03-10-2013
Force systems
Free-Body Diagram
Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
Force systems
Supports & Connections I
Section of Orthodontics, University of Aarhus, DK
Force systems
Supports & Connections II
Section of Orthodontics, University of Aarhus, DK
Force systems
Free-Body Diagram
Section of Orthodontics, University of Aarhus, DK
Force systems
Active & Reactive units
Section of Orthodontics, University of Aarhus, DK
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03-10-2013
Force systems
Force systems
Consistent force systems
Consistency & Inconsistency
The force system developed when a wire is inserted in a
Dependent on the desirability of the force
brack br acket et com compr pris ises es forces and
system developed, when a straight wire is
moments. If both the rotation moments. gene ge nera rate ted d by th the e moment and
tied into the bracket of the active and the reac re acti tive ve un unit it,, fo forc rce e sy syst stem ems s ca can n be cl clas assi sifi fied ed
the translation res resulti ulting ng fro from m the force ar are e le lead adin ing g to th the e pl plan anne ned d
as consistent or or inconsistent inconsistent..
tooth
movement,
the
force
syst sy stem em is sa said id to be consistent consistent..
Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
Force systems
Inconsistent force systems
Force systems
Statically determinate systems A force system is called static statically ally determ determinate inate whe hen n al alll
An inconsistent fo forc rce e sy syst stem em is
unkn un know own n fo forc rces es an and d mo mome ment nts s in th the e fo forc rce e sy syst stem em ca can n be
u na nable to pr od oduce the desire d combination of forces and
calculated from the force and mo mome ment nt eq equil uilib ibri rium um formulas.. formulas
moments. When the moment produc prod uced ed is de desi sire red, d, th the e fo forc rce e is undesir unde sirable able and vic vice e ver versa. sa.
Section of Orthodontics, University of Aarhus, DK
Force systems
Statically indeterminate systems A force system is called stat statica ically lly ind indeter etermin minate ate when some of the u nk nknown fo rc rces an d moments in the force syst sy stem em ca cann nnot ot be ca calc lcul ulat ated ed fr from om th the e force and moment equili equ ilibriu brium m form formulas ulas.. Ad Addi diti tion onal al in info form rmat atio ion n sh shou ould ld th then en
The cantilever cantilever is the mos mostt imp import ortant ant exampl exa mple e of a sta stati tical cally ly det determ ermina inate te orthodontic appliance.
Section of Orthodontics, University of Aarhus, DK
The Six Geometries
The fo The force rce sy syst stem em de deve velop loped ed in a tw two-t o-too ooth th seg segme ment nt wh when en conne con nect cted ed by a con conti tinu nuous ous st stra raigh ightt wi wire re is det deter ermi mined ned by the angles of the brackets with respect to the wire passing through the centers of the brackets and the interbracket interbr acket distanc distance. e.
be emp employ loyed ed to dete determi rmine ne thes these e unk unknow nown n qua quanti ntities ties.. In the V-bend the forces and moments at the brackets bracke ts cannot be calcul calculated ated straight away. However Howev er using symme symmetry try consi considerat derations, ions, the forc fo rces es mu must st be ze zero ro an and d th the e mo mome ment nts s opposite to one another. Burstone & Konig, AJO Konig, AJO,, 1974 Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
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03-10-2013
The Six Geometries
The Six Geometries
Geometry I
θ A/θB
= 1.0
F A = -FB M A/MB = 1.0 Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
The Six Geometries
Geometry II
The Six Geometries
Geometry III
θ A/θB
= 0.5
θ A/θB
= 0.0
F A = -FB
F A = -FB
M A/MB = 0.8
M A/MB = 0.5
Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
The Six Geometries
Geometry IV
θ A/θB
The Six Geometries
Geometry V
= -0.5
θ A/θB
= -0.75
F A = -FB
F A = -FB
M A/MB = 0.0
M A/MB = -0.4
Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
3
03-10-2013
The Six Geometries
The Six Geometries
Geometry VI MB = (K * θ A/θB
= -1.0
F A = FB = 0.0 M A/MB = -1.0
θB)
/ L,
F = (M A + MB) / L, with: K = (3.853 θ A/θB + 7.7089) * Ws Ws = Ms * Cs L - interbr interbracket acket distance distance Ms - materi material al stiffness stiffness Cs - crosscross-section sectional al stiffness
Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
The Six Geometries
Minor Bends
Step-bend force systems
Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
Minor Bends
Step-bends: forces
Section of Orthodontics, University of Aarhus, DK
Minor Bends
Step-bends: moments
Section of Orthodontics, University of Aarhus, DK
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03-10-2013
Minor Bends
Minor Bends
Step-bends: moments
V-bends: forces forc es
Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
Minor Bends
Minor Bends
V-bends: moments moment s
V-bends: moments m oments
Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
Minor Bends
Minor Bends
V-bends: special cases
☯
a / L = 0.5 0.5
☯ F A ☯
V-bends: special cases
= FB = 0.0
M A = - MB ☯
Section of Orthodontics, University of Aarhus, DK
1 / 3 < a / L< 2 / 3
→
M A & MB opposite
Section of Orthodontics, University of Aarhus, DK
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03-10-2013
Minor Bends
Minor Bends
V-bends: special cases
V-bends: special cases
☯
a / L = 2 / 3 → MB = 0;
☯
a / L > 2 / 3 → M A & MB same direction
☯
a / L = 1 / 3 → M A = 0
☯
a / L < 1 / 3 → M A & MB same direction
Section of Orthodontics, University of Aarhus, DK
Section of Orthodontics, University of Aarhus, DK
Minor Bends
V-bends in the occlusal plane
Section of Orthodontics, University of Aarhus, DK
Major Discrepancies
Force system L-loop influence of the vertical discrepancy
Major Discrepancies
Special loops
1. vertical loop
2. L-loop
3. rect cta angul ula ar loo oop p
4. T-lo loo op
Section of Orthodontics, University of Aarhus, DK
Major Discrepancies
Force system L-loop ∆
Section of Orthodontics, University of Aarhus, DK
influence of the horizontal length G
Section of Orthodontics, University of Aarhus, DK
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03-10-2013
Major Discrepancies
Force system rectangular loop influence of the vertical discrepancy
∆
Section of Orthodontics, University of Aarhus, DK
Major Discrepancies
Force system T-loop influence of the vertical discrepancy
Major Discrepancies
Force system rectangular loop influence of the horizontal length G
Section of Orthodontics, University of Aarhus, DK
Major Discrepancies
Force system T-loop ∆
Section of Orthodontics, University of Aarhus, DK
influence of the horizontal length G
Section of Orthodontics, University of Aarhus, DK
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