Purpose of this study was to obtain more information on motion of movable operating elements in the vibroimpact classifier, and final purpose was to improve efficiency and productivity of the mineral processing. A considerable interest presents a kinematic scheme in which a vibrating roller made in the form of a circular cylinder rolls on the inner surface of a spring-loaded square tube all points of which move circularly under the action of unbalanced vibratory drive. The studies focused on creating an analytical function, which could describe a trajectory of the roller’s mass center as close to its original as possible. Three variants of solving this problem are described. In the first variant, the analytical construction of the function is based on the integer function in a cylindrical coordinate system, in the second - on the inverse trigonometric functions such as ( ) sinarcsin ϕ and (cosarccos ϕ) in the Cartesian coordinate system, and in the third variant – on the sum of two trigonometric functions, one of which is an exponential. The obtained results can be used for qualitative and quantitative analysis of dynamics of the movable operating elements of vibroimpact roll classifier as they can reflect nay displacements, velocities and accelerations of the pendulum points. All of these three variants are also applicable for visualization and animation of the pendulum dynamics in any user-friendly graphical environment.
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