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A computational model of pinching a rigid 3D object with smooth geometry by a finger robot under rolling contact is presented. The object is pined at a fixed point in the inertial frame, but it can rotate freely around it. Dynamics of the finger-object system is integrated together with update equations of a moving frame at the contact point between a fingerend and an object. Normal curvatures are determined by geometrical structures but geodesic curvatures are determined by motion of the finger-object system. A control input is used to stabilize the object with smooth geometry. Numerical simulations are conducted to verify the effectiveness of the proposed model and control input.