本論文之目的在於針對能演生對稱耦桿點曲線的球面四連桿機構，建立其三角形列線圖集，以作為研究球面對稱耦桿點曲線之參考；同時依據三角形列線圖集所提供的資訊，配合最佳化方法來合成不具缺陷的球面四連桿路徑演生機構。
　　首先，分別探討球面曲柄搖桿機構、球面雙曲柄機構、球面雙搖桿機構與球面non-Grashof雙搖桿機構等四種能演生對稱耦桿點曲線的幾何條件，以及其設計參數與運動特性。根據這四種球面四連桿機構運動分析的結果，發現各種機構的尺寸參數在某些幾何條件下，能演生具有特殊幾何特徵的對稱耦桿點曲線。經由推導這些特殊耦桿點曲線與機構尺寸參數間的關係式，並將這些關係式表示在平面的等值曲線上，建立演生對稱耦桿點曲線的球面四連桿機構三角形列線圖集共九種。藉由機構的三角形列線圖集，選定所指定的對稱耦桿點曲線類型之後，不需複雜的計算即可迅速求得相對應的機構尺寸參數值，因此可當作設計球面路徑演生機構的重要參考工具。
　　接著，本論文利用最佳化方法，並根據球面四連桿機構三角形列線圖集，所提供的機構尺寸參數初始估測值，來合成符合設計需求的球面四連桿路徑演生機構。此外，為了使合成的結果不具次序、迴路與分支等缺陷問題，文中並提出了一套有效且快速辨識迴路與分支的方法，然後將此方法整合於球面四連桿路徑演生機構最佳設計問題中，並藉由將機構輸入桿的角度設定為設計變數的方式，如此即可避免各種缺陷問題存在於最佳設計結果中。
　　最後，本論文舉兩個設計實例，說明以最佳化方法來合成球面四連桿路徑演生機構的過程中，三角形列線圖集的確能提供合適的機構尺寸參數初始估測值，並因此得到不具缺陷的結果，藉以驗證本論文所建立的球面四連桿機構三角形列線圖集，與不具缺陷的球面路徑演生機構最佳化合成方法的可行性。

　　This dissertation presents the triangular nomograms for spherical four-bar linkages generating symmetrical coupler curves, and proposes a methodology for the optimal synthesis of spherical four-bar path generators without defects with the aid of the initial guesses provided by the triangular nomograms.
　　The geometric conditions, design parameters, and kinematic properties of the spherical crank-rockers, double-cranks, double-rockers, and non-Grashof double-rockers tracing symmetrical coupler curves are analyzed comprehensively. According to the results of kinematic analysis for these spherical four-bar linkages, some special symmetrical coupler curves are found and investigated, and the corresponding geometric relations for them are used to derive the implicit equations consisting of the dimensional parameters. Nine triangular nomograms for the spherical four-bar linkages are then presented for the determination of dimensional parameters of a linkage generating the desired coupler curve without further calculation. Therefore, these triangular nomograms can be served as important tools for the design of spherical four-bar path generators.
　　In order to avoid the order defect, circuit defect, and branch defect that may occur in the synthesis results, the dissertation studies the characteristics of circuits and branches of spherical four-bar path generators and also presents a suitable and effective identification method for each defect. Hence, the identification methods are integrated with the optimization problem for the dimensional synthesis of spherical four-bar path generators without defects based on the initial guesses obtained from the triangular nomograms.
　　Two examples are illustrated to show that the integration of the triangular nomograms with the optimization scheme presented in the dissertation is effective for the synthesis of spherical four-bar path generators.

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