The Bennett linkage 97
,
(5.48)
because in ΔAPC,
.
(5.49)
Comparing Eqs (5.44) with (5.49) yields
.
(5.50)
Similarly it can be obtained that
.
(5.51)
In ΔEPG, there is
,
(5.52)
and similarly
.
(5.53)
In general, ∠APC and ∠BQD cannot reach zero simultaneously. Substituting Eqs (5.52) and (5.53) into (5.43), noting that Eq. (5.43) holds only
when the linkage is fully folded, i.e. θ 1 = θ 1f and θ 2 = θ 2f , we have
,
(5.54a)
.
(5.54b)
The above equations show how the values of c and d are related to the
fully folded revolute angles θ 1f and θ 2f . Both values are negative, implying
that E, F, G and H must locate within lines PA, QB, PC and QD, respectively, rather than being at their extensions. In fact, c and d can be determined graphically, as Eq. (5.54) simply indicates that E and G should
move to a single point P, and F and H to Q, if the configuration shown
Figure 5.13(b) represents the fully folded configuration of linkage EFGH.
Having obtained the linkage corresponding to the most efficient folding
configuration, what is the form of Bennett linkage that covers the largest
,
(5.48)
because in ΔAPC,
.
(5.49)
Comparing Eqs (5.44) with (5.49) yields
.
(5.50)
Similarly it can be obtained that
.
(5.51)
In ΔEPG, there is
,
(5.52)
and similarly
.
(5.53)
In general, ∠APC and ∠BQD cannot reach zero simultaneously. Substituting Eqs (5.52) and (5.53) into (5.43), noting that Eq. (5.43) holds only
when the linkage is fully folded, i.e. θ 1 = θ 1f and θ 2 = θ 2f , we have
,
(5.54a)
.
(5.54b)
The above equations show how the values of c and d are related to the
fully folded revolute angles θ 1f and θ 2f . Both values are negative, implying
that E, F, G and H must locate within lines PA, QB, PC and QD, respectively, rather than being at their extensions. In fact, c and d can be determined graphically, as Eq. (5.54) simply indicates that E and G should
move to a single point P, and F and H to Q, if the configuration shown
Figure 5.13(b) represents the fully folded configuration of linkage EFGH.
Having obtained the linkage corresponding to the most efficient folding
configuration, what is the form of Bennett linkage that covers the largest