Resultant force

In this way, all of the forces acting on a body can be moved to the same point of application with associated torques.

To see this add the vector kF to the point of application R in the calculation of the associated torque, The right side of this equation can be separated into the original formula for T plus the additional term including kF, because the second term is zero.

To see this notice that F is the sum of the vectors Fi which yields thus the value of the associated torque is unchanged.

If this condition is not satisfied, then the system of forces includes a pure torque for every point of application.

The forces and torques acting on a rigid body can be assembled into the pair of vectors called a wrench.

, meaning that the single force F, acting at displacement R, can replace the system.