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Technical Briefs

Dynamic Analysis of a Motion Transformer Mimicking a Hula Hoop

[+] Author and Article Information
C. X. Lu, C. C. Wang

Department of Power Mechanical Engineering, National Tsing Hua University, Eng. 1, No. 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan 30013, R.O.C.

C. K. Sung1

Department of Power Mechanical Engineering, National Tsing Hua University, Eng. 1, No. 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan 30013, R.O.C.cksung@pme.nthu.edu.tw

Paul C.P. Chao

Department of Electrical Engineering, Institute of Imaging and Biophotonics, National Chiao Tung University, Hsinchu 30013, Taiwan

1

Corresponding author.

J. Vib. Acoust 133(1), 014501 (Jan 05, 2011) (8 pages) doi:10.1115/1.4001839 History: Received March 13, 2009; Revised April 29, 2010; Published January 05, 2011; Online January 05, 2011

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.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 2

(a) Amplitude of the main mass, (b) angular displacement, and (c) angular velocity of the free mass. All were solved by the homotopy perturbation method.

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Figure 3

(a) Amplitude of the main mass, (b) angular variation, and (c) angular velocity of the free mass. All were solved by direct numerical simulation.

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Figure 4

Stability of the approximate solutions

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Figure 5

Occurrence of hula-hoop motion obtained from direct numerical simulation

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Figure 6

Stability of the approximate solutions with the moment of inertia of free mass

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Figure 7

Occurrence of hula-hoop motion obtained from direct numerical simulation with the moment of inertia of free mass

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Figure 1

Physical model of hula-hoop motion with (a) a point mass and (b) a semicircular thin plate as the free masses

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