Chapter 2. Prehension

244 THE PHASES OF PREHENSION
necessary to increase the normal force at each finger to prevent
object displacement.
To restrain a rigid planar body from motion under conditions with
friction, two fingers are necessary. The fingertip forces F1 and F2
tone of friction
Figure 6.14 An applied force, F, has two components, a tangential
force, Ft, and a normal force, Fn. It makes an angle c1 with a
vector normal to the surface. The cone of friction is a geometric
interpretation of the relationship between the two contacting
surfaces.
applied by these two fingers to an object can be seen in Figure 6.15.
Each finger makes an angle aj with a normal to the surface, measured
in a counterclockwise sense. To prevent sliding, these angles must be
within the cone of friction, satisfying
4J > a, > -4J (17)
@'a?-@ (18)
For equilibrium, F1 and F2 must be colinear, of equal magnitude, and
opposite in sign to satisfy the first condition of a stable grasp. If they
are not colinear, rolling will occur. The two force angles are not
independent, and are related by
where y~ is the angle between the surface normals measured from the