Curvature Correction of a Notched Continuum Robot Based on a Static Model Considering Large Deformation and Friction Effect

Continuum robots are often used as wrist joints in medical robots because of their high dexterity and flexibility. Especially, the notched continuum robot (NCR) is used in the miniaturized wristed surgical robot. The Piecewise Constant Curvature (PCC) assumption is often used in the design of NCR. However, due to the friction effect, ideal PCC is difficult to achieve. Static analysis is a necessary means to correct the curvature of NCR. The static modeling of NCR is often based on the theory of small deformation. However, this cannot obtain accurate solutions at large bending angles. In this paper, a static model of a triangular-notched continuum robot is proposed. It presents a curvature correction method of NCR, considering large deformation. In addition, the friction effect is considered in the correction of PCC. The static model is derived from the end notch. Based on the Coulomb friction model, the recurrence relationship of the force on the cable is obtained. Then the elliptic integral solution corresponding to the large deformation assumption is calculated. The deformation parameters of the NCR are obtained by numerical iteration. Finally, the capability and validity of the static model proposed in this paper are verified in the experiment. This paper is of great significance for establishing an accurate static model for curvature correction and design of the notched continuum robot.