Force Closure

A grasp where friction at the contact points can resist an external force or torque in any direction, so the object can't be pulled free.

Force closure is the classic criterion in grasp mechanics for judging whether a grip is secure. Each contact point, thanks to friction, can apply force within a friction cone; stacking up all the force and torque (together called a wrench, 6 dimensions total) that every contact point can jointly produce, if the result covers the entire 6-dimensional space, the grasp is said to have force closure — no matter which direction an external push or twist comes from, the fingers can adjust their force to counteract it. Its counterpart is form closure, which pins the object down purely through contact geometry, without relying on friction, and usually needs more contact points. Force closure depends on the friction coefficient: the same fingertip positions might achieve it gripping a dry cardboard box but fail on an oily glass. It's the starting point for classical grasp planning and grasp quality metrics; for the planar case, a two-finger grasp achieves force closure exactly when the line connecting the two contact points falls inside both friction cones.

ExampleA two-finger gripper holding a block, with the two contact faces parallel and their normals pointing directly at each other (an antipodal grasp): as long as the line between the two points falls inside both friction cones, the block can't be pulled up or pushed sideways out of the grip — force closure, in the planar sense.

Related

Form Closure · Friction Cone · Wrench · Antipodal Grasp · Grasp Quality Metric · Grasp Matrix

Sources

Robotic Manipulation (MIT, Russ Tedrake) - Bin Picking: contact wrench cone, force closure