本研究針對三自由度並聯式機械手臂CaPaMan2及CaPaMan3，尋找其正向位置分析的解析解。解題過程首先是將原機構簡化為等效3RS機構，在此等效機構的座標系之內，利用活動平台上之球窩接頭間的距離為已知長度，可推導出三個多項式方程式，接著利用席維斯透析消去法(Sylvester dialytic elimination method)求得解答。在求得解答後，本研究亦利用圖形法進行逆向位置分析，以驗證正向分析之解答。

In this study analytical results for displacements of 3dof parallel manipulators CaPaMan2 and CaPaMan3 are obtained. The manipulators are firstly simplified into a 3RSmanipulator. Then in the simplified manipulator’s coordinate system three algebraic equations are obtained which constrain the distance between any two spherical joints on the moving platform to be a known value. Analytical solutions are obtained by using the Sylvester dialytic elimination method. Graphical inverse position analysis are also performed to verify the results.

目錄
中文摘要 ..............................................Ⅰ
英文摘要 ..............................................Ⅱ
目錄 ....................................................Ⅲ
圖目錄 .................................................Ⅴ
表目錄 .................................................Ⅶ
第一章  緒論 .......................................... 1
1.1前言 ................................................ 1
1.2文獻回顧 ......................................... 2
1.3研究動機 ......................................... 5
1.4研究目的 ......................................... 7
第二章  正向位置分析 ............................. 8
2.1 CaPaMan2 正向位置分析 ................. 8
2.2 等效3RS機構構 ............................. 10
2.3 CaPaMan2 正向位置分析流程圖 ..... 19
2.4 CaPaMan3 正向位置分析 ............... 21
第三章  結果與討論 ...............................23
3.1 CaPaMan2實例分析 ...................... 23
3.2 CaPaMan3實例分析 ....................... 31
第四章  逆向位置分析 ........................... 34
4.1 CaPaMan2逆向位置分析................. 34
4.2 CaPaMan3逆向位置分析................. 37
第五章  結論及預期結果 ........................ 39
5.1 結論 ............................................. 39
5.2 預期結果 ....................................... 39
參考文獻 ............................................ 40
附録A  席維斯透析消去法 ...................... 44
附録B  zxz尤拉角 ................................. 52


圖目錄
圖一  CaPaMan2 三自由度並聯式機械手臂 ..............2
圖二  第一代並聯式機械手臂CaPaMan  ....................3
圖三  第三代並聯式機械手臂CaPaMan3  ...................6
圖四  四連桿機構位置關係圖 ...................................9
圖五  等效3RS機構 ...............................................11
圖六  單位向量(n1',m1',l1')及(n1,m1,l1) ...................13
圖七  滑件曲柄機構位置關係圖 ..............................22
圖八  CaPaMan2之驅動四連桿機構 ........................23
圖九  CaPaMan2  90°-90°-90° 實例分析第1組解 .........24
圖十  CaPaMan2  90°-90°-90° 實例分析第3組解 .........26
圖十一  CaPaMan2  90°-90°-90° 實例分析第6組解 ......27
圖十二  CaPaMan2  45°-60°-90° 實例分析第1組解 ......29
圖十三  CaPaMan2  45°-60°-90° 實例分析第2組解 ......29
圖十四  CaPaMan2  45°-60°-90° 實例分析第3組解 ......30
圖十五  CaPaMan2  45°-60°-90° 實例分析第4組解 ......30
圖十六  CaPaMan3之驅動滑件曲柄機構 ..................31
圖十七  CaPaMan3  30°-45°-60° 實例分析第1組解 ......32
圖十八  CaPaMan3  30°-45°-60° 實例分析第2組解 ......33
圖十九  活動平台上之座標系 ..................................54


表目錄
表一 CaPaMan2實例分析機構尺寸表 .........................23
表二 CaPaMan2  90°-90°-90° 實例分析數據表 ...............25
表三 CaPaMan2  45°-60°-90° 實例分析數據表 ...............28
表四 CaPaMan3實例分析機構尺寸表 .........................31
表五 CaPaMan3  30°-45°-60° 實例分析數據表 ...............32
表六 CaPaMan2 逆向位置分析數據表 ........................36
表七CaPaMan3 逆向位置分析數據表 .........................38

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