The concept of reducing a system of forces and couple moments to an equivalent system is essential in simplifying the analysis of rigid bodies. This reduction allows for more straightforward computation and understanding of the external effects produced by the system. In particular, systems with an equivalent resultant force and a resultant couple moment having perpendicular lines of action can be further reduced to a single equivalent resultant force acting along a new line of action. There are three primary types of force systems that can be simplified in this manner: concurrent, coplanar, and parallel force systems.

A concurrent force system consists of forces with lines of action intersecting at a single point. Due to this intersection, no moment is produced at the point, and the system can be represented by a single resultant force acting at the intersection point. This simplification significantly reduces the complexity of the force system, allowing for a more straightforward analysis.

In a coplanar force system, the lines of action for all forces and the resultant force lie in the same plane. The resultant couple moment in this system is perpendicular to the resultant force, which allows for further simplification. Moving the resultant force by a perpendicular distance can produce the same moment as the original system.

A parallel force system consists of forces that are parallel to the same axis, with the resultant force also being parallel to that axis. In this case, the resultant couple moment lies perpendicular to the resultant force, allowing for simplification. The system can be reduced to an equivalent single resultant force acting on a point lying on the perpendicular axis.

In each of these force systems, the process of reducing the forces and couple moments into an equivalent single resultant force simplifies the analysis and understanding of the external effects on a rigid body. This reduction is beneficial in engineering applications, where complex force systems often need to be analyzed for design and safety purposes.

By understanding the underlying principles of concurrent, coplanar, and parallel force systems, engineers and other professionals can more effectively analyze and design structures, machines, and other systems subjected to various forces. Reducing complex force systems to an equivalent single resultant force allows for easier computation and more efficient and practical designs.