The gradient of FEix can be expressed as follow:
VFEiX = [0, JFEiX/3Y,, 3FEix/3Zm]T (4.32)
and points toward the outside of the boundary.
Let HiC and HiN be the points on the line of the
gradient such that the distance from these two points to
the boundary is L (the same as CiH), and the sense of CiHic
is opposite to that of the gradient and the sense of CiHiN
is the same as that of gradient. It is seen that when the
center H takes the position of HiC, the platform reaches a
limiting position in the direction of the gradient with
complete rotatability about H, provided we disregard link
interference and the constraints imposed by the other two
subchains. This means that the locus of points HiC
constitutes the external boundary of the CRSW with the
platform remaining in the given plane. Similarly, one can
see that the locus of points HiN constitutes the
intersection of the NRSS with the plane.
The coordinates of the points HiC and HiN when H is on
the plane can be expressed by Eq. (4.5) and (4.6) with X =
d. The simultaneous solution of Eqs. (4.5) and (4.29),
therefore, represents the intersection of the external
boundary of the CRSW with the plane X = d, and the
simultaneous solution of Eqs. (4.6) and (4.29) represents
the intersection of the NRSS with the plane X = d. Having
the equations of the intersection lines of the boundaries of