Hollow needles are the most frequently used medical equipment. The design of a hollow needle that best enables medical procedures requires a better understanding of needle tip geometry. Calculating the cutting angles of a needle for a complex surface topology is difficult. This article proposes a new method based on non-Euclidean geometry for the analysis of biopsy needle tip. The method can be used to calculate the cutting angles on any pipe needle. To verify the validity of this method, the normal rake angle and inclination angle on four types of needles (bias bevel needle, cylinder surface needle, curved surface needle and Cournand-type needle) were investigated. It was found that calculation of the cutting angles was simple and convenient using this method, especially for the curved surface needles. Images of the cutting angles from the Cournand-type needles revealed that the smaller bevel angle [Formula: see text] resulted in a higher normal rake angle [Formula: see text] and inclination angle [Formula: see text]. As [Formula: see text] increased, the range of the normal rake angle [Formula: see text] became larger at first and then became smaller.
Keywords: Cournand-type needle; Tissue cutting; curved surface needle; needle tip geometry; non-Euclidean geometry.