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 $5.4^{\circ }$ ($3.1\%$) and the position of each notch with an RMSE of as low as 0.33 mm ($2.5\%$) across its entire bending range ($0^{\circ }$ to ${180}^{\circ }$). The model was demonstrated for both tension and relaxation of the actuating wire.

由超弹性材料制成的带侧凹口的管结构正日益被外科手术机器人研究，因为它们可以轻松地集成到外科器械中，并为外科医生提供增强的灵活性。它们的简单设计以及实现大弯曲角度和小弯曲半径的能力使其特别适合用于受限工作空间手术。但是，到目前为止，还没有模型能够准确地预测这种类型的结构在大弯曲角度下的行为。因此，这项研究提出了一种新颖的方法来模拟侧凹管的大位移，该方法考虑了材料的超弹性，侧凹结构的非恒定曲率以及致动线引起的摩擦。更具体地说，是一个等效的，应变相关的，线性弹性模量用于模拟仪器材料的超弹性行为。依次计算侧凹管的每个单独部分的变形，以捕获NiTi主链的非恒定曲率。主导轴方程用于建模电缆摩擦。该模型在直径为2.3 mm的四个样品上进行了测试，并能够预测均方根误差（RMSE）低至$5。4^{\circ }$ （$3.1％$）以及每个槽口的位置，其RMSE低至0.33 mm（$2.5％$）在其整个弯曲范围内（$0^{\circ }$ 到 ${180}^{\circ }$）。证明了该模型对于致动线的张力和松弛。