The notched continuum mechanism is particularly suitable for natural orifice transluminal surgery benefiting from its small size and hollow structure. However, the widely used kinematic model based on constant curvature assumption does not reveal the actual deformation of the continuum mechanism, and its control accuracy is unstable, while the general mechanics model has the problem that the tension of the distal driving cable is difficult to measure. In this paper, a nonconstant curvature static model for a bidirectional V-shaped notched continuum mechanism is presented. The deformation of each part of the continuum mechanism from the distal end to the proximal end is analyzed in turn. The tension loss of the driving cable caused by the contact with the continuum mechanism is modeled using the capstan equation. The recursive equation between the deformation of each part of the continuum mechanism from the proximal end is derived, which can be solved numerically. The bending state of the continuum mechanism can then be estimated when only the tension of the proximal flexible cable is known. The model is experimentally verified by driving the continuum mechanism to move at a very low speed. The experiment results show that the estimation effect of the proposed model is significantly improved compared with that of the constant curvature model.
Journal of Mechanisms and Robotics Open Issues
