Cea(bC8b + a) sea(bsebCab sbSab)
sea(bCBb + a) + C8a(bSbbCab sbSab)
bSObSab + sbCab + da
1
(2.5)*
where the vector CO or its components CR (k= x, y and z)
denote the coordinates of point C with respect to the local
fixed coordinate system ox0Y0z0; the vector C3 denotes the
location of point C with respect to the coordinate system
Cx3Y3Z3; ea and eb are the rotation angles from xo to xl and
from x2 to x3, respectively; da is the translation of
cylindric joint A along the fixed axis z1 form the origin of
the local fixed coordinate system ox0YOz0; a and b are the
perpendicular distance between successive joint axes zl, z2
and z3, respectively; sb is the offset along the z2 axis; ab
is the twist angle between the axes zI and z2, and Ai, i = 1
and 2, represent the Hartenberg and Denavit [39] 4 x 4
homogeneous transformation matrices which relate the
kinematic properties of link i to link i-i and can be
derived as
COi -SeiCai SeiSai aiC8i
SEi CeiCai -ceiSai aiSEi
Ai = (2.6)
0 Sai Cai di
0 0 0 1
C can also be obtained by using the method in [44],
which is presented in Appendix A.1.