Chapter 2. Prehension

Chapter 6 - During Contact 247
the gradient VU I (o,o,o) must be zero (Equation 22). The grasp is
stable if and only if the potential function U(x,y,B) reaches a local
minimum. For this, the Hessian matrix HI po,o) must be positive
definite. This latter is true if and only if all its principal minors are
strickly greater than zero. Its first two principal minors are always
strictly positive, but there are two special cases for the third one. It is
strictly positive if the compliance center16 is at the common intersection
of the lines of action of the springs. It is also strictly positive if the
compliance center is such that the weighted sum of the virtual springs
is zero.
Nguyen (1987a) showed stable grasps in three dimensions using
soft finger contacts. While point contacts without friction were
modelled as one linear spring, soft finger contacts are modelled as four
springs. This system included three linear springs through the point
of contact that are oriented along the normal and along two tangential
directions to the surface contact, and one angular spring, with axis
going through the contact point that is oriented along the normal of the
contact surface. “With soft fingers, the larger the friction cone, the
more likely the grasp is force closure. This is why people tend to
grasp at sharp corners and edges (if parallel surfaces are not
available).” (Nguyen, 1987b, p. 241).
6.4 Force Application in Human Pad Opposition
6.4.1 Quantifying grip and load forces in pad
opposition
In an elegant series of experiments, Westling and Johansson have
investigated the force application in grasping (Johansson & Westling,
1990; Johansson & Westling, 1984b; Westling, 1986; Westling &
Johansson, 1984). Subjects grasped objects of varying weights (200,
400, or 800 grams) and surface textures (silk, suede, sandpaper)
using pad opposition between the index finger and the thumb. The
test object had force transducers placed as indicated in Figure 6.16,
providing measurement of grip forces for the thumb and index fingers,
and the load force (or vertical lifting force). An ultrasound transducer
and accelerometer measured object position and acceleration
respectively .
Manipulations of object weight affected both the load force and
l6The center of compliance is the point of rotation of the planar object.