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1. Common sense mechanics
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2. • Rational
• Reasonable
• Consistent
• and Coherent.

3. Biomechanics
• Mechanics-is the discipline that describes the effect of forces
on bodies.
• Biomechanics-study of mechanics as it affects the biologic
systems.
• Application of mechanics to the biology of tooth movement.

4. • Centre of Mass- All objects (finite) behave as if
the entire mass is concentrated onto a single point.
• Applicable in force - free state
• Behaviour- Predictable if forces acting in relation to
this point is known.

5. • Centre of Gravity- objects subject to gravitational
force
• Cmass / Cg -“ Balance point”

6. • Centre of Resistance- analogous to the Cmass for
restrained bodies.
– Function of a body in a system of constraints-supporting
tissues.

7. • Precise location-not known, conceptual awareness
needed.
• Relationship of force systems to Cres of tooth-type of
tooth movement

8. • Centre of Rotation- a point around which an
object rotates.
-The geometric point about which no movement
occurs
-Point around which an object seems to have
rotated as determined from its initial and final
positions

9. Principles of biomechanics
• Direction and magnitude of force -
Magnitude
Origin/
point of application
Line of action
Sense/Direction

10. Principles of biomechanics
• Multiple vectors can be combined through vector
addition
• Sum of 2 or more vectors- Resultant
F
1
ce
or
Resultant
Forc
e
2

11. Principles of biomechanics
• Different points of applicationForces can be combined using
the law of transmissibility
of force.
“When considering the external effects
of a force on a rigid body the force
may be considered to have a point of
application anywhere along its line of
action”

12. Principles of biomechanics
• Resolving a force into vectors-

13. Principles of biomechanics
• Moment –Rotational tendency of a force that is not
passing through the centre of resistance.
• The magnitude of the moment=
lar
Force x
distance of line of action (force) to
the Cres

14. Principles of biomechanics
• M=F x D

15. Principles of biomechanics
Couple –consists of two forces of equal magnitude,
with parallel but non-collinear lines of action and
opposite senses.
- Two equal and opposite parallel forces separated
by a perpendicular distance.
-Applied moments
• Pure rotation about the centre of resistance

16. Principles of biomechanics
• Magnitude of a couple=Mag.of 1 force x
perpendicular dist b/w them
• Unit-Gram.mm
Translational effects cancel out each other

17. Principles of biomechanics
• Moment arm of a couple-

18. Principles of biomechanics
• Couples result in pure rotational movement
regardless of where the couple is applied on the
object.
• 50 x 10=-500gm-mm
• 50x30=1500gm-mm
• 500gm-mm is negative Thus 1000gm-mm just
as in the previous case

19. Principles of biomechanics
• Clinically
Centre of rotation coincides with the centre of resistance.

20. Principles of biomechanics
• Forces indicated by• Moments indicated byMoment of force-rotational tendency of a single force
that does not pass though the Cres-(linear movement
occurs)
Moment of couple-two forces that produce pure rotation
(no linear movement)

21. Principles of biomechanics
• Important to distinguish between force and moment.
• “Cue ball concept”

22. Principles of biomechanics
• Static equilibrium-

23. Principles of biomechanics
• In orthodontics-equilibrium establishes itself
• We do not have to achieve static equilibrium but
recognize the forces and moments that have come
into existence to establish the static state.

24. Principles of biomechanics
• Newton’s laws of motion-underlie the fundamental
concept of mechanics.
1.Law of inertia
2.The law of acceleration
3.The law of action and reaction

25. Principles of biomechanics
• Application of these laws-orthodontics
• Wire engaged into poorly aligned teeth-1st & 3rd laws
• A more important application of Law of action and
reaction is static equilibrium.

26. Principles of biomechanics
• Static equilibrium implies -At any point within a
body, the sum of forces and moments acting on a
body is zero.
• The analysis of equilibrium as applied to
orthodontics can be stated as

27. Principles of biomechanics
• Sum of all vertical forces =0
• Anterior intrusion-have to deal with-the balancing
force-molar extrusion.

28. Principles of biomechanics
• Sum of all horizontal forces=0
• Correction of unilateral crossbite-not possible with
a single horizontal force

29. Principles of biomechanics

30. Principles of biomechanics
• Moment acting around any
point must = 0.
• Forces produced to
maintain static equilibrium
• Magnitude of forces exactly
–necessary to produce a
counter rotation.

31. Equilibrium situations
• Many appliances and bends placed in clinical
situations
• Many situations –unequal forces and moments
develop.
• “Additional forces”-develop to obtain equilibrium
• Determination of complete system in equilibriumside effects.

32. Equilibrium situations
• The forces and moments that determine a appliances
equilibrium –must exist.
• If not-Newton’s 2nd law-teeth will accelerate out of
the mouth!

33. Equilibrium situations
• Off-centered “V” bends (asymmetric bend
relationship)
• Creates unequal and opposite couples.
• The net equilibrium forces-intrude one unit, extrude
the other.
• Total magnitude of system-not certain, relative
magnitude can be determined.
• The larger moment-indicates the direction of
equilibrium forces.

34. Equilibrium situations

35. Equilibrium situations
• 1/3rd the way along the inter bracket span-no
moment on the distant tooth.
• Closure than 1/3rd moment generated in the same
direction.

36. Equilibrium situations
Centered “V” bend
Creates equal and opposite couples at the brackets.
The associated equilibrium forces at each bracket-equal
and opposite – cancel each other out.

37. Equilibrium situations
•The location of Cres has no effects on the reactions produced

38. Equilibrium situations
• Step bendsCreates 2 couples in the same direction-regardless of
location between brackets.
Location of step bend-no effect on either magnitude of
moments or equilibrium forces.

39. Equilibrium situations
Forces generated are
stronger than the offcentered “V” bend situation
If the Cres changes-similar
effect of that seen in Offcentre “V” bend .

40. Equilibrium situations

41. Equilibrium situations

42. Equilibrium situations

43. Equilibrium situations
• Visual inspection– Frequently used to determine the forces an arch wire will
produce
– May seem obvious-Faulty conclusions.
– Determine the forces and moments

44. Equilibrium situations

45. Equilibrium situations

46. A Simple Rule.
• Bend off center: short and long segment.
• Short segment engaged –long segment point in
direction of the force produced .
• Short segment points in the opposite direction of
the force.

47. Equilibrium situations
Bend at center: no short or long segments- forces as
cancel each other upon engagement leaving only
pure moments.

48. Determinate Vs Indeterminate force
systems
• Force systems can be• Statically determinate (One couple system)
The forces and moments can readily be discerned,
measured and evaluated.
• Statically indeterminate (Two couple
system) System is too complex for precisely
measuring all forces and moments involved in
equilibrium.

49. Biomechanical classification of
orthodontic appliances
• Equal and opposite force system
(No couple appliance system)
• One couple appliance system
• Two couple appliance system

50. Statically determinate

51. Statically Indeterminate
• Two couple system- When the free end of the
arch wire-inserted into a second bracket.
• For the purpose of establishing the direction of
associated equilibrium forces-sum of 2 successive 1
bracket systems
• Couples-each of 2 brackets

52. Clinical situations
• Forces and Moments acting on teeth-

54. Differential torque

56. Lingual Root TOrque

57. Commonsense!

58. Biomechanics of aligning
• Canine extrusion spring- Palatally placed
•Third order couple created at
molar-passive TPA

59. Biomechanics of aligning
Palatal to facial canine movement
•1st order couple at molar
tube
•Equilibrium forces-Facial
canine movement
•TPA- molar

60. Biomechanics of aligning
• Midline springs
•Wire lateral to incisors
in direction in which
movement required
•Force system-similar to
previous situation

61. Biomechanics of aligning
• Diastema closure

62. Biomechanics of aligning
• Molar rotations-Transverse corrections
– Can be done on a 2 x 2/4
– 2x6 –anterior segment –visualized as one large tooth.
– Predominantly molar movement

63. Biomechanics of aligning
• Symmetrical ‘V’ bends
Molar mesial- out rotations
Molar mesial- in rotations

64. Biomechanics of aligning
• Moments-Bilateral
toe-in
– Canine -distal out
– Molar –mesial out
• Anterior segment-large
tooth-cancel each
other
Increases arch perimeter
Correction of class II
malocclusion

65. Biomechanics of aligning
• Bilateral toe-outs
– Mesial-in molar
rotations
Correction of molar
rotation
Decrease the arch
perimeter

66. Biomechanics of aligning
• Asymmertrical ‘V’ bends
• Larger angle of entrydetermines direction and
not magnitude of
equilibrium forces
• Premolar should not be
engaged

67. Biomechanics of aligning

68. Biomechanics of aligning
• Molar mesial-out
rotationsMolar M-out rotations and
intermolar expansion

69. Biomechanics of aligning
• Molar mesial –in
rotations
• Reversal of situations
Bilateral molar M-in rotations
and constriction of inter molar
width

70. Biomechanics of aligning
• Molar constriction
• Bend-closure to canine
• Little or no molar
rotation
Constriction of intermolar width
with minimum molar rotations
are desired

71. Biomechanics of aligning
• Molar expansion
• Molar expansionminimal rotations

72. Biomechanics of aligning
• Step bends
• Magnitude of the 2 M of
couple need not be
equal-but associated
equilibrium forces are
always equal

73. Biomechanics of aligning
• Molar expansionToe-out
• M-out rotations &
enhanced expansive
equilibrium forces.

74. Biomechanics of aligning
• Molar constrictionToe-in
• M-out rotations and
greater constrictive forces

75. Bypass Arches
• The essence of activating a 2 x 4 –create and control
moments and their equilibrium forces.
• 2 x 4 –one couple

76. Bypass Arches

77. Bypass Arches
• 2 x 4 –two couple

78. Bypass Arches

79. Bypass Arches
• Mulligan’s 2 x 4 –can be used in the Begg set up• Upper molars do not require tipping-helix bent into
arch wire- 2-3mm mesial
• Anchor bend ,continuation of the helix
• No cuspid circles required

80. Knowledge is the antidote to fear.
- Ralph Waldo Emerson
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