Engineering Mechanics

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(^458) „„„„„ A Textbook of Engineering Mechanics
22.2.MOTION OF A RIGID LINK
Consider a rigid link AB, which moves from its initial position AB to its final position A 1 B 1.
It will be interesting to know that the link neither has, wholly a motion of translation nor wholly
rotational, but a combination of the two. But the point B moves faster than the point A as shown in
Fig. 22.1. (a).
Fig. 22.1. Motion of a rigid link AB to A 1 B 1.
If we split up the motion of the link AB, we shall find that the link has first motion of translation
from AB to A 1 B′, and then the motion of rotation about A 1 , till it occupies the final position A 1 B 1 as
shown in Fig. 22.1. (b).
The motion of link AB may also be considered to be first motion of rotation from AB to AB′
about A, and then motion of translation from AB′ to A 1 B 1 as shown in Fig. 22.1 (c)
Such a motion of AB to A 1 B 1 is an excellent example of combined motion of rotatiton and
translation ; it being immaterial, whether the motion of rotation takes place first, or the motion of
translation takes first.
22.3. INSTANTANEOUS CENTRE
We have discussed in the last article the motion of a
rigid link as an example of combined motion of rotation and
translation. Now consider the motion of link from AB to
A 1 B 1 as shown in fig. 22.2. In the last article, we had split up
such a motion for the sake of analysis into the following two
parts :



  1. Motion of rotation, and

  2. Motion of translation.
    Both these motions were considered to take place one
    after the other. But in actual practice the motion of link AB
    is so gradual, that it is difficult to see the two separate
    motions. But we see a smooth motion of the link, though
    the point B moves faster than the point A.
    This combined motion of rotation and translation, may
    be assumed to be a motion of pure rotation about some centre.
    As the position of link AB goes on changing, therefore the
    centre, about which the motion of rotation is assumed to take
    place, also goes on changing. Such a centre, which goes on
    changing, from one instant to another, is known as
    instantaneous centre. The locus of all such instantaneous
    centres, is known as centrode. The position of instantaneous
    centre may be located graphically as discussed below :


Fig. 22.2. Instantaneous centre.
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