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14
six above-mentioned movements
concerning the chosen system of
coordinates connected to the
second link. However, the link
joined into a kinematic pair with
another link, imposes conditions
of constraint on relative
movement of links. It is obvious,
that the number of these
conditions of constraint can be
only an integer and should be less
than six. If the constraint number is equal to six, the links lose relative
mobility and kinematic pair becomes a rigid connection of parts. At the same
time the number of conditions of constraint cannot be less than one, in this
case links do not contact and, therefore, kinematic pair ceases to exist. It will
be two bodies in space moving independently one from each other.
“S” is used to designate the number of conditions of constraint.
51
≤
≤
S
(I.1)
Hence, the number of degrees of freedom (commonly designated by H)
of a kinematic pair link in relative movement can be expressed by the
following relation:
H=6 – S. (I.2)
It is obvious that
1≤ Н ≤ 5. (I.3)
"H" determines the quantity of possible movements, which can either be
independent from each other, or connected by some additional geometrical
dependencies imposing functional constraint between movements (for
example as in kinematic pair a screw−lead nut).
Let's consider for example, some kinematic pairs, for which the separate
elementary movements are not functionally connected with each other.
Sphere - plane (Fig. II.8). As one can see links may perform five
relative movements - three rotational and two translational.
RRRTT Н = 5 S=6 – H=1.
Such kinematic pairs, having one constraint (S =1), are called first class
pairs and are designated P
1
(five-mobile pair of higher degree).
The legend for such pairs in accordance with GOST 2770-68
is:
Z
X
Y
Fig. II.7.
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