Center of Gravity in a 4-Bar Mechanism:

The center of gravity (CG) is the point where the entire weight of an object can be assumed to act. In a 4-bar mechanism, the coupler link is a connecting element between the input and output links. It has a certain mass distribution, and its center of gravity plays a crucial role in the overall behavior of the mechanism.

Effects of Acceleration:
Acceleration refers to the rate of change of velocity. In the context of a coupler link, acceleration can occur in two ways:

1. Linear Acceleration: Linear acceleration refers to the change in speed or direction of the CG along a straight line. It occurs when the coupler link moves in such a way that its CG experiences a force or torque resulting in linear motion.

2. Angular Acceleration: Angular acceleration refers to the change in rotational speed or direction of the CG. It occurs when the coupler link rotates about its CG due to applied forces or torques.

Explanation of the Correct Answer (Option D):
The correct answer is option D, which states that the center of gravity of the coupler link in a 4-bar mechanism would experience both linear and angular accelerations. This is because the coupler link is subjected to various forces and torques during the motion of the mechanism.

Forces and Torques Acting on the Coupler Link:
1. Tensile/Compressive Forces: The input and output links exert forces on the coupler link, which can lead to linear acceleration of the CG.

2. Frictional Forces: The contact points between the coupler link and other links may experience frictional forces, causing linear acceleration of the CG.

3. Rotational Torques: The forces acting on the coupler link may also create a rotational torque about its CG, resulting in angular acceleration.

4. Gravitational Forces: The weight of the coupler link acts vertically downward through its CG, contributing to both linear and angular accelerations.

Conclusion:
In a 4-bar mechanism, the center of gravity of the coupler link experiences both linear and angular accelerations due to various forces and torques acting on it. Understanding these acceleration effects is crucial for analyzing the motion and stability of the mechanism.