Consider this four bar mechanism:

Grashof law Four bar mechanism

s = length of the shortest link

l = length of the largest link

p and q = lengths of the other two links

By Grashof law, for at least one link to be capable of making a full revolution, the sum of the lengths of the shortest link and the largest link is less than or equal to the sum of the lengths of the other two links.

s + l ≤ p + q

The condition can be broken into two parts:

1. s + l < p + q

2. s + l = p + q

What happens if ‘s + l > p + q’?

For s + l > p + q, no link will be able to make a complete revolution. The mechanism so obtained is known as triple rocker mechanism.

Triple Rocker Mechanism

In the triple rocker mechanism, one link is fixed while the other three links oscillate.

Now let’s discuss the Grashof condition. We broke the condition into two parts:

1. s + l < p + q

2. s + l = p + q

1. s + l < p + q

Case 1: The shortest link is adjacent to the fixed link.

The mechanism obtained in this case is known as crank rocker mechanism.

Crank Rocker Mechanism

In the crank rocker mechanism, the shortest link rotates fully while the other link pivoted to the fixed link oscillates.

Case 2: The shortest link is the fixed link.

The mechanism obtained in this case is known as double crank mechanism.

Double Crank Mechanism

In the double crank mechanism, both the links pivoted to the fixed link rotates fully.

Case 3: The shortest link is opposite to the fixed link.

The mechanism obtained in this case is known as double rocker mechanism.

Double Rocker Mechanism

In the double rocker mechanism, both the links pivoted to the fixed link oscillate. The shortest link, which is the coupler, makes a full revolution.

2. s + l = p + q

Case 1: The length of the links is distinct.

Example: ‘s’ is 1 unit, ‘l’ is 4 units, ‘p’ is 2 units and ‘q’ is 3 units. In this case, s + l = p + q = 5 units.

In this case, all the inversions obtained are the same as in the case ‘s + l < p + q’.

a. Crank rocker: The link adjacent to the shortest link is fixed.

b. Double crank: The shortest link is fixed.

c. Double rocker: The shortest link is opposite to the fixed link.

Case 2: The length of the two links is same.

Example: p = s = 1 unit and l = 4 units. Now for ‘s + l = p + q’, q = l = 4 units. So, we have two pairs of equal length.

In this case, the links can be joined in two ways:

a. Equal links opposite to each other: The linkage so obtained is parallelogram linkage.

b. Equal links adjacent to each other: The linkage so obtained is deltoid linkage.

Parallelogram and Deltoid linkage

All the inversions are either crank rocker or double crank for this case.

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Grashof’s Law

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