronous rolling motion is used and its averaged equation is deduced. The first integral for the dynamical behavior of the synchronous rolling motion occuring in the power ball is obtained. The separatrix which identifies the basin of attraction of the synchronous rolling motion is derived, and the ranges of initial precession angle and the initial spin angular velocity for realizing the synchronous rolling motion are clarified. These theoretically obtained results are then experimentally confirmed. Furthermore, the influences of parameters to the basin of attraction are also clarified.

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