144 Layouts of spatial motion structures
(7.5b)
Eqs (7.5a) and (7.5b) in fact correspond to two different assemblies. Eq.
(7.5a) indicates that the guidelines are along AC direction. The large Bennett
linkages do not overlap along the guidelines but they do along the diagonals
parallel to BD direction. On the other hand, Eq. (7.5b) points to that the
guidelines are along BD direction. Again the Bennett linkages overlap along
the guidelines, but not so along the diagonals parallel to AC direction.
Nevertheless the lengths of each Bennett linkage in both assemblies must
satisfy
(i = 1, 2, . . ., 8),
(7.6)
because of Eq. (2.24).
The expansion sequence of models of the two mobile assemblies in this
case are given Figures 7.7(a) and (b), respectively.
Case IV assemblies can also be regarded as a special case of Case III if
we consider that the length of a link can have negative value. Readers may
refer to Chen and You (2008b) for detailed discussion.
(a)
(b)
Figure 7.6 (a) A Case IV building block based on the Bennett linkage and (b)
assembly of blocks.