determinate vs indeterminate force system

Contents
• Introduction
• Determinate vs indeterminate force system
• One couple system
• Two couple system

Introduction
• Mechanics (static / dynamic)
• Biomechanics
• Quantitative approach
• Qualitative approach

Frame of reference
(stationary/moving)
Ref:-Esthetics and biomechanics in orthodontics; ravindra nanda; 2nd edition

Force has four unique properties

Vector addition, or vector
composition
Vector Resolution

CENTER OF RESISTANCE,
CENTER OF GRAVITY, AND
CENTER OF MASS

Moment (Torque)

Couple (A Type of Moment)
Ref:-Esthetics and biomechanics in
orthodontics; ravindra nanda; 2nd
edition

EQUILIBRIUM AND NEWTON'S LAWS

Ref:-Esthetics and biomechanics in
orthodontics; ravindra nanda; 2nd
edition

 The moments as well as the forces generated by an orthodontic appliance
system must be balanced, in all three planes of space.
 Force systems can be defined as statically determinate, meaning that the
moments and forces can readily be discerned, measured and evaluated or as
indeterminate.
Ref:-Proffit;Contemporary orthodontics; 5th edition

 Statically indeterminate systems are too complex for precisely
measuring all forces and moments involved in the equilibrium.
 This is more of a problem in orthodontics because the eventual
action of the system is determined by the biologic response.

 The amount of tooth movement will be determined to a large extent by the
magnitude of the forces felt by anchor teeth and teeth whose movement is
intended, not just by the differential between those forces.
 If the force applied to the anchor teeth is high enough to pull them up onto
the plateau of the pressure response curve, reciprocal tooth movement will
occur despite a difference in PDL pressure.

 Whether intrusion of incisor teeth or extrusion of posterior teeth occurs is almost
totally a function of the magnitude of intrusive vs. extrusive forces, not their
direction or the difference between them.
 Determinate force systems therefore, are advantageous in orthodontics because
they provide much better control of the magnitude of forces and couples.
 Determinate systems in orthodontics are those in which a couple is created at one
end of an attachment, with only a force (no couple) at the other.

A wire that will serve as a
spring can be inserted into a
tube or bracket at one end,
but must be tied so that
there is only one point of
contact on the other.
When the wire is tied into a
bracket on both ends.

One-Couple Systems
One-couple systems are found when two conditions are met:
( 1) A cantilever spring or auxiliary arch wire is placed into a bracket or tube
(2)the other end of the cantilever spring or auxiliary arch wire is tied to a tooth
or group of teeth that are to be moved, with a single point of force
application

Cantilever Spring Applications
 Cantilever springs are used most frequently to
bring severely displaced (impacted) teeth into the
arch.
ADVANTAGES
•a long range of action,
• minimal decrease in
force as tooth movement
proceeds
•excellent control of force
magnitude
DISADVANTAGES
• If they are distorted by the
patient, significant tooth
movement in the wrong direction
is quite possible
•the moment of the force on an
unerupted tooth rotates the
crown lingually as the tooth is
brought toward the occlusal
plane, which is likely
to be undesirable

Auxiliary Intrusion/Extrusion Arches
 The major use of one couple systems is for intrusion, typically of incisors
that have erupted too much.
 light force against the teeth to be intruded is critical.
 An intrusion arch typically employs posterior (molar) anchorage against
two or four incisors.
 intrusive force must be light, and so will be the reaction force against
the anchor teeth.

Factors in the action of an intrusion arch are
 the relationship of the point of force application relative to the center of
resistance of the incisor segment and
 whether the incisor teeth are free to tip facially as they intrude or
 whether the arch is cinched back to produce lingual root torque.
no moment to rotate the
incisors faciolingually
lingual root torque on the
incisors as they intruded

Two-Couple Systems
A two couple system can be created by tying an intrusion arch into
brackets on incisor teeth, rather than tying it with one-point
contact.
For example, Ricketts arch wire
 formed from rectangular wire
 By passes the canine and premolar teeth
 provides excellent load deflection properties so that the light
force necessary for intrusion can be created

 When the utility arch is activated for intrusion, the moment
of the intrusive force tips the crowns facially.
 To prevent this:
o cinching or tying back the intrusion utility arch
o Place a twist in the anterior segment of the utility arch, to
torque the incisors lingually.Note that the "torque bend" in the utility arch wire
produces two problems:
•The reactive force generated by the couple within the bracket
•The magnitude of the reactive forces is not known with certainty, which
makes it impossible to accurately adjust the arch wire even if you do
anticipate the increase

Utility arch for intrusion
Intrusive force
Reactive force on
molar
Couple to tip crown
distally
Mf to tip crown facially
Mc within bracket
On torque bend:-
Moment to bring
crown ingually
Control facial tipping
as they intrude
Increased
intrusive,extrusive frce
& couple on molar
On cinch back:-
Force to bing incisor
lingually
Force to bring molar
mesially
Moment to tip molar
mesially

SYMMETRIC AND ASYMMETRIC BENDS
Symmetric V-bend, which
creates equal and opposite
couples at the brackets.
Asymmetric V -bend, which
creates unequal and
opposite couples, and net
equilibrium forces that
would intrude one unit and
extrude the other
Step bend, which creates
two couples in the same
direction regardless of its
location between the
brackets
When a wire is placed into two brackets, the forces of the equilibrium always act at
both brackets. There are three possibilities for placing a bend in the wire to
activate it:

one-couple torquing arch designed by Burstone
 prevents facial tipping
and extrusion of the
central incisors, the
result is lingual root
torque

TRANSVERSE MOVEMENT OF POSTERIOR TEETH
 Dental posterior crossbite requiring expansion or constriction of
molars, can be approached with two-couple arch wires.
 The anterior segment becomes the anchorage and movement of one
or both first molars is desired.
 Asymmetric expansion or constriction to correct unilateral crossbite
is often the indication.
 Teeth can be moved a considerable distance with a single activation
of the appliance.
 The disadvantage is that the system has poor fail-safe properties.

2 × 6 appliance
 toe-in bend at the molar results
in expansion and mesial-out
rotation of the molar
expansion of the molar, with little
or no rotation

Lingual Arches as Two-Couple systems
 Lingual arches are employed to prevent tooth movement.
 Steel lingual arches usually are 30mil when tooth movement is desired,
36mil when stabilization is needed.
 Replacing one with the other would require changing the tube on the
molar band.
 To prevent this, one possible approach is to use a 32 x 32 TMA wire for
active movement and 32 x 32 steel for stabilization, both of which will
fit into the same rectangular lingual tube.

 Its two-couple design predicts the effect of symmetric V, asymmetric
V and step bends.
 A lingual arch also can be activated to torque roots facially or
lingually.
 Another application of a lingual arch would be to tip one molar
distally thus, uprighting it; the reciprocal of which would be mesial
tipping of the opposite molar.

 Bilateral toe-in bends at the first
molars create equal and opposite
couples, so the mesiodistal forces
cancel and the teeth are rotated to
bring the mesiobuccal cusp
facially.
 When space has been lost in the
maxillary arch or when a Class II
molar relationship exists, this type
of rotation often is desired, but a
flexible rather than a rigid lingual
arch is needed to obtain it.
Lingual Arches as Two-Couple systems

 A unilateral toe-in bend rotates the
molar on the side of the bend, and
creates a force to move the other molar
distally.
 Although mesial movement of the
molar on the side of the bend is limited
by contact with the other teeth, mesial
movement may occur.
 Although net distalization of both
molars has been claimed, significant
distal movement of both teeth is
unlikely.

Bilateral expansion of molars can be created by
expansion of a transpalatal arch, which typically is
achieved by opening a loop in the middle.
The moment of the expansion force tips the crowns
facially.
Placing a twist in the wire creates a moment to torque
the roots facially.
The moment of the couple must be greater than the
moment of the force for this to occur.
A twist in the wire on one side can be used to create
stationary anchorage to tip the opposite molar facially.
This is particularly effective if the wire is rounded on
the movement side, so that a one-couple rather than
two-couple system exists in the faciolingual plane of
space.

Segmented Arch Mechanics
Advantages Disadvantages
a known force system is delivered to
teeth because there is no dissipation of
force by friction.
A good understanding of mechanics is required when
using retraction loops or springs because minor
errors in mechanics can result in major errors in
tooth movement.
Precise control over the anterior and
posterior anchorage.
More wire bending skill and chair time is required as
compared to friction mechanics.
It is fail safe; the tooth will move only
to the limit to which the loop is
activated.
Can lead to gingival irritation because of the loops.
Differential tooth movement is
possible.
Retraction loops may be uncomfortable to some
patients, especially with less vestibular depth
Retraction loops or springs offer more
controlled tooth movement than
continuous mechanics.

Simultaneous retraction and
intrusion of an anterior segment
A rigid bar in the anterior segment can be
extended posteriorly so that the point of
application of an intrusive force is at or distal
to the center of resistance of the incisor
segment.

Continuous Arch Mechanics
Advantages Disadvantages
Complicated wire configuration is not
required.
Confusion regarding the ideal force levels.
There are no essential guidelines
concerning the amount of force to be
used during space closure.
Initial wire placement is less time
consuming excellent fail safe properties.
Limited ability to produce differential
anchorage, optimal tooth movements or
control for adverse responses in complex
cases.
Enhances patient comfort. Tendency for initial over activation of
elastic and spring forces, causing initial
tipping and inadequate rebound time for
uprighting.

REFERENCES
• Proffit;Contemporary orthodontics; 5th edition
• Esthetics and biomechanics in orthodontics;
ravindra nanda; 2nd edition

determinate vs indeterminate force system

determinate vs indeterminate force system

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