n, r, s, 0 nx 0 ny2 + nf2 0
ny ry y 0 ny -nz -nxny 0
A = I
nz rz sz 0 nz ny -nxnz
0 0 0 1 0 0 0 1
J
Using the transformation of
X x xnx + z(ny2 + nz2)
Y y xny ynz znxny
Z z xnz + yny znxn,
1 1 1
the equation of the boundary of the SWIP originally
expressed with respect to the global system OXYZ can be
transformed to be expressed with respect to the new system
Oxyz. For example, Eq. (4.7) of the external boundary of
the SWIP of the first subchain can be transformed to be
expressed with respect to the new system as
FE1 = [Xmnx + Zm(ny2 + nz2)]2 + [Xmny Ymnz -
Zmnxnz + h]2 (al + bl)2 = 0 (4.45)
where Xm is a constant.
Eq. (4.45) represents the intersection of the boundary
with the given plane with respect to the new system Oxyz.
In the above equations the subscript m denotes that the