itself, it is important to design the manipulator so that
the condition ai + bi > L be satisfied. Otherwise, the
complete rotatability subworkspace does not exist. In fact,
to make the CRSW as large as possible, the length of CiH,
and thus the size of the platform, ought to be as small as
possible. Mathematically, the coordinates of the point on
the CRSW and the NRSS can be expressed respectively as
I FEi
Y = Ym L (4.5)
IVFEil
(CRSW)
and
X Xm
VFEi
Y = Ym + ------ L (4.6)
IVFEil
Z Z,
S(NRSS)
Generally the simultaneous solution of Eqs. (4.5) and
(4.3) represents the equation of the external boundary of
the CRSW, and the simultaneous solution of the Eqs. (4.6)
and (4.3) represents the equation of the NRSS, where both
are expressed in two of the three variables, Xm, Ym and Zm.
For obtaining the implicit equations of the boundaries of
the CRSW and NRSS correlating X, Y and Z, one can derive the
expressions of Xm, Y, and Zm in terms of X, Y and Z from
Eqs. (4.5) and (4.6), respectively, and then substitute the
resulting expressions into Eq. (4.3).