A universal solution to an applied problem related to the study of deviations occurring in the joints of manipulation robots, for example, due to elastic deformations or gaps in them, is proposed. A mathematical (dynamic) model obtained by the Lagrange–Euler method is presented, making it possible to investigate such deviations. Six generalized coordinates, three linear and three angulars, were used to describe the variations of each joint in the dynamic model. This made it possible to introduce into consideration joints with six degrees of freedom (6-DOF joints). In addition, mathematical models for external forces acting on the links of manipulation robots are presented. When composing matrices of coefficients of equations of motion, elements identically equal to zero were excluded, which significantly increased the computational efficiency of these equations. The dynamic model based on the obtained equations can be used in the computer simulation of manipulation robots.

The article deals with the concept of building an automated system for the harvesting of apple crops. This system is a robotic complex mounted on a tractor cart, including an industrial robot and a packaging system with a container for fruit collection. The robot is equipped with a vacuum gripper and a vision system. A generator for power supply, a vacuum pump for the gripper and an equipment control system are also installed on the cart. The developed automated system will have a high degree of reliability that meets the requirements of operation in the field.

An algorithm for parallel calculations in a dynamic model of manipulation robots obtained by the Lagrange–Euler method is developed. Independent components were identified in the structure of the dynamic model by its decomposition. Using the technology of object-oriented programming, classes corresponding to the structures of the selected components of the dynamic model were described. The algorithmization of parallel computing is based on the independence of the calculation of objects of individual classes and the sequence of matrix operations. The estimation of the execution time of parallel algorithms, the resulting acceleration, and the efficiency of using processors is given.

Mathematical models for the control systems of industrial robots permit calibration of the base, which is a single coordinate space for the industrial robot and the components being manipulated. Calib

The mathematical models underlying the methods of the calibration of the tool, fixed on the industrial robot installation flange, are considered. The software and mathematical support that implements these methods provides the functions of control systems of industrial robots connected with putting robots into operation. The calibration procedures are performed when the industrial robot is equipped with a new instrument. The tool calibration is performed in two steps. The first step is to determine the center point of the tool (TCP - Tool Center Point). The second step involves actions to determine the orientation of the rectangular coordinate system, which is associated with the instrument, the beginning of which is placed in TCP. This article is devoted to the study of the second final stage of instrument calibration.

Two mathematical models for determining the dynamic accuracy of manipulation systems of robots with elastic hinges are considered. Mathematical models are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical models make it possible to determine the elastic deviations of manipulation systems of robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. One model is the exact implementation of the Lagrange method and makes it possible to determine the total elastic deviation of the manipulation system from the programmed motion trajectory. Another mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by two models are compared to the example of a three-link manipulation system. The considered models can be used when performing investigations of the mathematical accuracy of the manipulation systems of robots.