本研究利用赫氏接觸原理以及力平衡方程式，推導出機械手臂抓取球形物件時的接觸力與夾緊位移關係式。只要給定手指的夾緊位移，即可代入關係式求出手指與物件間的正向及側向(摩擦)接觸力。此研究是針對二至四指抓取，在二指抓取方面，手指可以模擬成剛體或是可變形體，夾緊方式也可以是平移夾緊或是旋轉夾緊，另針對三指與四指抓取，手指模擬成剛體，夾緊系統為左右對稱，此研究皆以解析方式求出以上各情況的閉合形式解。

In this research Hertz contact theory and equilibrium equations are used to derive relations between contact forces and tightening displacements for a robot grasping a spherical object. By substituting a tightening displacement of robot fingers into these relations, the corresponding normal and tangential (frictional) components of fingers-to-object contact forces may be determined. For cases of two-fingered grasping, the fingers may be elastic or rigid, and tightening displacements may be linear or angular. As for three and four fingered grasping, the cases with rigid fingers are treated. Closed form solutions are obtained in all these cases.

中文摘要 I
英文摘要 II
目錄 III
圖目錄 V
符號說明 VII
第一章  緒論 1
1-1  研究動機與文獻回顧 1
1-2  Sinha and Abel所提出靜態模式之探討 3
1-3  赫氏接觸理論 8
1-4  研究架構 10
第二章  兩指平移挾持之探討 12
2-1  兩彈性指之平移挾持 12
2-2  兩指平移挾持之特例探討 19
2-3  兩指平移挾持之結果探討 21
第三章  兩指旋轉挾持之探討 23
3-1  兩彈性指之旋轉挾持 23
3-2  兩指旋轉挾持之特例探討 28
3-3  兩指旋轉挾持之結果探討 30
第四章  多剛性指圍繞抓取之探討 32
4-1  三剛性指之圍繞抓取 32
4-2  四剛性指之圍繞抓取 37
4-3  多剛性指圍繞抓取之結果探討 42
第五章  結論與未來展望 44
參考文獻 46

圖目錄
圖1  物體與手指接觸變形前示意圖[17] 51
圖2  圓盤受三指挾持示意圖[17] 52
圖3  一個立方體受三指挾持示意圖[17] 53
圖4  兩指平移挾持示意圖 54
圖5  兩指平移挾持不同角度時夾緊量與正向力關係圖(Es=Ef，I/(Rd3)=1) 55
圖6  兩指平移挾持不同材料時夾緊量與正向力關係圖(alpha=5度，I/(Rd3)=1) 56
圖7  兩指平移挾持不同慣性矩時夾緊量與正向力關係圖(alpha=5度，Es=Ef) 57
圖8  兩指平移挾持不同角度時夾緊量與正向力關係圖(I→∞，Es=Ef) 58
圖9  兩指平移挾持不同角度時夾緊量與正向力關係圖(Ef→∞) 59
圖10  兩指平移挾持不同角度時夾緊量與正向力關係圖(Es→∞) 60
圖11  兩指旋轉挾持示意圖 61
圖12  兩指旋轉挾持不同角度時夾緊量與正向力關係圖(Es=Ef，I/(Rd3)=1) 62
圖13  兩指旋轉挾持不同材料時夾緊量與正向力關係圖(alpha=5度，I/(Rd3)=1) 63
圖14  兩指旋轉挾持不同慣性矩時夾緊量與正向力關係圖(alpha=5度，Es=Ef) 64
圖15  兩指旋轉挾持不同角度時夾緊量與正向力關係圖(I→∞，Es=Ef) 65
圖16  兩指旋轉挾持不同角度時夾緊量與正向力關係圖(Ef→∞) 66
圖17  兩指旋轉挾持不同角度時夾緊量與正向力關係圖(Es→∞) 67
圖18  三指圍繞抓取示意圖 68
圖19  三指圍繞抓取不同角度時夾緊量與正向力N關係圖 69
圖20  三指圍繞抓取不同角度時夾緊量與正向力N3關係圖 70
圖21  四指圍繞抓取示意圖 71
圖22  四指圍繞抓取不同角度時夾緊量與正向力關係圖 72

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