臺灣博碩士論文加值系統

本研究主要目的在應用六自由度的史都華平台的機構模擬於三自由度並聯式機構特殊運動行為分析，藉由Newton-Euler方法推導出偏轉和俯轉之關係式，及應用滑移模態控制理論所具有的響應速度快、參數變動之強健性、高精準度等優點來控制此三軸平行機構，再加上史都華平台機構具備高精度與高剛性之特性，且可進行六自由度的運動，因此利用此特性，更是容易模擬三自由度的並聯式機構的特殊運動路徑。例如：工具機刀頭調整，就是姿態與位置的變換，但因刀頭有著先天的機構限制，所以只能調整可動平台的三個參數。在此研究中，探討當只有連接固定平台及活動平台之連桿長度可調時，各軸軸長與平台姿態的關連性，以數值驗證其正確性，及應用滑移控制之穩定性及快速移動使追蹤軌跡誤差趨於零的特性，模擬驗證及開發應用於三軸平台機構之動態特性的滑移控制器。

The purpose of this article is to analyze the kinematics behavior of a special parallel mechanism by restricting the six degree of freedom Stewart platform to 3 degree of freedom. As the superior properties of high precision and rigidity of Steward platform, it could be used for simulating the path of a 3 d.o.f system, such as adjusting the machine tooling head. As the genetic restriction, only three parameters of the moving platform could be used for adjustment. In this research, the linkage rods between the fixed and moving platforms are assumed to be adjustable. The relationship between the moving platform posture and linkage length are studied and verified by the numerical simulation. In this article, some important properties of the dynamics of this platform have been derived and exploited to develop a sliding mode controller which have stability and can drive the motion tracking error to zero asymptotically.

誌謝 II
摘要 III
ABSTRACT IV
目錄 V
圖目錄 VIII
符號與縮寫 XI
1. 緒論 1
1.1 研究動機 1
1.2 文獻回顧 3
1.3 研究方法 6
2. 三軸平行機構介紹 8
2.1 三軸平行機構運動平台機構說明 8
2.2 三軸平行機構平台自由度分析 9
2.3 座標系 10
2.4 動座標系與慣性座標系之座標轉換 11
2.5 活動平台角速度與座標轉換矩陣之關係 16
2.6 活動平台角速度與歐拉角速度之關係 20
3. 三軸平行機構之動力分析 24
3.1 運動學方程式推導（逆向運動學） 24
3.1.1 位置分析 27
3.1.2 速度分析 34
3.1.3 加速度分析 39
3.2 動力學推導 42
3.2.1 連桿動力學推導 42
3.2.2 活動平台動力學推導 48
3.2.3 致動力推導 53
3.3 NEWTON-EULER法程序 56
4. 三軸平行機構之控制 58
4.1 控制理論介紹 58
4.1.1 PID控制理論 58
4.1.2 滑移Sliding Mode控制理論 61
4.2 平台系統之實驗架構及流程 64
4.3.1 機構方程式 67
4.3.2 程式開發方面 79
4.3 模擬驗證結果 82
4.4 非線性控制模擬 87
4.4.1 平台動態方程式 88
4.4.2 滑移控制器設計 91
4.4.3 模擬結果 95
5. 結論與未來展望 96
5.1 結論 96
5.2 未來發展與應用 97
參考文獻 99
自傳 103

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