Four-bar linkage:
A four-bar linkage is a type of mechanical linkage that is composed of four links connected by four joints. The links can be of different lengths and the joints can be either revolute (rotational) or prismatic (linear).

Sum of lengths:
In this question, we are given that the sum of the lengths of the smallest and the longest link is less than the sum of the lengths of the other two links. Let's consider the lengths of the four links as a, b, c, and d, with a being the smallest and d being the longest.

a + d < b="" +="" />

Fixed smallest link:
Now, if we fix the smallest link (a) in the four-bar linkage, it means that it becomes a fixed link and cannot move. This leaves us with three remaining links (b, c, and d) that can move.

Classification of mechanisms:
Based on the relative motion of the links in a four-bar linkage, it can be classified into different types of mechanisms. Let's analyze the possible classifications based on the given conditions.

1. Grashof condition: The Grashof condition states that for a four-bar linkage to have continuous motion, the sum of the lengths of the shortest and longest links must be less than or equal to the sum of the lengths of the other two links.

a + d ≤ b + c

In our case, we are given that a + d < b="" +="" c,="" which="" means="" that="" the="" grashof="" condition="" is="" not="" />

2. Double-rocker mechanism: In a double-rocker mechanism, both the input and output links can rotate. This means that both the shortest and longest links can rotate. However, in our case, the smallest link (a) is fixed, so it cannot rotate. Therefore, the double-rocker mechanism is not applicable.

3. Double crank mechanism: In a double crank mechanism, both the input and output links are fixed. In our case, the smallest link (a) is fixed, which satisfies the condition of a double crank mechanism. This means that the remaining three links (b, c, and d) can rotate, allowing the mechanism to function as a double crank mechanism.

4. Crank-rocker mechanism: In a crank-rocker mechanism, one link is fixed and the other three links can rotate. In our case, the smallest link (a) is fixed, which satisfies the condition of a crank-rocker mechanism. This means that the remaining three links (b, c, and d) can rotate, allowing the mechanism to function as a crank-rocker mechanism.

Conclusion:
Based on the given conditions, if the smallest link is fixed in a four-bar linkage where the sum of the lengths of the smallest and the longest link is less than the sum of the lengths of the other two links, the linkage becomes a crank-rocker mechanism (option C).