Successful grasping of objects with robotic hands is still considered a difficult task. One aspect of the grasping problem is the physical contact interaction between the robotic fingertips and the object. Friction at the fingertip contacts can improve grasp robustness, but frictional fingertips may be difficult to precisely place on the object's perimeter. This paper describes a novel fingertip design that can switch from frictionless to frictional modes. The transformation from frictionless to frictional contact is achieved passively by the finger force exerted on the object at the target grasp. A novel swivel mechanism ensures that the force magnitude required to switch friction states is independent on the grasped object's contact normal direction, thus ensuring robustness. Analysis of the displacement and eventual sliding of the fingertip contacts in response to external torque is presented, taking into account the amount of friction and the compliant behavior of the fingertip mechanism. Experiments validate the analytic model and demonstrate the fingertip's ability to change friction modes by the applied force magnitude irrespective of the contact normal direction. In line with the analytic model predictions, the experiments show that when converted to frictional contacts, the fingertips provide a more robust and hence secure grasp in the presence of external disturbances. The robustness of the fingertips is further validated by real-world demonstrations shown in an external video referenced in the paper.