Chapter 2. Prehension

276 THE PHASES OF PREHENSION
In impacting an object with fingers, recall the cone of friction17
(see inset, Figure 6.23). Slip will not occur at the fingers if the
direction of the applied force Fis within the cone of friction.
However, the object will move as a pushing force is applied, and the
question to determine is what kind of motion will occur ; e.g., will the
pencil rotate clockwise or counterclockwise? Assuming Coulomb
friction (recall equation 13), planar motions are either translations or
rotations about some instantaneouly motionless point18. Mason
(1985) constructed an algorithm as a way to predict the direction of
rotation in spite of the indeterminancies of the problem. The sense of
rotation can be predicted from knowing the limits of the cone of
friction Rr and R1 and the direction of the velocity of the pusher F.
These three vectors ‘vote’ on a clockwise or counterclockwise
rotation, depending on their relationships to the center of mass. If Rr
and R1 (irregardless of F) are to the left or right of the center of mass,
the object will rotate clockwise or counterclockwise, respectively. If
Rr and R1 disagree (i.e., the center of mass lies within the cone of
friction), then the sense of the rotation is based on F.
Suppose, for example, as seen in Figure 6.23, a right hand is
picking up a glass in pad opposition and suppose that VF2 makes
contact with the glass before VF1. Will the glass rotate into the grasp
or out of the grasp? The cone of friction is drawn about a normal to the
surface. Assuming that the center of mass of the glass is at the center
of the glass, then the center of mass will be within the cone of friction
no matter where the glass is touched by VF1. The sense of rotation
will depend on the direction at which the finger is moving at contact F.
The glass will rotate out of the grasp (Figure 6.23a) if this direction is
to the near side of the center of mass. If, instead, it is to the far side
(Figure 6.23c), the glass will rotate into VF1. If, however, it is
through the center of mass, the glass will not rotate, and translate
instead, moving towards VF1.
An interesting analytic example of manipulation is seen in baton
twirling. Fearing (1986) showed how a third finger can be used to
twirl the pencil like a baton, in relocating the fingers in a dynamic,
serial tripod configuration using finger contacts modelled as point
contacts with friction. Forces applied within the cone of friction will
17See section 6.3.3 and Figure 6.14.
18During translation, a system of frictional forces reduces to a single force through
a point whose position is independent of the direction and velocity of motion and
whose direction is opposite to the direction of motion (no analagous reduction
occurs for rotation).