The Bricard linkages 131
alternative form of the original linkage. By extending the hinge axes of the
six- bar frame, we are able to identify the corresponding links of the original linkage, Figure 6.20.
Because of symmetry of the 6R frame, we have
.
(6.9)
Since axes of joints 2 and 3 meet at point A and axes of joints 5 and 6
meet at point B,
.
(6.10)
Following the convention given by Beggs (1966), we can define axes x i and
z i in the original 6R linkage shown in Figure 6.21. Let x 3 at point A be perpendicular to both z 2 and z 3 and point out of the paper, and x 6 at point B
be perpendicular to axes z 5 and z 6 and also point out of the paper, as
shown in Figure 6.21. So the twists of the linkage are
,
,
(6.11a)
,
(6.11b)
and offsets
and
.
(6.12)
Figure 6.20 The 6R frame and its original linkage.