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The closed few-parametrical dynamical model of the slider-crank WTWT is introduced and studied. The model takes into account aerodynamic action upon the wing and electromechanical load upon the rotor of the generator. Attractive periodical solutions of the system are studied that correspond to operation modes of motion of the WTWT. Estimations of the trapped power coefficient are given with respect to constructive parameters of the mechanism. Thus it is described how the behavior of one of the classical objects of mechanism science changes under the action of aerodynamic forces. It is interesting for further research to study behavior of the system with additional wings, to search for the construction with extended domain of attraction of high-power operation modes.