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.
