# Analysis and Design of a Minimalist Step Climbing Robot
## 4 Design Analysis
Hence, the higher the rear wheel torque, the lower the torque will be that is required by the front wheels for climbing over an obstacle. Table 5 shows the mean and standard deviation values of difference in allowable torque during the uncontrolled and controlled condition in the rear wheel with an increase in step number and change in height of the step. The decreasing value of mean and increasing value of standard deviation with higher step number implies that with the increase in the step number and the height of the step, the allowable torque in the controlled condition becomes higher than that of uncontrolled condition. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Required Torque (Nm)**} & \multicolumn{3}{c}{**Allowable Torque (Nm)**} \\ \cline{2-7}  & **Step 2** & **Step 3** & **Step 2** & **Step 3** \\ \hline Mean & \(-4.69\) & \(-3.44\) & -0.11 & \(-0.30\) \\ \hline Std. Dev. & \(0.93\) & \(2.45\) & \(0.33\) & \(0.30\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical analysis of variation in difference of required and allowable torque on front wheels during controlled and uncontrolled conditions with an active rear wheel and with respect to change in height of step. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Required Torque (Nm)**} & \multicolumn{3}{c}{**Allowable Torque (Nm)**} \\ \cline{2-7}  & **Step 1** & **Step 2** & **Step 3** & **Step 1** & **Step 2** & **Step 3** \\ \hline Mean & \(64.66\) & \(63.68\) & \(69.21\) & \(-57.18\) & \(-61.22\) & \(-65.47\) \\ \hline Std. Dev. & \(9.17\) & \(9.46\) & \(5.92\) & \(5.15\) & \(5.91\) & \(7.38\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical analysis of variation in difference of required and allowable torque on front wheels during controlled and uncontrolled conditions with respect to the change in the height of a step. The simulation conditions for the results plotted in the Figures 10 and 11 corresponds to a situation where the front wheel is considered on a step whereas the rear wheel in on a plane surface. Moreover, the height of the carried load is kept constant in the simulations. For a climbing robot, one of the most challenging conditions is when both the front and rear wheels overcome the steps simultaneously. In Figure 12, the effect of the height of the center of gravity of load is illustrated when both the front and rear wheels are at the edge of the steps. The height of the center of gravity of the load is varied from 50 mm to 1300 mm. The simulations for the cases wherein the inclination angle is actively controlled are performed for step 2 and step 3, only as the simulations at step 4, to maintain the inclination angle of the robot; the rear wheel has already climbed over the step 1. Figure 12a,b illustrates the variation in torque requirement in the front and rear wheels, respectively. It may be observed in Figure 12a that the required torque to overcome the step decreases in the case of controlled simulations as the front wheels are placed on higher steps. This phenomenon occurs because the connecting link is rotated to maintain the inclination angle, which in turn reduces the horizontal center distance of the front and rear wheels. As the center distance decreases, the center of the load proceeds closer to the rear wheel and a higher percentage of vertical load is shared by the rear wheels as compared to the front wheels. Moreover, the required torque on front wheels remains constant even with the increase in the height of the center of gravity (of the load). However, in the case of uncontrolled conditions, the variations in the required torque (required by the front wheels to overcome a step with respect to the changing heights of the center of gravity of the load) possess a negative slope. Moreover, the slope decreases with every higher step number. Eventually, the torque reduces to a negative value at the fourth step, while the height of the center of gravity (of the load) is close to 1300 mm.