本文是針對六自由度並聯式機械手臂HexaSlide，解出其正向位置分析的解析解。HexaSlide機械手臂可以有以下幾種形式：Hexaglide、HexaM、或Linapod，本研究計畫所建議的分析方法可以使用在以上任何形式的機械手臂，並求出其正向位置分析的解析解。方法是首先找出機械手臂的等效機構(equivalent mechanism)，亦即傾斜的3RS並聯式手臂，接著利用活動平台上三個球窩接頭間距離為已知常數，可得到三個多項式方程組，再利用席維斯透析消去法(Sylvester dialytic elimination method)，求解出方程組的實根並解出活動平台位置。本文亦發展出可判定桿件間是否交錯的方法，而且也利用逆向位置分析，來驗證正向位置分析結果。

The purpose of this study is to determine analytical solutions to the forward position analysis of the six degree-of-freedom parallel manipulator HexaSlide. A HexaSlide parallel manipulator may take the following three forms: Hexaglide, HexaM, and Linapod. The solution procedure suggested in this research may deal with any of these three forms. A HexaSlide manipulator is fist transformed into its equivalent mechanism, that is, an inclined 3RS parallel manipulator; then the condition that the three spherical joints on the moving platform form an equilateral triangle leads us to obtain three polynomial equations in three unknowns. These equations are solved by using Sylvester dialytic elimination method. Each set of real roots correspond to a movimg Platform’s position. A method to determine if the links are crossed is also developed in this study. Solutions so obtained are verified by performing inverse position analysis.

目  錄
中文摘要 ------------------------------------------------Ⅰ
英文摘要 ------------------------------------------------Ⅱ
目    錄 ------------------------------------------------Ⅳ
圖 目 錄 ------------------------------------------------Ⅴ
第一章 緒論 ----------------------------------------------1
第二章 等效平台 --------------------------------------5    
第三章 等效平台分析 -----------------------------------9   
第四章 結果與討論 ---------------------------------------17
第五章 結      論 ---------------------------------------37
參考文獻 ------------------------------------------------38
附錄A n1,m1,l1座標系與其他座標系間之座標轉換 ------------41
附錄B  --------------------------------------------------43
附錄C 程式  ---------------------------------------------45
圖 目 錄
圖一 Hexaglide並聯式機械手臂 ----------------------------52
圖二 HexaM並聯式機械手臂 --------------------------------53
圖三 Linapod並聯式機械手臂 ------------------------------54
圖四 兩圓球之交圓所在之平面 ---------------------------- 55
圖五 等效3RS機構 --------------------------------------- 56
圖六 (n1,m1,l1)及(n1',m1',l1')座標系 ------------------- 57
圖七 Hexaglide之位置圖 --------------------------------- 58
圖八 Hexaglide之位置圖 --------------------------------- 58
圖九 HexaSlide之位置圖 --------------------------------- 59
圖十 HexaSlide之位置圖 --------------------------------- 59
圖十一 HexaSlide之位置圖 ------------------------------- 60
圖十二 HexaSlide之位置圖 ------------------------------- 60
圖十三 HexaSlide之位置圖 ------------------------------- 61
圖十四 HexaSlide之位置圖 ------------------------------- 61
圖十五 HexaSlide之位置圖 ------------------------------- 62
圖十六 HexaSlide之位置圖 ------------------------------- 62
圖十七 HexaSlide之位置圖 ------------------------------- 63
圖十八 HexaSlide之位置圖 ------------------------------- 63
圖十九 HexaSlide之位置圖 ------------------------------- 64
圖二十 HexaSlide之位置圖 ------------------------------- 64
圖二十一 HexaSlide之位置圖 ----------------------------- 65
圖二十二 HexaSlide之位置圖 ----------------------------- 65
圖二十三 HexaSlide之位置圖 ----------------------------- 66
圖二十四 HexaSlide之位置圖 ----------------------------- 66
圖二十五 HexaSlide之位置圖 ----------------------------- 67
圖二十六 HexaSlide之位置圖 ----------------------------- 67
圖二十七 HexaSlide之位置圖 ----------------------------- 68
圖二十八 HexaSlide之位置圖 ----------------------------- 68

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