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.

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.

Using simple examples, an unconventional method for solving the inverse kinematic problem for manipulation robots is considered. The classical nonlinear formulation of this problem is reduced to the optimization problem. To solve which it is proposed to use the stochastic method, implemented based on a genetic algorithm. As the optimization criterion (fitness function), the square of the deviation of the position of the tool center point of the manipulation robot from the given trajectory point is selected. Various kinematic schemes of manipulation systems (flat, spatial, with kinematic redundancy) are investigated. The algorithm showed good convergence with a given accuracy, including multivariate solutions to the problem.

A method for compiling object schemes is proposed, which allows constructing algorithms for calculating the kinematic parameters of robotic manipulators. Examples of compiling object schemes for calculating the velocities and accelerations of points selected on the links of the robotic manipulator are considered. An analysis of the computational complexity of the obtained algorithms is carried out and a method for increasing their computational efficiency is proposed. An increase in computational efficiency is achieved based on the use of the associativity property due to the reduction of additional and multiplication operations performed by the algorithm. Graphs of computational processes illustrating the developed algorithms are presented. The developed algorithms allow parallel calculations; this will further increase the efficiency of calculations when using multiprocessor computing systems. As a result of the study, based on the object approach, an effective universal method for calculating the kinematic parameters of robotic manipulators has been developed. This will improve the quality of robot control.