Form closure

Holding an object through geometry#

A fixture can block every available translation and rotation of a workpiece by placing contact surfaces around it. The object cannot move without penetrating a fixture surface, even if the contacts are treated as frictionless. Modern Robotics defines this kinematic immobilization as form closure.

This makes form closure useful when reasoning about fixturing. Simply resting an object in a shallow tray does not establish form closure, because lifting may remain possible.

First-order analysis has a specific scope#

A first-order test examines contact positions and surface normals. It checks whether any nonzero instantaneous rigid-body motion remains feasible. If that test establishes form closure, the more detailed geometry also constrains the object.

Failure of the first-order test is less conclusive: surface curvature can prevent a motion that appears possible when only contact normals are considered. The source's examples show why higher-order geometry can establish closure in cases missed by the simpler test.

Different from force closure#

Force closure asks whether allowable contact forces can oppose every external wrench direction and may rely on friction, as explained in Modern Robotics. Form closure is a geometric condition. Neither description alone gives the fixture's load capacity: real contacts, supporting structures, and actuators can deform or fail under sufficiently large loads.