# A Stair-Climbing Wheelchair with Novel Spoke Wheels for Smooth Motion
## 4 Simulation Verification
### Flat Terrain Motion Simulation  
To evaluate the influence of different spring constants on the wheelchair's motion performance, we conducted simulations on wheelchair models equipped with various springs traversing flat terrain. The Flexwheel was driven at a rotational speed of 1.2 rad/s, and the fluctuation range of the body height was recorded as a function of the spring constant \(k\), as illustrated in Figure 9. The results indicate that as \(k\) increases, the fluctuation range of the body height initially decreases and then increases. When \(k=61.7N/m\), the fluctuation range reaches its minimum, demonstrating that this spring configuration effectively reduces oscillations during flat terrain motion. These findings align well with theoretical predictions, further validating the feasibility of the method proposed in Section 3.1.2.  
Figure 8: The maximum climbing height.  
However, the simulation also revealed significant variations in the model's pitch angle, suggesting an uneven load distribution between the front and rear wheels. During the rotation of the Flexwheel, the phase from the initial ground contact to the vertical position involves acceleration, where kinetic energy is converted into the spring's elastic potential energy. As the spoke rotates past the vertical position and lifts off, the stored elastic potential energy is released back into kinetic energy. The cyclic energy conversion influences the wheelchair's dynamic response, affecting load distribution. During acceleration, inertial forces induce a rearward thrust on the front wheel, causing slight lifting and shifting more load to the rear wheel [26]. Such variations in pitch angle could cause discomfort to the wheelchair user. To mitigate this issue, the front wheel should be equipped with a spring of lower \(k\). Figure 10 illustrates the variance of the body's pitch angle for different front-wheel spring constants. Through testing multiple front-wheel spring configurations, it was found that the pitch angle variance is minimized when \(k_{\text{FRONT}}=40.5\text{N}/\text{m}\).  
Therefore, the rear Flexwheels were assigned a spring constant of 61.7 \(\text{N}/\text{m}\), while the front Flexwheels were set to 40.5 \(\text{N}/\text{m}\). The parameter configuration of the simulation model is shown in Table 3.  
Figure 10: RMS of pitch varies with \(k\) value of the front wheel.  
Figure 9: The fluctuation range of the body height varies with the \(k\) value.  
Figure 11 compares body height variations between a traditional spoke wheel model and a Flexwheel-equipped model. The results show that the traditional spoke wheels experience significant body height fluctuations, with a range of 10.75 mm. In contrast, the Flexwheel model reduces this range to 3.39 mm. Oscillations in pitch angle contribute to variations in body height, leading to minor discrepancies between the simulation results and theoretical expectations. However, the Flexwheel model achieves a 68.47% reduction in body height fluctuation range compared to the traditional design, highlighting its effectiveness in height stabilization. Additionally, the average body height of the Flexwheel model is 79.87 mm. Accounting for the radius of the Flexwheel's foot pad, the average distance from the hub center to the foot pad's spherical center was 70.87 mm, which closely aligns with the theoretical value of 70.4 mm. A demonstration can be viewed in the supplementary video via [[https://youtu.be/jjpFh1](https://youtu.be/jjpFh1) ejd24]([https://youtu.be/jjpFh1](https://youtu.be/jjpFh1) ejd24) (accessed on 7 May 2025)