163
rsllT i110or,1 0 0 0 0 0 1
r21T 0 $210rS21 0 0 0 0 W21
S12 2a 120r12 T 0 o12
r22T 0 0 0 S220or22 0 0 W22
r113T 0 0 0 0 1130r113 0 f13
r 23T a 0 0 0 0 s230ri23 .w23J
(5.26)
or
[Al [$] = [B][wa] (5.27)
where the components of [Wa] = (Hll, w21', 12, w22' "13,
w23 T are the intensities of the motion screws of the
actuators, and for the linear actuators of the Ai joints,
"21 = v21,' 22 = v22 and 23 23-
If [A] is nonsingular, we can write
w[$] = [A]-l[B][wa] = [J][Wa] (5.28)
where [J] = [A]-1[B] may be called a Jacobian matrix.
5.6 Mechanical Error Analysis of the Platform
The term of mechanical error defined here means the
minor movements of the platform due to the inaccuracies in
displacements (rotation and translation) of the actuators
for a certain specified position and orientation of the
platform. Let the errors of the displacements of the
actuators, [86a], be expressed as