All force systems applied to a tooth are composed of either single forces and/or couples. The application of a force through the center of resistance of a tooth will result in translation of the tooth. The application of a force to act at points other than through the center of resistance of a tooth will produce different tendencies for rotation. Tooth rotation resulting from the application of a force always creates a simultaneous tendency to move the center of resistance of a tooth in the direction the force is acting. In contrast, the location of a couple on a tooth is irrelevant to the resulting tooth movement. A couple can never move the center of resistance, and with a couple the center of rotation and the center of resistance will always be coincident. The equilibrium forces, associated with a moment of a couple, also are single-point forces and can produce different tooth movements depending on where they are applied. All tooth movement must be either translation and/or rotation as defined at the tooth's center of resistance.
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