呼拉圈運動係透過人體與呼拉圈彼此間之交互運動所形成：由身體前後擺動過程，有效地將動力傳給呼拉圈，進而使呼拉圈產生旋轉運動稱之。故藉此運動機制，衍伸出呼拉圈轉換機構之設計概念，即經此呼拉圈運動機制，將外力造成之直線運動轉換為旋轉運動。由其機制，此呼拉圈轉換機構可搭配各式動力源，如：承載台振動力、車輛加減速慣性力，甚至於人體日間運動力等不同外力型式。
本研究首先評估各式動力源，了解可能存在之動力來源與搭配之能量轉換系統間的匹配問題，並由呼拉圈運動搭配可能應用之能量轉換機構。其中，電磁式機構除可由直線往復運動達到發電效果外，亦可透過旋轉運動進行發電，此與呼拉圈運動型態有所搭配。故，本研究主要整合電磁式發電裝置與呼拉圈轉換機構，作為發電裝置之輸入。另，以人體日常外力如：簡諧外力與脈衝外力為主，於此研究中作為外力來源進行討論。
首先，針對呼拉圈之運動狀態進行探討並建構物理模型，利用Lagrange方法推導出運動方程式，探討於簡諧外力下系統之動態行為，了解呼拉圈運動發生條件與系統參數之關係。進而針對運動方程式求取近似解析解，透過數值模擬驗證其準確性；再藉由Floquet理論進行穩定度分析，得出呼啦圈之發生區域，並與數值模擬進行探討比較。其後，由實驗結果進行驗證，與前述之數值模擬結果相符。故藉上述結果得到：於各式簡諧外力頻率與大小並搭配特定之參數情況下，系統發生呼拉圈之可能作動區域。
其次，藉脈衝力與系統初始速度之關係，探討系統於該外力情況，呼拉圈運動之暫態行為。透過數值模擬，進而驗證系統於脈衝外力下其運動方程式之正確性。同時，找出於不同初始條件下，系統發生呼拉圈運動之可能作動區域。最後，由實驗進一步驗證上述之模擬結果。
最後，透過法拉第定律，利用電磁機制有效擷取振動能量並轉換為電能，推得能量與呼拉圈運動之關係；並推知電磁阻尼與其對系統旋轉運動之影響。自理論得知，系統於特定外力大小與頻率下，可能輸出之能量，且於實驗與模擬結果，皆得一致之成果。最終，在最低外力大小為11.2 N與外力頻率為8 Hz時，系統輸出之最大能量為5 mW

Hula-hoop motion refers to the gyrating of a ring around a human body. This is made possible by the interactive forces between the human body and the moving ring. 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-spinning mass hinged eccentrically onto the center of the main mass. It is expected that the motion transformer can convert linear reciprocating motion into rotational one and accommodate various power sources, which mainly accompany with the vibrations of the vehicle suspension and machine base as well as the motion of human body.
This thesis aimed at designing an energy-harvesting device that can scavenge energy, especially, from human motion by integrating an electromagnetic generator with a hula-hoop motion transformer. The harmonic and impulsive forces caused by both machine vibration and human motion were investigated, individually.
First, a thorough dynamic analysis of the proposed transformer system with harmonic excitation was conducted in order to characterize the relationships between the various system parameters and the likelihood of hula-hoop motion occurring. The governing equations were derived using Lagrange method. This was followed by a search for steady-state solutions via the Homotopy perturbation method; meanwhile, a direct numerical simulation was performed to verify the correctness of the approximate analysis. The corresponding stability analysis was conducted via Floquet theory. In this manner, the feasibility of the proposed design and the occurrence criteria of hula-hoop motion were assessed. After that, an experimental study confirmed that the dynamic responses were well matched with the numerical simulation. The results imply the possibility of hula-hoop motion over a large set of combinations of excitation frequencies and amplitudes, which are confirmed by not only the dynamic analysis but also the experiment.
Secondly, the transient dynamic analysis was also performed based on the governing equations by applying an impulsive excitation to the main mass, which then created its initial velocity. A direct numerical simulation was performed to verify the correctness of the equations considering the impulsive excitation. Additionally, the occurrence of hula-hoop motion was investigated to find the dynamic matching between the initial conditions and the system parameters of the hula-hoop motion transformer. Moreover, the experimental responses were used to verify both the correctness of the equations considering impulsive excitation and the dynamic responses of the direct numerical integration.
Thirdly, for the generation of energy through electromagnetism, the equations describing the relation between induced voltage and power for the system were derived according to the Faraday theory. Herein, the equation of induced electrical damping was obtained as well, in which the effect of electrical damping was concerned for the system response. Moreover, the responses from the theoretical analysis, numerical simulation, and experiment were in good agreement with one another regarding the accuracy of the equations of the induced voltage and power from the generator.
Finally, the proposed energy-harvesting system was proved to generate power through electromagnetism after integrating the electromagnetic generator with the hula-hoop motion transformer. Specifically, the maximum power that the system can generate is approximately 5 mW when the frequency and amplitude of the external harmonic excitation are 8 Hz and 11.2 N, respectively.

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