The Bennett linkage 85
For given α, l 0 /a, r 0 /a vs deployed angle θ 1 curves can be plotted using Eqs
(5.18) and (5.22). Figure 5.7 shows such curves for α = π/3.
A couple of observations can be made from the diagram. The first is
when b/a = 1, i.e. the Bennett linkage is equilateral. The assembly folds in
two configurations which correspond to θ 1 = π, l 0 = 0 and, θ 1 = 0, r 0 = 0,
respectively. The deployment sequence, shown in Figure 5.8(a), starts from
a compact bundle when r 0 = 0, expands circumferentially to an intermediate arch profile and then folds flat with l 0 = 0. This makes it ideal as a frame
for expandable shelter. For assemblies made from non- equilateral Bennett
linkages, i.e. b/a ≠ 1, when θ changes from 0 to π, l 0 decreases whereas r 0
increases from 0 to a maximum value and then falls back to 0 again. This
leads to the second notable case when the twists are set to be
(5.23)
The assembly resumes a completely flat profile throughout folding and
expansion as shown in Figure 5.8(b).
(a)
(b)
Figure 5.7 (a) l 0 vs θ 1 and (b) r 0 /a vs θ 1 curves for a set of given b/a when α = π/3.