This research is a part of the work implemented by BSTU “VOENMEH” under the financial support of the Ministry of Education and Science of the Russian Federation for design and development of a precision mechanism with the parallel kinematics called “Hexapod”. The object of research is the mechanism, in which the control of leg lengths is implemented by linear drives with ball-screw gears. The article proposes the solution of the extended inverse kinematics of the hexapod. The neural networks solution of the forward kinematics of hexapod is presented, i.e. the calculation of the position and orientation of the moving platform for given rotation angles of the ball-screw drives. The results of the synthesis of neural networks to achieve a given accuracy of solving the forward kinematics are presented. An estimate of the implementation of kinematic problems in the hexapod control system based on an ARM microprocessor is obtained.