Electronic determination of centres of rotation produced by orthodontic force systems

Three-dimensional positions of the center of resistance of the maxillary canine distal movement under orthodontic force loading

Using finite-element analysis, we aimed to determine the center of resistance (CRes) of the maxillary canine for setting orthodontic forces. The inclination of the canine was measured by first loading from the mesial to the distal side of the mesial root surface, then the position and direction of the load that minimized the inclination were investigated. The CRes was defined as the set of midpoints of the minimum distances between two inclination lines. Twenty-one CRes values were calculated from a set of seven lines. These CRes data were then aggregated as a 95% confidence ellipsoid of width 0.170×0.016×0.009 mm with center points 4.269, 0.224, and 4.315 mm in the apical, mesial, and lingual directions from the origin, respectively. Further studies are required to effectively apply the CRes identified in this study to clinical applications.

The center of resistance of a tooth: a review of the literature

The center of resistance is considered the fundamental reference point for controlled tooth movement. Accurate determination of its location can greatly enhance the efficiency of orthodontic treatment. The purpose of this review was to analyse the scientific literature related to the location of center of resistance of tooth determined by various approaches. The literature describes three essential approaches to identify the center of resistance point, one being experimental in nature, one based on an analytical physical approach, and one using a numerical physical approach that uses a finite element simulation. A review on data referring to the location of the center of resistance, limited to single rooted tooth has been performed from electronic databases. It showed variation in its location related to the assumptions used in the model. The center of resistance of tooth therefore cannot be considered a static point, but rather as the composite point of all factors offering resistance to the applied force such as the tooth morphology and mass distribution within the tooth, the structure of the periodontium, the alveolar bone level, the adjacent teeth and direction of force applied.

In vivo measurements and numerical analysis of the biomechanical characteristics of the human periodontal ligament

The periodontal ligament is a complex tissue with respect to its biomechanical behaviour. It is important to understand the mechanical behaviour of the periodontal ligament during physiological loading in healthy patients as well as during the movement of the tooth in orthodontic treatment or in patients with periodontal disease, as these might affect the mechanical properties of the periodontal ligament (PDL). Up to now, only a limited amount of in vivo data is available concerning this issue. The aim of this study has been to determine the time dependent material properties of the PDL in an experimental in vivo study, using a novel device that is able to measure tooth displacement intraorally. Using the intraoral loading device, tooth deflections at various velocities were realised in vivo on human teeth. The in vivo investigations were performed on the upper left central incisors of five volunteers aged 21-33 years with healthy periodontal tissue. A deflection, applied at the centre of the crown, was linearly increased from 0 to 0.15mm in a loading period of between 0.1 and 5.0s. Individual numerical models were developed based on the experimental results to simulate the relationship between the applied force and tooth displacement. The numerical force/displacement curves were fitted to the experimental ones to obtain the material properties of the human PDL. For the shortest loading time of 0.1s, the experimentally determined forces were between 7.0 and 16.2N. The numerically calculated Young's modulus varied between 0.9MPa (5.0s) and 1.2MPa (0.1s). By considering the experimentally and numerically obtained force curves, forces decreased with increasing loading time. The experimental data gained in this study can be used for the further development and verification of a multiphasic constitutive law of the PDL.

Effect of archwire qualities and bracket designs on the force systems during leveling of malaligned teeth

OBJECTIVES

The force systems during multiband treatment are influenced by the selection of the bracket-archwire combinations. Resin models replicated from casts reflecting the pretreatment intraoral situation of a patient's mandible were used to explore how different bracket systems and archwire qualities would affect the force systems developing during simulated orthodontic leveling of several malaligned teeth.

MATERIALS AND METHODS

Leveling movements of the malaligned teeth 32, 33, and 34 were simulated using the orthodontic measurement and simulation system (OMSS). Two bracket types and three archwire qualities were compared, the former featuring a slot width of 0.022" (0.56 mm) and including one conventional (Freedom MIM Roth by ODS) and one passive self-ligating (Carriere MBT by ODS) design. Both were combined with three NiTi round 0.014" (0.36 mm) archwire products, two of them standard products (CuNiTi by Ormco; EuroArch by ODS) and one being a low-cost (NiTi Superelastic by Modern Arch) product. Measured parameters included force, torque, translation, and rotation.

RESULTS

Archwire qualities are critical to the force systems developing in the leveling stage. On the other hand, the finding that lower force/torque values result in less tooth movement is not primarily due to wire selection. Our most striking result was that the ODS EuroArch wire resulted in very low force and torque values both with the conventional and with the self-ligating brackets. Almost identical patterns with these two bracket designs were found, and none of the measured parameters revealed a significant advantage for any of the bracket-archwire combinations over the others.

CONCLUSION

In our experimental simulations of tooth leveling, wire-quality selection was found to be a key modifier of force, torque, translation, and rotation. Clearly, however, neither the wire qualities nor the bracket designs made a decisive difference to the amounts of leveling movement induced to malaligned teeth; other factors like tooth class or nature of the malalignment seem to be more important in this regard. A therapeutic benefit of self-ligating over conventional brackets was not demonstrable.

Force loss in archwire-guided tooth movement of conventional and self-ligating brackets

This study aimed to investigate the differences in the force loss during simulated archwire-guided canine retraction between various conventional and self-ligating brackets. Three types of orthodontic brackets have been investigated experimentally using a biomechanical set-up: 1. conventional ligating brackets (Victory Series and Mini-Taurus), 2. self-ligating brackets (SmartClip: passive self-ligating bracket, and Time3 and SPEED: active self-ligating brackets), and 3. a conventional low-friction bracket (Synergy). All brackets had a nominal 0.022″ slot size. The brackets were combined with three rectangular 0.019×0.025″ archwires: 1. Remanium (stainless steel), 2. Nitinol SE (nickel-titanium alloy, NiTi), and 3. Beta III Titanium (titanium-molybdenum alloy). Stainless steel ligatures were used with the conventional brackets. Archwire-guided tooth movement was simulated over a retraction path of up to 4mm using a superelastic NiTi coil spring (force: 1 N). Force loss was lowest for the Victory Series and SmartClip brackets in combination with the steel guiding archwire (35 and 37.6 per cent, respectively) and highest for the SPEED and Mini-Taurus brackets in combination with the titanium wire (73.7 and 64.4 per cent, respectively). Force loss gradually increased by 10 per cent for each bracket type in combination with the different wires in the following sequence: stainless steel, Nitinol, and beta-titanium. Self-ligating brackets did not show improved performance compared with conventional brackets. There was no consistent pattern of force loss when comparing conventional and self-ligating brackets or passive and active self-ligating brackets.

Determining the Center of Resistance of Maxillary Anterior Teeth Subjected to Retraction Forces in Sliding Mechanics

Objective: To determine the location of center of resistance and the relationship between height of retraction force on power arm (power-arm length) and movement of anterior teeth (degree of rotation) during sliding mechanics retraction.

Materials and Methods: Three human subjects with maxillary protrusion were selected for this study. Initial tooth displacements of maxillary right central incisor under sliding mechanics with various heights of retraction forces were measured in vivo using a two-point three-dimensional displacement magnetic sensor device. By calculating the angle of rotation from the displacements measured, the location of the center of resistance was determined.

Results: The results suggested that different heights of retraction forces could affect the direction of anterior tooth movement. The higher the retraction force was applied, the lower the degree of rotation (crown-lingual tipping) would be. The tooth rotation was in the opposite direction (from crown-lingual to crown-labial) if the height of the force was raised above the level of the center of resistance.

Conclusion: The location of the center of resistance of the maxillary central incisor was approximately 0.77 of the root length from the apex. During anterior tooth retraction with sliding mechanics, controlled crown-lingual tipping, bodily translation movement, and controlled crown-labial movement could be achieved by attaching a power-arm length that was lower, equivalent, or higher than the level of the center of resistance, respectively. The power-arm length could be the most easily modifiable clinical factor in determining the direction of anterior tooth movement during retraction with sliding mechanics.

Comparison of the finite helical axis and the rectangular coordinate system in representing orthodontic tooth movement

In orthodontics, tooth movement is typically described using the rectangular coordinate system (XYZ); however, this system has several disadvantages when performing biomechanical analyses. An alternative method is the finite helical axis (FHA) system, which describes movement as a rotation about and a translation along a single axis located in space. The purpose of this study was to examine differences between the FHA and the XYZ systems in analyzing orthodontic tooth movement. Maxillary canine retraction was done using sliding mechanics or a retraction spring with midpalatal orthodontic implants used as measuring references. Tooth movement calculated with the FHA was compared with the corresponding movement in the rectangular coordinate system weekly over a 2-month interval in eight patients. The FHA showed that sliding mechanics controlled rotation of the canine better than the retraction spring (Ricketts retractor), and that the Ricketts retractor controlled tipping better. Changes in the FHA direction and position vectors with time showed that the biomechanical forces are not uniform during the treatment period. In both mechanics, the FHA provided a simple biomechanical model for canine retraction.

Basic behavior of the finite helical axis in a simple tooth movement simulation

A finite helical axis (FHA) analysis can provide precise three-dimensional information on orthodontic tooth movement compared to an analysis based on a rectangular coordinate system. The FHA has already been applied in an analysis of orthodontic tooth movement. Interestingly, the position of the FHA changes dramatically in different stages of treatment; however, no previous report has provided detailed information of its basic behavior for clinicians. The purpose of this study was to clarify the basic behavior of the FHA in simple tooth movement, which could promote a better understanding of the 3-D orientation of and rotation about the FHA during tooth movement. Parameters of the FHA were calculated from a simulation of canine retraction. As the tipping angle of the canine was increased from 5 degrees to 30 degrees , the orientation vector of the FHA approached the most affected axis of rotation (on a rectangular coordinate system) in a non-linear manner. The angle of rotation about the FHA also increased in a non-linear manner. This non-linear problem was solved analytically. The basic behavior of the orientation vector of the FHA and the non-linear characteristics of the FHA parameters clarified in this study should be important for the future analysis of actual tooth movement based on the FHA. However, we must be aware that the non-linearity of the FHA itself may affect the analysis of the mechanical properties of the periodontal tissue.

Parametric finite element analysis and closed-form solutions in orthodontics

The goal and clinical relevance of this work was the development of closed formulas that are correct and simple enough for a fast decision making by the orthodontist in the daily praxis. This paper performs a parametric three-dimensional finite element linear analysis on a maxillary central incisor with a root of paraboloidal shape, which is subjected to typical orthodontic force-systems. Parameters of most importance, such as the tooth mobility in translation and in pure moment rotation including orthodontic centers, as well as the stresses inside the periodontal ligament are calculated for a large variety of over four hundred different couples of root lengths and root diameters around a nominal value. Regression analysis is afterwards performed and establishes closed-form solutions, which are also explained in terms of analytical strain energy and hydrostatic stress considerations within the periodontal ligament characterised by a small compressibility. The obtained expressions include both the root length as well as the root diameter.

A novel method for the three-dimensional (3-D) analysis of orthodontic tooth movement-calculation of rotation about and translation along the finite helical axis

The purpose of this study was to establish a novel method for evaluating orthodontic tooth movement in three-dimensional (3-D) space. The present system consisted of the following procedures at a given treatment period: (1) 3-D tooth positions were measured with a 3-D surface-scanning system using a slit laser beam; (2) the 3-D shape data were registered automatically at the maxillary first molars, and the coordinate systems were normalized; (3) the rotation matrix and translation vector were calculated from the automatic registration of the two position data for a given tooth; (4) the finite helical axes of teeth were calculated as the locus of zero rotational displacement; and (5) tooth movement was presented as rotation about and translation along the finite helical axis. To test this system, a male patient (age 22 yr 2 months) with Angle Class III malocclusion and moderate crowding of the anterior teeth, who had been treated using a standard multi-bracket appliance, was used as a model case in this study. Impressions for a dental cast model were taken at five phases; immediately before and after application of the appliance, and 10 days, 1 month and 2 months after beginning treatment. The results demonstrated that the present analytical method can more simply describe the movement of a given tooth by rotation about and translation along the finite helical axis, and provides quantitative visual 3-D information on complicated tooth movement during orthodontic treatment.

Experimental evaluation of initial tooth displacement, center of resistance, and center of rotation under the influence of an orthodontic force

The purpose of this study was to determine the location of the center of resistance and the center of rotation of the maxillary central incisors under the influence of a single simple force and to investigate related geometric parameters of the teeth and the surrounding periodontal tissues. By measuring the initial displacement of the central incisors with a magnetic sensing system, the location of the center of resistance and the centers of rotation associated with various forces were determined in 3 human subjects. The results show that the location of the center of resistance of the maxillary central incisor depends on the palatal bone level and is at approximately two-thirds of the palatal alveolar bone height, measured from the root apex. A greater moment-to-force ratio is needed for any controlled movement of the maxillary incisors during retraction in patients with reduced palatal alveolar bone height. This study suggests a method for estimating the location of the center of resistance of a tooth.

Numerical Estimation of the Centres of Rotation and Resistance in Orthodontic Tooth Movement

The position of the centre of resistance (Cre) as well as the centre of rotation (Cro) of a tooth under a force-system is still an open question. This paper presents a reliable and efficient three-dimensional rigid-body finite element technique to accurately estimate these centres. The influence of not only the root length but also the root diameter, the thickness of the periodontal ligament, as well as its material properties on the position of the Cre and Cro is investigated. Additionally, an explanation is given for the meaning of the coefficient (0.068 h(2) ) involved in Burstone's theoretical formula which is generalised and is expressed as the ratio of the flexibilities of tooth support in translation and pure moment rotation, respectively. The former ratio determines the position of the centres of rotation as a function of the applied moment-to-force ratio (M/F) and the relevant curve remains an isosceles hyperbola for any arbitrary-shaped tooth. The present study focuses on single-rooted teeth, such as maxillary canines and maxillary incisors, but the proposed methodology is generally applicable to any tooth.

A comparison between friction and frictionless mechanics with a new typodont simulation system

This study was designed to explore the differences between friction and frictionless mechanics for maxillary canine retraction with the use of a new typodont simulation system, the Calorific machine system. The unit was designed to observe the whole process of tooth movement and is composed of 3 parts: a temperature regulating system, electrothermodynamic teeth, and an artificial alveolar bone component. The efficiency of maxillary canine retraction was compared with the sliding mechanics (along a.016 x.022-in stainless steel labial arch and nickel-titanium closed coil spring) and a canine retraction spring. The patterns of tooth movement obtained with both of these mechanics were measured 5 times each. Friction mechanics were superior to frictionless mechanics in terms of rotational control and dimensional maintenance of the arch (P <.0001); frictionless mechanics were shown to be more effective at reducing tipping and extrusion (P <.0001). However, the observed differences between the 2 methods were relatively small in terms of their clinical significance, and no differences were found in anchorage control (P =.2078). In conclusion, this study indicated that friction and frictionless mechanics perform similarly.

Development of a magnetic sensing device for tooth displacement under orthodontic forces

We have developed a system for measuring tooth displacement from orthodontic force. Eight small magnetic sensors and a magnet are combined to measure three-dimensional displacement. Sensors, arranged cubically in the three planes of space, are placed in the mouth and fixed to the posterior teeth by a splint. A magnet is placed in the center of the eight sensors and attached to a front tooth that is subjected to orthodontic force. Sensors detect the magnet's movement as target tooth displacement. The system was designed to achieve displacement resolution of 1 microm. The mean percentage of measurement errors was determined to be less than 1% in a 600-cubic-microm volume from calibration. The system was tested clinically on human teeth. Although the oral environment, with high temperature and humidity, was not agreeable with the sensors, this system was stable and accurate enough for quantitative measurement of tooth displacement. The advantage of this system is the ability to detect tooth trajectories by decomposing displacement into translation and rotation and to determine the position of the center of rotation from these parameters.

A comparative FEM-study of tooth mobility using isotropic and anisotropic models of the periodontal ligament. Finite Element Method

Orthodontic tooth movement is usually characterized by two centres: the centre of resistance and the centre of rotation. A literature survey shows that both centres vary to a significant extent in both clinical and computational experiments. This paper reports on studies upon five different hypothetical mechanical representations of the periodontal ligament (PDL) which plays the most significant role in tooth mobility. The first model considers the PDL as an isotropic and linear-elastic continuum without fibres; it also discusses some preliminary visco-elastic aspects. The next three models assume a nonlinear and anisotropic material composed of fibres only that are arranged in three different orientations, two hypothetical that have appeared previously in the literature and one more consistent with actual morphological data. The fifth model considers the PDL as an orthotropic material consisting of both a continuum and of fibres. Results were obtained by applying the Finite Element Method (FEM) on a maxillary central incisor. It was found that the isotropic linear-elastic PDL leads to occlusal positions of both centres in comparison with those obtained through the well-known Burstone's theoretical formula, while histological anisotropic fibres locate them apically and eccentrically.

In vitro analysis of the initial tooth mobility in a novel optomechanical set-up

An optomechanical set-up was developed to accurately measure displacement/force curves of the initial tooth mobility in vitro. The system presented is capable of recording all six components of a tooth movement resulting from an applied orthodontic force system, and consists of a laser diode-based optical part and a six degree of freedom mechanical part. Three laser diodes were mounted in orthogonal arrangement on the tooth of a specimen and their light (lambda = 670 nm) was focused on the surfaces of three position sensing detectors. The laser beams thus defined a cartesian rigid body coordinate system and the movements of the tooth could directly be derived from the movements of the laser spots on the surfaces of the optical detectors. The force system was applied and simultaneously measured via a three-dimensional force-torque transducer mounted on a six-axis positioning table. Measuring accuracy of the tooth displacements was in the range of 9.0 microns and 0.022 deg for translations and rotations, respectively. Resolution and accuracy of the mechanical system was approx. 0.02 N for the measurement of forces and 0.5 Nmm for torques. Displacement/force diagrams of the specimen of a swine's mandible are presented, showing the relationships between applied force system and tooth displacement of the lower first premolar. The accuracy reached proved to be sufficient for the verification of numerical (Finite Element) models of the initial tooth mobility.

Analysis of forces and moments in arch guided molar protraction using Class I and Class II elastics. An in-vitro study

The use of class I and II elastics in arch guided tooth movement of the lower molars belongs to the proven clinical methods to achieve space closure even though risks are present. The vertical force component of class II elastics tends to interact with the sagittal force and thus the vertical force may change the desired sagittal force and movement direction. The objective of the study presented here was to investigate friction behavior and the movement dynamics of the arch guided protraction of the lower first molar being acted on by differing class I and class II elastic band geometries. The influence of class I and class II elastics at different force levels (1 N and 2 N) were studied. The pattern of the force line varied in the area of angulation from 0 degree to 40 degrees relative to the arch plane. The orthodontic measurement and simulation system (OMSS) was employed to determine force loss due to friction and to analyze side effects. In the arch guided mesialization of the lower first molar, the vertical component of class II elastics induces a minor force loss in comparison with class I elastics. This holds, however, only for the lower 1 N force level. When employing class II bands at a greater force level and with increased angulation, relatively greater force loss and increased side effects, such as extrusion and mesial tipping of the first molar, occur.

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 x 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.

[The practical aspects of using "superelastic" arch wires in the edgewise technic]

Ever increasing refinements in orthodontic treatment and the corresponding increase in technical demands are challenges to both the dentist in his/her practice and to the manufacturers of orthodontic materials. One interesting development has been the introduction of "super-elastic" arch wires, which have now been on the market for some years. Such arch wires are characterized by an excellent "shape memory", various levels of super-elasticity, a remarkable hysteresis, and temperature sensitivity. On the basis of findings from temperature controlled tests of arch wires in a "Lloyd 1000 R" testing machine, the following conclusions can be drawn. Shape memory can, from a clinical point of view, be regarded as being a positive feature. "Super-elasticity" is of lesser value, because conventional activation of edgewise arches rarely reaches the level of deformation necessary for super-elasticity to be called into play. Hysteresis and temperature sensitivity make a biomechanical control of the arch wires difficult. Reducing active forces by chilling the archwire brings relief to sore teeth. Whether this possibly leads to an improvement in blood circulation in the periodontal tissue, which would be biologically advantageous, should be made the subject of further research.

[Retraction of the upper incisors with pseudoelastic treatment elements. Their computational and biomechanical testing and clinical use]

Based on the favorable results achieved by the application of pseudoelastic T loops in the course of canine retraction, this study investigates their application to the retraction of maxillary incisors. A modified Burstone T loop was made of a pseudoelastic orthodontic nickel titanium wire and then subjected to experimental testing. The results obtained were compared with extensive numerical studies. The results of the tests showed that forces and moments generated by the T loop are suitable for the retraction of upper incisors. The clinical application of the pseudoelastic spring was performed using an individualized retraction arch enclosing the whole front segment. Whereas during canine retraction the experimental and clinical results corresponded very well, such was not observed during the retraction of upper incisors. This result implies that the location of the center of resistance of the upper incisors has not been completely clarified. It is thus recommended that this matter should be given further study.

[Frictional forces and movement dynamics in the mesialization of the second molar after the extraction of the sixth-year molar. An in-vitro study]

In this study the frictional forces and dynamics of arch guided molar mesialization were investigated. The influence of two different slot/arch combinations (.018" slot/.016" x .022" arch and .022" slot/.019" x .025" arch) as well as partial fortification of an .016" x .022" wire and the reduction of interbracket distance were studied. In guiding the arch wire, a convertible bracket was tested in tube and in bracket configurations. The tipping movement could be compensated by adding an uprighting spring. The orthodontic measurement and simulation system (OMSS) was employed to determine frictional loss in forces and to analyze side effects. Results showed that frictional forces were almost independent from the wire stiffness, whereas a reduced cross section resulted in distinct side effects. These effects can be countered either by employing a correctly dimensioned uprighting spring or by increasing the wire stiffness. The .019" x .025" wire in a .022" slot proved to be the optimum combination for molar mesialization.

[A pseudoelastic NiTi uprighting spring for the molars--its design, biomechanical testing and clinical use]

Uprighting inclined molars is one of the most common problems encountered in pre-restorative orthodontics. To prevent occlusal trauma, an intrusive force has to be applied to the molar in addition to the uprighting moment. Owing to their construction, current mechanical devices for uprighting either to not meet this requirement, or are difficult to adjust when in place. For this reason, an improved uprighting spring is described which utilizes the properties specific to super-elastic (pseudo-elastic) NiTi alloys. The most important property of super-elastic wires is the fact that they produce constant forces or moments within a specific deformation range. In order to utilize this useful property, certain design criteria have to be met. Recent measurements have shown that a super-elastic wire (Sentalloy, 0.016'' x 0.022'') having a length of 10 mm generates a constant moment of 7 to 8 Nmm within a bending angle of 50 degrees to 180 degrees. On the basis of these results, a table that permits the determination of the proper wire length needed to provide a constant moment within a given range of bending angles is proposed. The superelastic uprighting spring described here comprises an NiTi wire segment having a length of 7 mm and a mesial and distal steel wire segment. In the active state, the spring generates an uprighting moment of 8 Nmm and an intrusive force of 0.6 N. Numerical analysis using the finite element program, SOLF/MESY, and biomechanical testing with the orthodontic measuring and simulation system (OMSS) have shown that this force system remains stable throughout the entire uprighting process. The clinical application of the spring is demonstrated in a specific case.

An experimental apparatus for the simulation of three-dimensional movements in orthodontics

An apparatus for the study of three-dimensional force systems and the resulting movements during orthodontic treatment is presented. The instrument consists of two force-torque transducers which are capable of recording both forces and torques simultaneously, in all spatial directions. Each sensor has a measuring range of 15N (450 Nmm) and a resolution of 0.02 N (0.5 Nmm) and is mounted on a set of three translational and three rotational stages driven by stepping motors. Positioning accuracy is in the range of 1 micron and 0.01 degrees respectively. The apparatus is computer controlled and supported by comprehensive software.

[Orthodontic measuring and simulating systems (OMSS) for the static and dynamic analysis of tooth movement]

An orthodontic measurement and simulation system (OMSS) is presented. The major components of this system are two measuring tables each comprising a force/torque sensor and a motor driven, fully three-dimensionally adjustable positioning stage. The force/torque sensors are capable of measuring simultaneously all forces and torques acting on a tooth. Using the computer program "OMSS" which runs on a personal computer, several different measurements can be conducted. On the one hand, the system supports absolute measurements such as the registration of a force/deflection diagram. Furthermore, even multidimensional force/deflection- or torque/distance curves can be measured. On the other hand, simulations of orthodontic tooth movement can be conducted. In such simulations, the force system acting on a tooth is measured and the resulting tooth movements are calculated. By using this "computer typodont", not only the static but the dynamic behaviour of orthodontic appliances can be studied. The application of this system is demonstrated by the analysis of several orthodontic problems.

[Arch-guided tooth movement--its dynamics, efficacy and side effects]

Canine retraction on a continuous arch wire was simulated using the OMSS. The influence of wire dimension, force generating element (power chain, coil spring, powerhook, uprighting spring), bracket width and the position of the center of resistance on the effectiveness of the distalization of the canine and its side effects such as extrusion, rotation and tipping were examined. Stainless steel, nickel titanium and multi-stranded wires were tested. Employing the 0.018"-slot system, the use of an 0.016" X 0.022"-arch wire gave the best results. Comparing the NiTi coil spring with the elastic chain, the former should be preferred, because, due to its low load deflection it generates a nearly constant force over a wide range of activation. Using powerhooks or uprighting springs, a nearly bodily movement could be achieved. On the other hand, friction may increase if the uprighting is too strong. The rate of tooth movement decreases by increasing length of tooth root represented by the position of the center of resistance. Arch guided tooth movement along multi-stranded wires shows a high effectiveness, nevertheless, these wires should not be used for canine retraction because of the above mentioned side effects.