Planar double chain linkages 49
The conditions for it being closed loop linkage are identical to Eq. (3.10),
i.e.
.
(3.23)
Using the same approach utilising the complex number notation, we can
arrive at the mobility conditions as
,
(3.24a)
and
(3.24b)
as indicated in Figure 3.14(b). Hence, the double chain is mobile if Eqs
(3.24a) and (3.24b) are satisfied.
Other possible combinations for double chain assembly with five pairs
exist. For example, it can have two intersecting pairs followed by three
non- intersecting pairs, as shown in Figure 3.15. Let us now investigate the
mobility of this closed double chain.
To preserve the parallelogram constraint, the diagrams shown in Figure
13.15(b) can be drawn. There must be
,
(3.25a)
(a)
(b)
Figure 3.14 (a) A double chain with five pairs: three intersecting and two nonintersecting pairs, and (b) geometrical representation of its mobility
conditions.