## 1 Introduction
Thus, the matching and assembly interference of model design were tested, optimizing the compatibility between the stator and rotor of the improved single screw, and achieving dynamic interactive digital assembly in virtual reality environments. [PERSON] et al. [30; 31] analyzed the formation principles and geometric characteristics of the fixed rotor in the plasticizing conveying system of the eccentric rotor extruder. Through kinematic analysis of the relevant physical quantities of the fixed rotor, the movement characteristics of the fixed rotor in the cavity of the eccentric rotor extruder were described in detail; through disassembly experiments and theoretical modeling, the spatial variation law of material volume during the plasticizing conveying process of the eccentric rotor was analyzed. [PERSON] et al. [32] analyzed the kinematic relationships of the rotor in the straight section, the section with uniform pitch helical blades, and the section with variable pitch helical blades, revealing that the composite motion of rotor eccentric self-rotation and constant-speed reverse revolution is equivalent to the rotor rotating about its cross-sectional center while undergoing reciprocating linear pulsation motion within its corresponding stator cavity. Unlike progressive cavity pumps, which prioritize conveying efficiency, to enhance the stretching mixing performance of the internal meshing screw device, alternating straight and helical segments are arranged on the internal meshing screw and its corresponding stator, with small pitch and eccentricity distances, and parameters gradually decreasing axially. The arrangement of helical and straight segments allows for volumetric deformation of the material during transport, resulting in periodic volumetric stretching. Unlike extruders used in other fields, we used corn syrup and flour as experimental materials, eliminating the need for heating devices or extrusion molding. Therefore, there is no need for compression zones, melting zones, or extrusion zones, with a primary focus on mixing effectiveness. Furthermore, the viscosity of corn syrup is much greater than that of molten polymers, thus requiring additional adjustments specifically tailored for high-viscosity fluids. The studies mentioned above lay the groundwork for the application of internal meshing screw mixers in the food industry. However, they remain primarily theoretical and lack a comprehensive design methodology for internal meshing screw mixers. There is no trajectory and velocity analysis based on key points of the rotor, and there is no specific analysis on how to achieve the rotor's special epitrochoidal motion. This paper establishes a design method for internal meshing screw mixers based on the kinematic principles of internal cycloid formation. It derives motion equations for key points on the rotor, obtaining trajectories and velocity equations, and simulates the relative positions of the fixed rotor during the synchronous reverse motion of the transmission device, establishing the relationship between the transmission device and the motion positions of the fixed rotor. Based on this design methodology, an internal meshing screw mixer is designed and tested using corn syrup and flour as experimental materials. This study verifies the potential application of internal meshing screw mixers in the food industry and investigates the rheological properties of mixtures under different rotational speeds, laying a solid foundation for further research into the mixing mechanism of internal meshing screws in the food industry.