在空間連桿機構合成問題裡，以雙圓柱對連桿最具代表性，我們可以將其他空間雙接頭連桿視為其退化而成的特例。以往有關於這些合成問題的研究皆是利用該接頭的一些幾何限制來求解，很難將其完全推展至其他雙接頭連桿的合成應用上。所以本文希望能提出一較一般化的方法來求解這些問題，即希望能直接由這些雙接頭連桿的合成方程式下手。而我們選擇較具代表性的雙圓柱對連桿為我們探討的對象。
本論文首先會對Roth (1967a) 的幾何方法先做一說明，因其最先解出雙圓柱對連桿位置合成的問題有六個解。接著將求解合成方程式的問題分成數值解及解析解兩方面探討。在數值解方面我們引用多項式連續法來做為我們解題的工具，有別於一般傳統的數值方法，多項式連續法利用一同倫化的觀念使我們能找出合成方程式的所有根。本論文中再使用一些變數分群及變數變換的技巧來處理這些合成方程式，使得原本必須追蹤40000條的同倫路徑減少到僅剩6條。最後實際完成一電腦程式的撰寫，代入Roth (1967a) 所使用的輸入數據，驗證其結果。
在解析解方面，使用Dialyitc消去法為工具，來對四個方程式、四個未知數作處理，希望將其化簡至一單未知數的多項式。結果得到一12×12的係數矩陣。將其展開後，可得到一六次的單變數多項式，印證了雙圓柱對位置合成問題最多只有六組答案。同樣的將其結果寫成一電腦程式，實際做一數值例。

The position synthesis is considered the cylindrical-cylindrical (CC) dyad of the most general problem in the spatial linkage synthesis, most Spatial dyads can be thought of as the degeneration of the CC dyad. Previous solutions to the CC dyad synthesis problem, Roth''s and McCarthy''s solutions, are obtained geometrically, As a result, it is difficult to apply the existing solution methods to other spatial dyads. Therefore, this thesis seeks to develop more general methods to solve the position synthesis problem of the CC dyad. Two solution methods are developed, and, most importantly, the synthesis equations of other spatial dyads can be solved similarly.
In this thesis, we first review the exiting methods, including Roth''s screw geometry approach and McCarthy''s dual vector approach. Both methods showed that the CC dyad five-position synthesis gives at most 6 solutions. We then develop two new solution methods, a numerical method and an analytic method. In the numerical method, we use the continuation method to solve a system of polynomial equations. The key concept in the continuation method is that the homotopy allows us to find all solutions to the system of equations. By using the modern multi-homogeneous continuation method, we can simplify the equations and are required to track only 6 homotopy paths. The result confirms the existing solutions.
In the analytic approach, we utilizes the dialytic elimination method to reduce a system of 4 equations in 4 unknowns into a uni-variable polynomial equation. The dialytic elimination process gives a 12 by 12 square matrix. Expanding the determinant of the matrix yields a uni-variable polynomial equation of degree six, which again confirms the existing solutions. Both solution methods developed in this thesis can be easily applied to the synthesis of other spatial dyads.

第一章 緒言
1.1 文獻回顧
1.2 研究動機與目的
1.3 本文架構
第二章 問題描述
2.1 雙圓柱對連桿剛體導引運動的合成
2.2 雙圓柱對連桿在螺旋座標下的合成方程式
第三章 螺旋座標及一些特殊線座標系統於雙圓柱對連桿位置合成問題之應用
3.1 螺旋座標及其性質之探討
3.1.1座標系的建構
3.1.2螺旋三角形
3.1.3極點四邊形與螺旋四邊形
3.1.4 螺旋圓椎
3.2 線座標系
3.3 雙圓柱對連桿位置合成問題
3.3.1 雙圓柱對連桿
3.3.2 三個位置合成問題
3.3.3 四個位置合成問題
3.3.4 五個位置合成問題
3.4 電腦程式撰寫
3.4.1 程式流程及輸入資料
3.4.2 程式執行結果
第四章 多項式連續法及其在雙圓柱對連桿位置合成之應用
4.1 多項式連續法的基本觀念
4.1.1 同倫化
4.1.2 齊性化
4.1.3 Bezout數
4.2 新多項式連續法解雙圓柱對連桿位置合成方程式
4.2.1 雙圓柱對連桿合成方程式
4.2.2 變數分群及齊性化
4.2.3 建構起始系統
4.2.4 同倫化系統的建立
4.2.5 路徑追蹤
4.2.6 反齊性化
4.3 電腦程式撰寫
4.3.1 程式結構及流程
4.3.2 問題討論
4.4 結論
第五章 有關於雙圓柱對連桿位置合成問題的解析解
5.1 Dialytic消去法的基本觀念及步驟
5.2 雙圓柱對連桿位置合成問題之多項式解
5.3 Dialytic消去法與空間平台法的比較
5.4 問題與討論
5.5 結論
第六章 結論
參考文獻
附錄一 雙圓柱對連桿位置合成程式
附錄二 多項式連續法電腦程式
附錄三 Dialytic法電腦程式
附錄四 矩陣值的求法

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