The hinged attachment of the shaft is of interest with the use not only of standardized [1][2][3][4] high-speed mixers, but also of low-speed unsymmetrical mixers [5]. Investigations [6] of the technological characteristics of apparatus with unsymmetrical mixers on a hinged shaft have shown that, in such apparatus, the specific expenditures of power with the mixing of suspensions are considerably lower than in standard apparahis.The present article gives the results of theoretical and experimental investigations of the dynamic characteristics of an unsymmetrical paddle mixer on a hinged shaft: The angle of deviation of the shaft from the vertical axis of the apparatus is 0, and the angle of the path of the paddle is c~ (Fig. i). In the system under consideration, the shaft with the paddle performs a complex motion, rotating around its own axis with the angular velocity w, and around the vertical axis of the apparatus with the angular velocity ~2, which increases the rate of the mixing process over the whole volume of the apparatus. Experiments made by the present authors have shown that, originally, with small rates of rotation, the paddle is arranged at the angle c~ with respect to the projection of the shaft (Fig. la). With an increase in the rate of rotation, the angle decreases and, with some velocity Wer, called critical, the projection of the paddle coincides with the projection of the shaft (Fig. lb). With a further increase in the rate of rotation (under supercritical conditions), the projection of the paddle is located on the opposite side from the projection of the shaft (Fig. le). Under steady-state conditions, with which a = coast, 0 = coast, w = ~2, an unsymmetrical mixer on a hinged shaft has a stable trajectory of its motion.With the construction of apparatus with an unsymmetrical paddle on a hinged shaft, for fhe given conditions, it is necessary to determine the angles 0 and ~, which, as tests have shown, depend on the dimensions and the rate of rotation of the paddle and the shaft, as well as on the properties of the medium being mixed.With fully established suberitical conditions, under the action of the torque of the drive, the paddle originally turns with the instantaneous angular velocity ~l with respect to the point A (Fig. 2). The force of the resistance of the medium to the rotation of the paddle, applied at the point D, is denoted by S.In accordance with the rule of the transfer of force, at the point C of the paddle we apply the forces S~ and $2, equal in value to S. The moment of the pair of forces S and S 2, with uniform rotation of the paddle, is balanced by the torque of the drive. Under the action of the force S 1, the resultant force of the weight Pw and the force of the inertia of the shaft Pi, the paddle performs a translational motion, while the shaft rotates with the angular velocity co 2 with respect to the vertical axis of the apparatus. As a result of this motion, there arises the force S t of the resistance of the medium to the translational motion of the paddle, perpendi...