Friction

Dry Friction — Coulomb Friction

One solid point-surface against another. Depending on the situation, Coulomb friction can:

• hold an object in equilibrium (static friction)
• slow down the motion (kinetic friction)

$F_f\le \mu F_n$

Phases of Coulomb Friction

Friction in Grasping: Point on Plane Contact

Three options for this:

• Frictionless: only normal force is transmitted (picking up from under)
• With Friction: Normal and tangential force is transmitted, but $F=\{f|||f_{\text{tangent}}||\le {\mu }_s||f_{\text{normal}}||,f_z{\ge }_0\}$
• Soft finger contact: Normal and tangential forces are transmitted, and torques are too, but $F=\{(f,{\tau }_{\text{normal}})|||f_{\text{tangent}}||\le {\mu }_s||f_{\text{normal}}||,f_z\ge 0,|{\tau }_{\text{normal}}|\le \gamma f_z\}$

Friction Cone

Each normal force is associated to a maximum tangential force (given by the static friction parameter). Geometrically, this gives form to a cone. The angle of the cone is given by ${\tan }^{-1}$

Defining a Grasp

Each contact point creates a force/wrench.

Grasp: the combination of all applied forces/wrenches.

A grasp set corresponds to all possible sets of wrenches that can be used to grasp the object. If the grasp space is large, the grasp is very robust to disturbances.