102 The Bennett linkage
Finally, it should be pointed out that normally, for a given α, there are
two sets of θ 1e and θ 1f , in which configuration of the corresponding alternative form of Bennett linkage is square. However, when
or
,
there is only one solution,
and
.
In this case,
,
.
5.5 Physical model of alternative form of Bennett linkage
According to Crawford et al. (1973), for a close loop consisting of n links
with identical cross- section, the cross- section of the whole assembly in the
folded configuration should be n regular polygon if it can be packaged
most compactly. So for the alternative form of Bennett linkage, each link
could be made of four rods with square cross- section. The cross- section of
the folded linkage will then be a square. A model is shown in Figure 5.15,
which is defined by three design parameters: corner angle ω, tilting angle λ
and rod length L. The relationship linking the design parameters to the
geometric parameters of the alternative form of the Bennett linkage is
derived next.
Figure 5.15 The alternative form of Bennett linkage made from square crosssection bars in the deployed and folded configurations.