Form Closure

Immobilizing an object purely through the geometry of contact points, with no reliance on friction at all.

Form closure means a set of fixed constraints — fingers, jaws, locating pins, and so on — geometrically blocks every possible motion of an object: translating or rotating in any direction would push it directly into a constraint. When achieved with robot fingers, it's called a form-closure grasp. It doesn't depend on friction, which is what distinguishes it from force closure, where friction at the contact points is needed to resist forces in arbitrary directions. Lynch and Park's Modern Robotics gives the result that, under first-order analysis, a planar object needs at least 4 point contacts and a spatial object needs at least 7 (one more than the number of rigid-body degrees of freedom). Rotationally symmetric objects like disks and spheres can never achieve form closure no matter how many contact points are added, because they can always spin about their center. Form closure is common in fixture and jig design; robotic grasping usually can rely on friction and is more often analyzed in terms of force closure instead.

ExampleA square part sitting inside a flat fixture surrounded by locating pins can't move in any direction, even if its surface is oiled — that's form closure. Gripping the same part with a parallel jaw gripper instead relies on friction, which is force closure.

Also called

Geometric Closure, Form-Closure Grasp

Related

Force Closure · Grasping · Friction Cone · Grasp Quality Metric · Grasp Matrix · Contact Force

Sources

Lynch & Park, Modern Robotics（12.1.7 Form Closure, Theorem 12.6）