92 The Bennett linkage
a 4R loops denoted by even number subscripts alongside the guidelines,
e.g. I 2 , I 4 and I 6 , can always be connected by additional Bennett linkages of the same type but at a different layer forming a double- layer
assembly, see Figure 5.10(b);
b 4R loops in the other diagonal direction, e.g. I 1 , I 3 , I 5 and I 7 , can also
be connected provided that either
• twists of two smaller loops must be identical to those of the larger
loop that encircle them, e.g. to connect I 3 and I 5 , both of them
must be identical to I 4 , see Figure 5.10(c), or
• twists of two smaller loops are zero, e.g. to connect I 3 and I 5 , the
twists of I 3 and I 5 are 0, see Figure 5.10(d).
Note that here we say that two Bennett linkages are identical if both linkages have the same twists whereas the link lengths, obtainable from Eq.
(2.24), may be different.
The assemblies formed using the rules above will have double layers as
the bridging 4R loops are at a level different from that of the single- layer
assembly.
The solutions for forming double- layer mobile networks can be
extended to build multi- layer networks by repetition. For example, consider a single unit shown in Figure 5.9(c), If the bridging links at the upper
layer are extended, a larger Bennett linkage at a higher level can be connected to it. The process can be repeated, resulting in the formation of a
mobile multi- layer mast, see Figure 5.11(a). The same process can be
applied laterally. Figure 5.11(b) shows another possible lateral arrangement. Each of the 4R loops, including the ones whose sides have different
shades, is a Bennett linkage. Figure 5.12(a) shows the deployment of a
physical model of a multi- layer mobile assembly in which links are made
of Al- alloy rods.
(a)
(b)
Figure 5.11 (a) A multi-layer mast and (b) another possible layout for assembly of
Bennett linkages.
a 4R loops denoted by even number subscripts alongside the guidelines,
e.g. I 2 , I 4 and I 6 , can always be connected by additional Bennett linkages of the same type but at a different layer forming a double- layer
assembly, see Figure 5.10(b);
b 4R loops in the other diagonal direction, e.g. I 1 , I 3 , I 5 and I 7 , can also
be connected provided that either
• twists of two smaller loops must be identical to those of the larger
loop that encircle them, e.g. to connect I 3 and I 5 , both of them
must be identical to I 4 , see Figure 5.10(c), or
• twists of two smaller loops are zero, e.g. to connect I 3 and I 5 , the
twists of I 3 and I 5 are 0, see Figure 5.10(d).
Note that here we say that two Bennett linkages are identical if both linkages have the same twists whereas the link lengths, obtainable from Eq.
(2.24), may be different.
The assemblies formed using the rules above will have double layers as
the bridging 4R loops are at a level different from that of the single- layer
assembly.
The solutions for forming double- layer mobile networks can be
extended to build multi- layer networks by repetition. For example, consider a single unit shown in Figure 5.9(c), If the bridging links at the upper
layer are extended, a larger Bennett linkage at a higher level can be connected to it. The process can be repeated, resulting in the formation of a
mobile multi- layer mast, see Figure 5.11(a). The same process can be
applied laterally. Figure 5.11(b) shows another possible lateral arrangement. Each of the 4R loops, including the ones whose sides have different
shades, is a Bennett linkage. Figure 5.12(a) shows the deployment of a
physical model of a multi- layer mobile assembly in which links are made
of Al- alloy rods.
(a)
(b)
Figure 5.11 (a) A multi-layer mast and (b) another possible layout for assembly of
Bennett linkages.