Utilization of 2 N + 1 Units for 2-DOF Discrete Bending Joint to Transmit Perfect Axial Rotation for Laparoscopic Instruments

Laparoscopic instruments, which have traditionally been long and straight, have been equipped with wrist joints for executing complex procedures. Among the many methods for constructing a cable-driven wrist joint for such instruments, the use of pulleyless rolling unit joints has recently been demonstrated to be effective and applied to various surgical robots. Although it is a common practice to alternately stack 2 N one-degree-of-freedom (1-DOF) units to form a 2-DOF bending joint, it is cumbersome to determine the optimal stacking sequence, and the determined sequence might not satisfy performance requirements. Therefore, in this paper, we propose a new method to construct a 2-DOF discrete bending joint by using 2 N + 1 units. The advantages of the proposed method over the previous method of determining the optimal structure by using 2 N units are demonstrated quantitatively through kinematic modeling and calculation. As a result, the behavior of the proposed discrete bending joint becomes increasingly similar to that of a continuum joint as the number of units employed in the construction increases. In addition, it is confirmed that the 2 N + 1 model can accurately transfer proximal rotation to the distal tip, similarly to a constant velocity joint. It is expected that the proposed simple method for constructing bending joints will be applied to develop various surgical robot structures in the future.