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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.

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The article describes the main stages of developing a robotic system for the rehabilitation of the lower limbs based on the “tripteron” robot. The structure of a robotic system has been designed, consisting of a 3-PRRR parallel mechanism, which provides the angles of rotation of all joints of the patient’s leg required for rehabilitation and a passive orthosis for supporting the limb. At the first stage, the positions of the active mechanism links are determined. The output link of only one kinematic chain, making a translational movement in the vertical direction, will experience a maximum load. A design diagram of this kinematic chain was built, and the reactions of the supports were determined at the second stage. At the third stage, kinematic dependences were obtained, and an engine was selected that would provide the required torque at the required speeds.

The paper proposes the structure of the robotic system (RS) control system with and without the patient’s force feedback, describes the conditions for using each of them. The method for improving data reliability on applied forces using strain gauge readings in the absence of patient activity was developed. The method of motivating a patient to perform “correct” movements thus “assisting” the mechanism, which consists in changing the speed of movement to create an impression that the mechanism moves due to patient’s efforts was developed. Mathematical RS model was constructed, graphs reflecting the accuracy of the specified trajectory were obtained.