Passive and active closures by constraining mechanisms

This paper provides a unified theoretical framework for grasping and manipulation by robotic grippers and hands as well as for fixing works by fixtures and vises. The concept of passive closure and active closure for general constraining mechanisms is introduced. Passive closure is further classified into passive form closure and passive force closure. Conditions for these closures to hold are studied. Several new conditions are given for passive force closure. Especially, it is shown that, for the existence of passive force closure by frictionless point contacts, there must be at least six fixed contact points in the case of three dimensional space, and at least three in the case of two dimensional space. Conditions for other closures, which are mostly slight modifications of known results, are also included to show that they are naturally located in proper positions in the proposed unified framework