Grashof's Rule and Linkage Classification:
The Four-Bar Linkage has been discussed in the previous posts. Taking it a little further we will examine and understand Grashof's Rule and how it transformed the concept of Four-Bar Linkages.
The Rule states that "When the sum of the length of the shortest and the longest Links is less than or equal to the sum of the lengths of the other two links, the shortest link can rotate through 360° with respect to the other links.
Take a look at the diagram, posted above, the chains fulfilling Grashof's rule is to the left and the one which does not is to the right. It is important to note that Grashof's Linkages are the most useful linkages in Engineering applications i.e. machine tools.
On the other hand Non-Grashof Linkage do not find use in many applications since such linkage can only give us movement restricted to oscillation only.
Grashof's Linkage: Dead Centre phases:
In the Fig., posted above, The limiting phases of the four-bar Grashof linkage are shown. In these cases the fourth link has been formed, as can be seen, by fixing one to the links adjacent to the shortest link. Refer to Fig. (a) the sum of the shortest and the longest links is less than the sum of the other two sides. The formation of the linkage in Fig.(b) is similar to that of Fig.(a) except that the length of the linkage CD has been increased.
In Fig.(b). you can see that the sum of the length of the shortest and the longest links is equal to the sum of the lengths of the other two sides.
Both the linkages, mentioned above, have drivers (link 2) that rotates to make the follower link(4) oscillate, as such both fall in the category of Crank-rocker mechanisms, but there is a lot of difference between the two.
The mechanism of Fig.(a) has a driver 'without' a dead-centre-phase (look at the position of pin at position A') whereas in Fib.(b) we have a dead-centre-phase with A and B in simultaneous dead-centre-positions at A" and B" respectively.
The important point to note, therefore, is that at the simultaneous dead-centre-positions for links 2 and 4 are not totally constrained. It means that they are capable of rotating either way. Because of this the direction of rotation can change at A" and B". These points are, therefore, called change points. Another important point, worth taking note of, is that because of the simultaneous-dead-centre we have dead-centre-phases when either link 2 or link 4 happen to be the drivers.
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