## 3 Experiments And Discussion
### Experiment 2: Pick-and-Place and Experiment 3: Block-in-Hole  
In the pick-and-place task, the forceps were employed to grasp four silicon tubes (inside diameter: 3 mm, outside diameter: 5 mm, length: 8 mm) and place them on numbered pegs (see Figure 14b). The testbed was placed 100 mm away from the nostril. Right and left hands were alternated for each silicon tube. The task was repeated three times for each hand with both the conventional instruments and the proposed cooperative user interface. The block-in-hole task was similar to the pick-and-place task with an additional need for orientation adjustments while positioning the blocks. The forceps were employed to grasp three blocks (two 5 mm edge cube and one 4 mm edge tetrahedron) and place them on the corresponding hole located under the initial hole, with a similar shape, but different orientation (see Figure 14c). The testbed was located 100 mm away from the nostril. Right and left hands were alternated for each block. The task was repeated three times for each participant with both the conventional instruments and the proposed cooperative user interface.  
For the pick-and-place and block-in-hole tasks, a nose phantom was used (shown in Figure 14a). It comprised a 3D printed nose model and an acrylic platform for the testbeds. A magnetic motion capture system (Aurora, Northern Digital Inc., Ontario, Canada) was used to measure the motions of the surgical instrument for both the manual and robot task operation for evaluation purposes. For each trial, we considered the following aspects to evaluate the performance:  
* Task completion time (s): starting from the first contact with the tube/block until the release of the last tube/block.
* Motion smoothness: we used the root mean squared jerk (RMSJ) [33] as a metric, defined by: \[RMSJ=\sqrt{\frac{1}{t_{1}-t_{0}}\int_{t=t_{0}}^{t=t_{1}}\|\,\vec{x}\,\|^{2}dt}\.\] (25)  
Eight subjects between the ages of 20 and 35 who had no previous surgical training took part in these experiments. Before the experiments, each participant was instructed to practice for 5-10 min until they were familiarized with the operation. The results for the pick-and-place task are depicted in Figure 15.  
The time to complete the pick-and-place task was approximately 66% longer with the use of our proposed system than the case of the manual operation of conventional forceps. This was expected due to the velocity limitation of 10 mm/s imposed on the forceps tip motion on the robot arm. Despite this, the root mean squared jerk, used as a metric of smoothness, showed approximately a 20% reduction of the variability and mean values when using our proposed system. A higher dexterity in the right hand compared with the left hand was observed as lower variability in the manual operation. In the  
Figure 13: **(a)** Root mean squared error (RMSE) between the trajectory performed and the optimal trajectory. **(b)** Task completion time.  
The results for the block-in-hole are depicted in Figure 16. Similar to the pick-and-place task, the time to complete the block-in-hole task was approximately 66% longer with the use of our proposed system due to the velocity limitation. However, in this case, the root mean squared jerk showed more than a 40% reduction of the mean values when using our proposed system on both hands. The combined box confidence interval did not show any overlap, which indicated that the robotic system was able to provide a smoother motion compared with the use of conventional instruments when orientation adjustments and higher precision were required.