# A Mobile Robot with Omnidirectional Tracks--Design and Experimental Research
## 2 Materials and Methods
### Construction of a Mobile Robot with Multidirectional Tracks
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dimension Name and Symbol** & **Value** & **Dimension Name and Symbol** & **Value** \\ \hline robot mass \(m_{r}\) & 6 kg & working load \(u\) & 2 kg \\ track link height \(a\) & 45 mm & track link width \(b\) & 40 mm \\ roller radius \(r_{r}\) & 10 mm & distance between the axis of the roller & 5 mm \\  & & and the plane of the track link \(h_{r}\) & 270 mm \\ roller mounting angle \(\gamma\) & 45\({}^{\circ}\) & distance between pairs of continuous & 225 mm \\ distance between the continuous & & track systems \(c\) & 225 mm \\ track systems in pair \(d\) & 80 mm & distance between the axes of the & 225 mm \\ belt wheel radius on drive wheel \(r_{bs}\) & 60 mm & belt wheel radius on motor \(r_{s}\) & 15 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimension and construction assumptions of the mobile robot. Figure 5: Kinematic scheme of the robot with a continuous track system that has multidirectional tracks. Figure 6: General view (**a**) and bottom view (**b**) of the solid model of the robot with the continuous track system with multidirectional tracks. Figure 7 shows the views of a single continuous multidirectional track with its own drive system. The continuous track system is composed of a track, an idler and a drive wheel. In each track segment there is one cylindrical rotating roller. The drives are located in the central part of the robot. The active moment is shifted to the drive wheel using transmission with a toothed belt. The track drive systems, track links, rollers and the body of the robot were made using incremental FDM technology. The material used is PET-G, which is a polymer characterised by low shrinkage and high mechanical resistance. The free rollers rotate on steel axes. There are plastic slip rings between the rollers and the mount, which is connected to the track plate. The rollers consist of a printed core, onto which the tyres are pulled. The tyres of the rollers, also made using FDM technology, are made of thermoplastic polyurethane with a Shore scale hardness of 40D. The view of the finished prototype of the mobile robot is presented in Figure 8.  
The motor is connected to the drive wheel by a reduction pulley transmission system with a reduction ratio of \(i_{k}=r_{s}/r_{\text{ks}}=0.25\). For the assumed maximum robot motion speed \(v_{\text{r}}\) (Table 1), the maximum angular velocity of the motor \(\omega_{s}\) was determined from the following equation:  
\[\omega_{s}=\frac{v_{r}}{r_{ks}\,i_{k}}=10.67\,\,rad/s \tag{2}\]  
The rated active moment of motor \(M_{\text{s}}\) was selected using the simplified method of the experimental measurements of the robot's motion resistance in the longitudinal and transverse direction using a tensometric force sensor. The highest motion resistance was measured experimentally during motion in the direction perpendicular to the main axis,  
Figure 8: View of the finished robot prototype equipped with a continuous track system with multidirectional tracks. Figure 7: View of the continuous track system with multidirectional tracks: (**a**) side view and (**b**) front view (1—idler, 2—link with a rolling roller, 3—track, 4—motor pulley, 5—drive wheel, 6—toothed belt). and is expressed as the maximum force that excites motion in a set direction, which was \(F_{T}=13\) N. It was assumed that the motor moment \(M_{\mathrm{s}}\) should be greater than:  
\[M_{\mathrm{s}}>\frac{r_{\mathrm{s}}F_{T}}{4} \tag{3}\]  
On the basis of the calculations made to design the prototype construction, POLOLU-2274 motors were selected with a torque of \(M\)s = 0.57 Nm, and a nominal speed of \(n_{\mathrm{s}}\) = 21.99 rad/s. Each motor is equipped with a magnetic encoder that provides 48 counts per revolution, and therefore one complete revolution of the wheel will provide 2249 pulses, with a drive wheel accuracy of \(\Delta\phi_{\mathrm{s}}\) = 0.0007 rad.