and xi, yi and zi are unit vectors along the axes of
OixiYizi.
The coordinates of point Ci with respect to the system
oixiYizi can be used to determine the necessary joint
displacements by inverse kinematics, which is described in
detail in Chapter 2.5.1. It is noted that there are four
possible sets of solutions for a given location and
orientation of the hand. Each set of solutions corresponds
to a specific configuration of branches of the subchains.
Calculation of Jacobian and error analyses should be
performed in the same branch.
In Fig. 5.1, the position vectors OAi, OBi and unit
vectors oai and 0Zbi with respect to the global coordinate
system OXYZ can be calculated respectively by coordinate
transformation, and can be expressed as follows:
Ai = TiAi (5.7)
Bi = TiBi (5.8)
Oai = Tizai (5.9)
jbi = TiZbi (5.10)
5.3 Reciprocal Screws
A screw is defined by Ball [54] as a straight line with
which a definite linear magnitude termed the pitch is
associated. If (L, M, N; P, Q, R) are the PlUcker
coordinates, as shown in Fig. 5.2, of the screw axis, (L, M,