## 2 Design, Modeling, and Control
### Mechanical Design  
The vehicle has four legs, each one fully designed in Computer-Aided Design (CAD) and printed using 3D materials, for low-cost and fast development purposes. Throughout a previous research [21], a single leg for this vehicle was designed and modeled, and its control was tested in a practical context. Although the obtained results were quite satisfactory, the torsional moment required from the motors, especially on the rigid joint, was noteworthy.  
This can be explained since the rotational movements are sometimes sudden, and the combination of rigid and non-rigid joints makes it difficult, for example, to brake the joints, which is mechanically more critical. A way to solve this problem would be to use a motor with gearboxes built with more resistant materials, which can transmit and support larger torques. However, this solution increases the cost of the vehicle, which is not compatible with the low-cost paradigm. The solution that avoids these increased mechanical efforts and complies with the construction paradigm is the replacement of the rigid joint with a non-rigid one. However, the previously presented non-rigid joint revealed that the required torque could not be achieved. This torque is used for positioning over the \(z_{r}\)-axis. So, a planetary gearbox was added at that particular position. This reduction gearset increases the rotational torque to the desired values. Moreover, being planetary, it also helps in reducing the joint backlash. This additional gear has a 3.2:1 ratio, which maintains the system modularity, solving the reported problem. Figure 3 presents the improved non-rigid joint configuration, while Figure 4 presents the improved leg configuration.  
Figure 4: Improved leg configuration (front left leg).  
Figure 3: Improved non-rigid joint—explosion render.  
Each leg has a defined joint configuration, as shown in Figure 5. Their numbering goes from joint 0 to joint 2, from top to bottom, respectively. The linear and rotational axes are also represented.  
The hip joint also suffered from torsional moment, and could be damaged for this reason, since it is the only exactly vertical axis, and therefore more prone to impacts. Furthermore, this is also the joint responsible for steering the vehicle when it is moving, so it is extremely important that its positioning is as accurate as possible. Considering these, to improve the mechanical robustness of this joint, as well as to decrease the gearbox backlash, a reduction gear was added, with a 4:1 ratio, connected through a geared belt, that improves both specifications. The obtained rigid hip joint is the one present in Figure 6.  
The platform that was built to serve as a test bed is presented in Figure 7, which show the robot's rendering in CAD as well as its real version, respectively.  
As can be seen in the diagram of Figure 8a, the robot's maximum dimensions are 850 \(\times\) 465 mm (L \(\times\) W). Figure 8b shows that its height can vary between 320 and 505 mm. In its current configuration, the robot weighs approximately 18 kg. In Table 1, the data from the vehicle's dimensions are aggregated.  
Figure 5: Leg with axes, links, and joints numbering.  
Figure 6: Improved hip rigid joint (**left**—render, **right**—real).  
Figure 7: Rendered and real robot.