Introduction Physical principles Terminologies Tooth movement M/F Newton's laws Characteristics of force Equivalent force system Equilibrium principle Statically determinate vs. Indeterminate systems One couple Two couple Conclusion Bibliography

1. Biomechanics
Basic principles.
Presenter: Afaf Mohammed

2. Contents
• Introduction
• Physical principles
• Terminologies
• Tooth movement
• M/F
• Newton's laws
• Characteristics of force
• Equivalent force system
• Equilibrium principle
• Statically determinate vs. Indeterminate
systems
• One couple
• Two couple
• Conclusion
• Bibliography
2

3. Introduction
Every profession has its trade tools.
3

4. The scientific basis of orthodontics rests on a knowledge of anatomy, physiology
and growth, and in particular, biomechanics—the relationship between force
systems and dental or orthopedic correction.
Burstone. Orthodontics as a science: The role of biomechanics. American Journal of
Orthodontics and Dentofacial Orthopedics. 117(5): 599
5

5. Why Do We Need
Biomechanics??
1. Optimization of tooth movement
2. Anchorage control
3. Development and use of a scientific terminology
4. Evaluation of treatment results
5. Research
6. Minimization of tissue destruction
7. Reduction of patient cooperation
8. Evaluation and development of new appliances
9. Knowledge transfer from appliance to appliance
10. Reducing commercialization
6
Burstone C. Orthodontics as a science: The role of biomechanics. Am J Orthod Dentofac Orthop. 2000;11(5):598-600.

6. 1. Optimization of Tooth Movement The application of correct forces and
moments are necessary for full control of tooth movement.
2. Anchorage Control Anchorage control is based on combining force levels and
selective moments.
3. Development and Use of a Scientific Terminology : Universal biomechanical
language is the simplest way to describe how an appliance works and is to be
used. It allows communication with other disciplines so joint research becomes
simpler and more relevant. It also enhances the teaching of clinical orthodontics to
new resident
7

7. 4. Evaluation of Treatment Results To predict outcomes of treatment requires a
more precise control and understanding of the force systems used
5. Research
A biomechanical approach to orthodontics opens up new areas for research as what
is the relationship between force magnitudes, moment to force ratios, force
constancy on dental and orthopedic responses.
6. Minimization of Tissue Destruction
Histologic studies can demonstrate a relationship between force magnitude and
tissue destruct. the quality of our treatment suggests control over force magnitude.
As in medicine, dosage does count.
8

8. 7. Reduction of Patient Cooperation
• The reduction of undesirable side effects and the concomitant reduction in
treatment time can minimize the use of intermaxillary elastics or headgears and
other appliances that require patient compliance.
8. Evaluation/ dev of New Appliances
Tese appliances can be evaluated with the use of fundamental biomechanical
principles. The other approach is to try these appliances clinically and see how
they work. This trial and error approach is time consuming and is not fair to our
patients
9. Knowledge Transfer From Appliance to Appliance
lingual rather than on the facial surfaces, biomechanical principles allow an easy
transfer of equivalent force systems that should produce the same results.
9

9. 10. Reducing Commercialization
There has been much commercialization in orthodontics with exaggerated claims
made by both clinicians and orthodontic companies. Wires, brackets, systems, and
devices are claimed to be superior. Hyperbole is used to describe these appliances
such as “controlled ... hyper,” “super.
Knowledgeable clinicians with good biomechanical background are not easily
swayed by such presentations.
10

10. When the underlying principles are understood, what may
look possible becomes clearly impossible and what appears to
be impossible can be possible.
11

11. 12

12. Conventional vs. New wisdom
Shape-driven orthodontics
• Conventional wisdom in orthodontics has emphasized the appliance.
• Graduate students and orthodontists were taught to fabricate appliances or make
bends or adjustments in these appliances.
• Shapedriven orthodontics (where forces are not considered) is usually a standard
sequence or cookbook approach that does not adequately consider the individual
variation among patients.
14

13. Force driven approach
• The new wisdom is not appliance oriented.
• It involves a thinking process in which the clinician identifies treatment goals,
establishes a sequence of treatment, and then develops the force systems needed
for reaching those goals.
• Only after the force systems have been carefully established are the appliances
selected to obtain those force systems.
• This is quite a contrast to the older process in which the orthodontist considered
only wire shape, bracket formulas, tying mechanisms, friction, play, etc, without
any consideration whatsoever of the forces produced.
15

14. 16

15. 17
Biomechanics is
the _________________ of
orthodontics!
MAINSTAY

16. Physical Principles
There are a few basic physics concepts that warrant review prior to delving into
biomechanics in orthodontics and its applications in clinical cases.
18

17. Force
A load applied to an object that will tend to move it to a different position in
space.
• Force, though rigidly defined in units of Newton's (mass x the acceleration of
gravity), is usually measured clinically in weight units of grams or ounces.
19

18. Center of resistance (CR)
A point where force would result in translation of a constrained body (tooth or
group of teeth).
• For an object in free space, the center of resistance is the same as the center of
mass.
• If the object is partially restrained, as is the case for a fence post extending into the
earth or a tooth root embedded in bone, the center of resistance will be determined
by the nature of the external constraints.
20

19. 21

20. 22

21. 23

22. 24

23. 25

24. 26

25. 27

26. 28

27. 29

28. A point around which rotation actually occurs when an object is being
moved.
30
Center of rotation (Crot)

29. 31

30. A simple method for determining a center of rotation is to take any two points on the tooth and connect
the before and after positions of each point with a line. The intersection of the perpendicular bisectors of
these lines is the center of rotation
32

31. A measure of the tendency to rotate an object around some point.
• A moment is generated by a force acting at a distance.
• To calculate the moment of a force, multiply the magnitude of the force, and its
perpendicular distance from the centre of resistance about which the moment occurs.
• M = F x d
• Units: gram-millimetre
33
Moment

32. 34

33. Determine the direction of a moment
35

34. COUPLE
A couple is a pure moment and occurs when two forces (F1, F2 equal and
opposite) are separated by a perpendicular distance.
• No matter where the couple is applied, the object rotates about its center of
resistance—that is, the center of resistance and the center of rotation superimpose.
• With a moment of force, a body (eg, a tooth) will feel both a force and a moment.
With a couple, however, only the moment is felt.
36

35. 37

36. In fixed appliance, moment due to couple is generated due to
wire- bracket interaction.
In calculating the moment (M) of a couple, it is sufficient to
multiply the magnitude of one of the forces (F) by the
perpendicular distance (d) between the lines of action of
these forces.
38

37. 39

38. 40

39. 41

40. Rotation occurs in all views, not just from the occlusal view.
42

41. Correct bracket placement will produce couples at each tooth. The couples on each tooth produce rotation
of each tooth around its CR. (d) The midline was corrected using the couple acting at the brackets without
requiring any lateral force.
43

42. Tooth Movements
Pure rotation
• A rotation of a tooth about its center of rotation/ center of
resistance.
• It occurs when a couple is applied.
• Crot coincides with CR
44

43. Uncontrolled tipping
• When force is applied, the crown moves in one direction
while the root moves in the opposite direction
• Crot- near the centre of the root.
45

44. Controlled tipping
• Crown moves in the direction of force while the root
position remains same or is minimally displaced.
• Crot- near the apex or further apically.
46

45. Translation
• A type of movement by which all points on a body
move the same amount in a parallel direction.
• Both crown and root portion moves bodily in the
direction of force.
• Crot- infinity.
47

46. Root movement
• Root moves in the dierction of force while the crown
position remains same or minimally displaced.
• Crot- Incisal edge of the crown.
48

47. Modifying force system
• Tipping (uncontrolled) is the most common tooth movement in everyday
orthodontics but not always the preferred one. To modify this pattern of tooth
movement and create a new one, the force system acting on the tooth needs to be
altered.
• There are primarily two ways to accomplish this based on the mechanics involved:
1. Altering the point of force application.
2. Altering the moment-to-force ratio (to create a second moment opposite in
direction to the first one).
49

48. 50
Altering the point of force application

49. • In the orthodontic literature, the relationship between the force and the
counterbalancing couple often has been expressed in this way, a the "moment-to-
force" ratio.
• Understanding the M/F ratio concept is vital to the clinician in controlling tooth
movements.
• Clinically, the M/F ratio determines the types of movement or the location of the
center of resistance.
• According to the formula, M/F= F x d /F
• M/F= d.
• As the distance between the center of resistance and the line of action increases,
the M/F ratio also increases.
51
Moment- Force Ratio

50. Uncontrolled Tipping
52

51. Controlled Tipping
53

52. Bodily movement
54

53. Root movement
55

54. 56

55. 57

56. 58

57. 59

58. 60

59. Tooth Movement Mc/Mf M/F
Uncontrolled tipping Mc/Mf= 0 M/F= 0
Controlled tipping 0< Mc/Mf <1 M/F< d (1-7)
Bodily movement Mc/Mf= 1 M/F= d (8-10)
Root movement Mc/Mf >1 M/F > d (10)
61

60. Newton's laws
• Newton’s First Law (law of inertia)
An object at rest tends to stay at rest, and an object in motion tends to stay in
motion with the same velocity and in the same direction unless acted upon by
an unbalanced force.
62

61. 63

62. • Newton’s Second Law (law of acceleration)
Newton’s Second Law states that when force is applied to an object, it
accelerates proportional to the amount of force applied.
• The famous Newtonian formula is F = ma
65

63. • Newton’s Third Law (law of action and reaction)
Newton’s Third Law states that for every action there is always an equal and
opposite reaction (ie, for every force there is an equal and opposite force).
66

64. 67

65. Characteristics of a force
A force has three attributes:
• Magnitude
• Direction and sense
• Point of force application.
68

66. 69

67. • To specify the direction of a force vector, a proper coordinate system is required.
• There are several coordinate systems, but rectilinear Cartesian coordinates are
most frequently used.
70

68. 71

69. Part II
• Characteristics of force
• Equivalent force system
• Equilibrium principle
• Statically determinate vs.
Indeterminate systems
• One couple
• Two couple
• Conclusion
• Bibliography
72
Dr. Ravindra Nanda
Professor and Head of the Department of Craniofacial Sciences
and Chair of the Division of Orthodontics at the University of
Connecticut School of Dental Medicine.

70. Law of transmissibility of force.
A force acting anywhere along this line of
action has the same effect.
• In other words, a force can be moved along its
line of action without changing its effect.
• The appliance may differ with either an open or
closed coil spring, but if the force is along the
same line of action, the response should be the
same (assuming no other variables).
73

71. Components
• It is convenient to resolve a force into
rectilinear components (ie, two forces at
90 degrees to each other).
74

72. Resolving the force into rectilinear components tells us that there are both
mesial and lingual forces (yellow arrows).
75

73. Resultants
• The sum of all the forces is called the
resultant.
• The principle that forces along the same line
of action can be simply added together is
important for orthodontists.
76

74. Methods for adding forces. Forces F1 and F2 do not lie along the same line of
action. The addition must be done graphically.
77

75. 78

76. 79

77. Analytical method for determining a resultant Instead of the
graphic method, resultants can be calculated by using
trigonometric functions and the Pythagorean theorem.
80

78. Application
81

79. 82

80. 83

81. 84

82. 85

83. Equivalence of Forces
Forces that are interchangeable are called equivalent.
• Two force systems are equivalent if the sums of their
forces are equal and if the sums of their moments around
any arbitrary point are also equal.
• A system that replaces forces and/or moments with a
different set of forces and/or moments that bring about
the same basic translatory and rotational behaviour.
86

84. If a 200-g lingual force (red arrow) is placed on the root,
one might expect the root to move lingually with a center
of rotation on the crown (blue dot).
But it is not practical to place a force so far apically.
Let us replace the force at the bracket.
The bracket is picked as a convenient point to sum the
moments.
The original 200-g force times the 12-mm perpendicular
distance gives a +2,400-gmm moment.
The new replacement force has no moment (200 g × 0
mm = 0 gmm).
For equivalence, a couple of +2,400 gmm must be added
at the bracket (yellow curved arrow).
The red or yellow force systems do the same—the teeth
will not notice any difference. 87

85. Clinical examples of how an equivalence analysis can help us to
select the best possible elastic pull.
88

86. Typical cervical headgear
89

87. 90

88. Equilibrium Principle
• The most important concept from physics that can be applied to orthodontics is the
equilibrium principle.
• It is based on Newton’s First Law, which states that a body remains at rest or in
motion with a constant velocity unless acted upon by an external force.
• Once it is recognized that the appliance is in equilibrium (not pushing, pulling, or
rotating the patient), the laws of equilibrium can help us solve for unknown forces.
• In orthodontics we have the advantage of equilibrium automatically establishing
itself every time we engage an archwire into the brackets and tubes. We do not,
therefore, have to concern ourselves with how to create static equilibrium, but
rather with how to recognize the forces and moments (torques) that come into
existence to establish the static state.
91

89. 92

90. 93

91. 94

92. 95
Is the system in static equilibrium???
Yes
Yes

93. Statically determinate vs.
Indeterminate systems
• Force systems can be defined as statically determinate, meaning that the
moments and forces can readily be discerned, measured, and evaluated.
• Statically indeterminate systems are too complex for precisely calculating all
forces and moments involved in the equilibrium.
96

94. One-couple system
• One-couple orthodontic appliances are capable of applying well-defined forces
and couples to effect controlled tooth movement during treatment.
There are two sites of attachment:
1. In which the appliance is inserted into a bracket or tube where both a couple and
force is generated, and
2. At which the appliance is tied as a point contact where only a force is produced.
• Using relatively simple designs, powerful biomechanical force systems that are
easy to discern clinically can be applied to move teeth according to a prescribed
plan.
97

95. Canine extrusion spring.
(A) In its passive state, the spring is inserted into the molar auxiliary tube and its
anterior end is occlusal to the canine to be extruded.
(B) Activating the spring by tying it to the canine generates a couple to tip the molar in
a crown-mesial/root-distal direction, an intrusive force to the molar, and an
extrusive force to the canine.
Lindauer S J, Isaacson R J. One-Couple Orthodontic Appliance Systems. Seminars in Orthodontics. 1995;1(1):12-24.
98

96. Palatally impacted canine.
Frontal and occlusal view of a spring
designed to extrude and bring a
palatally impacted canine facially.
A. Passive spring extends from the
molar auxiliary tube and crosses to
the lingual through the canine site.
The anterior end is occlusal and facial
to the canine.
B. Activation of the spring by tying it to
the impacted canine creates a third-
order couple at the molar +
mesiolingual rotation, an intrusive +
lingual force at the molar, and an
extrusive + facial force at the canine.
99

97. Midline spring
Occlusal view of an anterior midline spring designed to shift the maxillary midline
to the patient's right.
(A) The passive spring extends from the molar auxiliary tube and has an anterior
hook that will be attached over the arch wire.
(B) Activation of the spring creates a couple at the molar to rotate it mesiolingually,
a lingual force at the molar, and a facial force at the point of anterior
attachment.
100

98. 101

99. 102

100. 103

101. 104

102. • These force systems are established between two attachments when a wire is
inserted in the bracket slots of two brackets/ tubes.
• As the name suggests, these force systems involve forces and couples at both the
attachments when a straight wire is placed in a pair of non-aligned brackets or
when a bend is placed between two aligned brackets.
• The force system generated by such appliances is complex and statically
indeterminate.
• One way of circumventing this problem is to reduce the multi-bracket system into
less complicated basic units.
• The smallest basic unit that one can study is the ‘two-teeth segment’ of an arch.
• This offers a basic building block for understanding more complex force systems
from multibracketed appliances
105
Two-couple system
Nanda R, Upadhya M. Skeletal and dental considerations in orthodontic treatment mechanics: a
contemporary views. European Journal of Orthodontics. 2013;35:634-43.

103. V- bends
• The force system produced by the V bends is a two couple system.
• When both the ends are engaged in edgewise brackets, moments are created at
both the brackets due to bracket slot - arch wire relationship.
• The magnitude of moments would depend on the angle of entry or, in other words,
how steep the wire is with respect to the slot orientation.
107
Burstone CJ, Koenig HA. The force system from step and V bends. Am J
Orthod Dentofac Orthop. 1988;93: 59-67.

104. A two-couple force system between two brackets
Symmetric V bend
Since the angles of entry at the two
brackets are identical but facing in
opposite directions, the moments created at
both the brackets are also equal in
magnitude but are acting in opposite
directions.
Therefore, the sum total of the two
moments comes to zero.
108
Nanda R, Upadhya M. Skeletal and dental considerations in orthodontic treatment mechanics: a
contemporary views. European Journal of Orthodontics. 2013;35:634-43.

105. Asymmetric V bends
The bracket A will experience a greater moment
than bracket B because angle of entry in bracket
A has increased while that in bracket B has
reduced.
Though the two moments are acting in opposite
directions, their sum total cannot become zero,
but will leave a residual moment.
Therefore, in order to establish equilibrium in
the overall system, another moment that is equal
in magnitude but opposite in direction to the
residual moment needs to be created. This
happens automatically by generation of two
veftical forces at the two brackets.
109

106. Asymmetric V bends
As the bend shifts more and more towards
bracket A, the moment within it will continue to
increase, and the moment at bracket B will
correspondingly continue to reduce.
The sum total of the moments at the two
brackets will leave a residual moment of
increasing magnitude.
The vertical forces will also continue to increase
in magnitude because they have to balance the
residual moment.
110

107. Asymmetric V bends
As the bend is shifted further towards
bracket A, a very interesting thing
happens: a moment is again created at
bracket B but it has the same direction as
that in bracket A.
The moments at both brackets add upp
together.
The equilibrium moment and the vertical
forces producing them are also
correspondingly larger
111

108. Symmetric V bend
Clinical use:
M-out rotations of the
molars are desired
without expansion of
intermolar width.
2x6
appliance
112

109. Asymmetric V bend
Clinical use:
M-out rotations of the
molars are desired with
expansion of intermolar
width.
113
2x6
appliance

110. TPA
appliance
Symmetric V bend
Clinical Uses
Bilateral M-Li molar rotations
are often required in finishing
cases of upper extractions for
camouflage of Class II
malocclusions.
This may help to close any
remaining posterior spaces that
resulted from tooth size
discrepancies and to seat the
molar cusps properly for a Class
II molar finish.
114
Rebellato J. Two-Couple Orthodontic Appliance Systems: Transpalatal Arches. Semin Orthod.
1995;1(1):44-54.

111. Asymmetric V bend
Clinical Uses
Palatally handing cusps.
Unilateral toe-in will produce a
facial root torque moment on
one molar and intrusive-
extrusive equilibrium forces.
115
TPA
appliance

112. Step bends
• Artistic, step-up, step-down, and anchorage bends in Tweed mechanics are
examples of step bends
• In these mechanics, the moments on both sides are equal and same-direction.
• In stepped arches, changing the location of a step bend between brackets does not
affect the force system.
• As the height of the step increases, moments on both sides also increases.
116

113. 117

114. Step bends
This activation of the 2 x 6
arch wire is useful when
molar M-in rotations are
required along with greater
molar constrictive forces than
can be obtained with
asymmetrical V-bends.
118
2x6
appliance

115. A wire with a V-bend in collinear brackets or Straight
wire in two non-collinear brackets
119
Nanda RS, Tosun YS. Biomechanics in Orthodontics Principles and Practice. Quintessence
Publishing Co, Inc. 2019.

116. Burstone geometry classification
• Different ratios between bracket angulations affect tooth movements.
• Burstone and Koenig named six geometry classes that can occur between two
teeth.
• In each of the six geometry classes proposed by Burstone and Koenig, the
angulation of the left bracket is changed while the right one is kept stationary.
120

117. Class I geometry
Both teeth make clockwise rotations, the right
one extruding and the left one intruding.
Analogous- Step bend
121

118. Class II geometry
Clockwise rotations on both sides; the right
tooth extrudes and the left one intrudes.
122

119. Class III geometry
Both teeth rotate in the clockwise direction and
the right tooth extrudes while the left one
intrudes.
Analogous- V bend at Bracket B
123

120. Class IV geometry
The right tooth rotates in the clockwise direction and extrudes
with, while the left tooth remains straight and intrudes with
the same amount of force.
Analogous- 1/3rd D distance Asymmetric V bend
124

121. Class V geometry
The tooth on the right rotates clockwise and
extrudes while the one on the left rotates
counter clockwise and intrudes.
125

122. Class VI geometry
Equal and opposite moments occur on both
sides, and the system is statically balanced.
Analogous- Symmetric V bend
126

123. 127

124. 128

125. 129

126. 130

127. 131
Modifying
the
geometry

128. 132
Modifying
the
geometry

129. Conclusion
An understanding of applied biomechanics allows the orthodontist to
determine both why a puzzling and problematic treatment change
occurred and also what to do to correct it.
133

130. Bibliography
1. Burstone CJ, Choy k. The biomechanical foundation of clinical orthodontics. Quintessence Publishing
Company, Incorporated. 2015.
2. Proffit WR, Fields HW, Sarver DM. Contemporary orthodontics. 5th ed. Elsevier/Mosby. 2013.
3. Nanda RS, Tosun YS. Biomechanics in Orthodontics Principles and Practice. Quintessence Publishing Co,
Inc. 2019.
4. Nanda RS. Esthetics and Biomechanics in Orthodontics. 1st ed. Chapter: Biomechanics in Orthodontics.
Saunders. 2019.
5. Jayade VP, Chetan VJ. Essentials of Orthodontic Biomechanics.
6. Nanda RS, Eliades T. Biomechanics and esthetic strategies in clinical orthodontics. European Journal of
Orthodontics. 2005; 27(6):616.
7. Kang A, Musilli M, Farella M. The six geometries revisited. Korean J Orthod. 2020;50:356-359.
8. Kuruthukulam RM. The center of resistance of a tooth: a review of the literature. Biophysical Reviews.
2023;15(4):23-29.
9. Lindauer SJ, Isaacson RJ. One-Couple Orthodontic Appliance Systems. Semin Orthod. 1995;1(1):12-24.
134

131. Bibliography
10. Isaacson RJ, Rebellato J. Two-Couple Orthodontic Appliance Systems: Torquing Arches. Semin Orthod.
1995;1(1):31-36.
11. Davidovitch M, Rebellato J. Two.-Couple Orthodontic Appliance Systems Unhty Arches: A Two-Couple
Intrusion Arch. Semin Orthod. 1995;1(1):25-30.
12. Rebellato J. Two-Couple Orthodontic Appliance Systems: Activations in the Transverse Dimension. Semin
Orthod. 1995;1(1):37-43.
13. Rebellato J. Two-Couple Orthodontic Appliance Systems: Transpalatal Arches. Semin Orthod. 1995;1(1):44-
54.
14. Lindauer SJ. Clinical Biomechanics Steven J. Lindauer. Semin Orthod. 2001;1(1):2-15.
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tooth movement. Semin Orthod 2000;6:145-154.
16. Smith RJ, Burstone CJ. Mechanics of tooth movement. Am J Orthod 1984;85:294-307.
17. Nanda R, Upadhya M. Skeletal and dental considerations in orthodontic treatment mechanics: a
contemporary views. European Journal of Orthodontics. 2013;35:634-43.
135

132. Bibliography
18. Burstone CJ, Koenig HA. The force system from step and V bends. Am J Orthod Dentofac Orthop. 1988;93:
59-67.
19. Ronay F, Kleinert MW, Meisen B. Force system developed by V bends in an elastic orthodontic wire. Am J
Orthod Dentofac Orthop. 1989;96:295-301.
20. Isaacson RJ, Lindauer SJ, Conley P. Responses of 3-d arch wires to vertical V bends. Semin Orthod 1995;
1:57- 63.
21. Burstone, CJ, Koenig HA. Force systems from an ideal arch. Am J Orthod Dentofacial Orthop .1998;65(3):
270-289.
22. Mulligan TF. Common Sense Mechanics in Everyday Orthodontics. Phoenix, AZ, Publishing. 1998:1-17.
23. Burstone CJ, Koenig HA. Creative wire bending—The force system from step and V bends. Am J Orthod
Dentofacial Orthop. 1988;93(1):59-67.
24. Burstone CJ. Application of bioengineering to clinical orthodontics. Graber TM, Swain BF: Orthodontics.
Current Principles and Techniques. St Louis, MO, Mosby. 1985:193-227.
25. Retrouvey JM, Kousaie K. Physics in orthodontics. Basic Mechanics Applied to Orthodontics. 2021.
26. Burstone C. Orthodontics as a science: The role of biomechanics. Am J Orthod Dentofac Orthop.
2000;11(5):598-600.
136

133. 137
THANK YOU!
“When you light a candle, you also cast a shadow.”
— Ursula K. Le Guin