Comments on "Equilibrium Clarified".
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Biomedical subjects
Publications and source records attributed to R J Nikolai.
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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.
The Hawley retainer is often prescribed by the practitioner for part-time wear during the retentive period subsequent to a program of active, maxillary arch, orthodontic therapy. The labial bow of this retainer, while engaged, may be subjected to contact forces from sources other than the maxillary anterior teeth. The bow also experiences small deformations during placement and removal of the appliance from the oral cavity. Potential failures of the bow are: 1) inelastic bending from individual masticatory actions that change its as-prepared shape; and 2) fracture due to fatigue arising from many cycles of removing and replacing the retainer. Reported in this paper, a sequel to a previous article, are the outcomes of two experiments and a nonparametric analysis that led to the development of a set of recommendations pertaining to the selection of the wire and preparation of the labial bow. Controlled variables in this study were as-received size, alloy and temper of the wire, and heat-treatment following fabrications of bow-specimens.
Removable Hawley orthodontic retainers have long been prescribed by clinicians following completion of active therapy. Only minor changes have occurred in the design of the retainer over the past 40 years. Structural, in-service failures of this appliance are typically: 1) permanent (inelastic) deformation of the as-prepared labial bow from masticatory action that induces unwanted force transmitted by the appliance to the dentition; or 2) accumulated material damage from removal and replacement of the retainer that eventually results in fracture of the labial bow. This paper reports the results of a series of experimental studies; the overall objective was the optimization of the appliance design, focusing on the labial bow. Wire size, material, temper, canine-loop height, markings for bend placements, heat-treatment of the prepared bow, and two procedures for removing and replacing the appliance were investigated. The collective outcomes suggest a combination of design-parameter values to help maximize the life of the labial bow of the retainer.
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.
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.
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.
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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.
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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.
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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.