臺灣博碩士論文加值系統

本文針對Hexaglide並聯式平台機構之反向運動學、奇異構型分析及運動軌跡規劃等問題提出研究。吾人首先利用活動平台與各驅動滑塊間之運動關係，推導出活動平台繞主軸旋轉之極限運動邊界。此外，並導出此機構之正、反向Jacobian矩陣之解析型式，並根據其物理意義分析此機構之正、反向奇異構型之形成原因，進而提出一種方法定義正向奇異性質指標。此方法可迅速判別此機構與正向奇異構型接近程度，再藉由活動平台之自轉以求得遠離正向奇異構型之最佳位置。吾人並依此方法提出一種避免於運動過程中產生正向奇異位置之最佳軌跡規劃法則，規劃活動平台點到點運動路徑與封閉運動路徑，再以三次樣條曲線合成最佳運動軌跡。

This thesis deals with the singularity analysis and trajectory planning algorithm of the Hexaglide, which is a spatial six degree-of-freedom parallel manipulator. The analytical equations for computing the rotational limitation of the moving platform around a specified rotation axis at a given point under the inverse kinematics constraints is first developed. The analytic forms of the direct and the inverse Jacobian matrices of the mechanism are then derived based on the velocity transformation equations. The corresponding singular configurations are further investigated based on the theory of instantaneous screw motions and Plücker vector representation of lines. An index for identifying the direct singularity of the manipulator at any specified configuration is then defined, and a simplified analytical approach for evaluating the singularity index is presented. Based on this approach and cubic-spline curve fitting technique, a numerical algorithm for synthesizing the singularity-free point-to-point and continuous motion trajectories of the manipulator is developed.

中文摘要……………………………………………………………….Ⅰ
英文摘要……………………………………………………………….Ⅱ
誌謝………………………………………………………………….. Ⅲ
目錄………………………………………………………………….…Ⅳ
圖表目錄………………………………………………………….……Ⅶ
第一章 緒論………………………………………………………...1
第二章 反向運動學分析…………………………………………….5
2.1 Hexaglide之構造………………………………………….5
2.2座標系統與桿件參數之定義……………………………...6
2.3反位移分析………………………………………………...8
2.4 活動平台繞主軸旋轉之最大正、反向角度…………….14
2.5 速度分析………………………………………………...17
第三章 正向奇異構型分析…………………………………………18
3.1 推導正向奇異構型之判別式…………………………...18
3.2 Hexaglide之各種正向奇異構型………………………..25
3.3判別正向奇異構型………………………………………..35
第四章 正向奇異性質指標…………………………………………39
4.1 Case 3 之正向奇異性質指標之定義…………………..39
4.2 提出一解析法則判別Case 3 之正向奇異構型………..41
4.3提出一改進方法判別Case 3 之正向奇異構型………...45
4.4 分析步驟………………………………………………...48
第五章 最佳運動軌跡規劃…………………………………………51
5.1 定義活動平台中心點之運動路徑……………………...51
5.2 三次樣條函數…………………………………………...53
5.3 分析步驟………………………………………………...59
第六章 數值範例……………………………………………………67
6.1 定義各種連桿組合之目標函數平均值………………...67
6.2 直線運動路徑…………………………………………...69
6.3 正圓運動路徑…………………………………………...77
第七章 結論與建議…………………………………………………84
參考文獻……………………………………………………………….85
附錄A 求解活動平台之最大旋轉角過程中方程式之係數展開式..87
附錄B 判別正向奇異構型解析法過程中方程式之係數展開式…..90
B.1 （4-15）式之係數……………………………………….90
B.2 （4-16）、（4-17）式之係數………………………….90
B.3 （4-19）式之係數……………………………………….91
作者簡介……………………………………………………………….92

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