This paper provides a unified theoretical framework for analytical characterization of grasping and manipulation capability of robotic grippers and hands as well as fixing capability of fixtures and vises. The concept of passive closure and active closure for general constraining mechanisms consisting of fixed and/or articulated constraining limbs is introduced. These concepts are useful for explicitly distinguishing the two kinds of capabilities of the constraining mechanism: Passive closure represents the ability of fixing devices and active closure represents the ability of manipulating devices. Passive closure is further classified into passive form closure and passive force closure. Passive form closure is essentially the same as Reuleaux’s classical form closure and passive force closure is a substantial generalization of classical force closure to the case where articulated constraining limbs exist. Conditions for these closures to hold are studied. After a brief review of conditions for passive form closure, several conditions for passive force closure are given. One outcome is that, under the assumption that the contact points are frictionless and the active contact points are independent, for the existence of passive force closure there must be at least six (three) fixed contact points and one active contact point in the case of three-dimensional (two-dimensional, respectively) space. Finally, a necessary and sufficient condition for active closure is given for the case of frictional point contacts by constraining limbs with enough degrees-of-freedom. This condition consists of a general positioning condition of contact points and the existence condition of nonzero internal force. This condition has a quite natural physical interpretation.

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