80 The Bennett linkage
Combining Eqs (5.3) to (5.6) gives
.
(5.7)
This is a non- linear equation and many solutions may exist. By observation, two solutions can be immediately determined, which are
(5.8)
and
(5.9)
Similar analysis can be applied to Bennett linkages around links BC, CD
and DA, see in Figure 5.2(a). Based on solutions (5.8) and (5.9), we can
conclude that twists of Bennett linkages 3, 4 and 5 should therefore satisfy
or
(5.10)
twists of Bennett linkages 5, 6 and 7 should satisfy
or
(5.11)
and twists of Bennett linkages 7, 8 and 1 should satisfy
or
(5.12)
Combining four sets of solutions Eqs (5.8) to (5.12), two common solutions which enable the network in Figure 5.2(a) to become mobile, are
obtained:
(5.13)
and
(5.14)