由於在平面連桿機構尺度合成過程中，常發生順序、迴路與分支缺陷等問題，為了合成無缺陷之機構，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，於尺度合成過程中剔除有缺陷之機構。本文之目的在於探討平面四連桿與六連桿機構之無缺陷尺度合成，所提出之方法可適用於函數機構、路徑演生機構與剛體導引機構之尺度合成。
針對平面四連桿機構，本文探討其無缺陷尺度合成，包括幾何法與最佳化方法。針對平面四連桿機構通過兩個有限分離位置之合成問題，本文根據幾何作圖法的步驟，提出一套辨識流程，有系統地求得輸出桿的固定軸樞或動軸樞之可行解範圍。另外，針對無缺陷最佳化尺度合成，本文利用機構位置分析閉合解，建立最佳化尺度合成之目標函數-演生機構輸出桿或其耦桿點之位置與需求位置之無因次化平均誤差，並配合避開順序、迴路與分支缺陷之限制式，使合成結果為無缺陷機構。
針對具閉合解的平面六連桿機構，本文利用子四連桿組耦桿點曲線、雙連桿與死點構形之幾何特徵等機構學基本原理，探討各機構迴路與分支缺陷形成之原因，並建立其辨識方法，據以歸納出避免迴路與分支缺陷之限制式。針對此類機構之無缺陷尺度合成，本文採用最佳化尺度合成之方法，其目標函數亦利用機構位置分析閉合解建立之，即演生機構輸出桿或其耦桿點之位置與需求位置之無因次化平均誤差，然後加入消除順序、迴路與分支缺陷之限制式，於機構尺度合成過程中即能自動消除順序、迴路與分支缺陷，合成滿足所有設計需求之無缺陷機構。
針對無閉合解的平面六連桿機構，本文利用設計變數之消除與整合，透過已知條件-輸入桿與輸出桿的指定通過位置，來求得演生機構輸出桿之位置表示式，進而建立最佳化尺度合成之目標函數，即演生機構輸出桿或其耦桿點之位置與需求位置之無因次化平均誤差。並藉由機構之迴路與分支特性及死點構形特徵之探討，歸納出避開順序、迴路與分支缺陷之限制式。然後，以最佳化方法進行機構尺度合成，同時加入所歸納之避開缺陷限制式，使合成結果為符合設計需求之無缺陷機構。

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 work is to propose a unified method for the defect-free dimensional synthesis of four- and six-bar linkages. The proposed method can be applied for the dimensional synthesis of four- and six-bar function generators, path generators, and motion generators.
The defect-free four-bar linkages are synthesized by using a geometric method and an optimization method, respectively. Based on an improved geometric method, an identification flowchart is proposed for obtaining feasible regions for the fixed pivot or moving pivot of the driven link of a four-bar linkage for a two-pose problem. For the defect-free optimal synthesis of four-bar linkages, the closed-form solutions for the positions of the output link of the mechanism are used to establish the objective function: the dimensionless average absolute deviations of the angular positions of the output link and/or the coupler point positions between the generated output and required positions. The constraint equations for avoiding order, circuit, and branch defects are included in the optimal synthesis, thus defect-free mechanisms are obtained.
For the dyadic six-bar linkages, using the concepts of the coupler curve of a four-bar linkage, the accessible region of a dyad, and the geometric feature of dead-center configurations, procedures are proposed for identifying the different circuits and branches of dyadic six-bar linkages. Using the characteristics of order, circuit, and branch defects, the constraint equations to avoid them are presented. The objective function is also established by using the position closed-form solutions of mechanisms. An optimization approach is then utilized for the defect-free dimensional synthesis of dyadic six-bar linkages.
For the nondyadic six-bar linkages, the explicit equations relating the generated output and specified variables are derived by eliminating and transforming angular variables on two loops and by using the specified values of input and output variables. Then, the objective function of the optimal synthesis is obtained. Using the characteristics of order, circuits, branches, and the geometric features of dead-center configurations for nondyadic six-bar linkages, the constraint equations for avoiding order, circuit, and branch defects are proposed for the defect-free optimal synthesis of nondyadic six-bar linkages.

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