A four bar mechanism is made up of links of length 100,200,300 and 350 mm. if the 350 mm link is fixed, the number of links that can rotate fully is ______

The correct answer is 1.

To determine the number of links that can rotate fully, we can apply Grashof's law for a four-bar mechanism.
Grashof's law states that for a four-bar linkage, if the sum of the shortest and longest link lengths is less than or equal to the sum of the remaining two link lengths, then at least one link can perform a full rotation (360 degrees) relative to the other links.

Let the lengths of the links be:
Shortest link, $s=100\text{mm}$
Longest link, $l=350\text{mm}$
Other two links, $p=200\text{mm}$ and $q=300\text{mm}$

Let us calculate the sum of the shortest and longest links:
$s+l=100+350=450\text{mm}$

Now, let us calculate the sum of the remaining two links:
$p+q=200+300=500\text{mm}$

Comparing the two sums:
$s+l<p+q$ (since $450<500$)

Since the inequality is satisfied, Grashof's condition holds. Under this condition, the behavior of the mechanism depends on which link is fixed:
1. If the shortest link ($s$) is fixed, we get a double-crank mechanism, where both links adjacent to the fixed link can rotate fully.
2. If the link opposite to the shortest link is fixed, we get a double-rocker mechanism, where no link connected to the frame can rotate fully.
3. If a link adjacent to the shortest link is fixed, we get a crank-rocker mechanism, where only the shortest link (which acts as the crank) can rotate fully.

In this question, the 350 mm link (which is adjacent to the shortest link of 100 mm) is fixed. Therefore, this mechanism functions as a crank-rocker mechanism.
Consequently, only the shortest link (100 mm link) can rotate fully.
Thus, the number of links that can rotate fully is 1.