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Malocclusion is the third largest oral disease in the world. At present, the most effective treatment method for malocclusion is the fixed orthodontic technique based on orthodontic archwires. Robotic archwire bending can overcome the shortcomings of manual bending such as low efficiency and low precision. The three-dimensional digital expression and robot bending method of orthodontic archwire are studied to realize the orthodontic archwire bending using a robot. Tooth is identified by the doctors’ common method. The shape, position, and constraint relationship of orthodontic archwire in three-dimensional space are expressed by the Bessel curve. The bending of the archwire curve is realized by transmitting the archwire curve into the alternative lines. The planning method of forming points and the spatial angle planning method are proposed. The archwire bending experiment is carried out with the maxillary information of a patient. The error rate of the experimental and ideal values is between 2.94% and 6.74%. It can meet the physician’s basic requirements after simple modification. Therefore, it can be considered that the method of using discrete Bessel curve to carry out the control point planning and angle planning is suitable for the orthodontic archwire-bending robot system, which has certain feasibility and practicability in clinical treatment.