相較於現今大部分工具機的串聯式結構，並聯式機構在結構特性上具備多個封閉迴路，使其相對優勢包含了高負載能力、較低的累積誤差與較好的加速性能，並且能將驅動器安裝於機架上藉此降低移動慣量，甚至基於多個相同機構迴路，簡化零組件種類與規格。然而，僅少數商品化的應用例子出現在工業界，市面常見的Delta robot皆應用於輕負載，學者與工程師們判斷關節撓性與末端效應器上非預期的動態響應為關鍵因子。因此，故本研究將針對3-UPU型具變化連桿長度之並聯式機構，在考量關節撓性下進行動態響應的探討。
本研究的兩個重點分別為：(1)關節撓性模型的建立以及(2)變化連桿長度造成之不同姿態下對於定位精度的影響。首先，將定義並聯式機構的重要運動學參數，並推導順逆向運動學之解析解。接著，轉換關節撓性為等效之質量彈簧阻尼系統，再將關節模型代入原機構系統，並利用拉格朗日方法求解整體機構的動態反應。最後，考量加速、減速後急煞與靜止時週期外力造成末端效應器之動態響應，並初步探討關節剛性變化對於軌跡偏差所帶來之影響。

A parallel kinematic machine (PKM) is expected to possess excellent performance of high load-carrying capacity, high speed and low accumulated position errors because of its superior rigidity caused by inherent multi-closed loop kinematic chains. Additionally, the actuators of PKM can be installed on the fixed frame to attenuate the dynamic effects and reduce the inertia of the moving components. Particularly, the components of PKM, including joints and linkages, are suitable for standardization and modularization for reducing manufacturing cost. However, most developed PKMs are not commercialized and only a few types of PKMs are practically used for various applications, especially for moving light-weight objects, for example the delta robot. Researchers attribute this consequence to insufficient stiffness of passive joints and undesirable dynamic response of the end-effector, which greatly reduce the precision performance of PKMs. Thus, the aim of this paper is to investigate the kineto-dynamic response of a 3-UPU PKM, which features three length-varying links connecting the moving end-effector by universal joints.
Attentions are mainly paid to two factors that affect the dynamic response of the PKM: (1) modeling of the universal joint that features unavoidable compliance and (2) link lengths varying during operation. This paper first investigates the kinematic characteristics of the PKM, and then explicit equations of forward and inverse kinematics are developed. The U-joint would be modeled as a mass-spring-damper system, combined with the original system. Using the method of Lagrangian mechanics, the equation of motion governing the kineto-dynamic response of the PKM is derived by considering its motion characteristics, namely, varying link lengths and joint compliance. Finally, these equations are used to evaluate the dynamic response of the end-effector under two specific motion scenarios and validated by simulation. One is the vibration of the end-effector stopped after fast acceleration and deceleration. The other is the kineto-dynamic response of the end-effector under periodic external forces.

摘要 I
ABSTRACT II
誌謝詞 IV
目錄 VI
符號表 VIII
圖表目錄 XIV
第一章 導論 1
1-1. 研究背景 1
1-2. 文獻回顧 4
1-2-1. 簡述並聯式機構之發展 4
1-2-2. 並聯式機構之靜態剛性分析 6
1-2-3. 並聯式機構之動態分析 7
1-2-4. 並聯式結構之關節撓性影響 10
1-3. 研究目的與研究方法 12
第二章 機構參數定義與運動學模型 14
2-1. 構型介紹與自由度計算 14
2-1-1. 構型簡介 14
2-1-2. 自由度計算 15
2-2. 座標與參數定義 16
2-3. 逆向運動學 18
2-4. 順向運動學 20
2-5. 運動靜力學 21
2-5-1. 連桿組之力與力矩平衡 21
2-5-2. 末端效應器之力與力矩平衡 23
第三章 動力學模型 28
3-1. 剛體動力學模型 28
3-2. 具關節撓性之動力學模型 36
3-2-1. 動力學模型架構 36
3-2-2. 關節模型之等效剛性與阻尼計算 41
3-3. 以曲柄滑塊機構案例說明 47
3-3-1. 座標與參數定義 47
3-3-2. 順向與逆向運動學 48
3-3-3. 剛體動力學推導 50
3-3-4. 關節撓性模型應用 57
第四章 結果與討論 65
4-1. 模擬設定與分析架構 65
4-2. 剛體模型–關節受力分析 68
4-3. 具關節撓性模型–頻域分析 79
4-4. 具關節撓性模型–靜止姿態受力分析 87
4-5. 具關節撓性模型–路徑誤差分析 92
第五章 結論與未來工作 100
參考文獻 102
附錄 110
A. 解析力學推導觀念簡述 110
B. 曲柄滑塊機構案例–剛體模型運動方程式彙整 113
C. 曲柄滑塊機構案例–關節撓性模型運動方程式彙整 115

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