Extension of the Form-Closure Property to Underactuated Hands

The property of form-closure of a grasp, as generally defined in the literature, is based on the assumption that contact points between the hand and the object are fixed in space. However, this assumption is false when considering a grasp exerted by an underactuated hand, since, in this case, it is not possible to control the position of each phalanx independently. In spite of researchers' interest in studying form-closure, none of the available published work on this subject takes into consideration the particular kinematics of underactuated hands. Actually, there are few available tools to qualify or quantify the stability of a grasp exerted by an underactuated hand; thus, the design of underactuated hands mostly results from an intuitive approach. This paper aims to reduce this gap. A classification of underactuated hands is proposed, which is based on the expression of contact forces. This highlights the influence of nonbackdrivable mechanisms introduced in the transmission of the closing motion of the hand on the stability of the grasp. After demonstrating that the original definition of form-closure is not suitable for the underactuated grasps, a more general definition is formulated, which checks the stability of the assembly ``object + hand.'' Using this new definition, a geometric method is proposed for the analysis of first-order form-closure of an underactuated grasp, as well as a simple rule to design a hand capable of achieving first-order form-closed grasps. Finally, a method is proposed for the analysis of higher order form-closure of an underactuated grasp, which is based on a first-order model of the grasp.