The external force
(consisting of pull and twist ) is applied to the end
effector of the articulated structure and results internal forces
and torques in the joints. The relation between the force and
the generalized forces is expressed as

The generalized forces could be expressed using either the joint variable accelerations or joint velocities [NN90]. The joint accelerations could be used for an accurate dynamic simulation of the manipulator motion. Because the method is not interested in the dynamic behavior, only the joint velocities are used for the necessity of this method. Thus equation (10) is supplied by another form:

The force is proportional to the velocity in equation (11). That means the object moves as long as the force takes effect. The inertia and torques are not applied. The scheme of the iterative model is demonstrated by the

The force corresponds to error function expressed by equation . is the error along the time-varying trajectory, is current position and is desired trajectory of the end effector.