Chapter 2. Prehension

Chapter 6 - During Contact 243
this will be considered here. The first has to do with the object
slipping from the grasp; the second has to do with counteracting
perturbations to the posture.
In terms of resistance to slipping, a stable grasp has three
necessary conditions (Fearing 1986):
1) The object must be in equilibrium (no net forces and torques). That
is to say,
where Fi are the force vectors acting on the object and ri are the
distance vectors from a point on the object to the location of force
application.
2) The direction of the applied forces must be within the cone of
friction, so that there is no slip at the fingers. As seen in Figure
6.14, a force applied to a surface generates a normal component, Fn
(due to surface stiffness), and a tangential component, Ft (due to
friction). As was mentioned in Section 6.1.1, the relationship
between these depends on surface properties of both the finger and
the object, and it is called the coefficient of friction, p, or
The arc-tangent of the coefficient of friction defines an angle, cp,
where
fJ = tan-lp (16)
The set of all vectors within twice this angle forms the cone of
friction. The applied force makes an angle a with respect to a
surface normal and as long as this angle is within this cone of
friction, there will be no slip of the fingertip along the edge of the
object.
3) It should be possible to increase the magnitude of the grasping force
to prevent any displacement due to an arbitrary applied force.
When the applied force is larger than the friction forces, it is