134
Y or Z of the fixed global system. All the points Ci are in
that same plane.
When the point Ci of subchain i is on the intersection
of the boundary of the SWIP with the plane, which plane is,
for example, perpendicular to the X axis as shown in Fig.
4.5, the platform can rotate in the plane about the axis
through H and normal to the plane in a portion of a circle.
The platform can rotate only in such a direction that the
point Ci moves inside the SWIP.
In general, the intersection of the SWIP with the plane
are lines. They can be symbolically expressed as
FEix(Xm Ym, Zm) = 0 (4.29)
and
Xm = d (4.30)
where the superscript x denotes the normal of the plane, the
subscript E implies the external boundary, d is a constant
distance from the origin and i = 1, 2 and 3. Since the
procedures of the analysis for the external and internal
boundaries are similar to each other, we discuss only
positions on the external boundary in the following section.
The workspace inside the external boundary is expressed by
inequality (one for each subchain):
FEix(Xm, Ym, Z,) < 0, i = 1, 2, 3
(4.31)