Inconstant curvature kinematics of parallel continuum robot without static model

In the study of minimally invasive surgical robots, a mini parallel continuum robot has shown motion advantage after passing through a long and winding working channel. However, due to the interaction force between the elastic wires of the parallel robots during motion generation processes, the constant curvature assumption has shown modeling errors. This causes the current geometric kinematic model to become unreliable. Therefore, there is a need for a more accurate kinematic model in the absence of a complicated static model. This paper aims to solve this issue. The simulation in ANSYS is carried out, and the shape of one of the driving wires, when bending, is fitted by a two-segment polynomial curve. Then, the position of the distal wrist tip can be calculated based on the curve shape. To verify the accuracy of the proposed model, bending simulation and experiment are carried out. The accuracy of the proposed model is compared with that of the kinematic model based on constant curvature assumption. The result shows that the proposed model can get more accurate results, especially when the driving wire displacement increases. For a 10 mm parallel robot, when the displacements of the two pairs of wires are both 3.0 mm, the errors of the two models are 0.42 mm and 5.79 mm (4.2% and 57.9%), respectively.