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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February 2011
Technical Briefs
Dynamic Analysis of a Motion Transformer Mimicking a Hula Hoop
C. X. Lu,
C. X. Lu
Department of Power Mechanical Engineering,
National Tsing Hua University
, Eng. 1, No. 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan 30013, R.O.C.
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C. C. Wang,
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.
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C. K. Sung,
C. K. Sung
Professor
Department of Power Mechanical Engineering,
e-mail: cksung@pme.nthu.edu.tw
National Tsing Hua University
, Eng. 1, No. 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan 30013, R.O.C.
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Paul C.P. Chao
Paul C.P. Chao
Department of Electrical Engineering, Institute of Imaging and Biophotonics,
National Chiao Tung University
, Hsinchu 30013, Taiwan
Search for other works by this author on:
C. X. Lu
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. 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. Sung
Professor
Department of Power Mechanical Engineering,
National Tsing Hua University
, Eng. 1, No. 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan 30013, R.O.C.e-mail: cksung@pme.nthu.edu.tw
Paul C.P. Chao
Department of Electrical Engineering, Institute of Imaging and Biophotonics,
National Chiao Tung University
, Hsinchu 30013, TaiwanJ. Vib. Acoust. Feb 2011, 133(1): 014501 (8 pages)
Published Online: January 5, 2011
Article history
Received:
March 13, 2009
Revised:
April 29, 2010
Online:
January 5, 2011
Published:
January 5, 2011
Citation
Lu, C. X., Wang, C. C., Sung, C. K., and Chao, P. C. (January 5, 2011). "Dynamic Analysis of a Motion Transformer Mimicking a Hula Hoop." ASME. J. Vib. Acoust. February 2011; 133(1): 014501. https://doi.org/10.1115/1.4001839
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