equivalent to three revolute joints with three mutually
perpendicular concurrent axes. Since the orientation and
position of the hand, H, is given, we thus can obtain the
following equations with the assumption that z3 is parallel
to z4:
nx Sx ax PX
H n s ay Py
nz Sz az Pz
0 0 0 1
C8a -SOa 0 aC@a Cebl 0 S8bl 0
Sea C8a 0 aSea Sebl 0 -C8bl 0
0 0 1 da 0 1 0 0
0 0 0 1 0 0 0 1
C8b2 0 S8b2 0 Ceb3 -SOb3 0 bceb3
S8b2 0 -C8b2 0 Sb3 -C8b3 0 bSeb3
0 1 0 0 0 0 1 0
0 0 0 1 0 0 0 1
Cac -Sec 0 cC8c
SBe cec 0 cSec
(2.18)
0 0 1 sc
0 0 0 1
J
where components of the position (Px, Py and pz) and
orientation (nx, ny, nz, sx, Sy, Sz, ax, ay and az) of
system Hx4Y4z4 with respect to the local fixed coordinate
system oxOy0z0 are all specified; and 8bl, Ob2 and 8b3 are