## 3 Implementation and Design
### Prototype Design  
Last but not least, along with the required force from the assessment above, electric actuators were chosen in preference to other common actuators, such as hydraulic and pneumatic actuators. As a result, the fluid or air from these actuators could leak, and also the electric ones could deliver both precise control and the compact design. To be specific, two stepper motors were chosen to control the **Roll** and **Pitch** motions. As their movement comprises discrete steps with high reliability, low cost, and high torque at low speeds, this makes stepper motors suitable for robotic applications both commercially and industrially when precision positioning is required. In this system, both stepper motors are part of an open loop system for computer-controlled holding and positioning of the uterine manipulator in place, as shown in Figure 15, along with the CAD model and the implemented prototype with all the details. M1 is the stepper motor controlling the \(\mathbf{\theta}\) in the **Roll** (rotating) panel, where M2 is a mechanical linear actuator with the other motor at the handle controlling the \(\mathbf{\varphi}\) in the **Pitch** (tilting) panel by converting the distance \(\mathbf{d}\) into the \(\mathbf{\varphi}\). Per the control interface for the proposed uterine manipulator robot, in order to control the robot in the distance without having to stand at the vaginal end where the uterine manipulator robot takes place, a common two-axes with one-enable-button joystick, adequate for controlling **Roll** and **Pitch** motions step by step, has been deployed in the system. Tilting the lever leftward or rightward controls the M1, increasing or decreasing the **Roll** angle by one degree. Similarly, tilting the lever forward or backward once controls the M2, increasing or decreasing the **Pitch** angle also by one degree. Meanwhile, holding the lever in any direction would change the angle every 0.5 s.  
Although the differences for each angle would be a positive value for the counter-clockwise direction and negative value for the clockwise direction, the number of motor steps for M1 and M2 is calculated based on the absolute angle difference values; \(\text{abs}(\mathbf{\theta})\) and \(\text{abs}(\mathbf{\varphi})\), respectively, as shown in Equations (8) and (9). The constants used in these equations are as follows: **SPR** is the number of steps per revolution; **SPD** is the number of steps per degree = \(\text{SPR}/360^{\circ}\); **L** is the axial distance traveled by the lead screw thread in a single revolution; \(\mathbf{d}_{max}\) is the stroke length, the maximum controlling distance at the handle; \(\mathbf{\varphi}_{max}\) is the maximum pitch angle, which is +90\({}^{\circ}\) in this case. Figure 14: The design (**a**) and experimental setup (**b**) for force assessment. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Pitch** & **0 g** & **100 g** & **200 g** & **300 g** & **400 g** & **500 g** \\ \hline
30\({}^{\circ}\) & 3.2 N & 3.8 N & 4.5 N & 6.0 N & 7.0 N & 10.2 N \\
60\({}^{\circ}\) & 3.9 N & 4.4 N & 5.7 N & 6.7 N & 7.0 N & 11.5 N \\
90\({}^{\circ}\) & 4.1 N & 7.9 N & 8.7 N & 9.6 N & 10.7 N & 12.3 N \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Measured force at different loads and **Pitch** angles (\(\mathbf{\varphi}\)). \[\#of\ M1\ Steps=\mathbf{SPD} \tag{8}\]  
\[\#of\ M2\ Steps=(\frac{(\frac{\mathbf{d_{max}}}{\mathbf{\hat{p}_{max}}})\ \times\ \mathbf{ SPR}}{\mathbf{L}}) \tag{9}\]  
After we obtained the maximum force of 12.3, which corresponds to the maximum possible weight (500 g) of a uterus at the **Pitch** angle of 90\({}^{\circ}\), it was determined that this would be the requirement for choosing an appropriate motor that can support this force. The NEMA17, a two-phase hybrid stepping motor, used as a bipolar stepper motor with a 1.8\({}^{\circ}\) step angle, has been chosen for the linear actuator, M2, in this study. Each phase draws 1.2 A at 4 V, allowing for a holding torque of 52 N-cm.