Geometric Model Of Tilted Implant Drills In Rigid Guide Tube

To overcome the limitations of current formulas for calculating the maximum deviation range of implant drills in guiding tubes. 1. Simplify implant drills and guide tubes as regular cylinders. Decompose the tilt into translation and rotation, and analyze using the median sagittal plane. 2. In a plane rectangular coordinate system, perform coordinate transformations to determine the positions of study points on the implant drill at maximum tilt. Derive equations for calculating linear and angular deviations. 3. Assign values to the parameters in the equations and analyze the results. 1. Equations for the maximum tilt angle and tilted center axis of various implant drills in single and combined rigid guide tubes were constructed. 2. For different guide tubes, the position range and variation pattern of the intersection point of the central axis before and after maximum tilt were determined. 3. The theoretical calculation value ranges of angular and linear deviations and their variation laws resulting from the maximum tilt of the implant drill were identified. 1. A series of geometric models for the maximum tilt of implant drills in rigid guiding channels were established. 2. The position of the intersection point of the central axis before and after maximum inclination can be quantified. 3. A quantifiable evaluation system for the maximum tilting state of different implant drills in different rigid channels was established, providing a numerical basis for preoperative instrument selection and individual surgical guide design.