134 The Bricard linkages
,
,
.
(6.15c)
Figure 6.23 shows the relationship of θ 2 vs θ 1 .
However, further analysis has uncovered that the linkage shown in
Figure 6.18 always has a bifurcation point as demonstrated in Figure 6.24
(Chen and You, 2009; Chen and Chai, 2011). For the 6R frame with
2l 1 ≤ l 2 and 0 ≤ μ ≤ π/2,
always holds because of the geometric relationship given by Eq. (6.13). By
analysing motion path, it is found that there is at least one bifurcation
between fully expanded and folded configurations.
Figure 6.23 The input–output curve for the Bricard linkage.
(a)
(b)
(c)
Figure 6.24 The bifurcation of a model frame. (a) Bifurcation point, (b) the configurations of the spherical 4R linkage in which the bottom left and top
right corner hinges are frozen and (c) configuration similar to (b) but
with other two hinges frozen.
,
,
.
(6.15c)
Figure 6.23 shows the relationship of θ 2 vs θ 1 .
However, further analysis has uncovered that the linkage shown in
Figure 6.18 always has a bifurcation point as demonstrated in Figure 6.24
(Chen and You, 2009; Chen and Chai, 2011). For the 6R frame with
2l 1 ≤ l 2 and 0 ≤ μ ≤ π/2,
always holds because of the geometric relationship given by Eq. (6.13). By
analysing motion path, it is found that there is at least one bifurcation
between fully expanded and folded configurations.
Figure 6.23 The input–output curve for the Bricard linkage.
(a)
(b)
(c)
Figure 6.24 The bifurcation of a model frame. (a) Bifurcation point, (b) the configurations of the spherical 4R linkage in which the bottom left and top
right corner hinges are frozen and (c) configuration similar to (b) but
with other two hinges frozen.