Table 3: Translation and rotation movements of the target tooth in the four different configurations.

Expected movementStandard alignerRectangular palatal attachmentRectangular buccal attachmentEllipsoid buccal attachment

Rotation x (°)00.1−0.090.150.15
Rotation y (°)0−0.13−0.17−0.11−0.18
Rotation z (°)0−0.55−0.41−0.01−0.11
Translation x (mm)00000
Translation y (mm)000.010.010.01
Translation z (mm)0.150.020.070.060.06