## 3 Component Design
### Motor Selection  
Based on the information provided from Table 1, the filter-wheel system is designed to switch between various spectral filters with a maximum of 10 work steps for any combination, with the motor capable of bidirectional rotation. For instance, A1 to C1 takes 10 steps, while A1 to B5 or D2 takes 9 steps. To meet these requirements, it is crucial to select a motor that can operate at the necessary speeds and has the torque to drive the filter-wheel mechanism effectively. The motor selection process is detailed in Figure 6. \begin{table}
\begin{tabular}{c c c c} \hline  & **Upper Gear** & \multicolumn{2}{c}{**Lower Gear**} \\ \hline
**Code** & **Transmission Wavelength** & **Code** & **Transmission Wavelength** \\ \hline
1 & \(\leq\)700 nm & A & \(\geq\)760 nm \\
2 & \(\leq\)800 nm & B & \(\geq\)400 nm \\
3 & \(\leq\)900 nm & C & \(\geq\)500 nm \\
4 & \(\leq\)1150 nm & D & \(\geq\)560 nm \\
5 & \(\leq\)1200 nm & & \\ \hline \end{tabular}
\end{table} 
Table 1: Design of transmission wavelength for the upper and lower filter wheel. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Work Step** & **Combination** & \multicolumn{2}{c}{**Spectral Details**} & \multicolumn{2}{c}{**Work Step**} & \multicolumn{2}{c}{**Combination**} & \multicolumn{2}{c}{**Spectral Details**} \\
**Number** & **Code** & & **Number** & **Code** & & **Size** \\ \hline
1 & A1 & 760 nm & 700 nm & 12 & D2 & 560 nm & 800 nm \\
2 & B2 & 400 nm & 800 nm & 13 & A3 & 760 nm & 900 nm \\
3 & C3 & 500 nm & 900 nm & 14 & B4 & 400 nm & 1150 nm \\
4 & D4 & 560 nm & 1150 nm & 15 & C5 & 500 nm & 1200 nm \\
5 & A5 & 760 nm & 1200 nm & 16 & D1 & 560 nm & 700 nm \\
6 & B1 & 400 nm & 700 nm & 17 & A2 & 760 nm & 800 nm \\
7 & C2 & 500 nm & 800 nm & 18 & B3 & 400 nm & 900 nm \\
8 & D3 & 560 nm & 900 nm & 19 & C4 & 500 nm & 1150 nm \\
9 & A4 & 760 nm & 1150 nm & 20 & D5 & 560 nm & 1200 nm \\
10 & B5 & 400 nm & 1200 nm & 21 & A1 & 760 nm & 700 nm \\
11 & C1 & 500 nm & 700 nm & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Detailed types of spectral bands and combination numbers for double-layer filter wheel. Figure 6: The process of motor selection. The motor's time-displacement curve typically forms a trapezoid, reflecting the process of acceleration, constant speed, and deceleration to reach the target. As seen in Figure 7a, if the target is nearby, the curve becomes triangular, indicating that the motor must begin decelerating before reaching full speed to prevent overshooting, as depicted in Figure 7b. To optimize the switching time, the preliminary motor selection is guided by the reference curve in Figure 7b. To ensure a safety margin, the design calculates the maximum switching time for any filter combination as 0.5 s. For adjacent combinations, the switching time is computed to be 0.1 s; the calculation method satisfies Formula (3). \[ \begin{split}\frac{t_{1}n_{1}}{2}=R_{1}\\ a_{1}=\frac{2n_{1}}{t_{1}}\\ \frac{t_{10}n_{10}}{2}=R_{10}\\ a_{10}=\frac{2n_{10}}{t_{10}}\end{split}  \tag{3}\]  
where \(t_{1}\) is the adjacent switching time, which is 0.1 s; \(n_{1}\) is the maximum speed of small gear during adjacent switching process, and the unit is r/s; \(R_{1}\) is the number of revolutions of the small gear during the adjacent switching process, which is 1 r/s. \(a_{1}\) is the acceleration of the small gear during the adjacent switching process, and the unit is r/s. \(t_{10}\) is the maximum switching time, which is 0.5 s; \(n_{10}\) is the maximum speed of the small gear during the maximum switching process, and the unit is r/s; \(R_{10}\) is the number of revolutions of the small gear during the maximum switching process, which is 10 revolutions; \(a_{10}\) is the acceleration of the small gear during the maximum switching process, and the unit is r/s. After calculation, \(n_{1}=20\) r/s, \(a_{1}=400\) r/s, \(n_{10}=40\) r/s, \(a_{1}=160\) r/s.