90 The Bennett linkage
From Eqs (5.24) to (5.29), the following relationships among the twists
can be obtained:
,
(5.30)
,
(5.31)
(5.32)
and
.
(5.33)
Two sets of solutions emerge for Eqs (5.30) to (5.33) if α, β ≠ 0 or π, which are
(5.34)
and
(5.35)
When α, β ≠ 0 or π, the assembly becomes a series of overlapped planar
crossed isograms or planar parallelograms.
Denote the lengths of links for small Bennett linkages JBKS, PVND and
RSTV as a 3 , b 3 , a 7 , b 7 and a 0 , b 0 . Obviously, there must be
,
(5.36)
and
,
.
(5.37)
From Eqs (5.24) to (5.29), the following relationships among the twists
can be obtained:
,
(5.30)
,
(5.31)
(5.32)
and
.
(5.33)
Two sets of solutions emerge for Eqs (5.30) to (5.33) if α, β ≠ 0 or π, which are
(5.34)
and
(5.35)
When α, β ≠ 0 or π, the assembly becomes a series of overlapped planar
crossed isograms or planar parallelograms.
Denote the lengths of links for small Bennett linkages JBKS, PVND and
RSTV as a 3 , b 3 , a 7 , b 7 and a 0 , b 0 . Obviously, there must be
,
(5.36)
and
,
.
(5.37)