A wind turbine with the working element based on an antiparallel link mechanism is proposed. A blade of the turbine is attached to the connecting rod. The flow acting on the blade is supposed to have a constant speed. A quasi-static model of an aerodynamic action is used. A rotor of the electric generator is attached to the axis of the crank. Electromechanical torque is supposed to be a linear function of the angular speed of the rotor of the generator. The mechanical system has one degree of freedom. The angle of rotation of the crank is chosen as a generalized coordinate. A mathematical model of the system was constructed. The attracting 2p- periodic trajectory of the dynamical system corresponds to the working periodic regime of the wind turbine. The Poincare-Pontryagin asymptotic approach is used to obtain the sufficient conditions for the existence and stability of the 2p-periodic trajectories and to estimate the mechanical power in the corresponding modes. Two types of asymptotic bifurcation diagrams of the trapped power were constructed: depending on the average speed of the center of pressure in the working modes, and depending on the coefficient of the external mechanical load. An asymptotic dependence of the average aerodynamic torque on the average speed of the center of pressure was constructed. A laboratory prototype of the turbine was constructed and tested. The prototype proved to be self-starting at the wind speed higher than 4m/s and with a sufficient initial position of a wind-receiving plate.