Chapter 2. Prehension

Chapter 6 - During Contact 237
of the fingerpad and one twisting motion of the finger (as if spinning
the basketball on the fingertip). These three twists define a twist
system at the point of contact. Another type of contact that more
closely models a human finger padl3 is the soft finger in contact with a
standard sized object such as a golf ball. A soft finger is similar to the
point contact with friction, but as seen in Figure 6.1 lc, this twist
system has only two twists (the two rotations around the radii of
curvature). This is because the fingerpad has a contact area large
enough to resist moments about the contact normal (no relative
spinning motion).
A set of forces and moments acting on an object acts as a single
force along a wrench axis and a moment exerted about the axis
(Salisbury, 1985). A wrench w = (fx,fy,fz,mx,my,mz) specifies the
forces and moments that can be resisted by the contact, where fx,fy,fz
are the components of net force, and mx,m ,mZ are the components of
net moment. A wrench system is the co Y lection of wrenches at the
point of contact. With the basketball example (Figure 6.1 lb), the
finger can resist forces along three axes: it can resist the force of the
basketball pushing against it along the contact normal, and it can resist
forces along the basketball surface tangential to the contact normal.
Since wrenches and twists are reciprocal to each other, four wrenches
are possible in the golf ball example (Figure 6.1 Id). These are the
three wrenches from the basketball example and in addition, the finger
can resist the moment about the contact normal.
Salisbury (1985) gives an example of two soft fingers in contact
with an object, as seen in Figure 6.12. Following Figure 6.1 1, each
finger has four wrenches resisting the external forces acting on the
object. The weight, acting at the object’s center of mass, is the
external force on the object. Wrench w 1 acts in a positive x direction.
Wrench wl and w2 are normal to the surface and are maintained
positive in order to assure contact with the object and to allow friction
to be active. Therefore, wrench wl=[ l,O,O,O,O,O]T and w2=
[-l,O,O,O,O,O]T (Wi are column vectors; the transpose of a column
vector, indicated by the T, is a row vector). Wrench w3 acts in a
positive y direction but also can resist a moment around z; the same is
true for w5. Wrenches w4 and w6 act in a positive z direction but also
13See Cutkosky and Wright (1986a) for a contact model that even more closely
resembles the human fingertip. It is a soft. curved finger which is a compliant
fingertip that conforms to the object surface and adheres slightly, while also
exhibiting the ability to roll, shifting the location of the contact point.