The solution of task of maintaining the dynamic accuracy of control of working tools of multilink manipulators (MM) when they move along arbitrary spatial trajectories is presented in this paper. In this case, constructive restrictions in all degrees of freedom (DoF) of manipulators and special cases of location of their links are taken into account. In the first part of the paper the features of the new solution to the inverse kinematics problem are considered and special (singular) positions for 6-DoF manipulators with PUMA kinematic schemes are described. These singular positions are characterized by ambiguity in solving inverse kinematics problem of these MM. The presented solution of the inverse kinematics problem takes into account various combinations of generalized coordinates of the MM, which ensure the movement of their working tools to the specified positions with the required spatial orientation. In the second part of the paper a method is considered, which, due to use of an additional (redundant) DoF of the MM, which ensures its movement near work objects, does not allow the manipulator to enter unpredictable in advance singular positions, excludes approaching of working tools to the boundaries of MM working area, as well as some of its DoFs — to restrictions leading to a sharp decrease in the accuracy of the manipulator in the process of performing any technological operations with previously unknown trajectories of movement. Based on this method, a system has been synthesized that makes it possible to automatically generate reference signals for all DoFs of MM, taking into account the current reference positions and orientations of the working tools specified in the absolute coordinate system. As a result, emergency situations are not created and the high quality of the prescribed operations and work is maintained. The results of the performed mathematical simulation confirmed the high efficiency of using the proposed approach to the contour control of the MM.