# Scoring of Human Body-Balance Ability on Wobble Board Based on the Geometric Solution
## 5 Results
### Results of Verification of Scoring Algorithm  
Figure 8 shows the results of some examples to score the HBBAWB based on the geometric solution. The blue-green colored circle on the human body indicates the location of the COM, the same colored circle on the plane shows that of COG, and the yellow-colored circle demonstrates that of the PPP.  
For the results of the score under the boundary condition in Figure 8a, the score became 100 points when the PPP was equal to the COG. On the other hand, the score was zero when the PPP was on the boundary condition, regardless of being on the left or right side on the ML plane. Furthermore, the proposed algorithm enabled the user to be instructed on how to improve the current balance condition, such as \"move left\" and \"move right\", as shown in Figure 8a. For the results of the score within the boundary condition in Figure 8b, the experimental results verified that the proposed scoring algorithm worked  
Figure 8: The results of some examples to score the human body-balance ability on the wobble board (HBBAWB) based on the geometric solution: (**a**) represents the results under the boundary condition and (**b**) represents within the boundary condition.  
Figure 7: The results of the specifications were displayed on the screen of the scoring system.  
well. Notably, the visualization for the location of the PPP helped the user keep a stable balance condition.  
Table 1 shows the results of boundary conditions for 10 participants. In this study, max_a is a variable, not a constant. Because the location of COM affected the value of max_a as shown in Figure 5.  
The different boundary conditions of max_a came from the different physical conditions of each participant.  
Figure 9 shows the results of the line plot between the angles of \(\alpha\) and \(\theta_{1}\). \(\alpha\) of the blue-colored plot represents the angle between the three points of the BOF, COM, and PPP, as shown in Figure 5, and \(\theta_{1}\) of the orange-colored plot represents the tilted slope of the wobble board, as shown in Figure 1b. If the \(\theta_{1}\) value increases and the \(\alpha\) value falls, they have an opposite direction, and the user is in a stable condition. Furthermore, the more change there is of the \(\theta_{1}\) value and the \(\alpha\) value, offset under the balance condition, the better the user maintains equilibrium. Conversely, when the \(\theta_{1}\) line and \(\alpha\) line go up or down together, meaning the \(\alpha\) value and \(\theta_{1}\) value increase or decrease together, the user is in an unstable condition.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ID** & **Age** & **Gender** & **Weight [kg]** & **Height [cm]** & **Max_a (\({}^{\circ}\))** \\ \hline
1 & 25 & Female & 60 & 155 & 10.47 \(\pm\) 0.42 \\
2 & 28 & Female & 57 & 156 & 10.35 \(\pm\) 0.32 \\
3 & 23 & Female & 50 & 162 & 8.40 \(\pm\) 0.26 \\
4 & 25 & Female & 52 & 162 & 8.40 \(\pm\) 0.33 \\
5 & 36 & Male & 80 & 170 & 8.77 \(\pm\) 0.68 \\
6 & 45 & Male & 80 & 170 & 9.3 \(\pm\) 0.54 \\
7 & 27 & Male & 81 & 170 & 9.70 \(\pm\) 0.74 \\
8 & 30 & Male & 69 & 173 & 9.28 \(\pm\) 0.59 \\
9 & 27 & Male & 73 & 176 & 8.32 \(\pm\) 0.82 \\
10 & 22 & Male & 59 & 180 & 8.06 \(\pm\) 0.33 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The results of boundary conditions for ten participants.  
Figure 9: The results of line plot between angles of \(\alpha\) and \(\theta_{1}\): \(\alpha\) of blue-colored plot represents the angle between three points of the base of the foot (BOF), the center of mass (COM), and the perpendicular-projection point (PPP), while \(\theta_{1}\) of orange-colored plot represents the tilted slope of the wobble board.  
That meant that the PPP of the proposed index played an essential role in explaining the reason and cause, compared with the trajectories of the COG.  
As a result, the proposed scoring algorithm enabled us to be able to score the HBBAWB, compared with a conventional method, such as the trajectories of the COG.