Related Experiment Video
Updated: Aug 2, 2026

A Finite Element Approach for Locating the Center of Resistance of Maxillary Teeth
Published on: April 8, 2020
[Three-dimensional analysis of force distribution on maxillary dentition while distalization of first and second
X H He1, Z X Yang1, X Y Zhang1
1Department of Orthodontics, School of Stomatology, The Fourth Military Medical University, State Key Laboratory of Oral & Maxillofacial Reconstruction and Regeneration, National Clinical Research Center for Oral Diseases, Shaanxi Clinical Research Center for Oral Diseases, Xi'an 710032, China.
Abstract:
Objective: To explore the force distribution on the maxillary dentition when the first and second molars distalized simultaneously with different step sizes using clear aligners in vitro in order to provide a theoretical basis for the rational design of molar distalization. Methods: Clear aligners were designed to simultaneously distalize the maxillary first and second molars bilaterally, with rectangular attachments placed on the buccal surfaces of the first and second premolars, as well as the second molars. Based on different step sizes, the aligners were divided into three groups: Group A (0.15 mm per step), Group B (0.20 mm per step), and Group C (0.25 mm per step). Ten aligners were fabricated for each group using 0.76 mm thick polyethylene terephthalate glycol (PET-G) sheets. A three-dimensional force measurement system was used to measure the forces exerted on each tooth by the aligners, the first and second molars served as the target teeth and the remaining teeth as anchorage teeth. The three-dimensional force data were compared among the three groups. Results: In the mesiodistal direction, the forces on the central and lateral incisors were relatively small among all three groups, with no statistically significant differences (P>0.05). However, significant differences were observed in the forces on the canines, first premolars, second premolars, first molars, and second molars (P<0.05). The distal forces on the second molars in Groups B and C were (6.13±1.45) N and (6.83±1.58) N, respectively, significantly higher than that in Group A [(3.51±1.01) N] (P<0.05). The distal force on the first molars in Group C [(6.62±0.89) N] was significantly higher than that in Groups A and B (P<0.05). The mesial reactive forces on the first and second premolars in Groups B and C were significantly higher than those in Group A (P<0.05). The mesial reactive force on the canines in Group C [(-2.98±1.33) N] was significantly higher than that in Group A [(-1.69±0.68) N] (P<0.05), while there were no significant differences between Groups B and C in the forces on the canines, first premolars, and second premolars (P>0.05). In the buccolingual direction, there were no statistically significant differences in the forces on the central and lateral incisors among three groups (P>0.05), but significant differences were observed in the forces on the canines, second premolars, and second molars (P<0.05). The buccolingual forces on the canines, second premolars, and second molars in Group B were (-0.56±0.54), (-2.07±0.95), (1.13±0.55) N, respectively, significantly higher than those in Group A (P<0.05), but there were no significant differences compared to Group C (P>0.05). Compared to the mesiodistal and buccolingual forces, the vertical forces on the target and anchorage teeth were relatively small in all three groups. Conclusions: When using 0.76 mm thick PET-G sheets to fabricate clear aligners for simultaneous molar distalization, a step size of 0.20 mm per step is recommended. To prevent buccal tipping of the molars during distalization, it is advisable to design lingual displacement for the molars and buccal displacement for the adjacent anchorage teeth to counteract the unfavorable forces, with attachments placed on the primary anchorage teeth.
Related Concept Videos
Three-Dimensional Force System
Three-Dimensional Force System:Problem Solving
To solve a three-dimensional force system, first resolve each force into its respective scalar components. Do this using...
Three Force Member
For example, consider a dumpster connected to a pin support at point A and a pin attached to a hydraulic cylinder at point B.
Distributed Loads: Problem Solving
Bearings: Problem Solving
Plastic Deformations of Members with a Single Plane of Symmetry

