Basic Biomechanics of Tooth Movement INDIAN DENTAL ACADEMY Leader in continuing dental education www.indiandentalacademy.com
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Introduction Scalars and vectors Orthodontic force: ď Ž ď Ž
Resultants and Components
Types of tooth movements Centers of rotation and resistance Equivalent systems www.indiandentalacademy.com
Moment of a force Moment of a couple Moment to force ratio Conclusion
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Mechanics An area of study within physical science that is concerned with the state of rest or motions of bodies subjected to forces. Understanding of mechanics is based on particle mechanics formulated by Sir Isaac Newton
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Newtonian Mechanics Static – body at rest and under action of forces Dynamic – moving bodies
Kinematics – study of motion itself Kinetics – relationship between the force systems and characteristics of body motion are explored
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Newton's Laws 1st law: particle subjected to balanced system of forces will remain at rest, if originally at rest, or move with constant speed in a straight line, if originally in motion. 2nd law: particle subjected to unbalanced system of forces will accelerate in the direction of the net force 3rd law: every action has an equal and opposite reaction. www.indiandentalacademy.com
Reduce empiricism or trail and error Relates concepts of stress distribution in the PDL to that of bone remodeling Increase efficiency and efficacy of the appliance.
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On a sub clinical level:
Control the centre of rotation of the tooth To maintain a desirable stress level in the pdl To maintain a relatively constant stress level
On a clinical level:
The M:F ratio The load deflection rate The maximal forces or moment of any component of an appliance
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Scalars and Vectors Scalars---- completely described by their magnitude alone. Eg. Mass, distance , temperature. Vectors---- described by magnitude and direction. Eg. Force www.indiandentalacademy.com
Force Is defined as an act on a body that changes or tends to change the state of rest or motion of the body. As per Newton's laws two bodies are always associated with a force i.e. one that exerts the force and the other that receives the force
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Smith and Burstone (1984)
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Resultants form a single point
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Resultant form two point of application www.indiandentalacademy.com
R2 = a2 + b2 – 2ab www.indiandentalacademy.com
p
q Tan theta = p/q R2 = p2 + q2 for mutually perpendicular forces R2 = p2 + q2 – 2pq (cos theta) for not perpendicular to Each other.
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Forces in general can be
Active and reactive (Newton) Concentrated or distributed External or internal
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Static equilibrium This states that for every appliance, not necessarily every tooth, the sum of moments and sum of forces be equal to zero, i.e. the net force should be zero, regardless of the type of appliance that is being used.
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Intrusive force on the incisors is balanced by an extrusive force on the molars
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Types of tooth movement
Pure translation
Pure rotation
Combination of both www.indiandentalacademy.com
When a tooth in the mouth move during orthodontic therapy there is no pure translation or pure rotation there is always a combination of the two. (Hurd and Nikolai)
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terminology Centre of Mass: is that point where all the mass of a body is concentrated when the body is in space. Centre of Gravity: is the same point but when gravity is acting on the body. Centre of Resistance: is that point, through which if a force is applied will move a object bodily, or produce a pure translation. www.indiandentalacademy.com
Centre of resistance in tooth Depends on the root length and Depends on the height of the alveolar bone. In a tooth of paraboloid shape the centre of resistance lies at h/3 where h is the length of the root.
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C res. Of a Single rooted tooth---on the long axis between 1/3rd and ½ of the root apical to alveolar crest. Multirooted tooth--- between the roots, 1 to 2 mm apical to the furcation. www.indiandentalacademy.com
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Effect of forces Translation: If the line of action of an applied force passes through the center of resistance of a tooth, the tooth will respond with pure bodily movement (translation) in the direction of the line of action of the applied force.
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A moment of a force is the rotational tendency of the force 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. m = f x d (gmm)
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(Note that there will be only a single net moment or net force on a tooth)
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Couple : ď Ž
Is a system consisting of two forces that are equal in magnitude, with parallel but non collinear lines of action and opposite senses.
M = 50x10 = 500gmm Net moment = 1000gmm
or
M = f x (distance between the two forces) M = 50 x 20 M = 1000gmm
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M =( f1d1) + ( f2d2)
M =( -50x10 ) + ( 50 x 30)
M = 1000gmm
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Center of rotation a centre of rotation can be defined as that point about which a body appears to have rotated as shown by the initial and final positions of the tooth
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Centre of rotation can also be defined as that point that has the least magnitude of moment (m = 0) or Can also be defined as the point that has moved the least during tooth movement
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Changing centre of rotations in A ( Nilkolai and Hurd) The centre of rotation for a combined translation and rotatory movement (Hocevar) www.indiandentalacademy.com
Forces within cross hatched areas will produce rotation as well as translation whereas the blank areas will produce simple tipping
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Forces in the shaded areas will produce translation And rotation at a rate that is continuously accelerating
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Changing the positions of the centers of rotation can bring about changes in the type of tooth movement but not the extent of tooth movement
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Equivalent systems
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Criteria for systems to be equivalent :
(1) the sums of forces in the x direction are identical, (2) the sums of forces in the y direction are identical, (3) the sums of moments about any point are identical. Smith and Burstone(1984)
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150gm
1200gmm
What would the force system at the bracket in B be so that It would be equivalent to the system in A www.indiandentalacademy.com
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Moment to Force ratio
The type of tooth movement would be determined by the ratio of the moment of the couple and the force applied at the bracket.
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What is the net moment here considering all forces to be 5 and distances to be 2 The type of movement occuring would depend on the location Of the center of rotation which is determined by the moment to force ratio (not their magnitudes) www.indiandentalacademy.com
10/1
Burstone and Pryputniewicz
A = uncontrolled tipping B = controlled tipping C = bodily movement D = bodily movement E = root movement F = pure rotation
7/1 0 20/1 12 or 13/1
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F3dc > F1d
F1d = F3dc
F1d>f3dc F3dc >> F1d
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Statically determinate systems (one couple system) ď Ž
This means that the magnitudes and the direction of the forces and moments exerted by the wire can be determined clinically once the appliance is inserted into the bracket
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One couple system-examples Cantilever springs used to bring severely displaced teeth into the arch Auxiliary intrusion or extrusion arches Begg intrusion arch
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Statically indeterminate systems (two couple systems) ď Ž
ď Ž
The ,magnitude of the force systems produced cannot be determined clinically but the direction can be. The force systems produced depend both on the wire geometry and the bracket angulations
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Conclusion The laws of physics are fundamental, and though their application in the different hands may vary the knowledge of the fundamentals is a necessary prerequisite to achieve the desired tooth movement in the most effective and efficient manner.
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references Graber and Swain :Orhtodontics: Current principles and practice Smith and Burstone: mechanics of tooth movement, AJO 1984; 85: 295 – 300. Hocevar: understanding, planning and managing tooth movement, AJO 1981; 457 -477 Mulligan: Common sense mechanics JCO – 13; 676 – 683 1979. Hurd and Nikolai: centers for rotation of combined vertical and transverse tooth movements, AJO 1976; 70 : 551 www.indiandentalacademy.com
Nikolai : bioengineering analysis of orthodontic mechanics Burstone and Koening, Forces in an ideal arch. AJO; 1974: 65, 2670 – 289. Demange C: Equilibirium situations in bend force systems. AJO – DO; 1990: 98, 333 – 339 Marcotte MR: AJO: 1969, 511 – 523, 1976. www.indiandentalacademy.com
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