A neurosurgical robot with 3-dimensional (3D) distal manipulation can increase instrument workspace for reaching peripheral regions of intracranial lesions to achieve complete lesion removal and minimal brain manipulation in a keyhole procedure. In this work, we designed a Nitinol-based symmetrically notched continuum robot based on the neurosurgical clinical constraints. A mechanics model is developed for the robot using a second order differential equation that exploits the shearing force formulation based upon the Euler $-$ Bernoulli moment-curvature equation. It affords non-constant curvature analysis, and integrates the piecewise linear material model with three stages that closely approximates the nonlinear superelastic property of Nitinol. A solution was introduced to this complex mechanics model based on the fourth order Runge-Kutta method with variable transformation, and an iterative approach. Comparison with the experimental data using our proposed model shows its high modeling accuracy in terms of the bending angle and tip position for a single symmetric notch bending as well as 2D bending motion of the robot. The significantly improved accuracy over previous models justifies the added complexity of our modeling approach and could better guide the determination of the notch parameters during robot design.

中文翻译：

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具有非恒定曲率和超弹性特性的对称缺口连续神经外科机器人建模

具有 3 维 (3D) 远端操作的神经外科机器人可以增加仪器工作空间，用于到达颅内病变的外围区域，以在锁孔手术中实现完整的病变去除和最少的大脑操作。在这项工作中，我们基于神经外科临床限制设计了一种基于镍钛诺的对称缺口连续体机器人。使用基于欧拉的剪切力公式的二阶微分方程为机器人开发了力学模型$-$伯努利弯矩方程。它提供非常规曲率分析，并将分段线性材料模型与三个阶段相结合，非常接近镍钛诺的非线性超弹性特性。基于带有变量变换的四阶 Runge-Kutta 方法和迭代方法，为这个复杂的力学模型引入了一个解决方案。与使用我们提出的模型的实验数据的比较表明，它在单个对称凹口弯曲的弯曲角度和尖端位置以及机器人的二维弯曲运动方面具有很高的建模精度。与以前的模型相比，精度的显着提高证明我们的建模方法增加了复杂性，并且可以更好地指导机器人设计过程中缺口参数的确定。