100 The Bennett linkage
α < arccos(1/3) or α > π – arccos(1/3), there is no pair of θ 1f and θ 1e satisfying
Eq. (5.63). Therefore the linkage is incapable of being flattened despite that
it can be folded up compactly, or vice versa.
The actual side length of the alternative form of the Bennett linkage, L,
can be obtained from Figure 5.13(b) as
.
(5.64)
Using c and d obtained from Eq. (5.54),
.
(5.65)
Denote by δ the angle between two adjacent sides of the alternative form
of the Bennett linkage in its flattened configuration when θ 1 = θ 1e and
θ 2 = θ 2e . Thus, δ = ∠FGH when S and T in Figure 5.13(c) become one point.
We have
.
Expressing FH and EG in terms of angles gives
Figure 5.14 θ 1f vs θ 1e for a set of given α.
α < arccos(1/3) or α > π – arccos(1/3), there is no pair of θ 1f and θ 1e satisfying
Eq. (5.63). Therefore the linkage is incapable of being flattened despite that
it can be folded up compactly, or vice versa.
The actual side length of the alternative form of the Bennett linkage, L,
can be obtained from Figure 5.13(b) as
.
(5.64)
Using c and d obtained from Eq. (5.54),
.
(5.65)
Denote by δ the angle between two adjacent sides of the alternative form
of the Bennett linkage in its flattened configuration when θ 1 = θ 1e and
θ 2 = θ 2e . Thus, δ = ∠FGH when S and T in Figure 5.13(c) become one point.
We have
.
Expressing FH and EG in terms of angles gives
Figure 5.14 θ 1f vs θ 1e for a set of given α.