123
FEi(Xm, Y,, Zm) 5 0 (4.1)
FIi(Xm, Y,, Z,) 0 (4.2)
Here the subscripts E and I denote respectively the external
and internal boundaries. For distinction of the coordinates
of the points on the boundaries of SWIP (SubWorkspace,
Infinitesimal Platform) from those of the points inside the
subworkspace of H, we use Xm, Ym and Zm to denote the
coordinates derived in Chapter 3 for infinitesimal platform,
and X, Y and Z are used in the following sections to denote
the coordinates when a finite size platform is considered.
The boundaries of the SWIP can then be respectively
expressed symbolically by the corresponding qualities as
FEi(Xm, Ym, Zm) = 0 (4.3)
Fi(Xm, Ym,, Zm) = 0 (4.4)
4.3 The Complete Rotatability Workspace (CRW) and
the Partial Rotatability Workspace (PRW)
The platform can rotate about point Ci describing a
whole sphere as the locus of point H, if we disregard link
interference and the constraints imposed by the other two
subchains, even when point Ci is already on the external
boundary of the i-th SWIP. This situation, with the finite
dimensions of the platform, is depicted in Fig. 4.2, where
Ci are at the vertices of an equilateral triangle with H at