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In this mechanism, we wish to determine omega 4 given omega 2.
We have already determined the location of centro 12. Centro 13 is not yet determined. Centro 14 is already determined.
Centro 23 is at infinity.
34 is here. That point.
We have to determine centro 24. 23 and 34 are already determined.
This point is point A in 2. There is also A in 3 and an A in body 4. They are coincident points.
A3 and A4 are sliding along body 2.
By Kennedy's theorem, we can determine the location of 13 and 24.
12 and 23 can give 13.
12 and 23 are along this line where we must be able to locate 13.
With 14 and 34, we can also locate 13.
That is centro 13.
The other one.
Centro 24: We can determine it with 12 and 14.
It must be along this line.
We can also determine 24 from 23 and 34.
Here, there is an intersection. And this is 24.
We can go now to the analysis of velocity. We can look at it this way.
The velocity of this point in 2 is given by this vector.
Velocity of A on 2.
The velocity of A on 4, to be given by the velocity vector perpendicular to this,
must have a certain magnitude which can be defined by
this vector, with this as the sliding velocity of A on 4 with respect to A on 2. This is the sliding velocity.
The velocity of A on 4 is this vector.
Again, this is the velocity of A on 2.
This is rotating.
And this is the velocity of A on 4.
This is the velocity of sliding of body 3 on 2.
By way of this centro (24), we can also do the same determination of velocity of 3 on 4.
If we make this arc (with centro 12 as center) passing through A2;
and transfer this velocity vector here;
that velocity vector is transferred here;
we can make this proportionality line (from centro 12) to determine the velocity of 24.
24 is very much a part of 2 and also a part of link 4.
24 is a part in body 4, so that we can also make this arc (with centro 14 as center).
From this point, we can make a proportionality line,
and by the proportinality line, we can determine the velocity of A on 4.
They may be some mistakes in the graphical method (since free hand was used in the drawing), but necessarily, the velocity of A before must be equal to velocity.
This is performed here, to determine the velocity of 24 knowing this velocity here.
And knowing this velocity, we were able to determine the magnitude of this velocity (centro 24),
which must be actually equal to the velocity of A on 4.
Omega 4 can be determined by dividing the velocity of A on 4 by the distance between centro 14 and 34.