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The purpose of this study was to analyze and clarify tooth movement during mesialization of the whole maxillary dentition with various force angulations (FAs).A finite element method was used to simulate the long-term orthodontic movement of the maxillary dentition by accumulating the initial displacement of teeth produced by elastic deformation of the periodontal ligament. A mesial force of 3 N was applied to the maxillary second molar at 5 different FAs (-30°, -15°, 0°, 15°, and 30°) to the occlusal plane.At an FA of 28°, the line of action of the force passed through the center of resistance of the maxillary whole dentition. With all FAs, the central incisors and molars tipped labially and mesially, respectively. The tipping angles gradually decreased as the FAs shifted from -30° to 30°. The molars tipped lingually with FAs of -30° and -15°, whereas they tipped buccally with FAs of 0°, 15°, and 30°. The molars tended to rotate mesiolingually more as the angle of force increased toward an FA of 30°. The occlusal plane rotated counterclockwise with FAs of -30°, -15°, and 0°, whereas it rotated clockwise with FAs of 15° and 30°. With an FA of 30°, buccal tipping and mesiolingual rotation of the molars, and the change in the occlusal plane angle decreased when the transpalatal arch (TPA) was fixed to the first molars and decreased, even more when the TPA was fixed to the second molars rather than the first molars, when a thicker TPA was used, and when the TPA was fixed to both molars rather than a single molar.There was a correlation between tooth movement during mesialization of the whole maxillary dentition and the angle at which the force was applied.

Class III malocclusions with mild to moderate skeletal discrepancies can be camouflaged by orthodontic tooth movement. Conventional methods using Class III elastics can correct Class III into Class I molar relationships. These mechanics show side-effects such as labioversion and intrusion of the maxillary incisors, extrusion of the maxillary molars, linguoversion and extrusion of the mandibular incisors, and intrusion of the mandibular molars along with flattening of the occlusal plane. Conventional mechanics can improve occlusal relationships and some profile esthetics but may produce detrimental smile esthetics by reducing the amount of maxillary incisor exposure. Recently, with the advent of temporary skeletal anchorage devices (TSADs), clinicians are able to achieve total distalization of the mandibular dentition and therefore improve the occlusal relationship without worsening smile esthetics. With the use of TSADs, the en masse movement of an entire dentition can be easily accomplished using a statically determinate force system, which makes treatment plans easier and treatment results more predictable. Finite element studies have identified the location of the center of resistance of the entire dentition and simulated displacement of the dentition depending on the force angulations and have thus provided the theoretical basis for 3-dimensional tooth movement patterns. This article provides the biomechanical considerations and clinical applications of total distalization of the mandibular dentition depending on various force angulations to the mandibular occlusal plane for camouflage treatment of various types of skeletal Class III malocclusions.

Objectives To clarify the mechanics of tooth movement in mesialization of the whole mandibular dentition when changing the force angulation. Setting A finite element method was used to simulate long-term movements of the whole mandibular dentition. Material and methods Tooth movement was simulated by accumulating the initial displacement, which was produced by elastic deformation of the periodontal ligament. Mesial forces of 3 N were applied to the second molar bracket at -30°, -15°, 0°, 15° and 30° to the occlusal plane. Results The whole dentition and occlusal plane were rotated depending on the direction of the force with respect to the centre of resistance (CR). At a force angulation of -30°, the line of action of the force passed near the CR, and the whole dentition translated without rotation of the occlusal plane. The second molar tipped buccally due to a clearance gap between the archwire and bracket slot. When increasing a force angulation from -30°, the line of action of the force passed above the CR, and thereby, the occlusal plane rotated clockwise. This rotation of the whole dentition induced tipping of the individual teeth. Buccal tipping of the molar due to an elastic deformation of the archwire was prevented by using a lingually pre-bent archwire. Conclusions Careful selection of force angulation and biomechanics is essential to obtain proper tooth movement in total mesialization of the mandibular dentition.

Objective The aim of this finite element study was to clarify the mechanics of tooth movement in palatal en-masse retraction of segmented maxillary anterior teeth by using anchor screws and lever arms. Methods A three-dimensional finite element method was used to simulate overall orthodontic tooth movements. The line of action of the force was varied by changing both the lever arm height and anchor screw position. Results When the line of action of the force passed through the center of resistance (CR), the anterior teeth showed translation. However, when the line of action was not perpendicular to the long axis of the anterior teeth, the anterior teeth moved bodily with an unexpected intrusion even though the force was transmitted horizontally. To move the anterior teeth bodily without intrusion and extrusion, a downward force passing through the CR was necessary. When the line of action of the force passed apical to the CR, the anterior teeth tipped counterclockwise during retraction, and when the line of action of the force passed coronal to the CR, the anterior teeth tipped clockwise during retraction. Conclusions The movement pattern of the anterior teeth changed depending on the combination of lever arm height and anchor screw position. However, this pattern may be unpredictable in clinical settings because the movement direction is not always equal to the force direction.

Objectives To estimate the optimal bending angles in the running loop for mesial translation of a mandibular second molar using indirect skeletal anchorage and to clarify the mechanics of tipping and rotating the molar. Methods A three-dimensional finite element model was developed for predicting tooth movement, and a mechanical model based on the beam theory was constructed for clarifying the force systems. Results When using a running loop without bends, the molar tipped mesially 14.4° and lingually 0.6°, rotated counterclockwise 4.1°, and the incisors retracted 0.02 mm and intruded 0.05 mm. These angles were about the same as those estimated by the beam theory. When the amount of tip back and toe-in angles was 11.0°, mesial translation of the molar was achieved, and incisors retracted 0.10 mm and intruded 0.30 mm. Conclusions Mesial translation of a mandibular second molar without any significant movement of anterior teeth was achieved during protraction by controlling the tip back and toe-in angles and enhancing anterior anchorage with the combined use of a running loop and indirect skeletal anchorage.

Introduction The purpose of this study was to analyze and clarify tooth movement during mesialization of the whole maxillary dentition with various force angulations (FAs). Methods A finite element method was used to simulate the long-term orthodontic movement of the maxillary dentition by accumulating the initial displacement of teeth produced by elastic deformation of the periodontal ligament. A mesial force of 3 N was applied to the maxillary second molar at 5 different FAs (−30°, −15°, 0°, 15°, and 30°) to the occlusal plane. Results At an FA of 28°, the line of action of the force passed through the center of resistance of the maxillary whole dentition. With all FAs, the central incisors and molars tipped labially and mesially, respectively. The tipping angles gradually decreased as the FAs shifted from −30° to 30°. The molars tipped lingually with FAs of −30° and −15°, whereas they tipped buccally with FAs of 0°, 15°, and 30°. The molars tended to rotate mesiolingually more as the angle of force increased toward an FA of 30°. The occlusal plane rotated counterclockwise with FAs of −30°, −15°, and 0°, whereas it rotated clockwise with FAs of 15° and 30°. With an FA of 30°, buccal tipping and mesiolingual rotation of the molars, and the change in the occlusal plane angle decreased when the transpalatal arch (TPA) was fixed to the first molars and decreased, even more when the TPA was fixed to the second molars rather than the first molars, when a thicker TPA was used, and when the TPA was fixed to both molars rather than a single molar. Conclusions There was a correlation between tooth movement during mesialization of the whole maxillary dentition and the angle at which the force was applied.

This paper proposes a WLAN system which has the transmission standby, that reduces radio interferences and effectively utilizes radio resources. In a WLAN system which has the transmission standby, devices whose SINRs are lower than the threshold wait for transmissions, and other devices can transmit frames without radio interferences from the devices which are waiting for transmissions. When radio interference is reduced, the SINR becomes higher and the transmission rate becomes higher. In this paper, we evaluate the transmission performance of the WLAN system based on DCF manner with the transmission standby. This paper asserts that reducing the radio interference by the function of the transmission standby brings an improvement of the transmission rate and a reduction of failed frames.

The aim of this finite element study was to analyze and clarify the mechanics of tooth movement patterns for total distalization of the mandibular dentition based on force angulation.Long-term orthodontic movement of the mandibular dentition was simulated by accumulating the initial displacement of teeth produced by elastic deformation of the periodontal ligament.Displacement of each tooth was caused by movement of the whole dentition, elastic deflection of the archwire, and clearance gap between the archwire and bracket slot. The whole dentition was rotated clockwise or counterclockwise when the line of action of the force passed below or above the center of resistance. Elastic deflection of the archwire induced a lingual tipping of the anterior teeth. It became larger when increasing the magnitude of angulation. The archwire could be rotated within the clearance gap between the archwire and the bracket slot, and thereby the teeth tipped.Mechanics of total mandibular distalization was clarified. Selective use of force angulation with a careful biomechanical understanding can achieve proper distalization of the whole mandibular dentition.

This clinical article reports an esthetic treatment option for managing a Class II malocclusion in an adult. The patient, a woman aged 24 years 2 months, had crowding and a convex profile. She was treated with maxillary first premolar extractions, a double J retractor, and temporary skeletal anchorage devices in the maxillary arch. Posttreatment records after 2 years showed excellent results with good occlusion and long-term stability.

Natural frequencies and vibration modes of four kinds of teeth were calculated by using a mechanical model. The alveolar bone and the tooth were assumed as rigid bodies, while the periodontal ligament was assumed as an elastic spring. All the natural frequencies were within a range of 1 to 10 kHz. The first natural frequencies of four teeth were about 1.5 kHz, and decreased as the root length decreased. Their vibration modes were tipping movements of the root. The natural frequency of the twisting vibration mode, or rotating movement around the tooth axis, was affected by root configuration. When subjected to a periodic force, the tooth and periodontal ligament would vibrate with the corresponding resonance mode. This phenomenon may be used as a method for the diagnosis and the treatment of a periodontal tissue.

Tooth movements produced by a canine retraction spring were calculated. Although a gable bend and an anti-rotational bend were incorporated into the spring, the canine tipped and rotated initially. Retraction force decreased and moment-to-force ratio increased after the spring legs closed. Then, the initial tipping and rotation began to be corrected. As a result, the canine moved almost bodily after a prolonged period of time. Such tooth movements cannot be estimated from the initial force system. The gable bend decreased tipping movement, but increased rotational movement. On the other hand, the anti-rotational bend decreased rotational movement but increased tipping movement. In other words, one bend decreased the effect of the other, when both bends were incorporated in the spring.

Objective The purpose of this study was to predict the optimal bending angles of a running loop for bodily protraction of the mandibular first molars and to clarify the mechanics of molar tipping and rotation. Methods A three-dimensional finite element model was developed for predicting tooth movement, and a mechanical model based on the beam theory was constructed for clarifying force systems. Results When a running loop without bends was used, the molar tipped mesially by 9.6° and rotated counterclockwise by 5.4°. These angles were almost similar to those predicted by the beam theory. When the amount of tip-back and toe-in angles were 11.5° and 9.9°, respectively, bodily movement of the molar was achieved. When the bend angles were increased to 14.2° and 18.7°, the molar tipped distally by 4.9° and rotated clockwise by 1.5°. Conclusions Bodily movement of a mandibular first molar was achieved during protraction by controlling the tip-back and toe-in angles with the use of a running loop. The beam theory was effective for understanding the mechanics of molar tipping and rotation, as well as for predicting the optimal bending angles.

The penetration of a viscous lubricating oil into a three-dimensional surface crack under a rolling contact stress was calculated. The finite element method was applied to solve the Reynolds equation coupled with the elastic deformation of the crack. The process of penetration is roughly the same as in the two-dimensional model. The lubricating oil begin to flow into the crack when the contact pressure passes the crack mouth. The lubricating oil enters the crack tip and increases the stress intensity factor when nondimensional viscosity β=ηvE2/(ap03) is small. The crack is not open when β is large, because the contact pressure passes before the lubricating oil flows into the crack. The critical value of β was calculated. The penetration of the lubricating oil in the three-dimensional model is not easy as compared with the two-dimensional model.

目的: オールセラミックスクラウンの破損は, 歯冠補綴において深刻な問題の1つである. この研究の目的は, 大臼歯オールセラミックスクラウンの咬合面形態の違いによる, 裂溝部の応力分布を明らかにすることである.方法: 解析モデルは下顎右側第一大臼歯の遠心片側の領域とし, その解析には三次元有限要素法を用いた. このモデルの形状因子である裂溝底の半径, 咬合面のクラウン厚さ, 咬頭傾斜角のそれぞれを変化させ, その応力分布を計算した. 負荷条件は食物摂取時を想定し, 円形の領域荷重とし, クラウンの中心窩に負荷を与えた. 特に, 応力の集中する裂溝部では要素分割を細分化することで, この部分の応力を正確に計算した. クラウン材料にはオリンパスキャスタブルセラミックスを, 支台歯には象牙質をそれぞれ想定した. 上述の事柄をANSYS5.5に入力し, 解析を行った.結果: 負荷した荷重が圧縮荷重であるにもかかわらず, 裂溝底部に大きな引張応力が生じた. この応力は, 裂溝底の半径を小さくした場合と, 咬頭傾斜角を大きくした場合に増加した. また, クラウンと支台歯の境界面にも, 引張応力が生じた. この応力は, 咬合面部のクラウン厚さが薄くなるに従って高くなった.結論: 破損の危険性の低いクラウンを作製するためには, 裂溝底の半径を大きめにすることと, 咬合面部のクラウン厚さを均一にすることが有効であった.

In the case of plane strain plastic compression, behavior of a viscous lubricating oil trapped in a small pit on a contact surface is calculated by a finite element method. The oil pressure is controlled by the yielding condition. When the oil pressure is constant over the surface, the oil does not flow and the pit is not flattened. When the lateral deformation of material is constrained and pressure gradient is produced, the oil in the pit flows out and the pit is flattened. Reduction in heigth required to flatten the pit is above several times of the pit depth. A decrease in the viscosity and an increase in the pit depth enhance the flattening. When the compression tool is slid with a high speed, a hydrodynamic effect of the oil causes a pressure change and the pit moves in the sliding direction.

Introduction En-masse sliding mechanics have been typically used for space closure. Because of friction created at the bracket-wire interface, the force system during tooth movement has not been clarified. Methods Long-term tooth movements in en-masse sliding mechanics were simulated with the finite element method. Results Tipping of the anterior teeth occurred immediately after application of retraction forces. The force system then changed so that the teeth moved almost bodily, and friction occurred at the bracket-wire interface. Net force transferred to the anterior teeth was approximately one fourth of the applied force. The amount of the mesial force acting on the posterior teeth was the same as that acting on the anterior teeth. Irrespective of the amount of friction, the ratio of movement distances between the posterior and anterior teeth was almost the same. By increasing the applied force or decreasing the frictional coefficient, the teeth moved rapidly, but the tipping angle of the anterior teeth increased because of the elastic deflection of the archwire. Conclusions Finite element simulation clarified the tooth movement and the force system in en-masse sliding mechanics. Long-term tooth movement could not be predicted from the initial force system. The friction was not detrimental to the anchorage. Increasing the applied force or decreasing the friction for rapid tooth movement might result in tipping of the teeth.

The penetration of a viscous lubricant into a three dimensional surface crack under a rolling contact stress was calculated. The finite element method was applied to solve the Reynolds equation coupled with the elastic deformation of the crack. The process of penetration is roughly the same as the two dimensional model. The lubricant begin to flow into the crack when the contact pressure is passing the crack mouth. The lubricant enters to the crack tip and increases the stress intensity factor, when a nondimensional parameter β=ηυE2/(ap30)is small. The crack does not open when β is large, because the contact pressure has passed before the lubricant flows into the crack. The critical value of β was calculated. The penetration of the lubricant is not easy as compared with the two dimensional model.

The penetration of a viscous lubricant into a two dimensional surface crack under a rolling contact stress was calculated. The finite element method was applied to solve the Reynolds equation coupled with the elastic deformation of the crack. The lubricant begins to flow into the crack when the contact pressure is passing the crack mouth. The lubricant enters to the crack tip and increases the stress intensity factor, when a nondimensional parameter β=ηνE2/(ap30) is small. The crack does not open when β is large, because the contact pressure has passed before the lubricant flows into crack. The critical values of β were calculated. The penetration of the lubricant becomes easy when a frictional stress acts as the crack opening.

Initial movements of a lower first premolar were analyzed by a three dimensional elastic finite element method. When the elastic constants of the periodontal ligament were the following : Young's modulus Ep=0.2 MPa, Poisson's ratio νp=0.47, the calculated mobility values almost agreed with measured ones. In these case where the ratio of Young's modulus in alveolar bone Ep to Eb, Eb/Ep, became greater than 104, only the periodontal ligament was subjected elastic deformation whereas the tooth and the alveolar bone hardly deformed. Stress values calculated by the two dimensional plane strain model were about the half of the three dimensional case, because the stiffness of the alveolar socket decreases. Assuming that the tooth and the alveolar bone were rigid bodies, the initial movements and the stress distributions in the periodontal ligament were able to calculate simply. The results calculated by the simple method almost agreed with those by the finite element method.

埋立地のしゃ水シートに使用されている合成ゴムシートに対して, 水を用いた溶出試験を行い, 溶出する有機化合物を検索した。その結果, ベンゾチアゾール, シクロヘキシルイソチオシアネート, 2-ベンゾチアゾロール, N, N'-ジシクロヘキシルウレアおよび2-メルカプトベンゾチアゾールを確認した。一方, これらの物質が埋立地の浸出水中に存在するか否かを調べたところ, 廃プラスチック類やゴムくずを廃棄している埋立地の浸出水から, 2-ベンゾチアゾロールとN, N'-ジシクロヘキシルウレアが検出された。これらの物質は, 廃棄物からの溶出と埋立地に用いた合成ゴム製のしゃ水シート自体から溶出したものがともに含まれることが考えられる。さらに, 埋立地の浸出水のGCチャート上に認められたピークについて検討を加え, N-ブチルベンゼンスルホンアミドの存在も併せて確認した。また, 2-メルカプトベンゾチアゾールの分解物である2-ベンゾチアゾロールの生物に対する影響についての知見が少ないことから, 2-メルカプトベンゾチアゾールと2-ベンゾチアゾロールについてエームス試験を行ったが, いずれも陰性であった。

Introduction Miniscrews placed in bone have been used as orthodontic anchorage in extraction space closure with sliding mechanics. The movement patterns of the teeth depend on the force directions. To move the teeth in a desired pattern, the appropriate direction of force must be selected. The purpose of this article is to clarify the relationship between force directions and movement patterns. Methods By using the finite element method, orthodontic movements were simulated based on the remodeling law of the alveolar bone. The power arm length and the miniscrew position were varied to change the force directions. Results When the power arm was lengthened, rotation of the entire maxillary dentition decreased. The posterior teeth were effective for preventing rotation of the anterior teeth through an archwire. In cases of a high position of a miniscrew, bodily tooth movement was almost achieved. The vertical component of the force produced intrusion or extrusion of the entire dentition. Conclusions Within the limits of the method, the mechanical simulations demonstrated the effect of force direction on movement patterns.

The purpose of this article is to simulate long-term movement of maxillary teeth connected with an archwire and to clarify the difference between the initial tooth movement and the long-term orthodontic movement. Initial tooth movement was calculated based on the elastic deformation of the periodontal ligament. Orthodontic tooth movement was simulated based on the bone remodeling law of the alveolar bone, while consequentially updating the force system. In the initial tooth movement, all teeth tipped individually due to an elastic deflection of the archwire. In the long-term movement, the maxillary teeth moved as one united body, as if the archwire were a rigid material. Difference of both movement patterns was due to the change in force system during tooth movement. The long-term movement could not be predicted from the initial tooth movement. Movement pattern and location of the centre of resistance in the long-term movement were almost the same as those in the initial tooth movement as calculated by assuming the archwire to be a rigid material.

This case report describes the treatment of an 18-year-old man with a skeletal Class III pattern and a full-step Class III malocclusion. The orthodontic treatment included distal movement of the mandibular dentition with temporary skeletal anchorage devices. The total active treatment time was 30 months. His occlusion and facial appearance were significantly improved by the orthodontic treatment. Posttreatment records 2 years later showed excellent results with good occlusion and facial balance.

A simple method for measuring contact pressure at a tool-workpiece interface is presented. The strain of the tool near the contact surface is measured using a pipe-type strain gage, and is converted into the pressure. The measured pressure distributions in plastic compression of rectangular blocks almost agreed with those estimated from the strain distribution. The pressure was distributed uniformly over the contact surface in the well-lubricated specimens regardless of the height-to-width ratio of the specimen, H0/L0 Friction hills were observed in the unlubricated specimens with H0/L0=0. 25 and 0. 5. A concave pressure distribution was obtained for the specimen with H0/L0=1, where the pressure increased from the center to the periphery of the contact surface. The present method can be applied to measure die pressure in practical metalworking processes.

The purpose of this study was to develop a new finite element method for simulating long-term tooth movements and to compare the movement process occurring in canine retraction using a T-loop spring having large bends and with that having small bends. Orthodontic tooth movement was assumed to occur in the same manner as the initial tooth movement, which was controlled by the moment-to-force (M/F) ratios acting on the tooth. The M/F ratios were calculated as the reaction forces from the spring ends. For these M/F ratios, the teeth were moved based on the initial tooth movements, which were calculated by using the bilinear elastic model of the periodontal ligament. Repeating these calculations, the teeth were moved step by step while updating the M/F ratio. In the spring with large bends, the canine at first moved bodily, followed by root distal tipping. The bodily movement was quickly achieved, but over a short distance. In the spring with small bends, the canine at first rotated and root mesial tipping occurred, subsequently the canine uprighted and the rotation decreased. After a long time elapsed, the canine moved bodily over a long distance. It was found that the long-term tooth movement produced by the T-loop springs could be simulated by the method proposed in this study. The force system acting on the teeth and the movement type remarkably changed during the long-term tooth movement. The spring with large bends could move the canine bodily faster than that with small bends.

Anomalous dyeing behaviour has been found when regular acrylic fibre treated in hydrochloric acid, in which the sulphonic acid group was present entirely in the acid form, was dyed in neutral condition with azo and anthraquinone disperse dyes. In the very early stages of dyeing there was an abnormally high degree of dye exhaustion, with bathochromic (azo) or hypsochromic (anthraquinone) colour changes on the fibre. These phenomena gradually disappeared after prolonged dyeing, with normal adsorption equilibria and colours eventually being obtained. The results were explained on the basis of protonation by the sulphonic acid groups of treated fibre which occurs at the azo nitrogen or the amino nitrogens of the substituents in the 1 — or 1,4-positions of anthraquinone. The normal adsorption equilibria after prolonged dyeing was attributed to hydrolysis of the cyano side group to form carboxylic acid. This produces ammonia to liberate neutral dye from the protonated dye cation adsorbed electrostatically by the sulphonic acid anion of the treated fibre.

A finite element method formulated by a total lagrangian method was used to calculate the nonlinear part of deformation. In the case of double beam load cells, when an off-center load is applied, axial forces of the beams produce a nonlinear bending strain. The nonlinear strain is proportional to the applied load and the off-center distance. The output of the nonlinear strain can be avoided by shifting strain gages to an appropriate position. The nonlinear strain distributions of load cells with thinned sections in beams are affected by the flexural rigidity along the beam. In the case of a center-beam load cell, the nonlinear strain is relatively small, but the deformation mode is more complicated compared to double-beam load cells.

Background: Bone remodeling laws have been used to simulate the movement of a single tooth, but the calculations for simulating the movement of several teeth simultaneously are time-consuming. The purpose of this article is to discuss a method that allows the simulation of more complex tooth movements. Methods: A 3-dimensional finite element method was used to simulate the orthodontic tooth movement (retraction) of a maxillary canine by sliding mechanics and any associated movement of the anchor teeth. Absorption and apposition of the alveolar bone were produced in proportion to the stress of the periodontal ligament. Results: In a reference case, the canine was retracted by a 2N force with 0.016-in square wire. The frictional coefficient between wire and bracket was 0.2. The movement of both the canine and the anchor teeth could be calculated with the elastic deformation of wire. The canine tipped during the initial unsteady state and then moved bodily during the steady state. It became upright when the orthodontic force was removed. The anchor teeth moved in the steady state and tipped in the mesial direction. The decrease in applied force by friction was about 70%. The tipping of the canine decreased when the wire size was increased or when the applied force was decreased. Conclusions: Simple assumptions were used in this calculation to simulate orthodontic tooth movements. The calculated results were reasonable in mechanical considerations. This method might enable one to estimate various tooth movements clinically. However, precise comparisons between calculated and clinical results, and the improvement of the calculation model, are left for a future study.

Introduction: Uprighting a tipped molar by using an uprighting spring is a fundamental orthodontic treatment technique. However, mechanical analyses have not been carried out for molar uprighting, and the mechanism of tooth movement has not been clarified. The purposes of this article were to clarify these mechanisms and to demonstrate the usefulness of mechanical simulations by which the effects of many factors on tooth movement can be estimated quantitatively. Methods: A 3-dimensional finite element method was used to simulate the uprighting of a second molar with a molar uprighting spring. The effects of a retainer and spring-arm bending on the tooth movements were shown quantitatively. Results: The retainer was useful to reduce the movement of anchor teeth. The same effect could be achieved by bending the spring arm in the lingual direction, but the molar was greatly rotated in the occlusal plane and was tipped in the buccal direction. Conclusions: The usefulness of a mechanical simulation method to predict orthodontic tooth movement in clinical situations was demonstrated.

Introduction: In orthodontic treatment, wires are bent and attached to teeth to move them via elastic recovery. To predict how a tooth will move, the initial force system produced from the wire is calculated. However, the initial force system changes as the tooth moves and may not be used to predict the final tooth position. The purpose of this study was to develop a comprehensive mechanical, 3-dimensional, numerical model for predicting tooth movement. Methods: Tooth movements produced by wire bending were simulated numerically. The teeth moved as a result of bone remodeling, which occurs in proportion to stress in the periodontal ligament. Results: With an off-center bend, a tooth near the bending position was subjected to a large moment and tipped more noticeably than the other teeth. Also, a tooth far from the bending position moved slightly in the mesial or the distal direction. With the center V-bend, when the second molar was added as an anchor tooth, the tipping angle and the intrusion of the canine increased, and movement of the first molar was prevented. When a wire with an inverse curve of Spee was placed in the mandibular arch, the calculated tendency of vertical tooth movements was the same as the measured result. In these tooth movements, the initial force system changed as the teeth moved. Tooth movement was influenced by the size of the root surface area. Conclusions: Tooth movements produced by wire bending could be estimated. It was difficult to predict final tooth positions from the initial force system.

Introduction The transpalatal arch (TPA), which splints together 2 maxillary molars, has been believed to preserve anchorage. The purpose of this study was to clarify this effect from a mechanical point of view. Methods The finite element method was used to simulate the movement of anchor teeth subjected to mesial forces with and without a TPA. Results In the initial movement produced by elastic deformation of the periodontal ligament, stress magnitude in the periodontal ligament was not changed by the TPA. In the orthodontic movement produced by bone remodeling, the mesial force tipped the anchor teeth irrespective of the TPA. The tipping angles of anchor teeth with and without the TPA were almost the same. The anchor teeth without the TPA were rotated in the occlusal plane and moved transversely. Conclusions The TPA had no effect on the initial movement. In the orthodontic movement, the TPA had almost no effect, preserving anchorage for mesial movement. However, the TPA prevented rotational and transverse movements of the anchor teeth. These results are valid when the assumptions used in this calculation are satisfied.

Introduction En-masse sliding mechanics have been typically used for space closure. Because of friction created at the bracket-wire interface, the force system during tooth movement has not been clarified. Methods Long-term tooth movements in en-masse sliding mechanics were simulated with the finite element method. Results Tipping of the anterior teeth occurred immediately after application of retraction forces. The force system then changed so that the teeth moved almost bodily, and friction occurred at the bracket-wire interface. Net force transferred to the anterior teeth was approximately one fourth of the applied force. The amount of the mesial force acting on the posterior teeth was the same as that acting on the anterior teeth. Irrespective of the amount of friction, the ratio of movement distances between the posterior and anterior teeth was almost the same. By increasing the applied force or decreasing the frictional coefficient, the teeth moved rapidly, but the tipping angle of the anterior teeth increased because of the elastic deflection of the archwire. Conclusions Finite element simulation clarified the tooth movement and the force system in en-masse sliding mechanics. Long-term tooth movement could not be predicted from the initial force system. The friction was not detrimental to the anchorage. Increasing the applied force or decreasing the friction for rapid tooth movement might result in tipping of the teeth.

Introduction: The transpalatal arch (TPA), which splints together 2 maxillary molars, has been believed to preserve anchorage. The purpose of this study was to clarify this effect from a mechanical point of view. Methods: The finite element method was used to simulate the movement of anchor teeth subjected to mesial forces with and without a TPA. Results: In the initial movement produced by elastic deformation of the periodontal ligament, stress magnitude in the periodontal ligament was not changed by the TPA. In the orthodontic movement produced by bone remodeling, the mesial force tipped the anchor teeth irrespective of the TPA. The tipping angles of anchor teeth with and without the TPA were almost the same. The anchor teeth without the TPA were rotated in the occlusal plane and moved transversely. Conclusions: The TPA had no effect on the initial movement. In the orthodontic movement, the TPA had almost no effect, preserving anchorage for mesial movement. However, the TPA prevented rotational and transverse movements of the anchor teeth. These results are valid when the assumptions used in this calculation are satisfied.

Introduction: The purposes of this article were to clarify the combined effect of friction and an archwire’s flexural rigidity on canine movement in sliding mechanics, and to explain how to select a suitable archwire and force level for efficient bodily movement. Methods: A numerical simulation was carried out by using a 3-dimensional finite element method. Results: As the frictional force decreased, both the net force acting on and the moving speed of the canine increased. The elastic deformation of the archwire increased, and the moving pattern of the canine changed from bodily movement to tipping, although there was no clearance between the archwire and the bracket slot. When a light wire was used, wire deformation increased, and the canine experienced greater tipping. These effects of friction and wire properties on canine movement (tipping and rotational angles) are combined by using a single parameter, EI/P , where EI is the flexural rigidity of the archwire, and P is the net force acting on the canine. A suitable combination of EI and P will cause canine bodily movement. The EI is determined from the archwire’s size and material. Conclusions: We propose a method for estimating a suitable combination in this article.

A method is presented for identifying the nonlinear relationship between voltage harmonics and the voltage distortion factor and controlling the latter. First, the nonlinear relationship between voltage harmonics and the voltage distortion factor is identified using the revised group method of data handling (RGMDH), which makes use of the self-organization technique. The nonlinear relationship is regarded as a black box, where the voltage distortion factor is expressed as a nonlinear function of some voltage harmonics. The RGMDH is very useful for nonlinear systems because it does not require so much data as the statistical method. Next, the paper deals with the problem of decreasing the voltage distortion factor by controlling the voltage harmonics that are input variables of the identified model. The optimum solution is achieved by minimizing this model of the voltage distortion factor with respect to the input variables. It is noted that decreasing a few harmonics does not necessarily mean that the voltage distortion factor is reduced. A nonlinear programming technique is utilized to obtain the optimum solution. The effectiveness of the proposed method is demonstrated with actual data obtained from a personal computer based measurement system.

In order to investigate load position errors due to dimensional errors, the strain changes caused by infinitesimal shape altering are calculated by using the three-dimensional finite element method. The strain changes which result in load position errors take place not only in the region of the beam which has been altered, but in all regions where the strain gage has bonded. In the case where the horizontal bending forces rise from a transverse load position movement, being some dimensional errors in the vicinity of one of the strain gage elements, both the local shift of the neutral axis for the bending in that region, and the global deformation due to the asymmetry of beams give rise to error in measurement. From the results presented in this report, particular modes of dimensional error resulting in serious load position errors are charified, so that the accuracy of dimensions to avoid load position errors may be estimated.