Moment-to-Force Ratios and Controlling RootNew Microsoft PowerPoint Presentation.pptx

moment force ratios and controlling root are presented

1. Moment-to-Force Ratios; Prof Dr Maher Fouda Mansoura Egypt applied to orthodontics

2. Moment-to-Force Ratios and Controlling Root Position The second and commonly employed method of controlling tooth movement with fixed appliances is with alteration of moment-to-force ratios , which is a description of the relationship between the applied force to move a tooth and the counterbalancing force couple (moment) required to prevent the rotational tendency produced as a result of the applied force being at a distance from the centre of resistance. Center or resistance of a single root tooth, Center of resistance of a molar Any force acting through the center of resistance of a tooth will make it translate in a bodily manner .

3. Moment-to-Force Ratios and Controlling Root Position What does this mean? The force applied to a tooth at the bracket will lead to a moment round the centre of resistance of the tooth; this is called the moment of the force , which will be in the direction of the applied force . (A) The moment of a force is equal to the magnitude of the force multiplied by the perpendicular distance from its line of action to the center of resistance. (B) The direction of the moment of a force can be determined by continuing the line of action around the center of resistance.

4. Moment In physics, a moment refers to the turning effect produced by a force acting at a distance on an object, usually defined with respect to a fixed reference point . In mechanics, the moment of a force describes the tendency of a force applied to a body to produce rotation . A force acting at a distance from the centre of mass of a free body in a vacuum will lead to rotation about the centre of mass, as well as a small amount of bodily translation in the direction of the applied force.

5. The application of orthodontic forces is typically at the crown of a tooth, and thereby the applied force is not through the tooth’s centre of resistance. A force applied at a distance from the centre of resistance will not produce bodily movement only, but will also result in rotation. In orthodontic biomechanics, the moment, or more accurately the moment of force , describes the tendency of a force applied to a tooth to produce rotation. The moment of a force (MF) is equal to the product of the force magnitude and the perpendicular distance (Ma) from its line of action to the centre of resistance (red circle). The point of force application in both (a) and (b) is the maxillary canine hook, but, for comparative reasons, the forces have different lines of action. The perpendicular distance from the line of action of each force to the centre of resistance is known as the moment arm (Ma).

6. The magnitude of this rotational effect produced by a force acting at a distance is expressed as the product of the force and the perpendicular distance from the line of action of that force to the centre of resistance. The direction of the moment may be found by following the line of action round the centre of resistance towards the point of force application . The direction of the moment may be found by following the line of action round the centre of resistance towards the point of force application.

7. The perpendicular distance from the line of action of the force from the point of force application to the centre of resistance is termed the moment arm (or lever arm) . The perpendicular distance from the line of action of the force from the point of force application (here the point of force application is the bracket slot) to the centre of resistance is termed the moment arm (Ma), also sometimes referred to as the lever arm.

8. In classical mechanics, the unit is the newton metre ( N ⋅ m ) or newton centimetre ( N ⋅ cm ), but in orthodontics the gram force- millimetre ( gf -mm) unit is more commonly employed (1 gf -mm = 0.98N ⋅ cm).

9. The magnitude of the moment of a force may be determined by two variables: • the magnitude of the force • the distance from the point of force application to the centre of resistance. The line of action of any force (F) not passing through the center of resistance creates a moment (M), which is a rotational or tipping effect on the tooth. According to the formula  M  =  F  ×  d , a moment is proportional to the magnitude of force and the distance (d) perpendicular from its line of action to the center of resistance

10. It is within the clinician’s capability to manipulate either of these variables in order to achieve the desired tooth movements. The edgewise orthodontic system can simultaneously deliver forces, moments and counterbalancing moments. Forces applied at a distance from the centre of resistance result in rotation of the tooth. This should be considered in all planes of space: ( i ) buccolingual , (ii) mesiodistal and (iii) occlusal.

11. Couple In mechanics, a couple refers to a pair of equal and parallel forces acting in opposite directions (i.e. opposite lines of action), and tending to cause rotation about an axis perpendicular to the plane containing them. An archwire in a bracket slot can be used to apply a couple in the: ( i ) mesiodistal , (ii) buccopalatal , and (iii) occlusal planes. (iv) The couple  created  between the bracket slot and archwire can be used to control the tipping caused by the moment of the force (F). In this way, bodily tooth movement can be achieved

12. A couple is a moment where the sum of the forces is zero. The magnitude of a couple is the product of the magnitude of one of the forces multiplied by the perpendicular distance to the opposite force . In order to determine the direction of the rotation, either force may be followed round the centre of resistance and towards the origin of the opposite force . The magnitude of a force couple is the product of the magnitude of one of the forces multiplied by the perpendicular distance to the opposite force. For example, the diagram shows the occlusal view of a premolar tooth which is to be rotated using a force couple. If the forces shown are each 60 g (a buccal elastic force applied to the bracket and an equal and opposite palatal force applied to a bonded button), and the distance (d) is 9 mm, the magnitude of the force couple (moment of the couple, MC) would be 60 × 9 = 540 gf -mm.

13. The moment created by a couple is always round the centre of resistance, no matter where the pair of forces is applied . As the distance between the two forces of the couple decreases, the overall magnitude of the couple also decreases. (a) The moment created by a force couple is always round the centre of resistance, no matter where the pair of forces is applied . A pair of equal and opposite forces is shown acting at a distance on a beam, resulting in rotation round its centre of resistance. (b) As the distance between the forces decreases, the magnitude of the force couple also decreases, but rotation still occurs round the centre of resistance. It should be noted that the pair of forces applied to the beam in this diagram resembles the position of a torquing force couple applied to a bracket on the crown of a maxillary incisor.

14. The clinical implication for fixed orthodontic appliances is that no matter where a bracket is positioned on the crown of a tooth, the moment of the couple will lead to rotation of the tooth round its centre of resistance . c) The clinical implication for fixed orthodontic appliances is that no matter where a bracket is positioned on the crown of a tooth, the moment of the force couple will lead to rotation of the tooth round its centre of resistance. In this diagram, a rectangular archwire with palatal root torque applied is engaged into the bracket slot on a maxillary central incisor. The torsional stress of the engaged archwire places a force couple in the bracket slot. The moment of this force couple (MC) will result in rotation of the maxillary incisor round its centre of resistance and thereby a change in the tooth’s inclination.

15. The magnitude of the couple depends on the magnitude of the forces and the distance between the two forces, with the moment of the created couple being the sum of the moments created by each of the two forces. Where the two forces creating the couple act on effectively opposing sides of the centre of resistance, their effect is additive. A couple created by two equal and opposite forces acting on a tooth. The total moment (M C ) is the vector addition of the two moments (m1, m2) generated by the two forces (F1, F2). Here, m1 = F1 × d1, m2 = F2 × d2. Because the two moments are in the opposite direction, one of the moments will be assigned a negative sign and the other positive. The net moment (M) will be obtained by adding the two: M = m1+ (−m2)

16. This applies to round or rectangular orthodontic archwires changing the angulation of a tooth by engaging in a bracket, and to rectangular archwires changing the inclination of a tooth by engaging in a bracket .

17. The magnitude of the couple depends on the magnitude of the forces (shown as two equal and opposite red arrows acting on the bracket) and the distance between the two forces, with the moment of the created force couple being the sum of the moments created by each of the two forces. Where the two forces creating the couple act on effectively opposing sides of the centre of resistance, their effect is additive. This applies to the settings illustrated in (a) and (b).

18. (a) Round or rectangular orthodontic archwires change the angulation of a tooth by engaging in a bracket slot. The expression of mesiodistal tip, i.e. the change in the angulation of the tooth, stops when the archwire becomes passive in the bracket slot. (b) Rectangular archwires change the inclination of a tooth by engaging in a bracket slot. The expression of buccolingual torque, i.e. the change in the inclination of the tooth, stops when the archwire becomes passive in the bracket slot.

19. To counteract the effect of the moment of the applied force , a force couple may be generated at the bracket, creating a new moment, called the moment of the couple , which can counterbalance themoment of the force .

20. If the moment of the couple is opposite the moment of the force, and equal in magnitude, rotational movement will be prevented, permitting bodily movement.

21. Moment-to-force ratios. The force applied to a tooth (F) will lead to a moment round the centre of resistance (CR) of the tooth; this is called the moment of the force (MF), which will be in the direction of the applied force. To counteract the effect of the moment of the applied force, a force couple may be generated at the bracket by engagement of an archwire , creating a new moment, called the moment of the couple (MC), which can counterbalance the moment of the force. If the moment of the couple is opposite the moment of the force, and equal in magnitude, rotational movement will be prevented, permitting bodily movement.

22. The following examples describe the biomechanics. (a) Application of a single point force (F) to the crown of a maxillary central incisor. This force may be from a labial spring or from a palatally directed elastic; in either case, there is a palatally directed retroclining force on the crown. The moment of the force (MF) will result in rotation round the centre of rotation, which in this situation is almost identical to the CR of the tooth, with the crown moving in the direction of the applied force.

23. (b) If a force couple is applied at the bracket on the crown of the incisor tooth by engaging a rectangular archwire , the tooth will rotate round its CR, leading to a change in the inclination of the tooth.

24. (c) However, if a palatal force is applied, as in (a), and a counterbalancing force couple is applied at the bracket, as in (b), the combination of the applied palatal force (and its moment, MF) and the force couple at the bracket (and its moment, MC) will mean that rotation of the tooth does not occur round its CR (red circle). The position of the centre of rotation (blue circle) will alter based on the ratio of the MF in relation to the MC .

25. Relationship between moment-to-force ratio and the type of tooth movement. The ratio between the moment of the applied force (MF) and the counterbalancing moment of the couple (MC) determines the type of tooth movement that will occur. This important concept requires further explanation in relation to a common orthodontic situation. Consider the maxillary arch in the space closure stage of fixed appliance treatment. A continuous archwire is in place, and a space-closing force is applied to move the maxillary incisors backwards towards the posterior anchor teeth. This force F is acting at the brackets. The force F will lead to a moment round the centre of resistance; this moment of the force is termed MF. In the following four examples, t he magnitude of the force F and the moment of this force, MF, will remain unchanged. (a) If the archwire is a relatively thin round wire, there will be no couple created at the bracket, i.e. MC = 0. The centre of rotation ( Crot , blue circle) will be very close to and just apical to the centre of resistance (CR, red circle), and the force F will lead to rotation round Crot . The incisors retrocline by simple tipping, i.e. the crown moves in the direction of the force and the root rotates in the opposite direction.

26. Relationship between moment-to-force ratio and the type of tooth movement. (b) A rectangular archwire is placed in the bracket. The space-closing force F remains the same, and MF thereby remains the same. The rectangular wire in the rectangular slot will lead to the formation of a force couple in the bracket, which is the moment of the couple (MC). If the bracket prescription is with palatal root torque, or if the archwire has palatal root torsional stress applied to it, MC will be the counterbalancing force to MF. As long as MC is less than MF, the tooth crown will still rotate in the direction of the original force F, but because of MC, Crot will move apically. There is less root movement and more crown movement, which is termed controlled tipping. The incisors are still retroclining , but the crowns are moving a greater distance in a palatal direction, with minimal root movement. If Crot moves to the apex, the apex will not move, and the crown will retrocline the greatest distance.

27. Relationship between moment-to-force ratio and the type of tooth movement. (c) If a larger rectangular archwire is placed, or greater palatal torsional root ‘ torquing ’ forces are applied, such that MC increases until MC = MF, the tendency to rotation is eliminated; i.e. because MC is the counterbalancing force to MF, the two moments cancel each other, and there is no rotation round CR. Crot moves apically towards infinity, and the effect of the original force F is to bodily translate the incisors in the direction of the force F, i.e. bodily retraction.

28. Relationship between moment-to-force ratio and the type of tooth movement. (d) If even greater torsional forces are placed by the rectangular archwire in the bracket slot, such that MC becomes greater than MF, Crot moves incisally , and there will be greater root movement in a palatal direction. If Crot moves to the incisal tip, the tip will not move, and the root will ‘torque’ the greatest distance in a palatal direction.

29. The ratio of the moment of the couple to the original applied force will determine the type of tooth movement that occurs; this is the moment-to-force ratio . Varying the moment-to-force ratio (by changing the magnitude of the applied force and/or the force couple at the bracket) allows the location of the centre of rotation of a tooth to be altered along its long axis, thereby giving control over the type of tooth movement .

30. Relationship between moment-to-force ratio and the type of tooth movement. The ratio between the moment of the applied force (MF) and the counterbalancing moment of the couple (MC) determines the type of tooth movement that will occur. This important concept requires further explanation in relation to a common orthodontic situation. Consider the maxillary arch in the space closure stage of fixed appliance treatment. A continuous archwire is in place, and a space-closing force is applied to move the maxillary incisors backwards towards the posterior anchor teeth. This force F is acting at the brackets . The force F will lead to a moment round the centre of resistance; this moment of the force is termed MF. In the following four examples, the magnitude of the force F and the moment of this force, MF, will remain unchanged.

31. (a) If the archwire is a relatively thin round wire, there will be no couple created at the bracket, i.e. MC = 0. The centre of rotation ( Crot , blue circle) will be very close to and just apical to the centre of resistance (CR, red circle), and F will lead to rotation round Crot . The incisors retrocline by simple tipping, i.e. the crown moves in the direction of the force and the root rotates in the opposite direction .

32. (b) A rectangular archwire is placed in the bracket. The space-closing force F remains the same, and MF thereby remains the same. The rectangular wire in the rectangular slot will lead to the formation of a force couple in the bracket, which is the moment of the couple (MC). If the bracket prescription is with palatal root torque, or if the archwire has palatal root torsional stress applied to it, MC will be the counterbalancing force to MF. As long as MC is less than MF, the tooth crown will still rotate in the direction of the original force F, but because of MC, Crot will move apically. There is less root movement and more crown movement, which is termed controlled tipping. The incisors are still retroclining , but the crowns are moving a greater distance in a palatal direction, with minimal root movement. If Crot moves to the apex, the apex will not move, and the crown will retrocline the greatest distance.

33. (c) If a larger rectangular archwire is placed, or greater palatal torsional root ‘ torquing ’ forces are applied, such that MC increases until MC = MF, the tendency to rotation is eliminated; i.e. because MC is the counterbalancing force to MF, the two moments cancel each other, and there is no rotation round CR. Crot moves apically towards infinity, and the effect of the original force F is to bodily translate the incisors in the direction of the force F, i.e. bodily retraction.

34. (d) If even greater torsional forces are placed by the rectangular archwire in the bracket slot, such that MC becomes greater than MF, Crot moves incisally , and there will be greater root movement in a palatal direction. If Crot moves to the incisal tip, the tip will not move, and the root will ‘torque’ the greatest distance in a palatal direction .

35. There is a direct relationship between the magnitude of the applied force and the magnitude of the counterbalancing couple, in that the heavier the applied force to the crown of a tooth, the larger the moment of the force, and thereby the larger the moment of the counterbalancing couple within the bracket required to prevent tipping. A couple created by two equal and opposite forces acting on a tooth. Te total moment (MC) is the vector addition of the two moments (m1, m2) generated by the two forces (F1, F2). Here, m1 = F1 × d1, m2 = F2 × d2. Because the two moments are in the opposite direction, one of the moments will be assigned a negative sign and the other a positive sign. Te net moment (M) will be obtained by adding the two: M = m1 + (–m2).

36. The orthodontic biomechanical mechanism for achieving such a system is a fixed bracket or other attachment on the tooth crown, constructed such that forces may be applied at two points on the tooth . This concept was elucidated by Calvin Case in 1921 based on round wires . A, Te moment created by a couple is always around the CRES or CG (MC = F × D). B, No matter where the pair of forces is applied, the couple created will always act around the CRES or CG. As the distance between the two forces decreases (d < D), the overall magnitude of the couple decreases (mc < MC).

37. The concept of bodily movement from a force couple applied to the crown was described by Calvin Case in 1921. ( a) Here, Case is describing a force being applied at point i , accomplished by attaching to the crown a rigid ‘root-wise extension or bar’, in order for the line of force to be sufficiently above the ‘point of greatest resistance’ at c . He suggests that a ‘more or less bodily movement’ would occur in the direction of the force, but that this would not be with the absolute certainty that would follow the more ‘scientific control of the force for this character of movement, described later’.

38. (b) The image marked A represents Edward Angle’s method. The force couple is represented by the two arrows at the bracket. The upper arrow represents the ‘ centre of work’ or ‘fulcrum’ (i.e. centre of resistance). The images marked B–D are Case’s gradual modifications of the appliance in order to decrease ‘the distance to the area of work or alveolar resistance, both of which greatly increase the mechanical advantage’.

39. (c) Combinations used to create couples for bodily tooth movement.

40. Alternatively, an auxiliary spring may be used together with a round base archwire . The auxiliary spring would be required to place a force on the facial surface of the incisor crown gingival to the bracket, with the force in a palatal direction, causing it to rotate round its transverse axis (which is the usual reason for using such auxiliary springs, i.e. palatal root ‘ torquing ’ forces).

41. However, in this situation, this force would need to be opposing the retroclining force at the bracket on the crown, the result being bodily retraction. Such torquing springs are used with traditional Begg appliances, but can be formed for use with some edgewise systems, and are rarely employed for the type of movement described here (Figure 2.31) (see Chapter 11, Figures 11.23 and 11.24), as the use of rectangular archwires has made such complex mechanics unnecessary. (a, b) Palatal root ‘ torquing ’ auxiliaries on the maxillary incisors, being used with a traditional Begg appliance. Source: courtesy of Dr David Spary .

42. The most common technique and mechanism for the application of a force couple is to use a rectangular archwire ligated into the rectangular edgewise bracket slot in order to generate the moment required to control the incisor inclination during retraction. The two points of contact are the opposite edges of the rectangular archwire within the bracket slot . A couple is applied to derotate a premolar. Before (A) and after (B)  Generation of a force couple by the interaction between the bracket slot and the archwire

43. The magnitude of the couple depends on the magnitude of the forces (shown as two equal and opposite red arrows acting on the bracket) and the distance between the two forces, with the moment of the created force couple being the sum of the moments created by each of the two forces. Where the two forces creating the couple act on effectively opposing sides of the centre of resistance, their effect is additive. This applies to the settings illustrated in (a) and (b).

44. (a) Round or rectangular orthodontic archwires change the angulation of a tooth by engaging in a bracket slot. The expression of mesiodistal tip, i.e. the change in the angulation of the tooth, stops when the archwire becomes passive in the bracket slot. (b) Rectangular archwires change the inclination of a tooth by engaging in a bracket slot. The expression of buccolingual torque, i.e. the change in the inclination of the tooth, stops when the archwire becomes passive in the bracket slot.