Layouts of spatial motion structures 141
can then be formed, Figure 7.4(b). Next, let us examine kinematically the
mobility of such an assembly.
Let
,
,
,
,
,
,
,
,
(7.1)
where k s is a constant with 0 < k s < 1. All of squares in Figure 7.4(b) have
zero offsets. Hence, they satisfy the geometric conditions for the Bennett
linkage, i.e. Eqs (2.23)–(2.25).
Considering Bennett linkages 1, 2, 3 and 4, there are
,
(7.2a)
,
(7.2b)
,
(7.2c)
and
.
(7.2d)
Combining Eqs (7.2a) and (7.2c), as well as (7.2b) and (7.2d), respectively,
gives
,
(7.3a)
can then be formed, Figure 7.4(b). Next, let us examine kinematically the
mobility of such an assembly.
Let
,
,
,
,
,
,
,
,
(7.1)
where k s is a constant with 0 < k s < 1. All of squares in Figure 7.4(b) have
zero offsets. Hence, they satisfy the geometric conditions for the Bennett
linkage, i.e. Eqs (2.23)–(2.25).
Considering Bennett linkages 1, 2, 3 and 4, there are
,
(7.2a)
,
(7.2b)
,
(7.2c)
and
.
(7.2d)
Combining Eqs (7.2a) and (7.2c), as well as (7.2b) and (7.2d), respectively,
gives
,
(7.3a)