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Forces and torques associated with second order bends

American Journal of Orthodontics
Publication Date
DOI: 10.1016/0002-9416(56)90044-6
  • Medicine


Abstract 1. 1. Mathematical expressions were given for calculating the forces and torques brought to bear against teeth by an arch wire containing second order bends. 2. 2. It was shown that the effective rotations which could be incorporated into the wire at any one adjustment varied between 1 and 2 degrees. The initial bends contain larger rotations of the bracket members because a certain amount of play must first be overcome before the teeth could be subjected to torques. 3. 3. In any arch wire containing second order bends, the torques created are balanced by a couple. This couple must intrude the teeth at one end of the segment and extrude the teeth at the other end. The direction or sense of the couple is always opposite to the sense of the torques. 4. 4. The torque received by either end tooth is about one-half as great as the torque taken by any one of the other teeth in the segment. 5. 5. For a given span distance, the relative lengths of the bracket and interbracket members have no practical effect on the action of the wire Furthermore, the angles made by the various interbracket members with the slots in the brackets need not be uniform. The bracket members, though, should be fabricated to be parallel to each other. 6. 6. Large forces and torques can be brought into existence through second order bends. Extrusive and intrusive forces as high as 2 pounds and torques as high as 0.5 pound-inch can act on the teeth immediately following the placement of the wire. These large forces and torques diminish quickly, however, because they are associated with very small angles of wire rotation. 7. 7. Wrought-gold wire, because of its lower modulus of elasticity, would exert a milder action than the usual types of stainless steel used. This is not meant to imply, however, that gold is superior to stainless steel in other respects. 8. 8. The second molar should be included in second order bend therapy. The additional span brought into action permits a greater storage of potential energy in the system which would be available for tooth movement. 9. 9. After the crowns have been moved distally and the uprighting of the axes is begun, it becomes essential to apply a continuous auxiliary force, distally directed, to the arch wire or brackets. Such a necessity represents an inherent weakness in second order bend therapy, because it is difficut to supply such a force continuously without the use of intermaxillary elastics. These elastics have a detrimental effect on the opposite arch, as stable anchorage cannot be found inside the oral cavity.

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