本文針對可變拓樸機構之動力學分析與最佳化尺度合成方法進行研究。文中提出一種利用能量流程圖模型來解決因機構拓樸變化而衍生的動力學問題，藉以進行機構分析與動作模擬。進而以此模型系統的動態輸出為性能目標函數，進行最佳化尺度合成。
從可變拓樸機構動力學的觀點考量，拓樸構形的變化往往伴隨著桿件間的接觸使接頭形式改變，其接觸可能為非碰撞接觸或碰撞接觸。吾人提出以切換式共流結與切換式共勢結的能量流程圖模型，來分別解決非碰撞接觸與碰撞接觸的不接續運動問題。特別是碰撞接觸類的機構動作涉及機械碰撞的拓樸構形變化，其動態模擬與碰撞衝擊力的演算很難以傳統的動力學分析方法處理。因此，本文採用能量流程圖中獨特的切換式共勢結來處理機構構形變化，以及Hertz 接觸理論計算碰撞衝擊所產生的連續接觸力，以建立能量流程圖模型，進行機構動力學分析與動作模擬。此外，並提出利用簡單的校正試驗取樣數據，求取模型系統中不易推算之物理參數的方法。
利用建構完成的能量流程圖模型及其參數化結構特性，吾人接著進行尺度合成最佳化方法的研究。首先分別採用採取統計理論中的田口方法與一般常用有限差分分析法進行靈敏度分析比較，以選定影響程度較大的系統參數作為最佳化的設計變數。接著提出一種多目標函數最佳化策略，來建立經濟學上最佳化理論中兩目標函數的Pareto 前線關係曲線，藉以暸解其物理關聯性，作為選定最佳化解的決策依據。
由於電力傳輸系統的高壓斷路器脫扣機構動作涉及機械碰撞的拓樸構形變化，是一種典型的可變拓樸機構。因此，將本文的分析方法與最佳化演算策略應用在24kV斷路器產品上，進行實際演練驗證。最佳化結果顯示，透過少數零件尺寸的小幅修改，便可獲得不錯的具體效果。並且經由實際修改產品零組件及實際測試，證實本演算法則的有效性。

This dissertation deals with dynamic analysis and optimal dimensional synthesis of mechanisms with variable topologies(MVT). An energy-based bond graph model is developed for solving the topological changing characteristics of the mechanism to simplify the tasks of dynamic analysis and motion simulation. The output of the model can also be utilized for evaluating the performance indices of the optimal dimensional synthesis problem of the mechanism.
From the dynamics point of view, topology change of mechanisms is due to the change of joint type of adjacent links, and which can be identified based on the form of contact. In general, the contacting form between two links can be classified into non-impact contact and impact contact. The discontinuity characteristics of these two types of contact can be handled in the bond graph model respectively by using switched one-junction and switched zero-junction. However, it is difficult to simulate the dynamic response of the MVT with impact contact by using traditional dynamic analysis methods, because it involves not only impact mechanics but also the change of topology. Therefore, in this dissertation, a special switched zero-junction module is employed in the bond graph to handle the topology change, and the Hertz contact theory is adopted for computing the continuous contacting force due to the impact contact. In addition, a method based on the use of simple experiment data is developed for calibrating some system parameters which are difficult to be estimated.
On the basis of the bond graph model and its parametric properties, an effective procedure is developed for synthesizing the optimal dimensions of the mechanism. The design variables of the optimization problem are first determined by performing sensitivity analysis toward the system parameters using the Taguchi method and finite difference algorithm. A multi-objective optimization is then developed for generating the Pareto frontier found in economics to evaluate the correlations between these two objective functions for making a favorable decision.
The trigger mechanism of high voltage circuit breaker is a typical MVT with impact contact, therefore it is chosen as a practical example to demonstrate the accuracy and effectiveness of the presented methods. It is shown that noticeable performance improvement of the device can be achieved with only minor modification of the dimensions. The simulation results are verified by performing real performance tests on a prototype mechanism fabricated based on the optimized dimensions.

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