160
through the center of spherical joint Ci and intersects both
the axes of joints Ai and Bi. A numerical example is given
to illustrate how to obtain such reciprocal screws as
follow:
Numerical example. With the base arrangement of the
manipulator shown in Fig. 3.37 and the dimensions of the
first subchain given as follows:
al = 3, b1 = 2, sbl = 1, h = 1, abl = -90 and C=
[4.000, 0.000, 2.732]T,
one set of the four possible solutions can be obtained as
dl = 1, eal = 00 and 8bl = -60" (see Section 2.5.1).
Therefore, the position vectors of joints A1 and B1 with
respect to the global coordinate system OXYZ can be
calculated as
0.000
oAl = -1.000
1.000
Therefore, the motion
the global coordinate
51 = (0, 1, 0; -2.732,
161 = (0, 0, 1; 0,
and OBI =
3.000
-1.000
1.000
screws of the joints with respect to
system OXYZ system can be expressed as
0, 0)
0, 1)
0, 3)
2.732, 0)
0, 4)
-4, 0)