DEPART. OF ORTHODONTICS
2023/2024
ASSIST. PROF. DR. MEHDI ALRUBAYEE
Biomechanics in Orthodontics
Mechanics is the science that describes the effect of force on the object. The
application of mechanics on the living body, whether on cellular and molecular levels or
on an organ of body, is called biomechanics. In the context of orthodontics, a proper
application of biomechanical principles will ensure an efficient tooth movement,
minimize a possible tissue damage, and may reduce the duration of the treatment
course.
Add to that a perfect understanding of the biomechanical principles may help in:
1- Planning the design of orthodontic appliance
2- Understanding the mode of action of the appliance in general as well as each
individual component in particular
3- Predicting the tooth and tissue reaction to the force applied
4- Selecting the appropriate appliance for a given case.
Force, Moment, and Couple are the three fundamental principles of biomechanics.
Force is defined as a load applied to an object and moves it from initial site to final one.
In orthodontics, the unit of force is commonly expressed in grams (g), although its unit in
general use is Newtons (N).
Centre of Mass/ or Centre of Gravity
Any free body has a point in its mass, which behaves as if the whole mass is
concentrated at that single point “center of mass/or gravity”. Any force loaded on the
body and passing through this center of mass in any direction will cause the whole body
to move as a one mass in that direction. Such a movement is called as “translation or
bodily movement.”
However, tooth is embedded in the alveolar bone and other supporting structures
(not free), this would restrain its movement. Hence, it has a point analogous to the
center of mass referred to as “center of resistance.”
Center of Resistance: is a point at which the resistance to tooth movement is
concentrated. By definition, a force with a line of action passing through the center of
resistance produces translation or displacement.
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DEPART. OF ORTHODONTICS
2023/2024
ASSIST. PROF. DR. MEHDI ALRUBAYEE
Figure 1: When a force in a certain direction passes through the center of resistance, all points along
the tooth move in same distance resulting in a bodily/translation movement of the tooth
The location of the center of resistance of a tooth is affected by several factors,
such as the root size and length, root morphology, number of roots and most
importantly on the level and density of alveolar bone support (Figure2).
Figure 2: Variation in the location of center of resistance in different teeth according to their size and
morphology
The center of resistance of a single-rooted tooth with normal alveolar bone level
is situated at about 1/4 to 1/3 the distance from the CEJ to the root apex (Figure 3A).
While in the case of multirooted teeth, the center of resistance is 1 to 2 mm apical to the
furcation (Figure 3B).
Figure 3: Center of resistance in single and multirooted teeth
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DEPART. OF ORTHODONTICS
2023/2024
ASSIST. PROF. DR. MEHDI ALRUBAYEE
The center of resistance shifts apically in case of alveolar bone loss (Figure 4A), while it
may shift coronally when the root is shortened due to its resorption (Figure 4B).
This is very important when treating a patient because the center of resistance
should be considered depending on tooth to be moved and the condition of the alveolar
bone.
Figure 4: Center of resistance shifts apically in alveolar bone loss but coronally in case of root resorption
Moreover, the center of resistance of the whole maxillary bone is situated 5-10
mm underneath the Orbitale point (the most inferior lateral point of orbit) (see Figure
5).
Figure 5: Center of resistance of maxilla
• Moment of force: is a measure of the tendency to rotate. If a force applied to a body is
not acting through its center of resistance, the force causes a tendency for the body to
rotate, the force will produce rotation rather than translation.
The moment of the force is determined by multiplying the magnitude of the force
by the perpendicular distance of the line of action of force on the center of resistance
(see Figure 6). The unit of measurement of moment is gram millimeters (gm.mm) or
sometimes Centi Newton millimeter (cN.mm).
Mf = F*d
MF is moment of force
F is magnitude of force
d is perpendicular distance between line of F application and the center of resistance
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DEPART. OF ORTHODONTICS
2023/2024
ASSIST. PROF. DR. MEHDI ALRUBAYEE
Figure 6: Moment is the force applied out of the center of resistance and tends to rotate the tooth rather than
bodily moves it.
A couple: is a pair of concentrated forces having equal magnitudes and opposite
directions with parallel but noncollinear line of action. In other words, a couple is a
system of two parallel forces of equal magnitude, acting in opposite directions and
separated by a distance (Figure 7). A couple brings about a pure rotation of the
body/tooth around its center of resistance. However, such movements have a great
tendency to relapse after orthodontic treatment due to re-coil action of supracrestal
fibers of gingiva and the PDLs.
Figure 7: The Force Couple is two forces equal in magnitude opposite in direction
In orthodontics, it is rarely possible to apply a force at the tooth center of
resistance, which is actually located on the root. This is because the brackets or
even removable appliance active components can only be placed directly on the
crown of the tooth. Therefore, if a force is applied to the tooth and the force does
not act through the center of resistance, then the force tends to rotate the tooth
rather than translating it. Rotation can be defined as the movement of a body
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DEPART. OF ORTHODONTICS
2023/2024
ASSIST. PROF. DR. MEHDI ALRUBAYEE
around a center where no two points on the body move to the same amount in
the same direction.
•
Center of rotation: can be defined as an arbitrary point about which a body
appears to have rotated, as determined from its initial and final positions.
Location of the center of rotation varies depending on how far the force is applied
from the center of resistance (8 A to D). Sometimes the center of rotation may
approach but can never reach the center of resistance (Figure 8 C). Other times it
could be positioned in an arbitrary point outside the tooth (Figure 8 D).
Figure 8: The concept of a center of rotation can be used to define any type of tooth movement in any plane of
space. (The red dot is center of rotation. The green dot is the center of resistance).
TYPES OF TOOTH MOVEMENTS
Most of the tooth movements, that occurring in daily routine orthodontic clinical
practice, are the combination of both translation and rotation. Clinically, the following
terms are used for various types of tooth movement:
Tipping, Bodily movement, Torque, Vertical tooth movements (Intrusion,
Extrusion), Multiple tooth movements, and Rotation.
1) Tipping or Inclination (proclination or retroclination)
a. Uncontrolled tipping
When the force applied at incisal 1/3 of the crown, there is a tooth movement
with the crown moves in one direction and the root apex moves in other direction. Here
the center of rotation is in some place between center of resistance and apex (see Figure
9A).
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DEPART. OF ORTHODONTICS
2023/2024
ASSIST. PROF. DR. MEHDI ALRUBAYEE
b. Controlled tipping: When the point of force application is closer to the center of
resistance, the center of rotation is at root apex. It is a very desirable type of tooth
movement because the position of the root apex is controlled or maintained (Figure 9B).
Figure 9: A, Uncontrolled tipping. B, Controlled tipping (Green circle represents the center of rotation)
2) Pure Translation/bodily movement: A tooth is said to be translated when all points on
the crown and root move the same amount in the same direction of force. Such a
movement can occur only when the force is acting through the center of resistance of
the tooth. Therefore, there is no rotation (zero moment) and the center of rotation is at
infinity (Figure 10).
Clinically, pure translation can be seen in: 1- Intrusion 2- Extrusion 3- Bodily
movement of tooth in mesiodistal or labiolingual direction
Figure 10: Pure labiolingual translation.
3) Vertical Movement: Sometimes considered as bodily movement, where the whole
tooth (crown and root) moved vertically either extrusion or intrusion
a. Extrusion: A translational type of tooth movement parallel to the long axis of the
tooth in the direction of the occlusal plane (resembling tooth eruption); e.g.,
extrusion of impacted central incisor (Figure 11).
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DEPART. OF ORTHODONTICS
2023/2024
ASSIST. PROF. DR. MEHDI ALRUBAYEE
Figure 11: Extrusion of impacted central incisor using orthodontic fixed appliance
b. Intrusion: The same definition of extrusion but in an apical direction, e.g.,
intrusion of upper and/or lower anterior teeth to reduce the deep bite or
intrusion of an extruded molar to the level of occlusal plane (Figure 12).
Figure 12: Intrusion of maxillary first molar
4) Root movement: It means a major movement of the root with minimal crown
movement. The center of rotation of a tooth is at the incisal edge, or bracket. Root
movement includes torque and upright.
a) Torquing means palatal or lingual root movement, while reverse (or negative)
torque means buccal or labial root movement. An example of torque movement is
the correction of maxillary central incisor root inclination in class II div2
malocclusion (Figure 13).
Figure 13: Class II div2 malocclusion can be treated by proclination of retroclined crowns plus root torque
b) Mesial or distal root movement is called root uprighting (see Figure 14).
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DEPART. OF ORTHODONTICS
ASSIST. PROF. DR. MEHDI ALRUBAYEE
2023/2024
Figure 14: Distally inclined crown and mesial root tilting can be corrected by uprighting
References
1- Singh. G. (2007). Textbook of Orthodontics. 2nd ed. Jaypee Brothers Medical Publishers (P)
Ltd, New Delhi.
2- Proffit, W. R., Fields, H. W., Larson, B. E., and Sarver, D. M. (2019). Contemporary
orthodontics. 6th ed. St Louis: Mosby Elsevier.
3- Phulari, B. S. (2017). Orthodontic Principles and Practice. 2nd ed. Jaypee Brothers Medical
Publishers.
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