the three rotational variables of the spherical joint B,
which play no part in the manipulation of the platform.
Equation (2.18) can be rewritten as
HO = A1A2A3
where
C8a
A1 = Se
0
SO
S8bl
A2 = 0
0
C(b3
Seb3
A3 =
0
b3
S8b3
0
0
(2.19)
S 0
a 0
1
0
SObl
-CObl
0
0
-Seb3
-Cab3
0
0
aCOa
ac(a
aS8a
da
1
-Ir
0 (
0
0
1
bCeb3
bSSb3
0
1
SEb2
-CGb2
0
0
-SOc
C8c
0
0
cC9c
cSOc
sc
1
Postmultiplying both sides of Eq. (2.19) by A3-1A2-1
yields Eq. (2.20). Premultiplying both sides of Eq. (2.19)
by A1-I and then postmultiplying both sides by A3-1 yields
Eq. (2.21).
H0 -1^
HOA3-A2-1
A1-1HOA3-1
(2.20)
(2.21)