Steerability and Kinematics of Bevel-Tip Flexible Needle

Steerable flexible needles with bevel-tip are designed for many medical diagnoses and treatments. In this paper we present a new kinematic model for the bevel-tip flexible needle. Based on the analysis of needle deflection, the procedure of needle insertion can be decomposed of n sub-procedures, which are independent on the depth of insertion. In each sub-procedure, the tip is steered though the base to generate three motions with respect to the body-frame Ox_iy_iz_i: the rotation about z_i, the translation along z_i and the rotation about y_i. The kinematics of flexible needle with bevel-tip is presented using the Denavit-Hartenberg method. The inverse kinematics of needle insertion is derived from the kinematic equation of flexible needle. The solution sets are discussed for the insertion consisting of consecutive rotation and insertion control actions. Furthermore, how to select suitable insertion position and orientation is discussed.