In minimally invasive surgery, flexible needle insertion is a popular application which has been extensively researched. However, needle steering is challenging for a bevel tip cannula flexible needle due to the nonholonomic constraints and the rebounds of the needle shaft when the needle tip is reoriented. We proposed a novel kinematic model for the bevel tip cannula flexible needle based on bicycle and unicycle models, taking consideration of the deflection of the bevel tip and the rebounds of the needle shaft. Aiming at different types of paths, forward kinematics of the model was analyzed and calculated. Each parameter of the kinematic models was identified based on the experimental data using the least square method. Furthermore, the changing rules of parameters were explored under different angles of the bevel tip. The experimental results show that the errors of the proposed kinematic models are within 2 mm, which is greatly reduced compared to the traditional bicycle or unicycle model, and fulfill a general clinical surgery.
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