# Design and Mechanical Behavior Research of Highway Guardrail Patrol Robot
## 2 Mechanism System Description
### Analysis of Falling Conditions and Guardrail Safety Conditions  
Since the guardrail inspection robot employs a tight-fitting double-sided wheel structure, a spring mechanism is required to provide the appropriate tension. This ensures effective power transmission while maintaining the robot's mobility and operational stability. The single-sided drive design also results in differing pulling force requirements on the driven and non-driven wheel sides. By adjusting the stiffness \(k_{1}\) of the spring on the driving wheel side and the stiffness \(k_{2}\) of the spring on the driven wheel side, the forces exerted on the wheel frames on both sides can be fine-tuned. The gravity distribution coefficients for the master and slave sides are defined as \(\lambda\), which satisfies the following relationship:  
\[\lambda=\frac{k_{1}}{k_{1}+k_{2}}, \tag{1}\]  
When the robot is in a critical situation where it is at risk of detaching from the guardrail, it is assumed that the load wheels no longer counteract the gravitational force. Figure 1: Structure of guardrail inspection robot. (**a**) Robotic mechanism composition. (**b**) Side view of the robot. (**c**) Stress condition of the rubber-coated wheel. In this scenario, the entire weight of the robot is supported by the rubber-coated wheels on both the master and slave sides, as illustrated in Figure 1c. At this point, the following equilibrium equation applies:  
\[\left\{ \begin{array}{l}\left({F_{N}}^{\prime}+{F_{N}}^{\prime\prime}\right)\cos \beta+\mu{F_{N}}^{\prime\prime}\sin\beta-{F}^{\prime}=0\\ \left({F_{N}}^{\prime}-{F_{N}}^{\prime\prime}\right)\sin\beta+\mu{F_{N}}^{ \prime\prime}\cos\beta+\lambda G=0\end{array} \right., \tag{2}\]  
When the wheel is in a critical falling-off state, where \({F_{N}}^{\prime}\) = 0, the spring tension on the driven wheel frame should satisfy the following formula:  
\[{F}^{\prime}+{F}^{\prime\prime}>G(\frac{\cos\beta}{\sin\beta}+\mu), \tag{3}\]  
Here, \(G\) represents the self-weight of the robot. The target mass for the patrol robot developed in this study is set at 30 kg. \(\mu\) denotes the static friction coefficient between the rubber-coated wheel and the corrugated beam guardrail, and \(\beta\) is the angle between the hypotenuse of the rubber-coated wheel and the vertical direction. \({F}^{\prime}\) and \({F}^{\prime\prime}\) represent the forces required for the driven wheel frame and the non-driven wheel frame, respectively, to prevent slippage. These forces depend on the spring stiffness values \(k_{1}\) and \(k_{2}\), the horizontal distance \(x\), the vertical distance \(h_{0}\), and the inclination angle \(\gamma\) of the spring. The relationship is expressed as follows:  
\[\left\{ \begin{array}{l}{F}^{\prime}=4k_{1}(x-x_{0}\cos\gamma)\\ {F}^{\prime\prime}=4k_{2}(x-x_{0}\cos\gamma)\\ {h_{0}}/{x}=\tan\gamma\end{array} \right., \tag{4}\]  
\(x_{0}\) in the formula is the initial length of the spring. In order to control the variables, the impact of the spring stiffness on the robot performance is analyzed separately, so the initial length of the spring on the active side and the driven side is ensured to be consistent. By changing the spring stiffness, the spring-tensioning force of the driving gear train and the driven gear train is changed. Based on the dimensions of the corrugated beam and the compatibility of the mechanical structure, the preset values for each parameter are shown in Table 1.  
Based on the above analysis, it can be concluded that, to ensure the inspection robot does not detach from the guardrail while operating on a stable track, the following relationship must be satisfied:  
\[k_{1}+k_{2}>1.21, \tag{5}\]  
If the sum cannot satisfy the aforementioned inequality, the robot will detach from the guardrail. It is important to note that the value of 1.21 is calculated based on the initial structural parameters of the robot and is specific to this configuration. Different robot dimensions may result in different corresponding values.