An analytical approach to 3D orthodontic load systems

Objective: To present and demonstrate a pseudo three-dimensional (3D) analytical approach for the characterization of orthodontic load (force and moment) systems. Materials and Methods: Previously measured 3D load systems were evaluated and compared using the traditional two-dimensional (2D) plane approach and the newly proposed vector method. Results: Although both methods demonstrated that the loop designs were not ideal for translatory space closure, they did so for entirely different and conflicting reasons. Conclusions: The traditional 2D approach to the analysis of 3D load systems is flawed, but the established 2D orthodontic concepts can be substantially preserved and adapted to 3D with the use of a modified coordinate system that is aligned with the desired tooth translation.