On force and form closure for multiple finger grasps

This paper considers the relationship between force and form closure. Based on a previously developed mobility theory, the authors give precise definitions for 1st and 2nd order form closure for frictionless grasps. The authors also introduce the new concept of 2nd order force closure. The authors show for the case of frictionless contacts, a grasp is 1st order force closure if and only if it is 1st order form closure. The authors further show that a grasp is 2nd order force closure if and only if it is also 2nd order form closure.