Basics of Orthodontic Force System

Force

• A load applied to an object that will move of tend to move it to a different position in space

• Force has Magnitude and Direction (Vector)

• F = m x a (mass × the acceleration of gravity)

• Units: Newton (N)

• Usually measured clinically in weight units of grams or ounces

• For all practical purposes, 1.0 N = 100 gm (the actual value is between 97 and 98 gm)

Addition of Force Vectors

Center of Resistance (CR)

• A point at which resistance to movement can be concentrated for mathematical analysis

• Center of resistance of an object in space

• Center of resistance of an object partially imbedded in a matter• The portion of object imbedded in a solid/semi-solid medium dictates the

amount of resistance to the movement of the object

• For a tooth partially imbedded in bone• Center of resistance is near the middle half of the root

THE CUE BALL CONCEPT

To summarize, there are three rules that can be directly applied to tooth movement.

• Rule 1 : If a force is applied through the center of a body, the body will move in the direction of the applied force.

• Rule 2 : When a force is applied away from the center of the body, the body will not only move in the direction of the applied force, but will also rotate because of the moment produced by the line of force acting at a perpendicular distance to the center of the body.

• Rule 3 : When equal and opposite forces act in the same plane of space, but parallel to each other, a pure moment is produced. In other words, the body undergoes pure rotation. This system refers to a couple.

Moment

• A measure of the tendency to rotate an object around some point

• A moment has magnitude and direction (Clockwise vs Anti-Clockwise)

• A moment is generated by a force acting at a distance from (CR)

• Quantitatively, it is the product of the force times the perpendicular distance from the point of force application to the center of resistance

• M = F x d

• Unit: Gram-millimeter (or equivalent)

• When an applied force does not pass through the center of resistance• The force tend to translate the object• Force will tend to rotate the object around the center of resistance

Couple

• Two non-colinear forces equal in magnitude and opposite in direction

• The translatory component of the force will be cancelled out

• Only rotational component of force will be left generating Pure Rotation

• The object will rotate around its center of resistance

• No matter where the couple is applied on a body, it will always rotate around its center of resistance

50 x 10 = 500 g.mm

50 x 10 = 500 g.mm

50 x 20 = 1000 g.mm

Force vs Couple

• Force has two components• 1. Translatory• 2. Rotational component (Moment) (if force is applied away from the CR)• Center of rotations can vary its place

• Couple has only one component• 1. Rotational component (Moment)• Center of rotation is always at its center of resistance

• Rotation can be resulted from• Rotational component of force (Moment of Force) MF

• Rotational component of couple (Moment of Couple) MC

Center of Rotation (CRot)

• The point around which rotation actually occurs when an object is being moved

• Controlling the Center of Rotation• When two forces are applied simultaneously to an object, the center of

rotation can be controlled and made to have any desired location

Addition and Subtraction of Forces and Moments• Forces:

• Left sided forces cancel out right sided forces

• Right sided forces cancel out left sided forces… and so on!

• Left vs Right

• Up vs Down

• Forward vs Backward

• Moments:• Clockwise Moments cancel out Anti Clockwise Moments

Types of Tooth Movement Revisited

• Uncontrolled Tipping

• Controlled Tipping

• Bodily Movement (Translation)

• Torquing

• Intrusion

• Extrusion

Rotation

• Rotation around:• Mesiodistal Axis

• Longitudinal Axis

• Faciolingual Axis

How to Achieve Desired Orthodontic Tooth Movement?

How to Achieve Uncontrolled Tipping?

• Apply force on crown• Crown will move on one side

• Apex will move to the other side

• Rotation of tooth occurring on MesioDistal Axis

• Center of Rotation• Between Center of Resistance and root apex

How to Achieve Bodily Tooth Movement?

How to Achieve Bodily Tooth Movement?

Force will tend to • Translate the tooth• Mf will tend to rotate the tooth

• We do not want tooth to rotate

• Nullify the effect the Mf with Mc

• Mc is generated by a couple by rectangular wire in bracket slot

• Center of Rotation• At infinity

• Mf = Mc

How to Achieve Controlled Tipping?

• Apply force on crown• Crown will move on one side

• Apex will move to the other side

• But for controlled tipping• We do not want the apex to move to the other side

• We want center of rotation at apex

• Apply some counter-clockwise couple (Mc) to partially nullify the effect of (Mf)

• Mf > Mc

How to Achieve Root Torque?

• Apply force on crown• Crown will move on one side

• Apex will move to the other side

• But for torque• We do not want the apex to move to the other side

• We do not want the crown to retract

• We want center of rotation at tip of crown

• Apply a lot of counter-clockwise couple (Mc) to over-ride the effect of (Mf)

• Mf < Mc

How to rotate a tooth?

• Apply force on crown away from its center of resistance• Force will tend to displace the tooth

• Moment of force will tend to rotate the tooth

• How to get pure rotation of tooth along the longitudinal axis?What if we do not want tooth displacement?

• Apply couple on the crown of the tooth

• Center/axis of Rotation• At the center of resistance along the longitudinal axis

MC/MF = 0Pure tipping (tooth rotates around center of resistance)

MC/MF < 1

Controlled tipping (inclination of tooth changes but the center of rotation is displaced away from the center of resistance, and the root and crown move in the same direction)

MC/MF = 1Bodily movement (equal movement of crown and root)

MC/MF > 1 Torque (root apex moves further than crown)

How to Generate Couple?

Questions?