In which movement does the center of rotation not exist?

In the context of orthodontic tooth movement, translation refers to the movement of a tooth in the same direction as a whole alongside the alveolar bone. This type of movement involves the entire tooth moving as a unit without any rotational activity. As such, translation does not have a defined center of rotation because the tooth is moving uniformly without pivoting around a fixed point.

In contrast, movements like controlled tipping, uncontrolled tipping, and reverse tipping involve a pivot point around which the tooth rotates to some extent. These types of movements have specific centers of rotation that determine how and where the tooth pivots. Therefore, since translation represents a simultaneous displacement of the tooth in the direction of applied force without rotation, it is characterized by the absence of a center of rotation. This foundational concept is essential in understanding how different orthodontic forces affect tooth movement.