# Study on the Propulsion Characteristics of a Flapping Flat-Plate Pumping Device
## 2 Physical Model  
### Structure and Working Principle of the Flapping Flut-Plate Device  
In this study, a flat-plate hydrofoil was selected as the hydrofoil profile, and a non-NACA profile device was used to simplify the model while maintaining control over experimental conditions. In the early stage of research, the flat-plate hydrofoil effectively captures the fundamental flapping and fluid interaction characteristics, reducing additional deviations caused by geometric complexity and facilitating parameter adjustment and result reproducibility. Moreover, experiments with flat-plate hydrofoils provide a theoretical foundation for subsequent studies involving more complex wing profiles, ensuring experimental controllability and continuity. The crank-slider drive mechanism consists of a stepper motor, gearbox, double crank-slider, connecting rod, flat-plate wing, and slide rail, as illustrated in Figure 1. The motor drives the connecting rod, and the crank-slider transmission induces the flat-plate wing to perform heaving and pitching quasi-harmonic motions.  
The synchronous belt drive mechanism mainly consists of a stepper motor, gearbox, synchronous belt module, slide platform, slider, connecting rod, flat-plate hydrofoil, and slide rail, as shown in Figure 2. The motor driver input signals are controlled by a microcontroller, enabling the synchronous belt module to drive the slide platform in reciprocating motion. The slide platform, via the connecting rod, drives the flat-plate hydrofoil to perform harmonic motion.  
In the experimental design, the crank-slider drive mechanism was chosen as the flapping hydrofoil drive due to its simple structure, low manufacturing cost, and ease of implementing periodic flapping motion. The drive system employs a stepper motor without closed-loop control, making real-time compensation for nonlinear acceleration during the mechanism's motion unattainable. Under these conditions, the slider displacement exhibits a nonlinear functional relationship with the crank angle. Especially near dead points, the slider acceleration changes abruptly, resulting in asymmetric and nonlinear quasi-harmonic motion of the hydrofoil during flapping.  
In contrast, the subsequently introduced synchronous belt drive mechanism, combined with a stepper motor and microcontroller system, modulates pulse signals to control the slider position following a sinusoidal trajectory, approximating ideal harmonic motion. The introduction of the control system effectively improves the tunability and precision of the motion trajectory, serving as a crucial prerequisite for achieving standardized harmonic motion. In summary, the crank-slider drive mechanism offers advantages in cost and assembly convenience but inherently produces quasi-harmonic motion due to its kine  
Figure 1: Schematic diagram of the crank-slider drive mechanism. (1. Double Crank 2. Coupling 3. Stepper Motor 4. Flapping Flat-Plate Hydrofoil 5. Slider 6. Slide Rail 7. Support Frame).  
Figure 2: Schematic diagram of the synchronous belt drive mechanism. (1. Stepper Motor 2. Slider 3. Connecting Rod 4. Flapping Flat-Plate Hydrofoil 5. Slide Platform 6. Synchronous Belt Module 7. Slide Rail 8. Support Frame).  
matic characteristics and control limitations. Conversely, the synchronous belt mechanism achieves a harmonic flapping motion closer to the ideal model through high-precision control strategies.