Common sense mechanics INDIAN DENTAL ACADEMY Leader in continuing dental education www.indiandentalacademy.com
• Rational • Reasonable • Consistent • and Coherent.
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.
• 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.
• Centre of Gravity- objects subject to gravitational force • Cmass / Cg -“ Balance point”
• Centre of Resistance- analogous to the Cmass for restrained bodies. – Function of a body in a system of constraints-supporting tissues.
• Precise location-not known, conceptual awareness needed.
• Relationship of force systems to Cres of tooth-type of tooth movement
• 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
Principles of biomechanics • Direction and magnitude of force -
Magnitude Origin/ point of application
Line of action
Sense/Direction
Principles of biomechanics • Multiple vectors can be combined through vector addition • Sum of 2 or more vectors- Resultant F
e1 c or
Resultant Forc e
2
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”
Principles of biomechanics • Resolving a force into vectors-
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
Principles of biomechanics • M=F x D
Principles of biomechanics Couple 窶田onsists 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 窶｢ Pure rotation about the centre of resistance
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
Principles of biomechanics • Moment arm of a couple-
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
Principles of biomechanics • Clinically
Centre of rotation coincides with the centre of resistance.
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)
Principles of biomechanics • Important to distinguish between force and moment. • “Cue ball concept”
Principles of biomechanics • Static equilibrium-
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.
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
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.
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
Principles of biomechanics • Sum of all vertical forces =0 • Anterior intrusion-have to deal with-the balancing force-molar extrusion.
Principles of biomechanics
• Sum of all horizontal forces=0
• Correction of unilateral crossbite-not possible with a single horizontal force
Principles of biomechanics
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.
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.
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!
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.
Equilibrium situations
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.
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.
Equilibrium situations
•The location of Cres has no effects on the reactions produced
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.
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 .
Equilibrium situations
Equilibrium situations
Equilibrium situations
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
Equilibrium situations
Equilibrium situations
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.
Equilibrium situations
Bend at center: no short or long segments- forces as cancel each other upon engagement leaving only pure moments.
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.
Biomechanical classification of orthodontic appliances • Equal and opposite force system (No couple appliance system) • One couple appliance system • Two couple appliance system
Statically determinate
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
Clinical situations • Forces and Moments acting on teeth-
Differential torque
Lingual Root TOrque
Commonsense!
Biomechanics of aligning • Canine extrusion spring- Palatally placed
•Third order couple created at molar-passive TPA
Biomechanics of aligning Palatal to facial canine movement •1st order couple at molar tube •Equilibrium forces-Facial canine movement •TPA- molar
Biomechanics of aligning • Midline springs •Wire lateral to incisors in direction in which movement required •Force system-similar to previous situation
Biomechanics of aligning • Diastema closure
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
Biomechanics of aligning • Symmetrical ‘V’ bends
Molar mesial- out rotations Molar mesial- in rotations
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
Biomechanics of aligning • Bilateral toe-outs – Mesial-in molar rotations
Correction of molar rotation Decrease the arch perimeter
Biomechanics of aligning • Asymmertrical ‘V’ bends • Larger angle of entrydetermines direction and not magnitude of equilibrium forces • Premolar should not be engaged
Biomechanics of aligning
Biomechanics of aligning • Molar mesial-out rotationsMolar M-out rotations and intermolar expansion
Biomechanics of aligning • Molar mesial –in rotations • Reversal of situations Bilateral molar M-in rotations and constriction of inter molar width
Biomechanics of aligning • Molar constriction • Bend-closure to canine • Little or no molar rotation
Constriction of intermolar width with minimum molar rotations are desired
Biomechanics of aligning • Molar expansion
• Molar expansionminimal rotations
Biomechanics of aligning • Step bends • Magnitude of the 2 M of couple need not be equal-but associated equilibrium forces are always equal
Biomechanics of aligning • Molar expansionToe-out • M-out rotations & enhanced expansive equilibrium forces.
Biomechanics of aligning • Molar constrictionToe-in • M-out rotations and greater constrictive forces
Bypass Arches • The essence of activating a 2 x 4 –create and control moments and their equilibrium forces. • 2 x 4 –one couple
Bypass Arches
Bypass Arches • 2 x 4 –two couple
Bypass Arches
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
Knowledge is the antidote to fear. - Ralph Waldo Emerson
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