本文針對史帝文生型平面六連桿機構之死點位置、分支與運動範圍之判斷準則與分析方法進行研究。於文中首先提出一套死點構型之解析分析方法，此方法係以連桿機構之輸入與輸出多項式（Input-Output Polynomial Equation，IOPE）之特性為基礎，配合史塔定理（Sturm Theorem）中的史塔函數（Sturm Function）之應用，導出死點位置之必要條件式為一僅含輸入變數之高次多項式。同時並提出一簡單的解析法以排除例外之狀況。由於此方法不受限於輸入接頭的選擇，且無需推導死點構型的特殊幾何條件，因此除史帝文生型六連桿機構之外，亦可泛用於其它各種平面或空間單自由度多迴路機構之死點位置分析。

其次於本文中提出一套系統化的分支構型與各分支運動範圍之分析方法。於此方法中，首先應用史塔定理，將機構之所有死點構型分為上死點與下死點兩類。再針對輸入接頭選擇於四連桿運動迴路的情況加以討論，並導出各上、下死點位置與分支構型間之對應關係與判斷準則，以獲得此類機構各分支構型之運動範圍與所屬之迴圈。之後再利用迴圈分析之結果，進一步導出輸入接頭選擇於五連桿運動迴路內時之各死點位置間之對應關係，並進而完成其分支、迴圈與運動範圍等分析。最後舉出數個數值範例以驗證本方法之可行性，並與其它現存之方法比較分析結果之正確性。

This dissertation deals with the branch identification and motion domain analysis of Stephenson type six-bar linkages. Firstly, a new method for analyzing the dead-center positions of such linkages is presented. This method uses the input-output polynomial equation (IOPE) of the linkage and the corresponding Sturm functions to formulate the necessary condition of the dead-center configurations as a polynomial equation in terms of the input parameter only. A simple analytical method for identifying the true dead-center positions among the real solutions to the condition equation is also developed. This method is conceptually straightforward and does not rely on any structure-related geometric conditions; therefore, it can be systematically applied to all types of Stephenson linkages and other multiple-loop, single degree-of-freedom linkages regardless of the selections of the input-output pair and the type of the joints.

Secondly, a systematic approach for identifying the branches of the linkage and their motion domains is presented. In this approach, the dead-center positions are first classified into two groups as the upper dead-center positions and the lower dead-center positions based on the application of the Sturm theorem to the IOPE. In addition, a unified methodology to attribute the branches and the dead-center positions is developed for determining the motion domains and the circuits of the linkage for the case where the input joint is chosen within the four-bar chain. The results of this analysis are then applied to identify the motion domains of the more complicate case where the input joint is selected to be one of the uncoupled joints within the five-bar chain. Finally, several numerical examples are presented to verify and demonstrate the effectiveness of the proposed methods.

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