The paper is devoted to preservation of dynamic control accuracy of working tools of multilink manipulators when they move along arbitrary spatial trajectories, taking into account the design limits in all degrees of freedom and special cases of position of their links. Preservation of control accuracy is proposed to be ensured by eliminating reach of all degrees of freedom of the manipulators to the limits and to indicated special positions, characterized by ambiguity in solving the inverse kinematic problems of the manipulators, as well as excluding the reach of their working tools to boundaries of working area due to use of a redundant degree of freedom when approaching indicated undesirable positions. The performed simulation has confirmed efficiency of the proposed method.