In hard-to-reach places, the performance of transportation and lifting operations with cargo is usually associated with significant financial costs and is a complex engineering task. One of the solutions can be the use of a lifting crane. It is a balloon filled with “light” gas, equipped with a cable system (sling) for suspending the load on the ball and connecting the ball with three drive motors reliably fixed on the ground, which rotate the drums with wound cables. The purpose of the work is to perform a mathematical description and simulation of the movement of objects of the electromechanical system of a "crane ball" with an automated electric drive, to assess the possibility of ensuring accurate positioning of the load when using a direct current electric drive with a subordinate control system. In the electromechanical system under consideration, the relocatable load has five degrees of freedom; dynamic processes are described by a system of five nonlinear differential Lagrange equations of the second kind in the corresponding coordinates. The linearization of the equations is performed by expanding into a Taylor series, limiting the representation of nonlinearity to the first two members of the series. Positioning of the ball and the load in space is provided by changing the lengths of the cables holding the ball. Therefore, during the synthesis of the positional control system for the electric drives of the drums, the dependences of the required cable lengths were determined as a function of the given coordinates of the ball (load) in the x, y, z coordinate space. Taking into account the accepted assumptions and requirements for limiting the oscillations of the cargo, a rather complex structural simulation model was obtained, containing several computational units interconnected in accordance with the system operation algorithm. The proposed mathematical model of the object and transient processes carried out during the Matlab structural simulation showed the ability to solve the load positioning problem by using a three-loop subordinate control system (control loops for the electromagnetic momentum, engine rotational speed and load position) for electric drums with cables holding the ball.