# Design and Development of an Omnidirectional Three-Wheeled Industrial Mobile Robot Platform
## 5 Mechatronic Design
### Mechanical System
#### 5.1.1 Omnidirectional Wheel Design  
The design process consists of the static and dynamic analyses, as well as the calculation of the stresses of each component. The load to be supported is 300 kgf as established by the objective required by the sponsor, but an estimated value of 100 kgf must also be added, which represents the dead load of the structure. Therefore, the total value to be supported is 400 kgf, and it will be divided among the three wheels. Based on existing designs such as HANGFA Robotics QLM Series ([[https://www.hangfa-europe.com/en/mecanum-wheels/qlm-series](https://www.hangfa-europe.com/en/mecanum-wheels/qlm-series)]([https://www.hangfa-europe.com/en/mecanum-wheels/qlm-series](https://www.hangfa-europe.com/en/mecanum-wheels/qlm-series)) [accessed on 29 April 2025]) Omnidirectional wheels, we opt for an initial diameter of 200 mm, similar to the 203.2 mm used by QLM Series omnidirectional wheels. This design incorporates twelve polyurethane rollers with an aluminum body and a load capacity of 160 kgf per wheel. In comparison, the mecanum wheels [26], while offering higher precision in motion due to optimized parameters such as  
Figure 11: Workflow of the mechatronic design process. Figure 12: Mechanical design schematic. the angle between the roller axes and the wheels (45\({}^{\circ}\)) and a more advanced roller design, present manufacturing complexities and higher costs. Our approach prioritizes the ease of construction and less need for complex adjustments, while maintaining adequate load capacity and sufficient functional characteristics for the proposed mobile system. The first step is to know the diameter of the roller axle, for which a length is estimated from a geometry-only design, using AutoCAD 2023 software and manipulating the dimensions in millimeters until a perfectly symmetrical wheel geometry is obtained as shown in the following Figure 13.  
Static study performed in SolidWorks 2023 to determine von Mises stress distribution. The arrow indicates the applied load direction. The corresponding value is shown in the following Figure 14.  
Figure 14: Roller shaft—von Mises stress. Figure 13: Omnidirectional wheel geometry. As can be seen from the results, the maximum stress is 70.2 MPa, without exceeding the allowable stress of 351.57 MPa, giving a reliable safety factor. Continuing with the wheel design, an important component is the roller because it adds a third degree of freedom, turning a conventional wheel into a omnidirectional one. The roller has a special ellipsoidal cylinder shape. In order to obtain a closer approximation to the actual geometry of the roller, the stresses exerted on an ellipsoid pressed from Duralon on a concrete plane are analyzed. The dimensions of the semi-axes of the ellipsoid are 25 mm and 40 mm as shown in Figure 15.  
Evidently, the geometrical form that comes closest is the ellipsoid. There is a program called \"Mesys Hertzian Stress\" that shows all the stresses and data that are calculated in spherical, cylindrical, and elliptical contact exercises as seen in Figure 16. The program shows the evolution of the variables with respect to the central \(Z\)-axis. The stress that has the highest \(\sigma Z\) value is \(-133.55\) MPa which, due to its sign, works in compression. Duralon has a compressive strength of 55 MPa, and is a material that, due to its own characteristics, tends to fail by wear. Finally, we have the base of the omnidirectional wheel that will be under the bending effect in the supports (blue arrows in Figure 17). The safety factor is determined by means of the finite element analysis. Figure 16: Graph of stress and shear evolution. Figure 17: Safety factor of the base plate. Figure 12:0 Dimensions of the ellipsoid. A reliable and ideal safety factor of 3.6 is obtained, reducing the weight of the wheel. However, the cost of machining that would result from reducing the thickness in the central body of the plate from 22 mm (due to the supports) to 8 mm would be high.