分支缺陷為機構在尺度合成過程中，最常發生的缺陷問題之一。若合成所得之機構在各指定通過位置之組合構形位於不同分支上，則在不同分支間，必有死點構形存在，使機構無法跨越死點運動到下一指定通過位置上，則稱此合成結果產生了分支缺陷。
本文的目的在於為檢驗出分支缺陷之存在，對於合成後之機構，探討其迴路、分支與死點構形等特性，並提出一套迴路與分支辨識的方法。首先本文對於文獻中針對平面四連桿與六連桿機構，具代表性的迴路與分支辨識方法，整理為幾何法、解析法及數值法等三類，並比較歸納其優缺點與適用範圍。接著本文以速度瞬心曲線、耦桿點曲線、傳動角與死點構形之幾何特徵，以平面四連桿機構為出發點，進而延伸至平面六連桿機構，探討其分支特性及辨識指標。最後，本文提出一套數值分析方法，針對機構合成後，針對各個指定通過位置進行位置分析，若其所處分支具有端點，便搜尋該位置所在分支上兩端對應之死點位置，以及靠近死點位置時各桿角度之收斂特性，藉此特性便可檢驗合成後之機構所指定通過位置是否具有分支缺陷。文中並應用此方法在各型平面六連桿機構，完成各指定通過位置之組合構形的分支辨識。

Branch defect is one of the major problems in the process of the dimensional synthesis of mechanisms. For a synthesized mechanism, if the assembly configurations of all specified positions do not fall on the same branch, the mechanism is said to have branch defect. The main purpose of this work is to propose criteria for the branch identification of mechanism synthesized. The existing methods for the circuit and branch identification of planar four-bar and six-bar mechanisms can be classified into three kinds, i.e., the geometric method, the analytic method and the numerical method. This study presents the advantages and disadvantages of these three kinds of methods in comparison. Based on the geometric feature of centrode, coupler curve, transmission angle and, dead-center configuration, a feasible criterion is proposed for the branch identification of some planar four-bar and six-bar mechanisms. This study also presents a numerical method for the branch identification of mechanisms. The position analysis of the mechanism synthesized starts from each specified position. If the branch exists ends, the two ends of the branch are dead-center positions. The analysis positions of all links on the two dead-center positions of a branch are found out for each specified position on its branch. The ways of approaching to the dead-center position and the values of angular positions of all links on the dead-center position are used for branch identification of mechanisms. Some examples are presented to illustrate the feasibility of the method proposed in this study.

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