# A Flexible Surgical Instrument for Robot-Assisted Minimally Invasive Surgery
## 1 Introduction
This research can be used to guide the design of soft actuators, thereby speeding up the design process. [PERSON] et al. proposed a method for solving the kinematics of a flexible robot [21] by analyzing the robot's mechanism, establishing a coordinate system, and using the geometric relationship and D-H method to solve the relationship between the pose and the three lines of the control end. Although this method can accurately obtain the kinematic equations, the solution process is too complicated, which is not conducive to the kinematics solution of complex structures. [PERSON] et al. presented a geometrical approach for solving the inverse kinematics of a continuum robot [22]. The position of each node on the continuum structure was assumed to be known and then compensated for the resulting change in direction; however, this approach cannot provide a general solution form. [PERSON] et al. designed and conducted a kinematics analysis of a series-parallel hybrid flexible surgical instrument [23]. The author obtained the kinematics equation of the robot according to the physical properties of the rigid Hooke hinge and the rod length constraint. Although this method can solve the relationship between each branch chain of the parallel mechanism and the rotation angle of the platform, due to the structural characteristics of the mechanism, it is not necessary to consider the kinematic characteristics of each branch chain, which has the disadvantage of lower accuracy. [PERSON] et al. designed a wire-driven flexible manipulator (WDM), using the robotics toolbox to model the WDM and verify its kinematics [24]. An optimized IK method was developed for the inverse kinematics solution of a WDM, and a geometric approximation was used as an initial guess for numerical optimization. Although this method does not provide an exact solution, it gives an approximate value of the angle of bending in WDM. Therefore, such an appropriate starting point can reduce the convergence time or even avoid local optimization. This method can provide fast and reliable inverse results, simplify kinematics calculations, and improve the real-time performance of the robot. However, it neither considers drive-by-wire control nor does it demonstrate the effectiveness of the method through prototype experiments. In summary, for kinematically redundant and flexible robotic structures, the standard Denavit-Hartenberg convention [25] for describing the position relationships of prismatic or revolute joints is not well suited for flexible robots, the development of kinematics to operate such robots repeatedly and reliably under real-time control remains an open research topic. In this study, a flexible surgical instrument was developed that realizes dexterous motion by means of the structure of a segment connected by a pin roll in sequence. Its forward kinematics were solved using geometrical methods, and the Newton-Raphson method was used to solve the inverse kinematics. The performed experiments verified that the method was quick and accurate. Finally, it was verified that the flexible surgical instrument had good dexterity in a long and narrow space and had a certain load-bearing capacity.