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write Eqs. (4.21) (4.23) for the NRSS (NonRotatability
SubSurface) directly by referring to Eqs. (4.18 4.20) as
follows:
FSN1 = X2 + (Y + h)2 (a1 + bI + L)2 = 0 (4.21)
FSN2 = X2 + (-Y/2 + ,3Z/2 + h)2 (a2 + b2 + L)2 = 0
(4.22)
FSN3 = X2 + (-Y/2 /Z/2 + h)2 (a3 + b3 + L)2 = 0
(4.23)
where the subscripts S and N denote surface and
nonrotatability, respectively.
Then we can obtain the external boundaries of the CRW
of the manipulator by solving Eqs. (4.18) (4.20)
simultaneously. The PRW (Partial Rotatability Workspace)
can be obtained as the following inequalities are satisfied:
FECi(X, Y, Z) > 0 (4.24)
and
FSNi(X, Y, Z) < 0 (4.25)
where i = 1, 2 and 3.
The equations of the internal boundary of the CRSW of
subchains 1, 2, and 3, which can be derived in a similar
way, are expressed as follows:
FICI = X2 + (Y + h)2 (rli + L)2 > 0
(4.26)