## 3 Speech-to-Text Transcriptor
### Database of Alphabet Models
#### 3.2.2 Inverse Kinematics  
The second step was to define the alphabet characters to be handwritten. In Figure 7, the alphabet considered in this work is presented. Each character can be drawn over a space defined by a set of points labeled from A-U, as presented in Figure 8. The height of this space is restricted by the limit specified in Figure 6 (3.0 cm). Figure 5: Speech recognition interface of the speech-to-text transcript. Any character presented in Figure 7 can be drawn based on a reference (center) coordinate (given by the point K) and a radius (r). The width of any character is equal to \(2\pi\), and the height of any character can be up to \(4\pi\), as deduced from Figures 7 and 8. Considering the writing line as defined by the points M-N-O, the height of the writing space can be expressed in terms of the radius as \(6\pi\). This is due to some characters having a height of \(4\pi\) above the writing line (e.g., h, l, k) and some others extending \(2\pi\) below the writing line (e.g., g, j, p). Curves and lines can be used to draw the alphabet characters by just considering the reference coordinate \([x_{0},y_{0}]\) (point K) and the radius/width (r). As presented in Figure 8, from \([x_{0},y_{0}]\), the coordinates for all other points can be computed and used as start-end points for drawing the segments that form each character. Consecutive characters can be drawn (written) by updating the reference coordinate given by K.  
For the task of drawing lines, just \"start\" and \"end\" points are required [28]. However, for the task of drawing curves, these points are given by angular ranges in terms of \(\pi\). Table 1 presents the  
Figure 8: Point-based approach for alphabet drawing (writing). Figure 6: Reachable \(x\)-\(y\) coordinates for all \(\theta_{1}\) and \(\theta_{2}\) combinations using forward kinematics equations. Figure 7: Mexican Spanish alphabet. set of points and angles that were defined to draw the segments for each alphabet character presented in Figure 7.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Alphabet**} & \multicolumn{2}{c}{**Straight Lines**} & \multicolumn{2}{c}{**Curved Lines-Circumferences**} \\ \cline{2-5}  & Start Point & End Point & Center, Radius & Angular Range \\ \hline a & I, where & O & K, r & \(0\leq\theta\leq 2\pi\) \\  & I(2) = I(2) - r/2 & & & \\ \hline b & A & M & K, r & \(0\leq\theta\leq 3\pi\) \\ \hline c & & & K, r & \(\pi/4\leq\theta\leq 7\pi/4\) \\ \hline d & C & O & K, r & \(0\leq\theta\leq 2\pi\) \\ \hline e & J & L & K, r & \(0\leq\theta\leq 7\pi/4\) \\ \hline f & D & M & E, r & \(\pi/4\leq\theta\leq\pi\) \\  & G & I & & \\ \hline g & R & I & Q, r & \(\pi\leq\theta\leq 2\pi\) \\  & & & K, r & \(0\leq\theta\leq 2\pi\) \\ \hline h & O & L & K, r & \(0\leq\theta\leq\pi\) \\  & M & A & & \\ \hline i & N & H & & \\  & H, where & H, where & & \\  & H(2) = H(2) + 0.2 & H(2) = H(2) + 0.3 & & \\ \hline j & R & I & Q, r & \(\pi\leq\theta\leq 2\pi\) \\  & I, where & I, where & & \\  & I(2) = I(2) + 0.2 & I(2) = I(2) + 0.3 & & \\ \hline k & A & M & & \\  & E & G & & \\  & G & O & & \\
1 & B & N & & \\ \hline ll & B, where & N, where & & \\  & B(1) = B(1) \(-\) 0.3 & N(1) = N(1) \(-\) 0.3 & & \\  & B, where & N, where & & \\  & B(1) = B(1) + 0.3 & N(1) = N(1) \(+\) 0.3 & & \\ \hline m & O & I, where & K, where & \(0\leq\theta\leq\pi\) \\  & & I(2) = I(2) \(-\) r/2 & K(1) = K(1) + r/2 and & & \\  & & K(2) = K(2) + r/2, r = r/2 & & \\  & N & H, where & K, where & \(0\leq\theta\leq\pi\) \\  & & H(2) = H(2) \(-\) r/2 & K(1) = K(1) \(-\) r/2 and & & \\  & & K(2) = K(2) + r/2, r = r/2 & & \\  & G & M & & \\ \hline n & O & L & K, r & \(0\leq\theta\leq\pi\) \\  & G & M & & \\ \hline fi & O & L & K, r & \(0\leq\theta\leq\pi\) \\  & G & M & & \\  & G, where & I, where & & \\  & G(2) = G(2) + 0.2 & I(2) = I(2) + 0.2 & & \\ \hline o & & & K, r & \(0\leq\theta\leq 2\pi\) \\Knowing the trajectories required to draw the alphabet characters is just part of the writing problem.