orthodontics dental

1. Begg mechanics

2. CONTENTS
ᵿ Introduction
ᵿ Basics of biomechanics
ᵿ Begg mechanics of
ᵿ Stage I
ᵿ Stage II
ᵿ Stage III
ᵿ Conclusion
ᵿ References
26 sep '12 2

3. INTRODUCTION
ᵿ Biomechanics - the study of mechanics as it affects the
biology of tooth movement
ᵿ Burstone deserves a lion’s share of credit for establishing
biomechanics as a vital ingredient of Orthodontic Treatment.
ᵿ Quick and predictable results with a minimum of tissue
damage and maximum patient comfort can only be obtained by
carefully planning the application of forces and moments on
the teeth
26 sep '12 3

4. Basics of biomechanics
Physical properties such as distance, weight, temperature
and force are treated mathematically as either
SCALARS or VECTORS.
SCALARS include temperature and weight, they have a definite
magnitude but do not have a direction.
They are completely described by their magnitude.
26 sep '12 4

5. ᵿ VECTORS include force, these have both magnitude and
direction.
ᵿ In case of force, along with magnitude and direction, point of
application must be taken into account.
FORCE:
It is defined as an act upon a body that changes or tends to
change the state of rest or motion of the body.
Force is a vector it has both magnitude and direction.
26 sep '12 5

6. In case of understanding the magnitude
and direction of tooth movement, point
of application of force is important
26 sep '12 6

7. Moment
ᵿ Is defined as a tendency to rotate
MOMENT is the product of the force times the perpendicular
distance from the point of force application to the center of
resistance.
M=Fxd
It is measured in grams – millimeters.
d
F
F x d(X) = M(X)
26 sep '12 7

8. If a line of action does not pass through the center of resistance
the force will produce some rotation. The potential for rotation
is measured as moment.
The direction of a moment can be determined by continuing
the line of action of the force around the center of resistance.
26 sep '12 8
F x d(X) = M(X)

9. A MOMENT may be referred as
Rotation
Tipping
Torquing.
26 sep '12 9

10. MOMENT OF FORCE:
When a force is applied at any point other than through the
center of resistance in addition of moving the center of
resistance in direction of the force, a moment is created.
In case of tooth, since it is embedded in the alveolar bone, we
cannot apply force directly on Cres, but can apply force on the
exposed part of the tooth, which is at a distance from Cres.
Therefore with a single force we invariably create a moment
called as moment of force.
26 sep '12 10

11.  Moment of force is always relative to point of application. It
means moment of a force will be:
 low relative to a point (point of application) close to line of
action
 high for a point (point of application) with a large
perpendicular distance to line of action.
 In case of Couple moment, it is not relative to any point.
26 sep '12 11

12. CENTER OF ROTATION:
It may be defined as a point about which a body appears to
have rotated as determined from its initial to final position.
A simple method of determining a Center of rotation - Draw the
long axis of the tooth in its initial and final positions; we will
see that both these lines intersect at a point.
This is the point around which the tooth rotates and is called
Center of rotation.
26 sep '12 12

13. Center of rotation could be at the center of resistance, apical or
incisal to Cres or at infinity. Its position will determine the
type of tooth movement.
The moment to force ratio controls the center of rotation for the
intended tooth movement.
26 sep '12 13

14. Controlled Tipping:
 In this situation, crown moves in the direction of force but the
root position remains the same or get minimally displaced.
Here Center of rotation lies at apex of the root.
26 sep '12 14

15. Uncontrolled tipping:
ᵿ In this situation, when force is applied the crown moves in one
direction and root moves in the opposite direction. Here
Center of rotation lies near to center of resistance.
26 sep '12 15

16. Translation/bodily movt.
ᵿ In this situation tooth moves bodily e.g. both crown and root
portion of tooth moves bodily in the direction of force. Here
Center of rotation lies at infinity.
ᵿ All the points in the tooth move by same distance in the same
direction in translation.
26 sep '12 16

17. Root movement
 In this situation, root moves in the direction of force but the
crown position remains the same or get minimally displaced.
 Here Center of rotation lies at incisal edge of the crown.
26 sep '12 17

18. COUPLE:
Two equal and opposite, non - collinear forces are called a
couple.
Couple consists of two forces of equal magnitude, which are
parallel to each other but not coincident and they face in
opposite direction.
The moment of this couple is equal to the magnitude of one of the
forces multiplied by the perpendicular distance between the two
lines of action of force.
26 sep '12 18

19. It seems that type of movement exhibited by a tooth is
determined by the ratio of the counter-balancing moment
produced to the net force that is applied to a tooth .
This is called as the moment to force ratio .
In terms of direction, the counter-balancing moment is always
going to be in the direction opposite the moment of force.
26 sep '12 19

20. M/F Ratio values
1. M/F ratio less than 5:1 causes uncontrolled tipping in
which the crown and the root apex move in opposite
directions.
2. M/F ratio between 5:1 and 8:1 causes controlled tipping in
which the root apex remains stationary and only the crown
moves.
3. M/F ratio of 10:1 causes translation. The crown and the root
apex move to same extent in the same direction of force.
4. M/F ratio of 12:1 causes root movement. The crown
remains stationary while only the root moves.
26 sep '12 20

21. Counter-balancing moment
Moment of force
Force
26 sep '12 21

22. STATE OF EQUILIBRIUM
ᵿ When an appliance is fitted in the mouth, it assumes a state of
equilibrium.
ᵿ The active elements in the appliance generate certain forces or
moments.
ᵿ Other forces or moments arise automatically in the system to
balance these forces or moments. Some of them may be
beneficial while others may be undesirable.
26 sep '12 22

23. ᵿ For example, tip back bend (like the bite opening bend in
Begg appliance) generates a moment which tends to tip the
molar tooth crown distally.
ᵿ This is balanced by an automatic creation of another moment
in the overall system in opposite direction comprising of two
forces an intrusive force at the anterior end and on extrusive
force on the molar.
26 sep '12 23

24. 26 sep '12 24

25. Begg Mechanics
There are three basic movements in the Begg mechanotherapy
 Incisor intrusion - intrusive force magnitude and direction.
 Tipping of teeth
 Root uprighting. basic of M/F ratio.
26 sep '12 25

26. Stage I
ᵿ Open the anterior bite
ᵿ Eliminate anterior crowding
ᵿ Close anterior spaces
ᵿ Over correct rotated cuspids and bicuspids
ᵿ Over correct the mesiodistal relationship of the buccal
segments
26 sep '12 26

27.  Open the anterior bite :
Proper amount of bite opening bends or curves in the arch wire.
Continuous wearing of Class II (intermaxillary) elastics as
required.
 Eliminate anterior crowding :
Vertical loops between crowded anterior teeth, with bracket
areas modified for desired overcorrection.
 Close anterior spaces :
Plain arch wire with latex elastic or elastomeric chain from
cuspid to cuspid.
26 sep '12 27

28.  Over correct rotated cuspids and bicuspids :
Rotating springs
Elastomeric traction into the arch wire
 Over correct the mesiodistal relationship of the buccal
segments
Continuous wearing of class II elastics.
Proper bite opening bends in both upper and lower arch wires.
26 sep '12 28

29. Mechanics in Stage I
ᵿ The orthodontic environment created during stage I is
conducive to rapid movement of anterior teeth under the light
forces generated by the arch wires and intermaxillary elastics
Stage I arch wire
26 sep '12 29

30. Intrusion
ᵿ All the six anterior teeth are intruded together in Begg
practice.
ᵿ The round archwire derives its bite opening force from the
anchor bends.
ᵿ This force acts on the teeth through the brackets which are
placed on the labial surfaces of the incisors, i.e. away from the
long axis of the teeth on which the CRes. of the individual
teeth are located.
26 sep '12 30

31. ᵿ Depending on the direction of the intrusive force in relation to
the long axis of the tooth, the tooth would undergo varying
amounts of intrusion (translation) and labial crown-lingual root
tipping (rotation).
ᵿ Such rotational displacement is generally undesirable (the
exception being lingually inclined incisors as in Cl. II div. 2
cases),
26 sep '12 31

32. 26 sep '12 32

33. ᵿ resisted in the case of upper incisors by using Cl. II elastics
during stage I.
ᵿ However, the Cl II force not only has a horizontal component
for providing this resistance, it also has a vertical component
which reduces the magnitude of the intrusive force of the wire.
ᵿ Further, the horizontal component of the elastic force affects
the direction of the net resultant force.
ᵿThus, the interplay between the wire generated
intrusive force and the elastic force determines
both the magnitude and direction of the net
resultant force acting on the teeth.
26 sep '12 33

34. 26 sep '12 34

35. Consideration of the magnitude of
intrusive force
Optimum intrusive force:
ᵿ Many authors have suggested optimum intrusive force values
ranging from 15-30 g per upper incisor and slightly higher
values for upper canines.
ᵿ Begg did not specify the precise force values in the Begg bite
opening mechanics.
26 sep '12 35

36. ᵿ Later, Kesling (1985) stated that the upper and lower bite
opening bends generate intrusive forces of approximately 1.5
oz and 1.2 oz magnitude respectively at the upper and lower
midlines.
ᵿ The extrusive component of the light Cl. II elastics on the
upper incisors is approximately 1 oz.
ᵿ Hence the net intrusive force on the upper incisors is
approximately 0.5 oz.
26 sep '12 36

37. Role of light Class II elastics
ᵿ A net intrusive force of 60 gm can be obtained by a
combination of 75 gm intrusive force , as follows :
ᵿ Jayade-By using light elastic force for longer periods (from 2
to 5 days), a very light Cl. II force is provided most of the
time, since the elastic force diminishes rapidly in the oral
environment. Such very low force values do not adversely
affect concomitant retraction, because forces in the vicinity of
5 gm are known to be capable of achieving tipping
movements.
ᵿ Sims has suggested the use of 3/8 ultra light elastics (e.g.,
“road-runner elastics” of M/s. Ormco) instead of the routinely
used 5/16 light elastics (e.g. T.P. yellow elastics). He goes to
the extent of continuing the same elastics for 4-5 days, till they
break.
26 sep '12 37

38. Consideration of the direction of the
resultant force
ᵿ Hocevar- teeth respond only to the resultant of the forces, and
not to the individual components of the force system.
ᵿ The anterior teeth would respond to a resultant of the wire
generated intrusive force and the elastic generated retractive
force.
ᵿ This resultant force should ideally pass through the center of
resistance of the upper incisors (which is very difficult to
achieve), or at least should lie very close to and directed as
much parallel to the long axis of the teeth as possible.
26 sep '12 38

39. The direction and the magnitude of the resultant force both
depend upon the interplay between
1. The magnitude of the intrusive force – its direction being
almost constant i.e. tangential to the arc which the anterior
segment of the archwire would subscribe if released from the
brackets.
2. The magnitude and direction both of the elastic force.
26 sep '12 39

40. ᵿ in case of severely proclined upper anteriors a low magnitude
of intrusive force along with light class II force would give a
desired resultant force, passing palatal to Cres, this will help
correcting the proclination of incisors .
ᵿ Once the inclination of upper incisors is corrected then the
class II elastics force is reduced helping in keeping the
resultant force close to Cres .
45gms 60 gms
26 sep '12 40
60gms 30gms

41. ᵿ In Class II Division 2 cases , where the upper centrals are
retroclined , only intrusive force should be used (Avoiding the
Class II elastics) The intrusive force acts labial to Cres and
corrects the retroclination. Once the inclination is corrected
then we can use Class II elastics .
40gms
50gms
20gms
26 sep '12 41

42. ᵿ Modifying the force system to achieve simultaneous intrusion
and retraction using Class I elastic instead of Class II elastics
was first illustrated by Shin Yang Liu (1981).
 In this arrangement the vectors are in the same direction as the
elastic pull and the archwire force are unidirectional and hence
synergistic
26 sep '12 42

43. Arch wire design
VARIOUS TYPES OF BITE OPENING BENDS:
 The Anchor bend the conventional bite opening bend causes
more intrusion of canines while the lateral and central incisors
progressively lag behind.
 A Gable bend causes a progressively more intrusion of central
and lateral incisor, as compared to canine
26 sep '12 43

44.  Swain modification: Mild
gingival curve is incorporated
in the anterior section, from
mesial of cuspid to mesial of
other side cuspid.
26 sep '12 44

45. Mechanics of tipping
ᵿ Reitan. -Generally, uncontrolled tipping is undesirable
because it leads to root resorption.There is more resorption
when uncontrolled tipping is in labio-lingual direction.
ᵿ Intrusion and tipping are intimately related not only because
they are carried out simultaneously but also, when both are
balanced judiciously it help in overcoming uncontrolled
tipping of incisors.
26 sep '12 45

46. ᵿ This is achieved by manipulating the intrusive force generated
by wire and retractive component of force from the Class II
elastics.
ᵿ Both the anchor bend in the wire and class ii
elastics produce moments in the same labio-lingual
plane but act in opposite directions.
26 sep '12 46

47. THE INTERPLAY BETWEEN THE
ANCHOR BEND AND CLASS II ELASTICS
INTRUSION FORC
26 sep '12 47

48. ᵿ The intrusive force produces crown labial-root lingual
moment e.g.. anticlockwise moment on the upper anteriors.
ᵿ While the retractive force produced the Class II elastics
generates clockwise moment e.g. crown lingual-root labial
moment
The moment from the intrusive force can act as the counter
balance moment against the moment produced by the elastic
force.
The ratio of the former to the retraction component of the
elastic force is the M/F ratio which governs the type of tipping
while retracting the anterior teeth.
26 sep '12 48

49. ᵿ The most important consideration is to keep light Class II
elastic and use adequate amount of intrusive force so that
correct M/F ratio (8:1) is obtained to have a controlled
tipping.
26 sep '12 49

50. PREVENTING
UNCONTROLLED TIPPING OF
LOWER INCISORS
The flaring can be avoided by two means;
1. Minimizing the clockwise force moment by reducing the
intrusive force or by placing the brakets much gingivally.
2. Secondly, cinching tightly the distal ends of the arch wire.
26 sep '12 50

51. 26 sep '12 51

52. ᵿ In case of severely lingually tipped lower anteriors, Cres will
be lying buccal to the point of application of the intrusive
force generated by the anchor bend so there is more chances to
tip the lower anteriors more lingually.
ᵿ So in that case we give a By pass arch wire in order to upright
26 sep '12 the lower incisors . 52

53. 26 sep '12 53

54. BEGG STAGE II
The sole or main purpose of II stage is closure of extraction
spaces.
ᵿ The extraction space can be closed by either retraction of the
anteriors or protraction of the posteriors or combination of
both.
During Stage II all the corrections achieved during Stage I should
be maintained
26 sep '12 54

55.  Maintain Edge to Edge relationship of anterior teeth:
Reduce the anchor bend in arch wire and wear intermaxillary
elastics as required
 Maintain anterior space closure :
To give cuspid ties either by elastomeric rings or steel
ligatures.
 To maintain overcorrected or normal mesiodistal molar
relationship :
Keep wearing of intermaxillary elastics as required during
posterior space closure.
26 sep '12 55

56. BIOMECHANICS OF STAGE II
ᵿ The anchor bend should be sufficient as to produce a
counter clockwise moment greater than the clockwise moment
produced by the Class I and Class II elastics in upper arch.
ᵿ The M/F ratio should be sufficient or around 8/1 so as to have
a controlled tipping movement.
If anticlockwise moment is less than clockwise moment produce
by Class I and Class II elastics on upper anterior, then M / F
ratio will less and it will uncontrolled tipping of upper anterior
teeth.
26 sep '12 56

57. “Class I Elastic”
Forces
INTRUSION FORC
CLASS I ELASTIC FORCE
At the end of Stage II
26 sep '12 57

58. ᵿ in lower arch the clockwise moment should be greater than
anticlockwise moment produced by Class I elastics. So as to
have controlled tipping movement
ᵿ Normally 0.016 upper and lower arch wires with reduced bite
opening bends are used.
ᵿ Some authors say use of heavy arch wire 0.020” as it will
function as retainers to maintain arch form and bite opening
achieved during stage I.
26 sep '12 58

59. ᵿ Dr. Swain advocated the use of lingual attachments on molars
and cuspids to allow the use of lingual space closing elastics to
aid the traditionally used buccal vector of intra maxillary
elastic force during stage II known as half strength elastics.
Two distinct advantages
 It gives a better positional control over the anchor molar thus
obviating the need for a mandatory compensate toe in bend
when using elastic force only from buccal side.
 Closure of extraction spaces becomes easier.
26 sep '12 59

60. 26 sep '12 60

61. BRAKING MECHANICS
ᵿ When further retraction of anterior teeth into the remaining
extraction space is deemed undesirable clinically , then the
posterior teeth are brought forward, that is posterior teeth are
mesialized.
ᵿ Mostly in extraction of 5’s cases
ᵿ To achieve mesialization of posterior teeth heavy elastic
forces are required with concurrent use of brakes in the
anterior region.
26 sep '12 61

62. ᵿThe brakes- reverse the anchorage site- from posterior to
anterior segment
ᵿ Permitting only the bodily movement of anterior teeth, instead
of allowing them the freedom of tipping
ᵿ the direction of resultant force should pass through the
center of resistance of anterior teeth (or close to it).
ᵿ Therefore, substituting Class II elastic forces by Class I
elastic forces would orient the resultant force more vertically
passing nearer to the center of resistance of anterior teeth.
26 sep '12 62

63. Various brakes are:
 Breaking springs (passive uprighting springs)
 Reverse torque to incisor roots (Udder arch and MAA)
 Using Angulated-T pins
Passive Uprighting Springs
UDDER ARCH
26 sep '12 63

64. Stage III BEGG
ᵿ The third stage of Begg treatment involves predominantly root
movements in a labiolingual or mesiodistal direction.
ᵿ A doubt is expressed by some edgewise operators as to how it
is possible to obtain a high M/F ratio required for the root
movements using the Begg torquing auxiliary and uprighting
springs.
ᵿ However, a careful scrutiny of the forces generated by the
torquing auxiliary and the uprighting springs in relation to the
light Cl.II elastic force will help in dispelling this
apprehension.
26 sep '12 64

65. Objectives of stage III
1.Maintaining all the corrections achieved during first and second
stages.
2.Achieve desired axial inclinations of all the teeth.
26 sep '12 65

66. Stage III arch-wire
26 sep '12 66

67. 1. Maintaining all the corrections achieved during stages I & II.
 Mesiodistal molar relationship maintained through the
wearing of class II or class III elastics as required.
 Original spaces between anterior teeth are prevented
from recurring by tying intermaxillry circles to the cuspid
brackets with steel ligature wire.
 Over corrections of cuspids are maintained by engaging the
brackets which have been offset on the teeth.
26 sep '12 67

68.  Over corrections of bicuspids are held by replacing elastic
threads with steel ligature ties.
 Over corrections of central and lateral incisors are
maintained through the continued use of bayonet bends in the
arch wires.
 Opening of a deep anterior overbite is maintained through
the continued use of bite-opening bends and class II or class
III elastics.
26 sep '12 68

69.  The correction of posterior crossbites is maintained by
modifying the archwire or by wearing of cross elastics as
necessary.
 Posterior spaces kept closed by bending the distal ends of
the arch wire around the buccal tubes.
 Arch form and overbite correction maintained by using
heavier (0.018 to 0.025) main archwire.
26 sep '12 69

70. 2. Achieve desired axial inclinations of the teeth.
 Changes in the mesiodistal inclinations of teeth are
accomplished by the use of individual root-tipping springs.
 Lingual or labial root torque is applied to anterior teeth
through the application of torqueing auxilaries.
26 sep '12 70

71. Auxiliaries used during stage III
The two main auxiliaries:
ᵿ Individual Root Springs or Mesio distal uprighting Springs.
ᵿ Torqueing auxiliaries.
26 sep '12 71

72. Torqueing Auxiliaries
ᵿ To torque roots of the maxillary anterior teeth lingually.
ᵿ Torqueing is nearly always necessary (especially with upper
incisors) in mild discrepancy cases that require extraction of
the four first premolars i,e in cases having only a mild excess
of tooth substance relative to jaw size.
ᵿ This is because crowns of the incisors tipped back a long way
lingually to close the extraction spaces.
26 sep '12 72

73. Spring - Pin
ᵿ A problem inherent in all uprighting springs is that, when
engaged and under tension, the coil presses against the
gingival edge of the beacket.
ᵿ If arch wire is not safely tied into the slot of the bracket, this
force from the coils can cause the bracket to move away from
the arch wire, with a subsequent elongation of the tooth.
26 sep '12 73

74. ᵿ As a solution to this problem authors have invented, Spring
Pin.
ᵿ A Combination of a Lock Pin and an Uprighting Spring.
ᵿ The leg of the pin portion passes lingual to the arch wire and
the tail fits labial to it in the space in the bracket that normaly
accepts the lock pin.
26 sep '12 74

75. Mechanics of stage III
ᵿ The torquing auxiliary - labio-lingual root movements and
ᵿ the uprighting springs - mesiodistal root movement generate
…..reciprocal reaction in all the three planes of space which
when not properly controlled, result in complication:
1. The lingual root-torquing auxiliary also tends to cause
labial crown movements, extrusion of the anteriors and
intrusion of posteriors, and buccal crown movement of
posteriors.
26 sep '12 75

76. 2. The labial root torquing auxiliary will have effect in opposite
direction.
ᵿThe uprighting springs for distal root movement also have
similar effects as the lingual root-torquing auxiliary in all
the three directions. The vertical and sagittal reactions are
easily appreciated.
ᵿ Reactions in the transverse direction arise because of the
vertical forces acting away from the centre of resistance of
posterior teeth.
26 sep '12 76

77. ᵿ The sagittal forces are easily appreciated.
ᵿ The uprighting springs on the anterior teeth for distal root
movement and the torquing auxiliary for palatal root torque,
both have an extrusive effect on the anteriors and an intrusive
effect on the molars.
ᵿ The intrusive effect on the molars is responsible for a
transverse buccal rolling action on the molars. Such undesired
reactions should be carefully monitored and neutralized.
26 sep '12 77

78. ᵿ The reciprocal mesial crown moving forces are commonly
reisted by:
1. Cinching the distal ends of archwires
2. Class II elastics
26 sep '12 78

79. Forces generated (in grams) by the commonly used four
spur and two spur torquing auxiliaries with 5 mm spur
length.
Wire Horizontal Vertical
Lateral Ce
ntr
al
010 14 18 11
4 Spurs 012 26 30 19
014 48 53 23
016 96 103 77
010 22 14
2 Spurs 012 42 28
014 64 28
016 112 78
26 sep '12 79

80. ᵿ The auxiliary commonly used is the one made in 0.012
premium plus wire.
ᵿ Although the forces produced by this auxiliary are low, the
moments generated by these forces are sufficient because the
moment arm is much greater in a torquing auxiliary than in a
rectangular archwire twisted for torquing effect.
26 sep '12 80

81. The forces generated by the
uprighting springs made from
different wires
Activation 75o 60o 45o 25o
Minispring 142.5 97.5 72.5 < 37.5
0.000 (s) 137.5 82.5 52.5 < 37.5
0.010 (s) 157.5 97.5 57.5 < 37.5
0.012 (s) 282.5 162.5 112.5 57.5
0.012 (p) 257.5 157.5 107.5 57.5
0.014 (sp+) 387.5 297.5 197.5 97.5
0.016 (p) 437.5 307.5 207.5 107.5
Spring pin 787.5 637.5 487.5 287.5
26 sep '12 81

82. ᵿ As Nikolai has pointed out, greater moments are required for
the mesio-distal root movements than for the bucco-lingual
root movements, since holding force for the former is greater
due to the mesio-distal crown contact.
ᵿ Thus the forces produced by the torquing auxiliary are smaller
than the forces generated by the uprighting springs for the
same individual teeth.
26 sep '12 82

83. Some other torquing auxiliary
design
ᵿ Single root torquing auxiliary proposed by Kesling
ᵿ Reciprocal torquing auxiliary (SPEC) design
ᵿ Reverse torquing auxiliary for controlling the roots of canines
or premolars
ᵿ Buccal root torque on molars
ᵿ Labial root torque only on lateral incisor
26 sep '12 83

84. Conclusion
ᵿ A common misconception is that the application of
biomechanical properties would make the begg technique too
cumbersome. On the contrary, biomechanically designed
appliance gives a predictable tooth movement, optimal
biologic tissue response and minimal side effects.
ᵿ In the lighthearted note - One can say that on the average, an
orthodontist spends half the treatment time on problems
presented by the patient and other half on problems resulting
from treatment side effects
ᵿOrthodontics could be in our hand if we use
efficient biomechanics
26 sep '12 84

85. References
ᵿ Vijay P.Jayade. Refined Begg for modern times.
ᵿ Nanda Ravindra. Biomechanics in clinical orthodontics.Philadelphia: W.B
Saunders Company ;1997
ᵿ Begg, P. R.: Begg orthodontic theory and technique, Philadelphia, 1965,
W. B. Saunders Company.
ᵿ Swain, B. F., and Ackerman, J. L.: An evaluation of the Begg technique,
AM. J. ORTHOD. 55: 668-687, 1969.
ᵿ Hocevar RA: Orthodontic force systems: Technical refinements for
increased efficiency. AM J ORTHOD 81: 1-11, 1982.
ᵿ Hocevar RA: Understanding, planning, and managing tooth movement:
Orthodontic force system theory. AM J ORTHOD 80: 457-477, 1981.
ᵿ Reitan K: Tissue behavior during orthodontic tooth movement. AM J
ORTHOD 46: 881-900, 1960.
26 sep '12 85