Chapter 2. Prehension

236 THE PHASES OF PREHENSION
A
Point Contac t with Friction
Twist System Wrench System
(motions) (forces and moments)
tl= (l,O,OPP,O)
t2= (O,l,OPP,O)
t3= (O,O,lPP,O)
wl= (1,0,0,0,0,0)
w = (0,1,0,0,0,0)
2
w3= (0,0,1,0,0,0)
c&-&4 2
Twist System
(motions)
tl= (l,O,OPP,O)
t2= (O,l,OPP,O)
w,
~ Wreich System
(forces and moments)
w = (lPP,O,O,O)
w' = (O,l~,O,O,O)
3 = (OP,l,O,O,O)
w4 = (OPP,l,O,O)
Figure 6.11 Two examples of contacts between two objects. A. A
point contact with friction allows relative rotational motions
about three twist axes B. A point contact with friction can resist
forces along three wrench axes C. A soft finger contact allows
relative rotational motions about two twist axes D. A soft finger
contact can resist forces along three wrench axes and it can resist a
moment about one wrench axis. A wrench system and a twist
system at a contact are reciprocal, or orthogonal, to each other
(from Salisbury, 1985; adapted by permission).
~=(T~,T~,T~,T~,Ts,T~),
where TI, T2, and T3 are infinitesimal
rotational motions about a twist axis and T4, T5, and T6 are
infinitesimal translations along a twist axis. A point contact with
friction is shown in Figure 6.1 la, where contacting a plane is used for
simplicity. The twists are two rotations around the radii of curvature