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In order to address the problems of low screening efficiency, easy blocking of screen holes, and short service life of key parts commonly used in vibrating screen equipment, the TRIZ (Theory of the Solution of Inventive Problems) was applied in the present work to design a four-degree-of-freedom (4-DOF; three translational and one rotational movements) chaotic vibrating screen with a chaotic vibration exciter as the main power source and a 3-DOF (three translational movements) parallel kinetic chain as the kinematic constraint mechanism of the outer screen frame. Based on the topological structure theory, a hybrid mechanism with structure [ 4 SOC − C i 1 ∥ R i 2 ∥ R i 3 − + R , i = 1,2,3,4 ] was constructed as the kinematic constraint mechanism of the inner screen box of the chaotic vibrating screen to solve the freedom of motion and POC (position and orientation characteristic) equations of parallel kinematic constraint mechanism of the outer screen frame and hybrid constraint mechanism of the inner screen box. The dynamic simulation of a virtual prototype of the chaotic vibrating screen was carried out in ADAMS software, and MATLAB was used to chaos recognition of the simulation results. It was found that the chaotic exciter moved aperiodically in X-, Y-, and Z-directions when the chaotic exciter motor rotated at uniform speed, and the amplitude, velocity, and acceleration of the outer screen frame of the vibrating screen had characteristics of reciprocating aperiodic and irregular changes. Through the phase trajectories of the eccentric block and inner screen box of the exciter in all directions, it was observed that the motion output of the vibrating screen was a chaotic vibration. Therefore, the present paper can provide an important reference for the design and application of chaotic vibrating screens. [ABSTRACT FROM AUTHOR]