FIC2 = X2 + [-Y/2 + (j3/2)2 + h]2 (ri + L)2 > 0
(4.27)
FIC3 = X2 + [-Y/2 (.r/2)Z + h]2 (rri + L)2 > 0
(4.28)
where ryi denotes r2i or r3i (see Fig. 3.36) and i = 1, 2
and 3. Once the internal boundaries of the three CRSWs have
been obtained, the internal boundary of the CRW can be found
as the common areas of the three CRSWs.
Numerical example. The given parameters are as
follows:
al = a2 = a3 = 3", b1 = b2 = b3 = 3", h = 2", L = 1"
and X = 4"
In Fig. 4.4, a cross section of the workspace of the
manipulator is plotted on the plane OYZ, with X = 4. It is
noticed that the complete rotatability workspace is very
limited for this kind of manipulator, especially when the
size of the platform is not small compared to the length of
the links.
4.4 The Workspace of the Platform with
Given Orientation
The workspace of the platform with given orientation on
a plane is defined here as the reachable region on a plane
of the center H of the platform, while the platform keeps
moving with a given orientation. The simplest case is that
the plane is perpendicular to one of the coordinate axes, X,