Analysis and design of multiple-beam appliances

Abstract

A new approach for the analysis of multiple-beam structures, such as headgear bows, is developed for beams which contain arbitrary curvatures, twists, and material properties. The generalized transfer matrix of a single-beam analysis is converted to a stiffness matrix and inserted into a global matrix which describes the entire system. The effect of inner bow wire size (0.044 inch and 0.051 inch) on the force system is demonstrated. The inner bow with the larger cross section shows only a slight (not clinically significant) reduction in rotational moment and buccal force applied because of its greater ability to resist deformation during the loading process. Small amounts of tooth and/or tube rotations ("play") result in a significant reduction of the crown rotational moment. With increasing rotation of the tube to the inner bow, the high lateral forces and large moments found about the long axis of the teeth are found to reduce. Symmetrical headgears are chosen to illustrate the analysis and to indicate the manner in which this approach may be used to study and design similar orthodontic appliances.