# Research on the Decoupling of the Parallel Vehicle Tilting and Steering Mechanism
## 3 Simulation and Experiment
### Experiment  
A prototype was produced for the experiment. The proposed parallel mechanism was applied to the prototype. The prototype is shown in Figure 8a. The parallel mechanism is shown in Figure 8b. The parameters of the prototype are the same as those that are shown in Table 1. In order to facilitate the manufacture of the prototype, the parameters that were optimized by the mathematical model were approximated. As such, \(DE\) = 166 mm, \(FF^{\prime}\)= 118.7 mm, \(DC\) = 55 mm, \(GF\) = \(G^{\prime}F^{\prime}\) = 301.5 mm, and \(\varphi\) = 100 deg. The prototype uses two DC servo motors to drive \(\theta_{\text{t}}\) and \(\delta_{\text{t}}\), respectively. \(\theta_{\text{t}}\) and \(\delta_{\text{t}}\) were controlled by a given program. \(\theta_{\text{t}}\) and \(\theta_{\text{t}}\)\({}^{\prime}\) were linked through the mechanical structure, as are shown by the red part in Figure 8b. The manner that was used to read and record the experiment data is shown in Table 2. The equipment of the experiment is shown in Figure 9. \begin{table}
\begin{tabular}{c c} \hline \hline
**Function** & **Hardware** \\ \hline Read \(\theta_{\text{v}}\), yaw rate \(\hat{\varphi_{\text{v}}}\), and fit trajectory. & Inertial measurement unit: VG427C-CAN. \\ Read \(\delta_{\text{t}}\), \(\delta\), and \(\delta^{\prime}\). & Angle sensor: KD-701. \\ Read \(v\). & Wheel speed sensor: TE-ABS-181. \\ Record the experimental data. & Data logger: CANDTU-100 UR. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Equipment list of the experiment. Figure 8: The prototype. (**a**) The prototype; (**b**) The parallel mechanism. Figure 9: The equipment of the experiment. (**a**) Inertial measurement unit; (**b**) angle sensor; (**c**) wheel speed sensor; (**d**) data logger. Taking the prototype steering left as an example, the prototype drives on the road with the same \(\delta_{\text{t}}\) and \(v\), but different \(\theta_{\text{v}}\), where the speed is \(v=25\) km/h. The results of the experiment are shown in Figure 10.  
Figure 10: The result of the experiment. (**a**) Entered steering information; (**b**) the yaw rate of the prototype; (**c**) steering angle of the left wheel; (**d**) steering angle of the right wheel; (**e**) steering angle error of the left wheel; (**f**) steering angle error of the right wheel; (**g**) the SGCR; (**h**) the trajectory. The \(\delta_{\rm t}\) and \(\theta_{\rm v}\) values that were obtained by the experiment were input into the mathematical model. The \(\delta\) and \(\delta^{\prime}\) values that were calculated by the model were compared with the results of the experiment. The average relative errors of the steering angles are shown in Table 3.  
In order to facilitate the manufacture of the prototype, the mechanism's parameters were approximated. The established mathematical model is infinitely rigid, ignoring the effects of vehicle dynamics. The experiment made the prototype drive at a constant speed with different tilting angles in order to dilute the influence of the nonlinear change of the tires. These three points are the main reasons for the errors in the experiment. Compared with \(\theta_{\rm v}\) = 0 deg, the maximum relative errors of the steering angles, the yaw rate, and the trajectory of when the prototype drove at different tilting angles are shown in Table 4.  
The parallel mechanism that was designed by this method can reduce the influence of the vehicle tilting on the steering angle of the outer and inner wheels by up to 0.64% and 0.78%, respectively. This shows that when the vehicle is traveling at a low, constant speed, the influence of the vehicle tilting on the steering angle is small. In contrast, vehicle tilting affects the inner wheels more so than the outer wheels. As the vehicle's tilting angle increased, the influence of the vehicle tilting on the steering angle was greater. This effect is most obvious in the yaw rate. When \(\theta_{\rm v}\) = 20 deg, the relative error of the yaw rate was 2.49%.