# A Flexible Surgical Instrument for Robot-Assisted Minimally Invasive Surgery
## 4 Experiment  
In order to verify the accuracy of the kinematics and some functions of the flexible instruments, we built a robot system that adopted a master-slave control method [32; 33]. As shown in Figure 6a, the flexible instrument was installed at the end of the telecentric mechanism of the robot slave hand part. Figure 6b shows the main manipulator of the robot system. Figure 6c shows the flexible surgical instrument, which used stainless-steel 304 material for the model. The flexible part was composed of multiple segments, the outer diameter of the end effector was 8 mm, and cables of different lengths and with diameters of 0.5 mm were used for power transmission. The cables used in this instrument were produced by Japan N.M.R Company, the structure was 7 \(\times\) 6-IWR, the standard breaking load was 0.176 KN, the standard weight was 0.81 g/m, and the cables' material was high-strength and high-melting tungsten, which is suitable for complex mechanical driving or repeated bending requiring a long service life. The movements of the flexible instrument and robotic arms were driven by motors. In order to measure the range of motion of the end effector of the flexible instrument and the effect of real-time control, we controlled the flexible instrument to swing in the bending plane (the range of each swing was approximately 30\({}^{\circ}\)), and we recorded the corresponding time of each swing. Figure 7 illustrates the practical effect of the flexible instrument in bending degrees of freedom of \(\pm\)90 swing. As shown in Figure 7b, we gave the motor the proper running speed, and the time of each movement was approximately  
Figure 6: The prototype of the developed flexible surgical instrument: (**a**) minimally invasive surgical robot system; (**b**) the main manipulator of the robot; (**c**) flexible surgical instrument. 1 to 2 s. We believe that, in the need for visual feedback, in some cases, the proposed instrument can be moved very quickly to the desired position. During the experiment, no obvious problems were encountered such as the failure of wires and cables. In order to verify the accuracy of inverse kinematics, we extracted the bending trajectory of the flexible instrument. The position given by the master-slave mapping was compared with the position given by the kinematic equation calculation. For the given position, the bending angle \(\theta\) of each segment can be calculated through the inverse kinematics equation. Through the relationship between the wire rope length variation and the bending angle, the corresponding wire rope length variation controlled by the motor could be calculated, and the motor could be controlled to make the end of the instrument run to the given position. A motion capture system (Fusion Track 500, Atracsys, Puidoux, Switzerland) was used to collect movement information and obtain the actual motion trajectory through the collected position information. As shown in Figure 8, an optical reflector was fixed to the end effectors of the instrument. Data were collected from the motor's encoder, and the resulting values were applied to the forward kinematics equation to obtain the theoretical trajectory of the end of the instrument. The theoretical and actual motion trajectories of the flexible device are shown in Figure 9a. Taking the points of the trajectory in MATLAB, the coordinates of the obtained points were entered into the inverse kinematics solver, and the inverse kinematics were obtained in a very short period of time. The position deviations of the planned and collected trajectories are shown in Figure 9. E\({}_{x}\) is the deviation along the direction of the \(x\)-axis, E\({}_{y}\) is the deviation along the direction of the \(y\)-axis, and E\({}_{z}\) is the deviation along the direction of the \(z\)-axis. As shown in Figure 8, the maximum deviation of the simulation results for each coordinate point did not exceed 0.4 mm. Because the positioning accuracy of human vision is less than 0.1 mm [34], the accuracy could meet a doctor's operational needs.