## 4 Dynamics and Experiments
### Gripping Force Test  
To ensure that the landing gear can withstand the expected operational loads, we tested the gripping force of the landing gear on spherical objects with different radii under tension springs of various stiffness coefficients. As shown in Figure 10a, the dual-function landing gear was mounted on the end effector of a Siasun GCR5-910 robotic arm, positioned vertically to simulate the landing gear's orientation during UAV flight. The landing gear was tested with acrylic spheres of 8 mm, 12 mm, and 16 mm radii. A linear guide rail was vertically placed below the spheres via a support. An electronic dynamometer, manufactured by Yueqing Handpi Instruments, fixed to the guide rail, was connected to the bottom of the sphere using a lightweight string, ensuring the string direction was collinear with the gravitational force of the sphere.  
During the experiment, the linear guide rail moved downward at a constant speed, pulling the sphere downward with the string. The landing gear gradually opened under the interaction with the sphere until it could no longer withstand the load, causing the sphere to drop. The experimental results are shown in Figure 10b. The results indicate that the gripping force of the landing gear decreases as the opening degree increases. The initial gripping force is greater for smaller radius spheres. This is because smaller spheres exert a smaller horizontal component of the initial interaction force with the supporting fingers, requiring a greater tensile force to rotate the main rods.  
Experimental results indicate that as the model radius increases (e.g., 16 mm), the initial gripping force is significantly lower than that of smaller radii (e.g., 8 mm). This phenomenon is attributed to the reduction in contact pressure under identical loading conditions, which directly results in a decreased initial gripping force. Furthermore, the  
Figure 10: (**a**) Experimental setup for the gripping force test. (**b**) Comparison of the model prediction versus the experimental results for the gripping force.  
gripping force exhibits a similar decay trend over time across different model radii. However, models with larger radii (e.g., 16 mm) consistently exhibit lower gripping forces throughout the time range compared to smaller-radius models (e.g., 8 mm and 12 mm). The model predictions closely match the experimental data, particularly in capturing the decay trend of the gripping force across varying radii. Nevertheless, for certain radii (e.g., 8 mm and 12 mm), the model slightly overestimates the gripping force in the later stages of decay. This discrepancy may arise from nonlinear factors in the experiments, such as material relaxation effects or external disturbances, which were not fully accounted for in the model.  
In summary, an increase in model radius (representing a larger opening of the gripping mechanism) leads to a reduction in gripping force, but this relationship is nonlinear. Larger radii not only diminish the initial gripping force but also reduce the overall gripping force over time. Therefore, the design of gripping mechanisms must balance the trade-offs between radius size, gripping force, and stability to achieve optimal performance.