Jacobson 1979

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    LONG *

    :.-. ,

    .‘,’ ,I’

    ,:’

    X8’

    ‘*

    I,

    I,

    Jr

    MEDIUM ,--I

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    Fig. 1. Diagram illustratin g face-bow with short, me dium , and long outer bow lengths

    teeth, certain mechanical principles need to be understood and defined. This is essential

    since the key to an understanding of the effects of extraoral forces on a molar tooth is an

    appreciation of the relationship of the line of action of a,force to the center of resistance of

    a tooth.

    The mechanical principles that need to be defined include the following:

    A force. A force is that which changes or tends to change the position of rest of a body

    or its uniform motion in a straight line. The forces used in orthodontics are created by

    elastic or spring traction.

    Center of resistance. Teeth may be moved by tipping or translation. In tipping, the

    center of rotation for any tooth must be located between the neck of the tooth and its apex,

    its exact position being unknown.3 Most investigators”. I3 agree that the fulcrum of the

    tipping movements is in the region between the middle and apical thirds of the root portion

    of the tooth. In discussions of tipping or translatory tooth movements, the terms center of

    rotation and center of resistance are sometimes not clearly differentiated4 and tend to be

    used loosely. Since one is a fixed point and the other movable: the points warrant

    definition.

    The center of resistance of a body i s that point through which the resultant of the

    constraining forces acting upon it may be considered to act. The center of resistance of a

    single-rooted tooth with a parabolic shape is at a point 0.4 times the distance from the

    alveolar crest to the apex.* In the maxillary first molar the center of resistance is estimated

    to be in the middle third of the root near the junction of the cervical third, or approxi-

    mately at the trifurcation of the roots. The center of resistance of a tooth cannot be

    changed by external force application.

    Center of rotation. The center of rotation of a body is a point around which the body

    wi ll rotate or tip. The center of rotation, unlike the center of resistance, can be changed,

    the latter being dependent upon external force application. When a force is applied to a

    tooth and its line of action does not pass through the center of resistance, then tipping of

    the tooth wi ll occur around a center of rotation which may be located anywhere between

    the center of resistance of the tooth and infinity. No tipping wi li occur when the force

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    363

    Fig. 2. The three planes of space in which a tooth may be moved.

    application is such that its line of action results in the centers of resistance and rotation

    coinciding.

    Force resolution. Forces may be resolved into component vectors which, in a single

    plane of space, are at right angles to each other. The extraoral force application to molars

    is considered to be the resultant force which, in the discussion, are resolved into its

    components in the various planes of space.

    Line ofaction. The line of action of a force is usually represented by an arrow and is

    the direction in which the force acts.

    Clinica l application of above principles

    Teeth can be moved in only three planes of space: sagittal, coronal, and transverse

    (Fig. 2). One or more planes of space may be involved in orthodontic tooth movement.

    However, to facilitate understanding of the mechanical principles involved in extraoral

    force application, each will be discussed separately, under the following headings:

    (1) sagittal plane, (2) coronal plane, and (3) transverse plane.

    Sagittal plane. The extraoral force applied to the molars is the resultant force. This

    force has direction, in which the line of action of a force is that line connecting the point of

    origin of the force (head- or neckgear assembly hook) to the point of attachment (hook) on

    the outer bow. The resultant force component acting on the banded molar tooth is the

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    Fig.

    3. C, Center of resistance. R, Center of rotation. 7, Line of action of force.

    C*

    l3

    1

    A

    M

    Fig.

    4. C, Center of resistance. T, Tension (line of action of force). P, Perpendicu lar distance. M,

    Moment.

    relationship of the line of action to the center of resistance of the tooth. The center of

    resistance of the tooth remains constant. The variables are, therefore, (a) the distance of

    the line of action from the center of resistance and, (b) the inclination (or steepness) of the

    line of action.

    D~STANCEOFTHELINEOFACTIONFROM THECENTEROFRESISTANCE.

    Whenthelineof

    action passes through the center of resistance of a tooth, no tipping wi ll occur. Tipping,

    however, will occur if the line of action does

    not

    pass through the center of resistance

    (C). The tipping takes place around a center of rotation (R) (Fig. 3). The center of rotation

    varies and is dependent upon the relationsh ip of the line of action to the center of

    resistance of the tooth.

    Should the line of action (T) pass occlusally through the center of resistance, the

    crown of the tooth will tip dista lly (and the root apex mesially). The farther the line of

    action is from the center of resistance of a tooth, the greater is its tipping effect.

    This principle is easily analyzed by applying the simple formula

    M=TxP

    M represents he moment producing the tipping

    T represents he tension (extraoral traction)

    P represents he perpendicular distance rom the center of resistance o the line of action.

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    Fig. 5. Type s of extra-oral anchorage. P, Parietal. 0, O ccipital. C, Cervical.

    If the line of action (T) passes through the center of resistance, P must be zero, in

    which case no tipping moment w ill occur. In other words, the line of action and the center

    of resistance of the tooth are in a straight line (Fig. 4, A).

    On the other hand, if the line of action is moved farther away (above or below) from

    the center of resistance of the tooth (Fig. 4,

    B

    and C), P is increased. Since M = T

    X

    P,

    the tipping moment is proportionately increased. Thus, the control of tipping force to a

    molar tooth

    based

    on the above principle is readily applicable.

    THE INCLINATION OF THE LINE OF ACTION.

    The inclination or steepness Ofthe line

    Of

    action can be varied and is dependent upon (1) The point of origin of the force and (2) The

    point of attachment of the force.

    The poinr of origin of the force is dependent upon the type of assembly that is used.

    The numerous extraoral assemblies available may be grouped conveniently into three

    major categories (Fig. 5): namely:

    Cervical: Anchorage obtained from the nape of the neck.

    Occipital: Anchorage obtained from the back of the head.

    Parietal: The upper part of the back of the head is used as anchorage.

    The point of attachm ent of the force is the hook on the outer bow of the extraoral

    assembly. In the sagittal plane the point of attachment of the force (outer bow hooks)

    could be located anteroposteriorly anywhere along the AP axis, where point A represents

    the point of attachment anteriorly of a short outer bow and point P represents the point of

    attachment posteriorly of a long outer bow (Fig. 6).

    Vertically, in the same sagittal rectangle, the location of the outer bow hook could

    extend anywhere along the V V, axis, where points V and V, represent vertical ex-

    tremities of points of attachment above and below the first molar teeth created by angulat-

    ing the outer arms of the face-bow.

    Theoretically, therefore, the points of attachment of a force (outer bow hooks) in the

    sagitta l plane could be located anywhere within the confines of a rectangle formed by the

    AP and V Vi axes.

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    ,1 ,I / Orrhod

    4rwrl 1979

    Fig. 6. Sagi ttal rectangle. Theoretically, the outer bow hooks could be located anywhere along the AP

    and VV, axes.

    The shape of the outer bow is of no consequence and has no effect on the applicat ion

    of force to molar teeth, provided the relationship of the point of attachment (outer bow

    hook) to the site of origin of the force remains unaltered, namely, D1 = D, (Fig. 7). This

    contention applies only if it is assumed that the arms of the headgear are rigid.

    The points of attachment of the outer bow hooks are variab le and may be altered to fit

    anywhere in the sagittal rectangle by (1) varying the length of the outer bow, (2) varying

    the angle between the inner and outer bows, and (3) varying the length and the angle of the

    outer bow.

    The inclination or steepness of the line of action is dependent upon the location of its

    points of origin and attachment. The location of the point of origin of the force is

    dependent upon the type of assembly that is being used, that is, whether it is cervical,

    occipital , or parietal. The point of attachment of the force must be located within the

    “sagittal rectangle” and is dependent upon the length of the outer bow and its angular

    relationship with that of the inner bow.

    Extrusive and intrusive force components. Essential in extraoral force application in

    orthodontics is a knowledge of whether the force during treatment is designed to intrude or

    extrude molar teeth.

    The determinant of whether the vertical force component upon a tooth is extrusive or

    intrusive is the location of the origin of the line of action. Should the origin of the line of

    action be below the center of resistance of the tooth, as in cervical traction, the most

    widely used type,’ an extrusive component of force will be present in its clinical appli-

    cations. Should the point of origin of the line of action be located above the center of

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    Fig.

    7. The shape of the outer bow is of no consequence and has no effect on force application to molar

    teeth, provided the distances of the points of attachm ent (0, and Or) to the midline axis are equal.

    resistance of a tooth, as in a parietal assembly, the vertical force component to the tooth

    will be intrusive.

    In occipital traction the point of origin of the force is more or less in line with the

    center of resistance of the molar. Under these circumstances, slight intrusive or extrusive

    vertical force components may result, depending upon whether the point of origin is

    slightly above or below the center of resistance of the tooth.

    The magnitude of the intrusive or extrusive vertical components is dependent upon the

    inclination or steepness of the line of action of the force. The steeper the line of action, the

    more intrusive or extrusive the vertical force component. Horizontal forces will neither

    intrude nor extrude molars. The inclination of the line of action of the force is determined

    by the point of attachment of the outer bow hook (and this, in turn, is determined by the

    type of extraoral assembly that is used) and the location of the point of attachment (outer

    bow hook of the face-bow). The location of the latter can be controlled by altering the

    length and angle of the outer bow to that of the inner.

    Translatory, crown, or root-tipping move men t. The translatory or bodily movement,

    or the crown or root-tipping effect upon the molar teeth of the various extraoral orthodon-

    tic appliances is dependent upon the relationsh ip of the line of action to the center of

    resistance of these teeth.

    If the line of action is in line with the center of resistance of the tooth, it will translate

    distally with no tipping effect to either crown or root.

    In a cervical type of assembly the point of orig in is fixed. The point of attachment, the

    outer bow hook of the face-bow, may be adjusted within the confines of the sagittal

    rectangle. In Fig. 8, the angle and length of the outer bow hook have been adjusted so that

    the line of action passes through the center of resistance of the tooth, in which case the

    tooth will translate distally.

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    Fig. 9. C, Cervical traction. Heavy stipplin g depicts distal crown tip. Light stipplin g depicts distal root tip.

    Fig. 10. Since the angles and lengths of the arms in the diagram are adjusted to be in line with the line of

    action, the molar teeth will move distally in a bodily manner. 0, Occipital traction.

    Fig. 11. 0, Occipital traction. Heavy stipplin g depicts distal crown tip. Light stipplin g depicts distal root

    tip.

    Fig. 12. Diagramm atic illustratio n of parietal type of extraoral assembly (P) acting o n outer bow hooks

    which are adjusted in length and angula tion to allow the line of action to pass through the center of

    resistance of the tooth, causing it to translate.

    Fig. 13. P, Pariet al traction. Heavy stipplin g depicts distal crown tip. Light stipplin g depicts distal root tip.

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    370 Jwohwt~

    t, 3

    B

    t

    c

    Fig. 14. Diagram to illustrate the principles of molar intrusion (or extrusion). t, Line of action of force. d,

    Distal force componen t. i, Intrusive force component. (Y, Ang le of line of action. obh, Outer bow hook.

    can be mathematically calculated. These effects on molars relate to the inclination or the

    steepness of the line of action of the force. In analyzing the force system, a parallelogram

    of force diagram is used. In Fig. 1.5, the force system is reduced to a right-angled triangle

    (ABC ) in which a is the adjacent side, o the opposite side, and h the hypotenuse. Angle CY

    is formed by the base of the triangle and the line of action of the force. The steeper the line

    of action of the force, the greater the angle CX.

    The classic formulas are:

    (1) Since= j+ arid(2) &sol=+

    The parallelogram of force diagram can be applied. The hypotenuse of the triangle is

    the line of action of the force T. The steepness of the line of action is measured in degrees

    (a). Lines D and I would be the adjacent and opposite s ides of the triangle and would

    represent the distal and intrusive (or extrusive when applicable) force components.

    Application of the formula would be as follows:

    A Sin cy= r

    T

    I = T Sin cy

    1. If T was constant, the magnitude of intrusion would be directly proportional to the Sin

    LY,viz., the steepnessor inclination of the line of action of the force.

    The extrusive

    component is directly related to the steepness f the line of action. The greater the angle

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    Fig. 15. Parall elogram of force diagram. o, Opposite side. h, Hypotenuse.

    a,

    Adjacent side. LY, Angle of

    line of action. I, Intrusive force com ponent. T, Line of action of force. D, Distal force co mponent.

    Fig. 16. Intrusive force in a coronal plane acting on the buccal tube of a molar, causing it to “roll.” C,

    Center of resistance of tooth. P, Perpendicul ar distance of buccal tube to center of resistance line.

    or the steeper he inclination of the line of action, the greater the extrusive effect on the

    tooth.

    2. If angle cywas constant, I would be directly proportional to T. In other words, if the

    angle of the line of action of the force was constant, the magnitude of the intrusive force

    I would be directly proportional to the magnitude of the applied force.

    In sum, therefore, the amount of distal or intrusive (or extrusive) force that i s clin ically

    applied to molars with the use of extraora l appliances is dependent upon the steepness of

    the line of action of the extraoral force. The steeper the line of action, the greater the

    intrusive (or extrusive) force. A horizontal line of action exerts maximal distal force to

    molars with no extrusive or intrusive force. As the line of action steepens, so do the

    extrusive or intrusive forces at the expense of reducing the dista l force component to the

    molars.

    Coronal plane

    In the coronal plane, molar teeth can be moved vertically (intruded or extruded) and/or

    laterally or medially.

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    Fig. 17. Pala tal bar soldered to molar bands wil l cause teeth to intrude bodily on intrusive force

    application.

    Extrusion or intrusion. If the origin of the line of action of the force is located above

    the center of resistance, as in parietal headgear, the effect on the molar wi ll be to intrude

    it. Locating the origin of the line of action below the center of resistance of a tooth, as in

    cervical gear, will tend to extrude the tooth.

    The inner bow of the extraoral appliance fits snugly into the buccal tube of the molar

    tooth. This means that the line of action does not pass through the center of resistance of

    the tooth which is located somewhere along i ts midline between the root apex and the

    alveolar crest (Fig. 16). Since the line of action of the force during intrusion or extrusion

    passes buccally to the center of resistance of the molars, these teeth will tend to “roll.”

    The crowns of these teeth will rotate bucca lly (and the roots lingually) during intrusion

    and palatally (and the roots bucca lly) during extrusion. The moment, or rotation effect, is

    dependent upon the perpendicular distance of the buccal tube to the center of resistance.

    Clinica lly, this distance, albeit small, will cause molars to “roll” during extended periods

    of extrusive or intrusive activity, particularly if the line of action of the force is steep.

    Soldering a palatal bar to the lingual aspect of both molars can obviate this effect. This

    will cause both teeth to translate vertically with intrusive or extrusive force application

    (Fig. 17).

    Lateral or medial action. Lateral movement of both molars can be achieved by

    expanding the inner bow of the face-bow and inserting its end in the buccal tubes of the

    molars. Medial movements can be simi larly achieved by contracting the inner arch of the

    face-bow.

    Since the buccal tubes of the molars are located below the center of resistance of the

    teeth, any expansion or contraction of the inner arch of the face-bow wi ll cause the crowns

    of these teeth to tip buccally or palatally, respectively, and their roots to move in the

    opposite direction to the crowns (Fig. 18). Since the ends of the inner arch of face-bows

    are round and these, in turn, are inserted into round tubes, molar teeth can only be tipped

    bucca lly or palatally by means of headgear. Translatory buccal or palatal movements of

    molars using only headgear could be achieved if square, rectangular, or ovoid arches were

    slotted into similarly shaped buccal tubes.

    Transverse plane

    In the transverse plane teeth can be moved distally and/or medially or laterally. Since

    round tubes on molar teeth snugly receive the distal ends of the inner arch of headgear,

    these teeth are prevented from rotating in the transverse plane with any force application to

    the face-bow. Expansion or contraction of the inner arch of the face-bow wi ll translate the

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    Contract ion

    Fig. 18. Buccal or ling ual crown tip in the coronal plane caused by expansion or contraction of inner

    arch of face-bow. C, Center of resistance. P, Perpendicul ar distance of buccal tube to center of

    resistance of tooth.

    crowns of the molars laterally or medially, respectively, in this plane (but not necessarily

    in the coronal plane). Likewise, the long tubes which receive the inner arch of the

    face-bow cause it to act as a fixed unit, thereby obviating any rotation effect or moment to

    molars on distal force application.

    In other words, dista l or lateral force application to molar teeth with conventional

    extraoral face-bows wil l cause these teeth to translate distally and/or medially and later-

    ally in the transverse plane. The force application to the molars is generally of the same

    magnitude if symmetrical extraoral assemblies are used. However, there are many clin ical

    situations which require a greater force delivery on one side of the arch. In these instances,

    face-bows of the asymmetric or unilateral type are used.

    Unilateral face-bows

    To achieve asymmetric molar force delivery to molar teeth, various face-bows have

    been designed, many of which have been mathematically shown to be effective.“, ‘I In

    computing the effects of extraoral forces by mathematical means, many variables have

    had to be ignored. Among these are the indeterminate characteristics of bone and teeth,

    both of which exhibit a certain amount of flexibility. Add to this the flexibilities of the

    geometry of the face-bow which cause the line of action to vary with the amount of pull

    and degree of flexibility of the material. Together, these produce a myriad of variables

    which make the practicability of computing the results of force application to molar teeth

    in three planes of space by mathematical means almost impossible.

    Because of these inherent difficulties and interpretations in calculating molar forces, it

    was deemed desirable to design and construct a mechanical device which would measure

    the magnitude and direction of the forces transmitted to the molars by various extraoral

    face-bows.

    Method and materials

    To test mechanically the effect of various extraoral appliances on molars in a trans-

    verse plane, a model comprising a number of “frictionless” pulleys located between two

    sheets of inch acry lic plastic was constructed (Figs. 19 and 20). The pulley system was

    designed to measure the various force applications to the outer and inner bows of the

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    Fig. 19. Mod el of device used to mechanical ly test effects of force applic ation to various face-bows

    (see text).

    headgear appliance by attaching aluminum containers which

    could

    be weighted by adding

    lead shot. Dental handpiece ballbearing assemblies were used in the construction of the

    pulley wheels to minimize friction.

    The ends of the inner arch of the extraora l appliance were accurately fitted into s lots

    drilled into two L-shaped flat pieces of acry lic plastic. The two free-floating pieces of

    acryl ic plastic represented the left and right molar teeth, ML and MR. Fig. 21 presents a

    diagrammatic representation of the pulley principle of the apparatus.

    Equally weighted containers A and A, were attached to the outer bow hooks of the

    headgear appliance. These weights represented the extraoral force application of

    headgear. The effect of adding weights to the outer bow of the headgear would be to move

    “molars” ML and MR vertically downward.

    To counteract the downward movement of “molars” ML and MR, containers 5 and B 1

    were loaded with lead shot.

    Since pulley friction was minimal in a symmetrical type of face-bow, it was antici-

    pated that weights A and AI and B and B r would be of equal magnitude. In effect, the total

    force application to the outer bow would be transmitted via the solder joint to the inner

    bow and to the molars.

    In an effort to determine whether any lateral displacing forces on molar teeth are

    introduced with the use of headgear, two additional pulley systems were added to each

    molar attachment ML and MR (Fig . 22). The amount of lateral or medial displacement

    could be measured by loading the appropriate receptacles with lead shot. For example, if

    the effect of the force application to the outer bow was to move ML latera lly, receptacle R

    would drop downward and Q would be elevated. To counteract this lateral force, lead shot

    could be added and the amount of weight measured to receptable Q until ML was in its

    original position and balanced. The medial and lateral forces on MR may be simi larly

    measured by loading receptacles S and T.

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    Fig.

    20. Pulleys N and N, adjusted to simul ate line of action of force from outer bow hooks to tangent to

    back of neck. W ithout the additi on of these pulleys, the line of action would be vertical.

    Finally, to simulate the direction of pull of the elas tic traction from the outer bow

    hooks to the back of the neck, pulleys N and N, were added to the apparatus. Without the

    addition of these pulleys, the traction forces (line of action) would always be vertical and

    not tangent to the back of the neck (Fig. 20).

    Findings

    1. The first exercise involved determining whether a force applied to the outer bow of

    a symmetrical headgear could exert an expansion force in the molar region of the inner

    bow. The possib ility of obtaining a lateral force is based on the premise that if relatively

    lightweight legs supporting a heavy body or weight (W) were parallel, no lateral forces or

    widening effect of the legs on a flat surface would be produced (F ig. 23 A). However, if

    the legs were divergent as in B, they would tend to splay. The more divergent the legs, the

    greater the splaying effect. On the other hand, if the legs were rigid as in diagram C, they

    would not splay with weight application in spite of being divergent.

    Two symmetric headgears were tested, the first having a narrow inner arch with more

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    Fig. 21. Diagram matic representation of distal force pulley system. A and A,, Force applic ation to outer

    bow hooks. ML and MR, Left and right “molar teeth.” B and B,, Containers for lead shot required to

    counteract force applica tion to A and A,,

    or less parallel distal ends and the second having a wide inner arch with divergent distal

    ends. The inner bows were contoured to conform to dental arches which would be

    considered as being particularly narrow and wide, respectively.

    Face-bows in which the anterior section of the inner arches were stiffened or rein-

    forced by the addition of tubing or constructed of thicker material showed no discernible

    molar expansion with the application of up to 3 pounds of force on either side. This

    finding applied to both wide and narrow inner arches.

    Inner arches constructed from uniform 0.045 inch (diameter) steel evinced consider-

    able expansion or lateral forces in the molar region, particularly in the wide arch. Fortu-

    nately, inner arches of commercially marketed face-bows now usually are reinforced

    anteriorly, making them adequately rigid.

    2. The next exercise entailed testing

    a face-bow

    in which the solder joint was offset.

    The face-bow was designed to exert more distal molar force on the side of the solder joint.

    On applying a force of 16 ounces on each side to the outer bow hooks, the forces

    transmitted to the molars were 18 ounces on the side of the solder joint and 14

    ounces

    on

    the opposite side (Fig. 24).

    The 4 ounce discrepancy in the molar reading is ascribed to the flexibility of the outer

    bow arms and not to the offset solder joint. This is not shown here. Theoretically, if the

    outer bow arms were constructed of a rigid, nonyielding material, the forces to the molar

    teeth in this type of headgear would be ident ical to that of a symmetric type.

    The rationale of the unequal force d istribution to the molars relates to the distance of

    the

    outer

    bow hooks to the midsagittal plane. In the model tested, the distance between the

    outer bow hooks to the midsagittal plane in a nonstressed face-bow was 70 mm. on each

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    Fig. 22. Diagram to illustrate method of measuring lateral forces to “molars.” Q, Med ial force to left

    molar (ML). R, Lateral force to left molar (ML). S, Med ial force to right molar (MR). T, Lateral force to

    right molar (MR).

    Fig. 23. A, Para llel l ightw eight legs supporting heavy body (W). B, Divergent lightw eight legs splaying

    under the effect of weight of a body (W). C, Rigi d divergent legs exhibit no splaying effect with weight

    application.

    side. On applying forces (weights) to the outer bow hooks and counterbalancing there, the

    distance of the outer bow hooks (A and B) to the midsagittal plane was reduced to 69 and

    65 mm., respectively. The flexibility of the longer arm allowed the outer bow hook on that

    side to be located nearer the midline (midsagittal plane), thus reducing the force on the

    molar on that side. What determines the different dista l molar forces is the line of action of

    the force to the outer bow hook. This is discussed later. As you can see in comparing Figs.

    24 and 25, we are not incorporating the neck pad shift that might occur in a patient.

    3. The next test entailed measuring the forces upon molars using a symmetrically

    soldered outer bow, the arms of which were of different lengths. The second part of this

    experiment involved bending the longer arm away from the contour of the cheek and

    measuring the effect of applying extraoral force to these hooks in this manner.

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    Fig. 24. Testing o f face-bow with offset solder joint. No te flexibil ity o f arm on side opposite solder joint.

    (See text.)

    On applying a force of 16 ounces on each side to the outer bow hooks, it was found

    that forces of 8 ounces and 24 ounces were transferred to the molars of the shorter and

    longer sides, respectively. This configuration introduced considerable lateral force on both

    molars. When the longer arm was extended away from the cheek, it was found that an

    even stronger lateral force component was introduced. The amount of lateral force re-

    quired to counterbalance the outer bow force was 5 ounces on each side, a total of 10

    ounces (Fig. 25).

    The lateral force component cannot be disregarded in clinica l procedures. This com-

    ponent is dependent upon the direction of pull of the line of action of the force (the elas tic

    stretching between the outer bow hook on the longer arm and the point of attachment) of

    the neck and headgear assembly. The amount of dista l or lateral forces on the molars does

    depend on the lengths of the outer arms of the headgear. It i s dependent on the angulation

    of the line of action of the force from the outer bow hooks. If the outer bow arms were of

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    5

    -I

    24

    Fig. 25. Testing of face-bow with sym me tricalty soldered joint but with arms of different lengths. In one

    experiment the longer arm was bent outward. (See text for findings.)

    different lengths, but the line of action of the forces (elastic traction) on either side were

    paral lel (Fig. 26), the force application to the molars would be the same. Bending the

    larger arm outward locates the outer bow hook laterally. The origin of the line of action of

    the force is thus moved outward. From here the line of action of the force is directed

    toward a tangent to the back of the patient’s neck (Fig. 25). The line of action on the

    longer arm side is thus considerably angulated, whereas the line of action of the short arm

    side is minimally angulated as it passes toward the back of the neck.

    If the line of action of the extraoral force to the outer bows (the line of traction of the

    elastics of the extraoral assembly) was parallel to the midsagittal plane, its angulation

    would be 0 degrees to this plane. Angulating the line of action of the force (by bending the

    other bow laterally) increases the molar force on that side, but it also introduces a lateral

    component. If the angulation of the elas tic pull (line of action) was 30 degrees, the amount

    of lateral force exerted on the molar on that side would be reduced by as much as 50 per-

    cent of the total force. If the line of action were reduced to 20 degrees, the amount of force

    on the molar would be 34 percent of the total pull on that side. The amount of force to the

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    i

    c6

    Fig. 26. Illustration to show that if the outer bow arms were of different lengths, but the line of action of

    the forces on the outer bow hooks was parallel, the force applica tion to the molars would be the same

    on either side.

    Table I. Relation of reduction in magnitude of total molar tooth force to angle of line

    of action of face-bow

    Angle of l i ne of action to midl in e axis

    (degrees)

    I

    Percentage reduct ion of total distal force

    to molar

    0 0

    10 17

    15 26

    20 34

    25 42

    30 50

    molars can be mathematically computed by relating it to the angle of the line of force to

    the midline axis . Table I relates the amount of force to the molar relative to the line of

    action.

    In its clinical application, lengthening the arm of a symmetrical face-bow within

    certain limits will increase the force application to the molar tooth on that side. Consider-

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    Fig. 27. A swivel asymmetric type of extraoral face-bow of excellent design (insert), permit ting move-

    ment only in the transverse plane. Outer bow arms are of different lengths.

    able reduction in length of the one arm of the face-bow and some lengthening of the other

    wi ll introduce a difference in the line of action of the extraoral forces on both sides. The

    effect w ill be much the same as bending one arm of the face-bow outward. The effect is

    that of increasing the force to the molar tooth on the side of the lengthened or laterally bent

    arm. Accompanying angulated extraoral line-of-force actions is the lateral force compo-

    nent which has been shown to be quite considerable.

    A mild expansion of the inner bow of the appliance will counteract the lateral force

    component on the lengthened side and increase the lateral force on the molar tooth of the

    opposite side. This could be useful for correction of specific cross-bites. Contracting the

    inner bow wi ll have exactly the opposite effect. There is no way that the lateral forces on

    both molars can be neutralized with the use of th is type of headgear.

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    Fig. 28. The effects on the molar teeth on force applica tion to the swivel type of face-bow shown in

    Fig. 27. (See text.)

    4. The swivel type of unilateral extraoral face-bow tested provided the most satisfac-

    tory unilateral force delivery without the usual accompanying lateral components to both

    molars. The swivel arrangement comprised a heavy outer bow with a soldered extension

    having a vertical pivot section fitting into a vertical tube soldered asymmetrically to the

    inner arch of the face-bow (Fig. 27). The particular swivel arrangement was good in that

    the appliance permitted movement in only the horizontal plane of space. Flexibility in the

    other plane of space was reduced to a minimum by the rigid ity of the material from which

    the face-bow was constructed.

    An application of 16 ounces of force to either s ide of the outer bow hooks delivered 25

    ounces of force to the molar in the swivel side and only 8 ounces to the opposite molar.

    Unfortunately, on the face-bow tested, the inner bow was not reinforced anter iorly, in

    which case a total expansion force of 10 ounces was delivered to the molars on loading of

    the outer bow hooks with a 16 ounce weight on each side.

    The design of the face-bow is such that the outer arm on the swivel side is considerably

    shorter than that of the opposite side. The applica tion of 16 ounces of force on each of the

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    .Jtrc~ohso~,

    opposite the swivel to bend too far inward. The bending would cause the arm to impinge

    upon the cheek of the patient during the application of force. Thus, the manufacturer’s

    method of compensating for th is (by lengthening the arm on the swivel s ide) was emi-

    nently satisfactory. It was believed that stiffening the inner bow of the face-bow anteriorly

    would have added to the effic iency of the design of the appliance.

    5. Three additional asymmetric face-bow designs were tested (Fig. 29).

    In design A, a fairly heavy bar was soldered eccentr ically to the inner arch and

    centrically on the outer bow. The effect of loading the outer bow was that the outer arm on

    the side opposite the solder joint was more flexible (because of the added length of the bar)

    and consequently became positioned closer to the midline axis . The effect of this was the

    introduction of a lateral force component to the molars because of the line of action of the

    elastic traction.

    Designs B and C proved unsatisfactory, inasmuch as the swivel and helix types of

    attachment were too flexible and allowed movement in three planes of space in force

    application to the face-bow.

    6. The final experiment was designed to test the claim that an open coil spring slid on

    the inner arch of a symmetric type of face-bow immediately ahead of one or another of the

    molar teeth would produce a unilatera l dista l force on that molar.

    On application of 16 ounces of force to each of the outer bow hooks, the measured

    force to the molars proved to be identical to the force applied to the outer bow of the

    face-bow (in this instance, 16 ounces to each molar). On complete compression of the coil

    spring, the compressed coil acts as a solid unit. On partial compression of the coil spring,

    the force required to partially compress the coil is balanced by the same amount of force as

    the tension to the outer bow hooks of the face-bow. The mechanics of the appliance

    clearly illustrate that coil springs applied unilaterally to the inner arch of a face-bow

    cannot effect unilateral distal forces to molar teeth.

    Discussion

    Awareness of the intrusive or extrusive effect on molars cannot be, and has not been,

    overlooked by clinicians.

    ‘3 -‘. ‘. lo, ii The key to the appreciation of the effects on molar

    teeth of the numerous extraoral neck- and headgear appliances marketed is the understand-

    ing of the relationship of the line of action of a force to the center of resistance of a tooth.

    The center of resistance of a tooth is fixed. The line of action of an extraoral force is

    variable and is dependent upon the locations of the outer bow and head- or neckgear

    assembly hooks and not the point of attachment. The inclination of this line of action to

    the center of resistance of the molars must be analyzed in three planes of space.

    In analyzing the effects on the molars of the various symmetric types of extraoral

    assembly, it is found that certain generalities are pervasive.

    Occipital headgears will tend to intrude molars,

    whereas cervical assemblies will

    extrude these teeth. The degree of intrusion or extrusion is dependent upon the inclination

    of the line of action of the force; the steeper the inclination, the greater the intruding or

    extruding effect. Tipping root or crown movements are readily controlled if the principle

    of relating the line of action to the center of resistance of the molars is borne in mind.

    Application of maximum distal force to molar teeth with minimal intrusion or extru-

    sion is achieved with the use of horizontal-pull extraoral assemblies.

    “Rolling” of molars due to the application of intrusive or extrusive orthodontic forces

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    may be prevented by connecting the two molar bands with a palatal bar. Soldering a

    palatal bar to the molars will thus cause these teeth to translate vertical ly rather than to

    roll.

    Inner arches of face-bows of 0.045 inch (1.143 mm.) and less wi ll cause molars to

    expand laterally on force application. Fortunately, most commercially available face-

    bows have inner arches which are reinforced anteriorly and prevent this from occurring.

    The various eccentric or asymmetric face-bows have been designed to effect unilateral

    molar movements. The various designs may be divided conveniently into two basic types,

    the fixed and the swivel type, in which the inner and outer arches of the face-bows are

    either soldered together or attached by means of a swivel or free-moving attachment.

    Haack and Weinstein5 mathematically computed that no matter where the rigid at-

    tachment of face-bow to arch wire is placed, as long as the applied forces on the cervical

    region are symmetric with respect to the midsagittal plane, the reactionary forces on both

    right and left molars should be equal. Th is report did show a discrepancy of 4 ounces from

    side to side. To obtain rigidity, they advocate an outer bow wire 0.075 inch (1.905 mm.)

    in diameter since this would be five times as still as a 0.050 inch (1.270 mm.) wire. I agree

    with this contention, particularly since they stress a rigid outer bow. The ultimate deter-

    minant of molar force application is dependent upon the relationship of the outer bow

    hooks to the midline axis. Unless the outer bow is constructed from extremely rigid metal,

    the outer bow opposite the solder joint is usually more flexible (being longer), in which

    case the outer bow hook tends to be pulled closer toward the midsagittal plane. In clinical

    pract ice the longer arm is frequently bent outward to compensate for its flex ibil ity, but, on

    application of traction, the force to the molars tends to be ident ical in spite of the

    asymmetrically soldered inner and outer bows.

    Haack and Weinstein5 used strain gauges to demonstrate that the force exerted on the

    molar on the side of a long face-bow arm is considerably greater than the force exerted on

    the side of the short face-bow arm. Oosthuizen and associates” illustrated mathematically

    that asymmetric force de livery is achieved by lengthening the one outer arm of the

    face-bow.

    These researchers were aware of the lateral forces on the molars on application of this

    type of face-bow design. Whereas extending one arm laterally or lengthening it does

    increase the distal force to the molar on that side, it also introduces a lateral force which

    cannot be ignored in clinical situations. The relative force delivered to each side is

    dependent upon the angulation of the line of action to the midline axis ; the greater the

    angle, the greater the lateral force component.

    The most effective extraoral face-bow design encountered for effecting a unilateral

    distal movement of a molar is that of the swivel-type attachment. The outer arms are of

    unequal length and the swivel arrangement is rigid, allowing movement in only one plane

    of space. The flex ibil ity and leverage of the arms are such that the lines of action to the

    midline axis on both sides are more or less equal on application of traction. The force

    delivery to the molar on the swive l side is directed primar ily distally with a minimal lateral

    component.

    Summary

    By following certain basic principles, the effects, advantages, and disadvantages of

    the wide assortment of extraoral assemblies marketed are easily understood. The key to

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    this understanding is the appreciation of the relationship of the

    line of action of the force

    application to the center of resistance of the tooth.

    These principles are discussed in three planes of space: sagittal, coronal, and trans-

    verse.

    Because

    of the many

    variables

    and complexity of mathematically computing the

    force effects of unilateral or asymmetric extraoral assemblies on molar teeth, a mechanical

    testing apparatus was designed to accommodate the various face-bows. Not all the designs

    proved effective, and many of the clinical

    side

    effects of the respective

    face-bow

    designs

    became manifest on mechanical testing.

    I would like to express my gratitude to Dr. P. L. Sadowsky. Assistant

    Professor

    n Orthodontics

    at the University of Alab ama Schoo l o f Dentistry. whose assistance in the mechanic al testing of the

    various face-bows is greatly appreciated. My thanks also to the UAB Orthodontic Alu mn i members

    and the Southern Society of Orthodontists who contributed to the UAB Orthodontic Research Fund

    which was responsible for financing the construction of the testing apparatus and the photography.

    REFERENCES

    1. Armstrong, M. A.: Control ling the magn itude, direction and duration of extraoral force,

    AM. J. OKTHOD.

    59: 217-243, 1971.

    2. Burstone, C. J.: The biomechanics of tooth movement. In Kraus, B. S., and Riede l. R. A. (editor): Vistas

    in Orthodontics, Philadelphi a, 1962, Lea & Febiger, pp. 197-213.

    3. Gould 1. E.: Mechanic al principles in extra-oral anchorage, AM. J. ORTHOD. 43: 319-333. 1957.

    4. Greenspan, R. A.: Reference charts for controlled extra-oral force to maxillary molars, AM. J. ORPHOD. 58:

    486.491, 1970.

    5. Haack, D. C., and Weinstein, S.: The mechanics of centric and eccentric cervical tractions.

    AM. J.

    ORTHOD. 44: 346-357, 1958.

    6. Haaa, A. J.: Pala tal expansion: Just the begin ning of dentofacial orthopedics,

    AM. J. ORTHOD. 57: 219-255,

    1970.

    7. Huettner, R. J., and Young , R. W.: Movabil ity of vital and devitalized teeth, AM. J. ORTHOD. 41: 601-602,

    1955.

    8. Kloeh n, S. J.: An appraisal of the results of treatment of Class II malocclusio n with extra-oral forces. In

    Kraus, B. S., and Riede l, R. A. (editors): Vistas in orthodontics. Phil adel phia, 1962. Lea & Febiger, pp.

    227-258.

    9. Massler, M.: Changes in lamina dura during tooth movement,

    AM. J. ORTHOD. 40: 369, 1954.

    10. Merrifiel d, L. L., and Cross, .I. J.: Directional forces,

    AM. J. ORTHOD. 57: 435-475, lY70.

    1 I. Oosthuizen, L., Dijkm an, J. F. P., and Evans. W. G.: A mechanic al appraisal of the Kloe hn extra-oral

    assembly. Ang le Orthod. 43: 221-232, 1973.

    12. Oppenhe im, A. I.: Biol ogic orthodontic therapy and reality, Angl e Orthod. 6: 77-81, 1936.

    13. Thurow, R. C.: Perio dontal memb rane in function, Ang le Orthod. 15: 20, 1975.

    I919 7th AIY. South (35294)