Chapter 2. Prehension

Chapter 6 - During Contact 245
Figure 6.15 Two fingers applying point contact with friction
against an object. Each finger makes an angle ai with a normal to
the surface. For equilibrium, F1 and F2 must be colinear, of equal
magnitude, and opposite in sign.
normal at F2 to the normal of F1. Substituting, we get
Fearing (1986) mentions that the closer the sides are to parallel, the
smaller the coefficient of friction required to grasp them stably.
The second aspect of a stable grasp is counteracting perturbations;
i.e., determining whether the grasp posture will return to its initial
configuration after being disturbed by an external force or moment.
This could occur, for example, when a grasped hammer comes into
contact with a nail. Will the hammer stay in the grasp, or will it go
flying out of the hand? While modelling a three dimensional stable
grasp with soft fingers has been done (Nguyen, 1987a, b), a much
simpler model will be presented here for clarity.
Nguyen (1986b) models two-dimensional grasps using point
contacts without friction. A grasp consists of a set of fingers making
contact with the object (planar in this case). A finger Fi is modelled as
a virtual spring1s with linear stiffness ki. Ths stiffness can come from
the stiffness of the tendons, the viscoelastic properties of the fingers,
or even from using active stiffness to control the fingers. The finger
compresses when the object is moved away by (x,y,e) from its
equilibrium. Assuming that the object’s weight is perpendicular to the
1
15The potential energy of a spring is U = - b2.
2