Bracket Width Research Articles

Effect of Bracket Width on Bending Deformation of NiTi Arch Wire: A Finite Element Study

The force transferred from the NiTi arch wire to the tooth during orthodontic treatment is strongly dependent on the geometry of the wire and brackets used by the orthodontist. This study investigated the effect of orthodontic bracket geometry on the bending behaviour of superelastic NiTi arch wire. A three-dimensional finite element models of wire bending in three-brackets configuration was developed by employing superelastic user material subroutine and contact interaction. The finite element model was used to anticipate the bending forces and stresses of NiTi wires as they were engaged in various slot width dental brackets. Four different bracket widths were considered, ranging from 1.5 mm to 4.5 mm. Throughout the bending course, the superelastic NiTi wire bent in the 4.5 mm width bracket continuously demonstrated the highest bending force in comparison to the other bracket widths. As the bracket width was raised from 1.5 mm to 4.5 mm, the wire unloading force measured at 2.5 mm deflection increased gradually from 0.40 N to 1.7 N. The bending stress of the wire deformed in the 1.5 mm width bracket was 543 MPa, band it increased to 1051 MPa when the 4.5 mm width bracket was used. The proportion of complete martensite structure at the wire curvature gradually increased as the width of the bracket slot was increased.

Bracket width of simple Lie algebras

The notion of commutator width of a group, defined as the smallest number of commutators needed to represent each element of the derived group as their product, has been extensively studied over the past decades. In particular, in 1992 Barge and Ghys discovered the first example of a simple group of commutator width greater than one among groups of diffeomorphisms of smooth manifolds. We consider a parallel notion of bracket width of a Lie algebra and present the first examples of simple Lie algebras of bracket width greater than one. They are found among the algebras of polynomial vector fields on smooth affine varieties.

Comparative Analysis of Sliding Resistance of Different Lingual Systems

Objective: To analyse and compare the frictional properties of 4 lingual systems combined with two types of stainless steel archwire (0.016x0.022, 0.018x0.025) and a 0.018x0.025 TMA archwire by simulating different misalignment situations in vitro. Material and Methods: Five randomly chosen brackets from each system (e-Brace, Harmony, Incognito, and STb) were used for the measurements and to simulate an upper first premolar extraction case. The friction tests were performed using a material testing machine in combination with a specialized test rig. Results: The lowest absolute friction values were found with the 0.016x0.022 SS wire in a passive configuration. STb provided the lowest mean friction, while Harmony brackets displayed the highest friction. The TMA Beta Titanium wire showed the highest friction values, but maintained proportions similar to those of the other wires as tip and torsion increased. Conclusion: The type of bracket has a significant impact on friction, and there is a positive correlation between mesiodistal bracket width and resistance to sliding. The archwire sections and materials and the vertical displacement, also significantly affect the friction generated by the system.

In-vitro investigation of the mechanical friction properties of a computer-aided design and computer-aided manufacturing lingual bracket system under diverse tooth displacement condition.

ObjectiveThe purpose of this study was to compare the static (SFF) and kinetic frictional forces (KFF) of a computer-aided design and computer-aided manufacturing lingual bracket (CAD/CAM-LB) with those of conventional LB (Con-LB) and Con-LB with narrow bracket width (Con-LB-NBW) under 3 tooth displacement conditions.MethodsThe samples were divided into 9 groups according to combinations of 3 LB types (CAD/CAM-LB [Incognito], Con-LB [7th Generation, 7G], and Con-LB-NBW [STb]) with 3 displacement conditions (no displacement [control], maxillary right lateral incisor with 1-mm palatal displacement [MXLI-PD], and maxillary right canine with 1-mm gingival displacement [MXC-GD]; n = 6/group). While drawing a 0.016-inch copper or super-elastic nickel-titanium archwire with 0.5 mm/min for 5 minutes in a chamber maintained at 36.5℃, SFF and KFF were measured. The Kruskal-Wallis method with Bonferroni correction was performed.ResultsThe Incognito group demonstrated the highest SFF, followed by the 7G and STb groups ([STb-control, STb-MXLI-PD, Stb-MXC-GD] < [7G-MXC-GD, 7G-MXLI-PD, 7G-control] < [Incognito-MXLI-PD, Incognito-control, Incognito-MXC-GD]; p < 0.001). However, there were no significant differences in SFF among the 3 displacement conditions within each bracket group. Within each displacement condition, the Incognito group demonstrated the highest KFF, followed by the 7G and STb groups ([STb-control, STb-MXLI-PD] < Stb-MXC-GD < 7G-MXLI-PD < [7G-control, 7G-MXC-GD] < [7G-MXC-GD, Incognito-MXLI-PD, Incognito-control] < [Incognito-control, Incognito-MXC-GD]; p < 0.001). MXC-GD exhibited higher KFFs than MXLI-PD in the same bracket group.ConclusionsThe slot design and ligation method of the CAD/CAM-LB system should be modified to reduce SFF and KFF during the leveling/alignment stage.

Frictional property comparisons of conventional and self-ligating lingual brackets according to tooth displacement during initial leveling and alignment: an in vitro mechanical study.

ObjectiveWe evaluated the effects of tooth displacement on frictional force when conventional ligating lingual brackets (CL-LBs), CL-LBs with a narrow bracket width, and self-ligating lingual brackets (SL-LBs) were used with initial leveling and alignment wires.MethodsCL-LBs (7th Generation), CL-LBs with a narrow bracket width (STb), and SL-LBs (In-Ovation L) were tested under three tooth displacement conditions: no displacement (control); a 2-mm palatal displacement (PD) of the maxillary right lateral incisor (MXLI); and a 2-mm gingival displacement (GD) of the maxillary right canine (MXC) (nine groups, n = 7 per group). A stereolithographic typodont system and artificial saliva were used. Static and kinetic frictional forces (SFF and KFF, respectively) were measured while drawing a 0.013-inch copper-nickel-titanium archwire through brackets at 0.5 mm/min for 5 minutes at 36.5℃.ResultsThe In-Ovation L exhibited lower SFF under control conditions and lower KFF under all displacement conditions than the 7th Generation and STb (all p < 0.001). No significant difference in SFF existed between the In-Ovation L and STb for a 2-mm GD of the MXC and 2-mm PD of the MXLI. A 2-mm GD of the MXC produced higher SFF and KFF than a 2-mm PD of the MXLI in all brackets (all p < 0.001).ConclusionsCL-LBs with narrow bracket widths exhibited higher KFF than SL-LBs under tooth displacement conditions. CL-LBs and ligation methods should be developed to produce SFF and KFF as low as those in SL-LBs during the initial and leveling stage.

Molecular and morphological variability of Satureja bachtiarica in Iran

Satureja bachtiarica is a valuable medicinal plant that belongs to family Lamiaceae. In this research, genotypic and phenotypic variations among 57 individuals of this species were assessed based on three marker systems, namely, ISSR, RAPD and morphological traits. Principal component analysis showed that 75.91 % of the morphological variability was explained by all components for the studied individuals. Variables such as stem number, plant diameter, total weight, leaf and flower weight, stem weight, sepal length, petal length, petal tube length, sepal diameter, bracket length and bracket width were predominant in the first three components and contributed to most of the total variation. Leaf dimensions were in significant positive correlation with flower and inflorescence characteristics. Also, plant height showed significant positive correlation with characteristics related to inflorescence and weight. Clustering from morphological data allocated individuals into two main clusters with high variations. Profile patterns of 15 ISSR and 11 RAPD primers revealed 135 (98.78 %) and 84 (97.94 %) polymorphic fragments, respectively. The range of similarity coefficient by ISSR and RAPD markers were 0.08–0.63 and 0.09–0.69, respectively, indicating high genetic variation among individuals that originated from different geographic sites. UPGMA dendrograms based on ISSRs, RAPDs and ISSRs+RAPDs revealed high genetic diversity between studied individuals and grouped them into two main groups. Some cases of similarity and dissimilarity were observed between clustering based on ISSR and RAPD data. Also, the results showed that grouping based on molecular markers and morphological traits were different so these two systems could not discriminate individuals as the same way. The genetic relatedness among the studied individuals could provide useful information for conservation and selection of cross-parents in breeding.

The Effect of Various Ligation Methods on Friction in Sliding Mechanics

Aim: To evaluate the effect of ligation method on friction and the efficacy of the new slick elastomeric modules (TP Orthodontics, USA) and slide elastomeric modules (Leone Orthodontics, Italy) which claim to reduce friction at the module/wire interface. Materials and methods: Slick and slide modules were compared with regular modules, modules tied in figure of eight fashion, tight stainless steel ligatures, and loose stainless steel ligatures. Brackets used for the study were 0.022 × 0.028 maxillary first premolar twin brackets (MBT Prescription, Gemini series, 3M Unitek USA.) The effect of bracket width on friction produced with four different methods of ligation was also studied using 0.022 × 0.028 maxillary first premolar single width brackets (Alexander prescription, Leone Co. Italy). Results: When considering tooth movement along a 0.019 × 0.025 in stainless steel archwire, Super slick module produce less friction when compared to regular module, module tied in ‘figure of 8’ pattern and tight SS ligation produced more friction when compared to loose SS ligation and slide module. Slide modules produce least friction when compared to other available methods of ligation. Modules tied in a ‘figure of 8’ pattern generate highest friction. Conclusion: Slide modules produce least friction followed by loose SS ligation, slick modules, regular modules, tight SS ligation and highest friction was produced by regular modules tied in a ‘figure of 8’ pattern. Width of bracket had no influence on friction produced.

Torque capabilities of self‐ligating and conventional brackets under the effect of bracket width and free wire length

To numerically investigate the torque capacity of conventional and self-ligating brackets under the effect of varying bracket width and free wire length. Finite element models of three kinds of orthodontic brackets in the 0.022-inch slot size were investigated: Discovery, Damon 3MX, Speed. Additionally, finite element (FE) models of Speed and Damon brackets were generated with the same width as the Discovery. From the left upper incisor to the right upper canine, four brackets each were modelled. The total wire length at the upper right incisor was kept constant at 12 mm for all brackets types. For the Discovery brackets, the wire length was increased from 12 to 16 mm in 2-mm steps. A torque of 20° was applied to the upper right incisor with 0.46 × 0.64 mm(2) (0.018″ × 0.025″) and 0.48 × 0.64 mm(2) (0.019″ × 0.025″) wires. Wires made of stainless steel, titanium molybdenum and nickel titanium were studied. Torque angle/moment characteristics were recorded. Wider brackets showed more torque control capability (e.g. Discovery: 10.6 Nmm, Damon: 9.2 Nmm, Speed: 4.0 Nmm for the NiTi wire). Even with the same width as the Discovery bracket, Damon and Speed brackets showed lower torque capability than the Discovery bracket. Increasing the free wire length decreased the torsional stiffness of the wire and thus decreased the torque capability. The results showed that the bracket design has less influence on the torquing moment than other parameters, such as bracket width, free wire length, wire/slot play or misalignment.

Frictional Resistance between Orthodontic Brackets and Archwire: An in vitro Study

The purpose of this investigation was to determine the kinetic frictional resistance offered by stainless steel and Titanium bracket used in combination with rectangular stainless steel wire during in vitro translatory displacement of brackets. In this study. Brackets: (All brackets used had a torque of - 7° and an angulation of 0°): (1) Dynalock (Unitek) 0.018'' slot, 3.3 mm bracket width, (2) Mini Uni-Twin (Unitek) 0.018'' slot, 1.6 mm bracket width, (3) Ultra-Minitrim (Dentaurum) 0.022'' slot 3.3 mm bracket width, (4) Titanium (Dentaurum) 0.022'' slot, 3.3 mm bracket width. WIRES: (1) 0.016 x 0.022'' stainless steel (Dentaurum), (2) 0.017 x 0.025''stainless steel (Unitek), (3) 0.018 x 0.025'' stainless steel (Dentaurum), elastomeric modules (Ortho Organisers), 0. 009'' stainless steel ligature wires, hooks made of 0.021 x 0.025'' stainless steel wires, super glue to bond the hooks to the base of the bracket, acetone to condition the bracket and wires before testing and artificial saliva. Brackets were moved along the wire by means of an Instron universal testing machine (1101) and forces were measured by a load cell. All values were recorded in Newtons and then converted into gms (1N-102 gm). 200 gm was then subtracted from these values to find out the frictional force for each archwire/bracket combination. For each archwire/ bracket combination three readings were taken under wet and dry condition and also with stainless steel ligature and elastomeric modules separately. The results showed that narrow brackets generated more friction than wider brackets. Frictional force was directly proportional to wire dimension. Titanium brackets generated more friction than stainless steel brackets. Archwire and bracket ligated with elastomeric module generated more friction than when ligated with stainless steel ligature wire. Frictional forces in the wet condition were greater than in the dry condition for all archwire to bracket combinations. Frictional force was seen to be inversely proportional to bracket width, frictional force was inversely proportional to bracket width, and in the wet condition were greater than in the dry condition for all archwire to bracket combinations. This study of friction is its role in lessening the force actually received by a tooth from an active component such as a spring, loop or elastic. Hence greater applied force is needed to move a tooth with a bracket archwire combination demonstrating high magnitudes of friction compared with one with a low frictional value.

Canine retraction rate with self-ligating brackets vs conventional edgewise brackets

To compare the rates of retraction down an archwire of maxillary canine teeth when bracketed with a self-ligating bracket was used on one side and a conventional bracket on the other. In 43 patients requiring maxillary premolar extraction, a self-ligating bracket (Damon3, SmartClip) was used on the maxillary canine on one side and a conventional bracket (Victory Series) on the other. The teeth were retracted down a 0.018-inch stainless steel archwire, using a medium Sentalloy retraction spring (150 g). The rates of retraction were analyzed using a paired t-test. The mean movement per 28 days for the conventional bracket was 1.17 mm. For the Damon bracket it was 0.9 mm and for the SmartClip bracket it was 1.10 mm. The differences between the conventional and self-ligating brackets were statistically significant: paired t-test, SmartClip, P < .0043; Damon3, P < .0001). The retraction rate is faster with the conventional bracket, probably because of the narrower bracket width of the self-ligating brackets.

The effects of a newly designed twin-slot bracket on severely malpositioned teeth--a typodont experimental study

The aims of this study were to design a twin-slot bracket featuring two horizontal slots and to examine its efficiency in tooth displacement. Based on the structure of a traditional edgewise bracket, an additional slot was added to a twin-slot bracket and the prototype products were fabricated for the typodont experiments. The orthodontic correction of malpositioned canines was conducted on a typodont to examine the efficiency of the twin-slot bracket in tooth displacement compared with a single-slot edgewise bracket. Three modalities of tooth movement requiring a heavy force moment, namely, axial rotation, mesiodistal tipping, and bodily translation, were conducted. The canine positions before and after simulation were measured and the changes identified. Statistical analysis was undertaken using a t-test to determine the significance of the differences in canine repositioning between the two bracket types. The results showed that in the twin-slot bracket group, the treatment changes in the canine position by derotation and uprighting were 40 +/- 3 and 25 +/- 2 degrees, respectively, compared with 20 +/- 5 and 10 +/- 2 degrees in the edgewise group (P < 0.01). When retracted into an extraction space with an initial 10 degrees of mesial tip, the mesiodistal angulation of the canines in the twin-slot bracket group remained unchanged while in the edgewise group the canines became distally tipped by 5 +/- 2 degrees (P < 0.01). The twin-slot bracket significantly increased the bracket width without reducing the interbracket span and therefore can generate increased force moments within the bracket, leading to an improved manipulation in tooth repositioning.

DYNAMIC ANALYSIS OF HEAD IMPACT TEST OF PASSENGER AIR-BAG MODULE ASSEMBLY OF VEHICLE USING FEM

In this study, dynamic impact analysis for the passenger air-bag(PAB) module has been carried out by using FEM to predict the dynamic characteristics of vehicle ride safety against head impact. To carry out the dynamic analysis of head impact test of the PAB module assembly of automobile, the FE models, which are consist of instrument panel, PAB Module, and head part, are combined to the whole module system. Then, impact analysis is carried out by the explicit solution procedure with assembled FE model. And the dynamic characteristics of the head impact are observed to prove the effectiveness of the proposed method by comparing with the experimental results. As a result, the better optimized impact characteristics are proposed by changing the tie bracket's width and thickness of module. The proposed approach of impact analysis will provides an efficient vehicle to improve the design quality and reduce the design period and cost.

In-vitro evaluation of frictional resistance between brackets with passive-ligation designs

The lower frictional resistance produced by passive self-ligating brackets can be helpful during orthodontic sliding mechanics. The aims of this study were to evaluate the frictional resistance of brackets with passive ligation and to compare these values with corresponding controls. Two passive self-ligating brackets (Damon SL II, Sybron Dental Specialties/Ormco, Orange, Calif; SmartClip, 3M Unitek, Monrovia, Calif) and 1 novel bracket with passive elastic ligation (Synergy, Rocky Mountain Orthodontics, Denver, Colo) were used. The brackets were coupled with 3 nickel-titanium archwires (0.014-in round, 0.016 x 0.022-in, 0.019 x 0.025-in) in a simulated ideal arch introducing first-order rotations of 3 degrees and 6 degrees, second-order intrusions of 0.5 and 1.0 mm, and a third-order labial crown inclination of 3 degrees . The dimensions of the brackets were measured with scanning electron micrographs. The results of initial maximum drawing forces (IMDF) were analyzed by 2-way ANOVA and 1-way ANOVA tests. The SmartClip bracket had larger critical angles and distances for binding than the other 2 brackets. When coupled with 0.019 x 0.025-in archwires in an ideal arch alignment, SmartClip brackets had lower IMDF than the other brackets. For the first-order rotations, Synergy brackets had significantly lower IMDF than the other brackets. Damon SL II brackets with smaller critical angles had greater IMDF. For the third-order inclination, the Damon SL II brackets with less torsional play also had greater IMDF. No significant differences of IMDF were found for all the brackets tested in second-order intrusions. However, IMDF increased as the severity of the malocclusion increased. No significant bracket differences were found when binding occurred in second-order distances. In an ideal arch alignment, brackets with greater slot lumen have lower frictional resistance. First-order rotational control was influenced by slot depth, bracket width, and labial cover of the brackets with the same archwire. When a sliding mechanism was used with a third-order inclination change, the brackets with smaller third-order critical contact angles had greater frictional resistance.

Influence on binding of third-order torque to second-order angulation

Using an earlier model, which described the critical contact angle for binding from second-order angulation alone, a more generalized model is derived that combines the effects of angulation and torque. From this vantage point, the onset of binding is evaluated for 3 scenarios: second-order angulation alone, third-order torque only, and a combination of second-order angulation and third-order torque. These scenarios are detailed by plotting the critical contact angle for binding against the torque angle as a function of 10 wire dimensions (16 × 16, 16 × 22, 17 × 17, 17 × 22, 17 × 25, 18 × 18, 18 × 22, 18 × 25, 19 × 25, and 21 × 25 mil), 4 bracket widths (70, 100, 130, and 160 mil), and 4 bracket slots (18, 20.5, 22, and 24.5 mil). From these plots, we learn that each wire base dimension (eg, an 18-mil base as found in 18 × 18-mil, 18 × 22-mil and 18 × 25-mil archwires) has a common maximum critical contact angle for binding. Moreover, each wire-slot combination has a common maximum torque angle, which is independent of bracket width. Finally, we learn that archwire-bracket combinations that use a metric 0.5-mm slot might have some advantages with regard to torquing—given the current philosophy that light, continuous forces are more favorable.

Frictional resistances of different bracket – wire combinations

Abstract Background: It has been suggested that the frictional resistance of ceramic brackets can be reduced by either lining the slots with stainless steel or by contouring the base of the slot. Objectives: The objectives of this investigation were to compare in vitro the static and kinetic frictional resistances of ceramic brackets with metal lined slots (“Clarity”, CL), stainless steel brackets (“Miniature Twin”, MT), and two ceramic brackets with different slot designs (“Contour”, CO; “Transcend”, TR). Method: Two sizes (0.018 x 0.025 inch; 0.021 x 0.025 inch) of stainless steel (SS), nickel titanium (NiTi) and ß titanium (ß-Ti) wires were drawn through the brackets. All brackets had 0.022 inch slots, and the brackets and wires were used once. The brackets were of different widths: CL, 0.180 inch; CO, 0.114 inch; MT, 0.118 inch; TR, 0.138 inch. An Instron Universal Testing Machine was used in this study. Results: There were no significant static or kinetic frictional differences when the smaller 0.018 x 0.025 inch wires were drawn through the brackets. There were no statistically significant static or kinetic frictional differences between the CL-CO, CL-MT and CO-MT bracket pairs when the 0.021 x 0.025 inch wires (SS, NiTi, ß-Ti) were used. There were no significant kinetic frictional resistance differences between the CL-TR and MT-TR when the SS wires were used. In general the static and kinetic resistances of the 0.021 x 0.025 inch wires of NiTi wire &lt; SS wire &lt; ß-Ti wire. Regardless of wire type some of the lowest kinetic resistances were found with the narrow CO brackets with the rounded slot bases. The highest static and kinetic frictional resistances were found with the wide TR bracket, and with stainless steel and ß-Ti wires. Conclusion: The high static and kinetic frictional resistances of ceramic brackets can be reduced either by lining the slots with stainless steel or by reducing the bracket width and rounding the slot base.

Structural behaviour of silos supported on discrete, eccentric brackets

Abstract Supporting steel silos on discrete, eccentric brackets offers an attractive alternative to using traditional ring beam supports in terms of both cost and simplicity of construction. A range of silos of typical geometries are analysed and the structural behaviour presented. Collapse modes are found to include buckling, plastic collapse and combined mechanisms. The results of a finite element parametric study that considers the effects of bracket width, bracket height and geometric imperfections are then presented. It is found that the strength of bracket-supported silos is strongly but non-linearly dependent on bracket width. Increasing the bracket height also increases the silo strength. Bracket-supported silos are found to be generally imperfection insensitive. However, a weld imperfection placed above the bracket can result is significantly increased strength.

Three-dimensional relationship between the critical contact angle and the torque angle

The purpose of this study was to analyze the relationship between the critical contact angle and the torque angle in an orthodontic bracket and archwire assembly in 3 dimensions. Three-dimensional mathematical models were created with geometric bracket-archwire parameters that included 2 slot sizes, 3 bracket widths, and 3 to 4 wire sizes. From this, 3-dimensional mathematical equations (3DMEs) for the critical contact angle and the maximum torque that result in critical contact angles of 0 were derived and calculated. To evaluate the effects of archwire-bracket parameters on critical contact angles, analysis of variance (ANOVA) was performed at the significance level of P ≤.05. For all bracket-archwire combinations, the critical contact angle decreased as bracket width, torque angle, and wire size increased. Therefore, all bracket-archwire parameters except slot height had an effect on the critical contact angle. Results of the critical contact angle produced from our 3DMEs were the same as those produced by 3D computer-aided design (SolidWorks Corp, Concord, Mass), thus confirming the validity of our derived equations. In addition, the effect of a beveled edge was investigated in some archwires. Furthermore, torsional play angles were calculated and found to be similar to those in previous reports. The results of this study provide theoretic and experimental bases for clinical orthodontic practice and indicate that torque angles should be included in the evaluation of the critical contact angle. (Am J. Orthod Dentofacial Orthop 2003;123:64-73)

A formula for the displacement of an arch wire when subjected to a second-order couple

A new formula, expressing the local angular displacement of an orthodontic beam when subjected to a second-order couple applied at midspan, has been developed and analyzed. The computed displacements were compared with the results of ex vivo testing. There was good agreement between the results from the theoretical evaluation and the bench testing. Second-order activation of an orthodontic beam can be described in four sequential phases. The initial displacement is influenced by the second-order clearance between bracket-slot and wire as well as the relationship between the bracket-slot width and interbracket distance. During phase II there is a nonlinear relationship between applied couple and rotational displacement. Within phases three and four displacement is linearly related to the interbracket distance, provided the relationship between the bracket-slot width and interbracket distance remains constant. For a given tooth size, the second-order beam stiffness is exponentially related to bracket width. The experiments also show that even small deflections of thin stainless steel wires can lead to second-order couples of large magnitudes when using a clinically relevant interbracket distance. Consequently, it is important that the orthodontist evaluates his or her choice of bracket width and arch wire stiffness in each clinical case in order to avoid supra-physiologic force levels. (Am J Orthod Dentofacial Orthop 1998;113:632-40)

Relative friction minimization in fixed orthodontic bracket appliances

The biomechanical and mathematical analysis of friction on an arch wire/bracket combination and the wire supports has demonstrated that there is an optimal relationship, i.e. minimal friction forces, between the bracket width and the distance between the adjacent brackets on the neighboring teeth. With this optimal situation, less force will develop for a given deflection of the arch wire. This, in turn, will lead to fewer frictional effects when the friction forces are assumed to be proportional to the concentrated perpendicular forces on the arch wire. As long as the contacting surface can be regarded as a point, Coulomb's law of friction can be applied in its simplest form. Relative friction minimization can thereby be qualitatively and quantitatively obtained by linear theory for any specified angulation, wire properties and coefficients of friction. Literature stating that narrow brackets will lead to less friction for specified angulation cannot be confirmed according to the presented analysis. The other extreme statement ‘Use the widest bracket possible’ also cannot be used in principle. Since the analysis shows a mathematical relationship between most of the relevant design variables of an arch wire/bracket combination and the magnitude of friction forces, empirical results can be sorted and ranked by their physical figures instead of by statistical distribution. In addition, it is possible to make recommendations about the appropriate bracket sizes for various cases. The dependences of the coefficients of friction themselves on material, surface roughness, lubrication, etc. are not investigated here. These factors are also very relevant, especially in reduction of the absolute magnitude of frictional forces, but this problem is left to tribologists.

A study of force application, amount of retarding force, and bracket width in sliding mechanics

We investigated the relationship of the retraction force to the location of force application, retarding force and bracket width during simulated sliding tooth movement along an arch wire. Point 1 for retraction was located at the center of the bracket, and points 2 and 3 were at 4.0 mm and 6.0 mm from the bracket slot, respectively. Weights of 100 gm, 200 gm, and 400 gm were suspended at 9.0 mm from the bracket slot as the point of simulated center of resistance. Stainless steel standard edgewise wide, medium, and narrow twin brackets were engaged with two elastomeric ligatures on a stainless steel wire (0.016 × 0.016 inch). The bracket was retracted at the rate of 0.1 mm per second for a distance of 2.0 mm. Measurements were repeated six times, and the results were compared with multiple ANOVA tests. For all brackets, with an increase of the retarding weight, the mean retraction force at points 1 and 2 increased but decreased at point 3. The mean retraction force at point 1 for the narrow twin bracket was significantly p < 0.05) higher than that for the wide twin bracket at all retarding force levels. However, the mean retraction force at points 2 and 3 for the narrow twin bracket was significantly ( p < 0.05) lower than for the wide twin bracket at all retarding force levels. These findings indicated that the point of force application, the resistance force of a tooth, and the width of the bracket are crucial in consideration of the tipping moments on the bracket. (A M J O RTHOD D ENTOFAC O RTHOP 1996;109:50-6.)