十六個平面八連桿組中，僅雙蝴蝶連桿組不含子四連桿組，其任何倒置機構皆屬無閉合解機構，為構造最複雜之八桿機構，而此機構之尺度合成也是最難處理之問題。在平面連桿機構的尺度合成過程中，常發生順序、迴路與分支缺陷等問題，為了合成可用之無缺陷機構，須先探討各機構發生順序、迴路與分支缺陷之原因，進而建立其避開缺陷之限制式，於尺度合成的過程中剔除有缺陷之機構。本文之目的在於探討平面八連桿雙蝴蝶機構之無缺陷尺度合成，所提出之方法可適用於函數機構、路徑演生機構以及剛體導引機構之尺度合成。
針對各型平面八連桿雙蝴蝶機構的構造，本文首先根據已知條件──輸入桿及輸出桿之需求角位置，提出一套獨立迴路篩選法則，選擇出最適當的三個獨立迴路。再以此三個獨立迴路的位移方程式，透過變數消去與轉換，以及輸出桿拆解之方法，來求得演生機構輸出桿角位置與耦桿點位置之顯函數表示式。由於演生機構之輸出桿角位置或耦桿點位置，會與原輸出桿之需求角位置或耦桿點位置存在誤差值，求得此誤差值之方均根並無因次化後，即可建立最佳化尺度合成之目標函數。另外，並藉由探討雙蝴蝶機構之相鄰分支與死點之Jacobian值，歸納出避開順序、迴路與分支缺陷之限制式。然後，將目標函數配合所歸納出之避開缺陷限制式，以SQP最佳化方法進行尺度合成，得到符合設計需求之無缺陷機構。其中，最佳化尺度合成所需之初始值，本文提出一套幾何作圖法來提供。
本文針對各種不同設計問題，利用上述方法推導出各型雙蝴蝶機構最佳化尺度合成所需之目標函數，並以範例驗證其正確性。藉由範例之結果可得知，以本文提出之方法所合成出之機構，不僅能夠達成所給定之設計需求，且在運動過程中亦能夠確實地避開各類缺陷問題。

The double butterfly linkage is the only eight-bar linkage without any four-bar loops. Each inversion of the linkage is a complex non-dyadic mechanism which is difficult to deal with its dimensional synthesis. Order, circuit, and branch defects are frequently encountered in the dimensional synthesis of linkages. In order to obtain mechanisms without defects, it is necessary to investigate the causes for occurring dead-center, order defects, circuit defects, and branch defects for each mechanism, and then propose suitable constraint equations for avoiding defects in the dimensional synthesis processes. The main purpose of this thesis is to propose a unified method for the defect-free dimensional synthesis of planar double butterfly linkages for function generation, motion generation and path generation.
For each double butterfly linkage, a selective methodology is proposed for choosing three suitable independent loops according to the specified input and output variables. The explicit equations relating the generated output variables and coupler point positions are then derived by eliminating and transforming some angular variables in the three independent loops and by separating the output link into two links. The objective function of the optimal synthesis is defined as the dimensionless root mean square of deviation of the angular positions of the output link and/or the coupler point positions between the generated output and required positions. The Jacobian limit of each double butterfly linkage is used as the constraint equation for avoiding order, circuit, and branch defects in the optimal synthesis. Thus, defect-free mechanisms can be synthesized by using the Sequential Quadratic Programming method. Furthermore, the thesis uses a geometric approach for obtaining the initial values of design parameters for the optimal synthesis.
For different design problems, this thesis provides several examples to demonstrate the feasibility of the proposed method. The results of the examples show that the synthesized mechanisms not only satisfy the design requirements but also avoid defect problems.

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