Force closure

Resisting disturbances through contacts#

Each finger contact contributes a set of forces allowed by its friction cone. Those forces also create moments about the object. A grasp has force closure when positive combinations of its available contact wrenches span the full wrench space, as described in Modern Robotics.

This is stronger than holding an object against gravity in one orientation. A grasp may support a downward load while still allowing the object to rotate or escape under another disturbance.

How it differs from form closure#

Form closure blocks motion through geometry without depending on friction. Force closure allows frictional forces to contribute. In the frictionless point-contact model, force closure is equivalent to first-order form closure; with friction, fewer contacts can sometimes suffice.

A capability condition, not unlimited strength#

The mathematical test does not mean a real hand can resist arbitrarily large forces. Modern Robotics explicitly notes that finger actuators may be unable to generate the squeezing forces the test permits.

The contact model also matters. Two ideal point contacts on a spatial object cannot resist torque about the line joining them, while soft contact patches can supply additional torsional resistance. State friction and contact assumptions when reporting force closure.