The couple moment and the force is divided to get the distance of the axis from the point of action of the force in free body diagrams.

In free body diagrams, the forces and moments acting on a body are represented by vectors. These diagrams are used to analyze and solve problems in mechanics and engineering.

Couple Moment:
A couple moment is a pair of equal and opposite forces that act on a body but do not have a resultant force. Instead, they create a moment or torque that tends to rotate the body. The couple moment is represented by a vector perpendicular to the plane of the couple, with its magnitude equal to the product of one of the forces and the perpendicular distance between the forces.

Axis of Rotation:
In order to determine the distance of the axis from the point of action of the force, we need to identify the axis of rotation. The axis of rotation is an imaginary line around which the body rotates when subjected to a couple moment.

Dividing the Force:
To determine the distance of the axis from the point of action of the force, we need to divide the force vector into two components: one component parallel to the axis of rotation and another component perpendicular to the axis of rotation.

Parallel Component:
The parallel component of the force lies along the axis of rotation. This component does not contribute to the moment about the axis and can be ignored when calculating the distance of the axis from the point of action of the force.

Perpendicular Component:
The perpendicular component of the force is the one that creates the moment about the axis of rotation. This component is used to calculate the moment arm or the distance between the axis and the point of action of the force.

Calculating the Distance:
Once we have the perpendicular component of the force, we can calculate the moment arm by dividing the magnitude of the moment created by the force by the magnitude of the perpendicular component of the force.

Conclusion:
In free body diagrams, the couple moment and the force are divided to determine the distance of the axis from the point of action of the force. The parallel component of the force is disregarded, while the perpendicular component is used to calculate the moment arm. This approach allows us to accurately analyze and solve problems involving moments and forces in mechanical systems.