Third-Order Torque and Self-Ligating Orthodontic Bracket–Type Effects on Sliding Friction

Objective: To examine the influence of third-order torque on kinetic friction in sliding mechanics involving active and passive self-ligating brackets.

Materials and Methods: Wire-slot frictional forces were quantified and compared across five sets of brackets and tubes within a simulated posterior dental segment with −15°, −10°, −5°, 0°, +5°, +10°, and +15° of torque placed in the second-premolar bracket; a working archwire was pulled through the slots.

Results: Increasing the torque from 0° to ±15° produced significant increases in frictional resistance with all five sets of brackets and tubes. At 0° and ±5° of torque, generally less friction was created within the passive than within the active self-ligating bracket sets, and the conventional bracket sets with elastomeric ligation generated the most friction. At ±10° of torque, apparently with wire-slot clearance eliminated, all bracket-and-tube sets displayed similar resistances, with one exception at +10°. At ±15° of torque, one passive set and one active set produced significantly larger frictional resistances than the other three sets.

Conclusions: Third-order torque in posterior dental segments can generate frictional resistance during anterior retraction with the archwire sliding through self-ligating bracket slots. With small torque angles, friction is less with passive than with active self-ligating brackets, but bracket design is a factor. Frictional forces are substantial, regardless of ligation if the wire-slot torque exceeds the third-order clearance.

Controlled localized buckling responses of orthodontic arch wires

The orthodontic arch wire is often activated locally, in transverse bending and/or longitudinal torsion, to engage an individual malaligned tooth. Arch wires with substantial flexibilities and elastic ranges in bending are available. Several clinical reports of distal displacements of molars with appliances activated by locally buckling the arch wire have appeared in the recent published literature. This article contains an explanation of buckling or "column" action and the postbuckling response of a wire, and a report of the results of a controlled, in-vitro study of a sample of 256 wire segments subjected to activation-deactivation, buckling-postbuckling-unbuckling cycles. Continuous force-displacement diagrams were obtained from mechanical tests run at oral temperature. Four orthodontics-relevant, mechanical characteristics were quantified from each diagram, and each specimen was subjected to posttest evaluation for inelastic behavior. Although the deformation of the buckled wire is, in fact, bending, the force-displacement diagrams obtained differed substantially from their familiar counterparts generated in transverse bending. Judging from the force magnitudes induced as the deactivation half-cycles commenced as well as the deactivation rates, not all of the 8 wires seem to be clinically suitable for activation initiated by buckling. Magnitudes of springback were substantial from activations as large as 6 mm, and only 2 of the 8 wires exhibited full deactivations less than 80% of their activating displacements. This relatively new mode of arch wire activation that enables delivery to the dentition of mesiodistal pushing forces has substantial potential for clinical application from several biomechanical standpoints.

Orthodontic wire: a continuing evolution

Wires have substantial structural presence in active and retentive orthodontic therapy. Wires, and auxiliaries fabricated from wire, may deliver force to produce dental displacements, they may attempt to prevent unwanted displacements, or they may simply carry force from one location to another within the dentofacial complex. Wires may have relatively simple or rather convoluted geometries. The most prominent wire in clinical orthodontic treatment is the "arch wire." Marketed in just two, symmetrical, cross-sectional shapes, its sizes are numerous, and arch wires are manufactured of a variety of metallic alloys and compositions. The primary objective of this article is to trace the history of arch wires over the past century, considering the evolution from the stiff arch bow to the wire exhibiting Hookean material behavior, from the precious metal to the stainless steel to the titanium alloys, and into the era of the "superelastic" wire and a thermomechanical behavior decidedly more complex than its predecessors. Timely, relevant questions that are addressed herein pertain to the current "state-of-the-art" of orthodontic wires, the extent to which the mechanics of the "old" and new wires are understood, and the anticipated arch wire advancements in the near future as a new millennium approaches.

Elastic responses to longitudinal torsion of single-strand, rectangular, orthodontic archwire segments

OBJECTIVES

This study was undertaken to characterize elastic responses of orthodontic archwire segments in longitudinal torsion, to compare experimental results with predictions from structural engineering theory, and to examine the potential interaction between flexural and torsional responses of archwires.

METHODS

Passively straight and deflected rectangular wire segments were activated in torsion to states beyond their elastic limits. The wire parameters that were controlled included: the alloy, the cross-sectional size, and the gauge length. The research design included 48 cells and 240 separate tests. From torque-twist plots, values of elastic stiffness, elastic range, and unit elastic range were obtained. Raw experimental data were subjected to analyses of variance and means to a Tukey's post-hoc test. Mean stiffness and elastic range outcomes were compared with theoretical values.

RESULTS

Most plots were generally characteristic of Hookean materials. All three wire parameters significantly influenced the three dependent variables; few statistical interactions emerged. Theoretical stiffness values were reasonably comparable to those obtained experimentally; however, the elastic range predictions were conservative. Torsion theory predicts unit elastic ranges independent of gauge length; the experimental data displayed a nonlinear relationship. The minor influences of flexural deformations on the responses of wire segments activated in torsion are suggested as clinically inconsequential.

SIGNIFICANCE

Few clinically relevant, controlled studies of archwire torsion have been published. A modified or new formula is needed to predict elastic range magnitudes of archwires in torsion. When flexure and torsion exist in an archwire, it may be possible to separate them to determine overall structural response.

Flexural activation and de-activation responses of orthodontic wires in single-tooth, occlusogingival corrections

An experimental design was developed to simulate the processes of the activation in flexure of a wire segment to engage an occlusogingivally-malposed tooth and the correction of that malalignment. Independent, controlled parameters, clinically referred, were wire material, mesiodistal bracket width, and inter-bracket distance. Full-cycle, activation/de-activation diagrams were generated for 96 specimens. Each load-deflection diagram was in five segments. Slope discontinuities occurred at the states of disappearance and reappearance of "second-order" clearances at the support sites. Ratios of the slopes of the diagrams above these discontinuities to their counterparts beneath the discontinuities were typically between 2:1 and 4:1. A segment of the diagram was distinct at the initiation of de-activation, and was related to the reversal of frictional forces at the supports. Generalizing, in some cases activation may not eliminate the cited clearances; in others, clearances may be negligibly small in the passive states. Apparently, analyses should ordinarily recognize the segmented formats of the activation and de-activation plots. In comparisons of activation with de-activation plots within the individual diagrams, differences in quantified properties for the cobalt-chromium- and nickel-titanium-alloy wires were sufficient to suggest further study toward an objective of predicting de-activation behavior from outcomes of an activation analysis.

Structural responses of orthodontic wires in flexure from a proposed alternative to the existing specification test

To be reaffirmed in 1987 for lack of a ready replacement, the flexural (elastic-bending) test protocol of ADA Specification No. 32 is judged inadequate. The protocol is problematic because of potentials for erroneous use of the theoretical component, incompatible with the flexible titanium alloy and multistrand stainless steel wires marketed subsequent to the preparation of the specification, and obscure to the clinician because it dictates quantifications of mechanical (pertaining to material only) rather than structural properties (including wire shape and size influences). A five-point elastic-bending test is proposed that stimulates wire activation toward engagement of a single, malaligned tooth crown. An experimental study was undertaken to determine values of transverse stiffness and corresponding elastic range for a broad sample of orthodontic wires and in the process to evaluate the proposed alternative test. Reduced test results are presented; comparisons of rankings and ratios from available theoretical developments and other experimental outcomes, including findings from the existing standard test, were completed. The difficulties with the existing protocol are largely eliminated with the alternative test; a test fixture and procedures are relatively straightforward to fabricate and follow, and the structural characteristics quantified are more meaningful to the practitioner.

Localized, transverse, flexural stiffnesses of continuous arch wires

Elastic bending (flexure) theory, although apparently extendable to the arch wire, incorporates assumptions that are violated in orthodontic application, and neglects several influences confined to the clinical arena. The standard elastic-bending test for orthodontic wires uses a passively straight segment of wire, and a rotational bending stiffness rather than the force-deflection ratio akin to the transverse deformation of a leveling wire is determined. In this study the transverse flexural stiffnesses of five preformed arch wires were quantified in each of three activation directions at five separate sites on simulated dental arches to which appliances were affixed. The influences of elastic moduli, numbers of strands, and interbracket distances were found to be less substantial than theory suggests. Other parameters, including wire curvature at the activation site, malalignment direction relative to that curvature, bracket-wire friction, and preactivation fit of the preformed arch to the dentition, also affected the localized, transverse, flexural stiffnesses.

Stiffness of incisor segments of edgewise arches in torsion and bending

A mechanical model dentition is used in a laboratory study to relate incisor segment third-order activation to actual torque induced upon engagement of maxillary Edgewise arches. A portion of the sample of stainless-steel aches was subjected to stress-relief heat treatment. Torsional stiffness values are calculated, and the accompanying vertical displacement force on the incisor segment is evaluated. The results seem to warrant the following conclusions. Broad ranges of incisor segment torque magnitudes may be obtained from rectangular orthodontic wires and arch designs presently in common clinical use. Torsional behavior is associated with the elastic shear modulus or modulus of rigidity, which is essentially the same for all stainless and chrome-cobalt alloys. Vertical extrusive force is generated as a secondary effect directly related to the torsional stiffness and torque activation. Compensation is possible through archwire adjustments to cause the wire to lie above the bracket slots of the incisor segment before activation of lingual root torque. Stress relief of rectangular stainless steel arches following placement of V-bends, twists, or loops did not have a significant effect on force values. Further investigation, modeling other configurations such as labiolingual movements of the six maxillary anterior teeth to determine the torsional stiffnesses for commonly-used arches could be worthwhile. Similarly, the quantification of torsional stiffnesses of arches fabricated in rectangular nickel-titanium, titanium-molybdenum, and braided stainless-steel wires may be of value.

A comparative study of frictional resistances between orthodontic bracket and arch wire

Practitioners are aware of the presence of friction in those orthodontic appliances where relative motion between bracket system and arch wire occurs in ordinary deactivation processes. Numerous comments on friction have appeared in the published dental/orthodontic literature, but little controlled research into the problem has been reported. The objective of this investigation was to evaluate and compare frictional forces generated in an experimental stimulation of the canine-retraction procedure on a continuous arch wire. Six independent variables were chosen for study: arch wire size and shape, bracket width and style, second-order angulation between bracket and passive arch wire, arch wire material, ligature force and type of ligation, and interbracket distances. Frictional resistance was found to be nonlinearly dependent upon bracket/arch wire angulation. With small and generally nonbinding angulations, bracket width and ligature force were the dominant influences on level of friction. As angulations were increased, producing binding between wire and bracket, this variable itself became the controlling parameter. Wire shape and arch wire stiffness in bending, a function of three of the variables studied, apparently exerted substantial influence on frictional-force magnitude at relatively high angulations. The reduced data, together with structural computations, were employed to deduce a minimum frictional-resistance combination of edgewise appliance components.

Relaxation of orthodontic elastomeric chains and modules in vitro and in vivo

Relaxation patterns for two orthodontic polyurethane-based elastics have been quantified in dry air and water bath environments and in vivo. Water bath simulation of in vivo behavior is apparently valid for up to a week following initial activation, but it becomes somewhat erroneous thereafter.

Centers of rotation for combined vertical and transverse tooth movements

For purely transverse orthodontic tooth movements, the center of rotation is defined as that point on the long axis or its extension which remains stationary during the movement and around which the rotational component of the tooth displacement takes place. For tooth movements having both vertical and transverse components, no point on the long-axis line remains fixed in space. The two-dimensional theory proposed herein suggests the more general definition of the center of rotation as that point on the long-axis line which displaced the shortest distance during the tooth movement. The center of rotation can be located for the combined transverse and vertical tooth displacement. It is found to move along a path coincident with a segment of a line in a position depicting the tooth angulation midway through the movement. Formulas, which can be used in conjunction with a composite pre- and post-displacement cephalometric tracing, are presented herein to define the center-of-rotation location for such tooth movements.

On optimum orthodontic force theory as applied to canine retraction

The study reported here was undertaken in an attempt to contribute, from a theoretical standpoint, to the knowledge and understanding of optimum force theory, particularly as it may be relevant to canine retraction. The following statements are derived from my analysis of the applicable published literature and the results of the present investigation: 1. This study lends support to the beliefs, from the findings of previous investigations, 20, 22 that the center of rotation for simple tipping is three tenths to four tenths of the distance from the root apex to the alveolar crest and that the center of resistance is at approximately midroot for the single-rooted tooth. 2. For a given distal driving force, increasing the countertipping couple from zero causes the center of rotation to "move" from a point near the apical end of the middle third of the root to the root apex and then to infinity. That is, the couple to be developed by the appliance to produce crown movement is smaller than required for bodily movement. Also, increasing the rotational stiffness of a canine-retraction appliance will result in greater inherent potential for canine root control and a greater probability of achieving bodily movement. 3. In a specific orthodontic case, an average periodontal stress value (active force divided by root area) can be used as a basis of comparison of suggested active force magnitudes among several single-rooted teeth having different root surface areas, provided all teeth are to experience the same form of displacement (for example, bodily movement). Similarly, differences in average stress magnitudes developed in the periodontium, rather than differences in root surface areas, are actually the basis for the differential force theory. 4. Clinical studies have suggested that the size of active force for bodily movement or root movement of a given tooth be two to three times that employed in simple tipping of the same tooth. Induced stress levels in the periodontium, especially at the root apex and alveolar crest locations, can be related to suggested magnitudes of aplied crown force components.