## 4 Conclusions  
Modeling robot positioning error makes it possible to take into account the main factors affecting positioning accuracy at the stage of robot programming. The change in the geometric dimensions of the links of the robot manipulator is considered through the example of temperature influence. This makes it possible to programmatically calibrate the manipulator depending on the conditions of the production environment. The available elastic pliable elements cause elastic deformations. Evaluation of the displacement of the gripper from the positioning point vertically and horizontally, as well as the roll angle, respectively, provide data for correcting the initial model of the movement of the robot manipulator links. For our case, the positioning error for the partial motion system is \(1.008\cdot 10^{-4}\) degrees, or \(6.048\cdot 10^{-3}\) min. More precise movement can be obtained by changing the drive characteristics of the robot links. For example, changing the power supply voltage of the electric drive. The available elastic pliable elements cause elastic deformations. The calculation of elastic forces of deformation makes it possible to determine the vector of errors, which is the first column of the compliance matrix of the gripper. Calculations were made for the conditions of the gripper holding a longitudinal object weighing 200 N and the center of gravity of the object being placed at a distance of 0.5 m in the horizontal direction from the pole of the gripper. Their results showed that, due to the load, the gripper shifted to the right by \(0.48\cdot 10^{-3}\) m and down by \(2\cdot 10^{-3}\) m, and also tilted at an angle of \(0.8\cdot 10^{-3}\) rad clockwise around the \(x_{0}\) axis. As an option to improve accuracy, the positioning process can be carried out in the form of successive partial movements. Such a task of synthesizing the \(i\)-th transmission mechanism by the method of partial movement makes it possible to maximally unload the drives of the mechanisms. For this method, it is necessary to have a system of equations that describe the movement of the link of the robot manipulator and the drive of this link. Synthesis of the drive law of the robot mechanism characterizes program control under the condition of ideal motor characteristics. The dynamic assessment of the positioning error characterizes the adequacy of the robot manipulator link movement model. Static geometric and elastic evaluation of the deviation of the gripper pole from the positioning point characterizes the design of the robot itself for the given conditions of its operation. The existing mathematical model of positioning errors makes it possible to compensate for the positioning error by changing the speed of movement of the reference point of the gripper before determining the direct kinematic task. The method is focused on the accuracy of approaching the destination point under given arbitrary positions of the robot. Conceptualization, V.D. and I.D. ; methodology V.D., I.D., I.H. ([PERSON]) and S.K. ; software, I.D., T.H. and R.B. ; validation, V.D., LH. ([PERSON]) and J.C.; resources, M.P. and S.P. ; writing--original draft preparation, I.D. and V.D. ; writing--review and editing, LH. ([PERSON]) and M.K. ; visualization, J.C. and S.P. ; formal analysis, LH. ([PERSON]); project administration, V.D., S.K., M.K. and M.P. ; Supervision, T.H. All authors have read and agreed to the published version of the manuscript. Funding: Publication was co-financed from the funds of the Ministry of Education and Science under contract No. KONF/SP/0507/2023/01 dated 13 January 2024 in the amount of 92,113.85 PLN. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Abstracted data is available from the corresponding author on reasonable request. Anonymous reviewers are gratefully acknowledged for their constructive review that significantly improved this manuscript as is the Ukrainian University in Europe (universityque.com).