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25
3. Five-link chain (Fig. II.23.). n = 4 P
4
= 0 P
5
= 5
205243
=
−
⋅
−
⋅
=W .
In order for such kinematic chain to become a mechanism, it is
necessary to initialize motion to its two links and only then all others receive
the certain movement.
Therefore, the number of motion freedom is a number of independent
parameters, for which it is necessary to preset values in order for a given KC
to be a mechanism.
One can see that Chebyshev's formula incorporates only P
4
and P
5
kinematic pairs and it means that any flat mechanism may be created by only
4th and 5th classes kinematic pairs.
Let's consider two more examples:
1. Articulated parallelogram (Fig. II.24.).
n = 4 P
4
= 0 P
5
= 6
006243 =
−
⋅
−
⋅
=
W .
According to Chebyshev`s formula
the given construction is motionless, but
this fact does not correspond to the reality,
as at equality of links 1, 3, 4 and pairwise
equality of О
1
О
2
and АВ, О
2
О
3
and ВС this
is an articulated parallelogram. Having
removed link 4 with its kinematic pairs B
and O
2
, movements of links 2 and 3 with
driver link 1 does not change at all.
n′ = 3 P
4
= 0 P
5
= 4. 14233
=
⋅
−
⋅
=
W .
Links which are not influenced by the driven links movement laws are
called
passive. Link 4 is passive.
2. Cam mechanism with translating pusher 3 and intermediate roller 2
(Fig. I.25.).
n =3 P
5
= 3 (R
1,4
, R
2,3
, T
3,4
) P
4
= 1 (RT
2,1
)
O
1
O
2
O
3
A B C
1
2
34
5
Fig. II.24.
O
1
O
2
O
3
A
B
C
1
2
3
4
5
O
1
O
2
A
B
C
1
2
3
4
5
Fig. II.22.
Fig. II.23.
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