Force Closure

• Also called: force-closure grasp
• Category: Planning & manipulation › Manipulation
• Tags: grasping, contact, statics, manipulation, grasp-quality

A grasp property: the contacts, using friction, can together apply a wrench that resists any external force and torque on the held object.

Definition

A grasp has force closure when the forces its contacts are able to apply can balance any external wrench on the object, that is, any combination of force and torque. Each contact can only push, not pull, and with Coulomb friction it can apply forces anywhere inside its friction cone. Mapping those cone forces into the object's wrench space gives a set of contact wrenches; the grasp is force closure when nonnegative combinations of them span the whole space (three dimensions for a planar object, six for a spatial one). An equivalent test is that the origin of wrench space lies strictly inside the convex hull of the contact wrenches.

Force closure differs from form closure, in which the object is immobilized by the geometry of frictionless contacts alone. Form closure needs more contacts (at least four for a planar object and seven for a spatial one) but does not depend on friction. Force closure typically needs fewer contacts because friction adds tangential force, but it relies on the hand actively squeezing: internal forces between the fingers press the contacts into their friction cones. A classic result for planar grasps, due to Nguyen (1988), is that two frictional contacts give force closure when the line joining them lies inside both friction cones. In 3D, two point contacts with friction cannot resist torque about that line, so either soft-finger contacts, which add torsional friction, or a third contact are needed.

Force closure is a yes-or-no property, so grasp planners usually pair it with a quality measure. The best known, from Ferrari and Canny (1992), is the radius of the largest ball around the origin that fits inside the convex hull of contact wrenches: a larger radius means the worst-case disturbance the grasp can resist, per unit of finger force, is larger. Analytic grasp planners and many learned grasp pipelines use force closure or such metrics to label training data, even when the deployed system never computes them online.

Why it matters

Force closure is the standard formal answer to the question of whether a grasp will hold. It explains why finger placement, friction and squeezing force all matter, and it underpins grasp quality metrics, simulated grasp labels and the analysis of multi-fingered hands.

Key applications

• Labeling grasps for training learned grasp detectors
• Analytic grasp planning for parallel-jaw and multi-fingered hands
• Grasp quality metrics in wrench space
• Fixture and workholding design
• Checking in-hand regrasps and finger gaits for stability

In practice

A team building a dataset for a learned grasp detector samples thousands of candidate parallel-jaw grasps on object meshes. For each candidate they find the two contact points and their surface normals, approximate each friction cone with eight edges using an assumed friction coefficient of about 0.5, and assemble the resulting contact wrenches with soft-finger torsional terms. A linear program or convex-hull test checks whether the origin lies strictly inside the wrench set, and the Ferrari-Canny metric ranks the passing grasps. Because the friction coefficient is uncertain, they repeat the test with a lower coefficient and keep only grasps that stay force closure, which removes candidates near the edge of the friction cone.

Common misconceptions

• Force closure means the grasp cannot fail — it says the contacts could resist any wrench given enough squeezing force; actuator limits, slip and object deformation still matter
• Force closure and form closure are the same — form closure comes from geometry alone without friction, while force closure depends on friction and active squeezing
• Two opposing fingers always give force closure in 3D — two point contacts cannot resist rotation about the line between them unless the contact patches provide torsional friction
• A force-closure grasp is a good grasp — force closure is binary; quality metrics are needed to tell a marginal grasp from a robust one

Who should know this

• Grasp planning and manipulation researchers
• Engineers designing grippers and robot hands
• Developers generating grasp datasets in simulation
• Robotics students studying contact mechanics

Related technologies

• Grasp Wrench Space
• Ferrari-Canny Metric
• Friction Cone Linearization
• Dex-Net
• GraspIt!

Related terms

• Wrench
• Friction Cone
• Antipodal Grasp
• Grasp Planning
• Coulomb Friction
• Dexterous Manipulation

Related projects

• LeRobot: HuggingFace ML library for real-world robotics in PyTorch
• Isaac Lab: NVIDIA robot learning framework: one task API across Newton, PhysX and Isaac Sim
• NVIDIA Isaac GR00T: NVIDIA open foundation model for humanoid robot reasoning and skills
• OpenVLA: 7B-parameter Vision-Language-Action model for robotic manipulation
• Drake: MIT robotics toolbox for model-based dynamics, optimization, and control system design
• OpenArm: 7DOF humanoid arm for physical AI research in contact-rich environments

Videos

• Modern Robotics, Chapter 12.2.3: Force Closure: Northwestern Robotics