164
[68a] = [wa]6t, (5.29)
where &t denotes a very short period of time.
Then we have
w6t[$] = [J][wa]6t (5.30)
or
(8[$] = [J][68a] (5.31)
where 6e denotes the minor angular displacement of the
platform about its axis due to the error input, 66a, of the
actuators.
The movement of the platform is generally specified by
the linear displacement of the center, H, and the angular
displacements of the hand coordinate system embedded in the
platform about the axes of the global coordinate system
OXYZ. In order to calculate the components of the minor
movements of the platform, the motion screws of the platform
may be expressed as
m$ = w(s + So] = t[S + e(r x S + hS)] (5.32)
where r is the global position vector of an arbitrary point
on the axis of the motion screw of the platform, e denotes
the dual part of a vector and h is the pitch; this screw is
shown in Fig. 5.6.
Now, we have
h = S So
(5.33)