Describe grashorf’s law and explain its importance in mechanism design [2]
Answers
Answer:
Grashoff’s law for a four bar mechanism , the sum of the shortest and longest link lengths should not be greater than the sum of the remaining two link lengths if there is to be continuous relative motion between the two links.
Kinematic chain is a combination of a four or more kinematic pairs, such that the relative motion between the links or elements is completely constrained. The simplest and basic kinematic chain is a four bar chain or quadric cycle chain, as shown in fig.4. it consists of four links, each of them forms a turning pair at A,B,C and D. the four links may be of different lengths. According to Grashoff’s law for a four bar mechanism , the sum of the shortest and longest link lengths should not be greater than the sum of the remaining two link lengths if there is to be continuous relative motion between the two links.A very important consideration in designing a mechanism is to ensure that the input crank makes a complete revolution relative to the other links. The mechanism in which no link makes a complete revolution will not be useful. In four bar chain ,one of the links, in particular the shortest link, will make a complete revolution relative to the other three links,if it satisfies the Grashof’s law. Such a link is known as crank and driver. In fig.4, AD (link 4) is a crank. The link BC (link 2) which makes a partial rotation or oscillates is known as lever or rocker or follower and the link CD (link 3) which connects the crank and lever is called connecting rod or coupler. The fixed link AB (link 1) is known as frame of the mechanism.
Explanation:
Consider this 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.

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.

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.

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.