本論文探討機械手指夾取圓柱的接觸問題，利用套裝軟體ANSYS從事有限元素接觸分析，本文先進行圓柱與平面以及圓球與平面的接觸分析，數值結果先與赫氏接觸之解析解比較，再進行機械手指夾取圓柱的接觸分析。
分析的情況包括兩個部分，第一部分是針對手指以平移方式夾緊圓柱，而二部分是機械手指用旋轉的方式夾取圓柱。在第一部分機械手指可以有傾斜角度，並以平移方式夾取圓柱，本文求出不同傾斜角度情況下夾緊位移與正向力之間的關係；以及機械手指夾取不同材料圓柱時夾緊位移與正向力之間的關係；並探討手指夾取鋁製圓柱的降伏問題。本文第二部分首先推導出模擬旋轉夾緊的位移邊界條件，利用此條件所求出的有限元素分析結果非常接近利用材料力學懸臂樑公式求出的估計值。

Contact analysis in robot grasping is performed in this thesis. Commercial software ANSYS is used in finite element analysis. Two dimensional cylindrical contact analysis and axisymmetric spherical contact analysis are first performed, and the results are compared to Hertz solutions.
Then two situations are treated in this study: cases with linear tightening displacements and cases with rotational tightening displacements. In the first situation, translational tightening displacements may be imposed by inclined robot fingers. The relation between normal grasping force and linear tightening displacements are obtained for various inclination angles of the fingers, and for cylinders with various material properties. Also the critical linear displacement that causes yielding is obtained for an Aluminum cylinder. In the second situation, displacement boundary conditions to simulate rotational tightening are obtained. Results obtained by imposing these conditions agree well with estimated values found by using fixed-end beam formula.

目錄
中文摘要	Ⅰ
英文摘要	Ⅱ
目錄	Ⅲ
圖目錄	Ⅳ
第一章 緒論	1
第二章 有限元素法	3
2.1 有限元素法簡介	3
2.2 有限元素法之接觸分析	11
2.3 ANSYS接觸分析	16
第三章 接觸範例	17
3.1 圓柱與平面接觸	17
3.2 圓球與平面接觸分析	25
第四章 結果與討論	29
4.1 機械手指平移夾取圓柱	29
4.2 傾斜手指平移抓取圓柱	41
4.3 機械手指平移夾取不同材料之圓柱	46
4.4 手指夾取圓柱的降伏問題	50
4.5 手指以旋轉方式夾取圓柱	52
第五章 結論	59
參考文獻	60

圖目錄

圖1 將物件分割成有限個元素	3
圖2 圖1中之元素j 及其上一點P.	4
圖3 ξ-η座標系	4
圖4 兩物體在接觸狀態(已變形)	11
圖5 兩物體在接觸狀態	12
圖6 圓柱(或圓球)與平面接觸	20
圖7 圓柱(或圓球)接觸分析，分布力q之合力為F/2.	21
圖8 圓柱(或圓球)與平面接觸網格圖	22
圖9 圓柱與平面接觸應力分布圖	23
圖10 圓柱所受外力與接觸寬度關係圖	24
圖11 圓球與平面接觸應力分布圖	27
圖12 圓球所受外力與接觸區域半徑關係	28
圖13 手指平移夾取物件示意圖	29
圖14 手指夾取圓柱網格圖	31
圖15 剛性手指平移挾取圓柱位移u	32
圖16 剛性手指平移挾取圓柱應力x 33
圖17 剛性手指平移挾取圓柱應力y 34
圖18 彈性手指夾取圓柱位移u 36
圖19 彈性手指夾取圓柱應力x 37
圖20 彈性手指夾取圓柱應力y 38
圖21 夾緊位移x 與接觸區域內應力x 最大值關係圖 39
圖22 夾緊位移x 與接觸區域a 關係圖 40
圖23 傾斜θ 角度的手指平移夾取物件示意圖 42
圖24 傾斜30°手指平移夾取圓柱網格圖 43
圖25 手指傾斜45°夾取圓柱網格圖 44
圖26 不同角度手指平移夾取圓柱時夾緊量與正向力關係圖 45
圖27 傾斜0°手指夾取不同材料之圓柱時夾緊量與正向力關係圖 47
圖28 傾斜30°手指夾取不同材料圓柱時夾緊量與正向力關係圖 48
圖29 傾斜45°手指夾取不同材料圓柱時夾緊量與正向力關係圖 49
圖30 手指挾取鋁製圓柱時夾緊位移與圓柱最大von Mises 應力關係圖 51
圖31 手指旋轉一微小角度 54
圖32 手指旋轉示意圖 55
圖33 機械手指傾斜θ 角旋轉夾持物件示意圖 58

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