A large displacement model for superelastic material side-notched tube instruments

Abstract

Side-notched tube structures made of superelastic material are increasingly being studied in surgical robotics as they can easily be integrated into surgical instruments and offer the surgeon enhanced dexterity. Their simple design and ability to achieve large bending angles and small bending radii make them particularly suited for use in constrained workspace surgery. Up to now, however, no model has been able to accurately predict the behavior of such types of structures for large bending angles. This study, therefore, proposes a novel approach to model large displacements of side-notched tubes taking into account the superelasticity of the material, the non-constant curvature of the side-notched structure, as well as the friction induced by the actuating wire. More specifically, an equivalent, strain dependent, linear elastic modulus is used to model the superelastic behavior of the instrument’s material. The deformation of each separate section of the side-notched tube is calculated successively to capture the non-constant curvature of the NiTi backbone. The capstan equation is used to model cable friction. The model was tested on four samples of 2.3 mm diameter and was able to predict the bending angle of the side-notched tubes with a root mean square error (RMSE) of as low as 5.4∘ (3.1%) and the position of each notch with an RMSE of as low as 0.33 mm (2.5%) across its entire bending range (0∘ to 180∘). The model was demonstrated for both tension and relaxation of the actuating wire.