46 Planar double chain linkages
3.2.3 Double chains with non- intersecting elements
First consider a double chain linkage with four non- intersecting pairs as
shown in Figure 3.11. The assembly is constructed so that it meets the loop
parallelogram constraint. The loop parallelogram constraint gives
,
(3.16a)
and
.
(3.16b)
For the double chain shown in Figure 3.11 bringing A and D together will
enable the double chain to be closed. Hence,
.
(3.17)
Introducing complex number notations,
,
(3.18)
or
.
(3.19)
(a)
(b)
Figure 3.11 (a) Angulated beams forming a non-intersecting element and (b) a
double chain linkage with four non-intersecting pairs prior to closure.