## 3 Implementation and Design
### Chosen Instrument  
As per the previous section, with the aim to of simplifying the robotic system to ensure its compatibility with an existing instrument, the uterine manipulator used here has been selected from the available reusable tiltable-tip uterine contraction instruments. Similarly to other tiltable-tip uterine manipulators, the chosen uterine manipulator, which is almost identical to the Tintara uterine manipulator [20] shown in Figure 6, consists of three parts; a handle, a body, and a tiltable tip. Its body comprises two stainless-steel rods and a spring hook retaining its contact with the tenaculum. At the joint connecting the body and the tiltable-tip, a plate is connected to the changeable pivot head with a screw. The head has a diameter of 5 mm with three standard lengths of 6, 8, and 10 cm. This instrument allows anteversion of the uterus up to 90\({}^{\circ}\) and lateral motion of about 150\({}^{\circ}\) bilaterally.  
Unlike other uterine manipulator robots, which may require 3 DoFs [8,10,14], 5 DoFs [12] or up to 7 DoFs [13], the 2 DoFs of the chosen uterine manipulator could provide a considerably sufficient coverage of uterine movements, delineate the vaginal follicles nicely and allow the uterus to flex on itself.  
Figure 5: Diagram of robot prototype implementation and preoperative performance evaluation in soft-tissue cadavers.  
Figure 6: The chosen tiltable-tip uterine manipulator.  
Though the movement control range of the chosen instrument could achieve nearly the full coverage of an entire sphere, it is not that straightforward for the **Roll**, **Yaw** and **Pitch** motions. As shown in Figure 7, there are two joints in the chosen instrument at the handle and the tip at which the handle can only roll while the tip can only tilt; these will be referred to as (handle) **Roll** and (tip) **Pitch**, respectively, from now on. Though the instrument can only maneuver \(\pm 150^{\circ}\) (not the full \(360^{\circ}\) in the **Roll** panel due to the handle of the instrument, which is the most unwieldy part) in roll motion, and only (0\(\sim\)90\({}^{\circ}\)) in tilt or pitch motion due to its structure, with the combination of these roll and tilt maneuvers, **Pitch** and **Yaw** panels can be achieved. In total, generally speaking, the chosen instrument can move \(\pm 150^{\circ}\) in the **Roll** panel and \(\pm 90^{\circ}\) in both **Pitch** and **Yaw** panels.  
Figure 8 illustrates the movements in the **Roll**, **Yaw**, and **Pitch** panels of the chosen manipulator, with the body pointing towards the front, showing the best views of the tip: the front views, as shown in Figure 8a,c, and the side view, as shown in Figure 8b,d, where the vertical stick is the pole, holding the instrument. Figure 8a shows the **Roll** motion of \(\pm 150^{\circ}\) with the **Pitch** angle fixed to \(90^{\circ}\). Though the distal **Yaw** motion cannot be manipulated directly via the manipulator, any designated position in the **Yaw** panel could be achieved as shown in Figure 8c by controlling the **Roll** motion followed by the **Pitch** motion. Lastly, both Figure 8b,d depict the movement in the **Pitch** panel. Although the **Pitch** motion can be directly achieved by varying the **Pitch** angle, the movement in Figure 8b is limited to only (0\(\sim\)90\({}^{\circ}\)) in the **Pitch** panel, as the instrument cannot roll down to \(180^{\circ}\) due to the bulky handle, while Figure 8d shows all \(\pm 90^{\circ}\) in the **Pitch** panel when the instruments rolls to other available angles. Here, the first half of the **Pitch** angles (0\(\sim\)90\({}^{\circ}\)) can be obtained with a **Roll** angle (30\({}^{\circ}\)) and the last half of the **Pitch** angles (0\(\sim\)\(-\)90\({}^{\circ}\)) can be obtained with the flipped **Roll** angle (\(-150^{\circ}\)).  
Figure 7: Configuration of the 2 DoFs of the chosen instrument.