靜音鏈早在百年前就已經開始被應用於動力傳送上，但是在文獻上，至今一直無完整的數學模型來描述它的運動，而相關的研究多是實驗分析。故本文嘗試建立靜音鏈的數學模型以便作為設計的依據。據此模型便可以更改鏈片及鏈輪齒形狀，用電腦模擬出鏈片與鏈輪的嚙合運動分析，以得知鏈片與鏈輪嚙合的運動情況。
本論文針對靜音鏈作嚙合運動分析，將其歸類為多剛體連接的接觸運動，根據二維的嚙合理論來做鏈片和鏈輪的齒面接觸分析(Tooth Contact Analysis, TCA)，建立分析靜音鏈的數學模型。並依照鏈片實際的運轉情形，採用緊邊鏈條作分析，並把靜音鏈作正規化，再求得鏈片固定住時的高度及節圓半徑、兩固定片的夾角，鏈片固定角，再假設兩種鏈片固定的模式，以作為以後鏈片運動分析的依據，並分別求出兩種鏈片假設固定模式接觸的初始點與三個不同的鏈片運動階段。
從兩種假設固定模式的數值模擬中得知，接觸的初始點是相同的，嚙合擺動期也相同，從中可確定鏈片真實固定的位置，重新再做一次數值模擬，確定暫時固定期、懸空期及嚙合擺動期。接著解出鏈輪轉動參數與鏈輪齒的漸開線參數、鏈片接觸的內緣參數及相鄰兩鏈片的轉動參數的相互關係，得知鏈輪轉動與鏈條的運動及接觸情況，藉此解釋靜音鏈鏈片在嚙合過程中運動模式及為何會比較安靜及較無振動問題。

In mechanical power transmission applications, two of the most popular chain drive types are the roller chain and the silent chain, both of which have been employed in industry for decades. Silent chains have many advantages. It is quieter and more efficient than roller chains. However, there are not many research reports of silent chains in literature. This thesis aims to investigate the kinematics of pin-jointed silent chains.

Based upon conjugate theory, this thesis studies the motion analysis of silent chains. We analyze silent chains by using the techniques of tooth contact analysis with force equilibrium equations incorporated. First, we assume two fixed models of link with respect to the sprocket. Second, we establish four stages of the motion of a link, starting from tight chain span until it is fixed with respect to the sprocket. These four stages are conjugate contact stage, stationary contact stage, pulled suspension stage, and conjugate suspension stage. Finally, we change the curvature of the inner curve of the link to investigate the relationship between the curvature of links and the chain motion. Some animations of the engagement process are demonstrated to illustrate the results.

In conclusion, we have proposed a systematic approach for analyzing the motion of silent chains. The results of this research can also be applied to mechanical system with multiple bodies in contact.

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