The article describes the application of optimization algorithms for solving the problem of determining the workspace of robots as a serial and parallel structure based on the tripod. The method of approximating the set of solutions of nonlinear inequalities system describing constraints on the geometric parameters of the robot and based on the concept of non-uniform coverings is considered. The internal approximations defined as a set of parallelepipeds are obtained on the basis of the method. The influence of various geometric parameters on the volume of the workspace of the robot is analyzed. To approximate the workspace, the developed algorithm and its modifications with different dimensions of parallelepipeds and approaches to the transfer of constraints from the space of input to the space of output coordinates due to the complexity of the computational problem are used. A software package in the C ++ language is developed to implement the algorithms. The results of mathematical modeling are presented. Various dimensions of the grid to calculate the functions, as well as the accuracy of the approximation are experimentally conducted. The obtained results can be used in the selection of geometric parameters of robots, which determine their limitations when moving as part of a multi-robotic system.