Unilateral Cervical Traction With A KloehnExtraoral MechanismE. W. DRENKER, D. D. S., M. S. D.Twin Falls, IdahoThere exis@ a lack of understandingregarding the production of unilateralcervical traction with a Kloehn extra-oral mechanism. The present methodof offsetting the joint between the ex-traoral and oral bows is not theoretic-ally correct unless the joint is a knife-edge. In the following material twosteps are presented which can be utiliz-ed to achieve unilateral action. Thesesteps do not involve changes in thelocation of the joint between the twobows. Instead, the aim is to alter thepositions of the lines of action of theapplied forces so that the line of ac-tion of the resultant lies closer to themolar against which greater force ac-tion is desired.Figure 1 represents a plan view ofa Kloehn mechanism. Points m and nof the oral bow are inserted into buccaltubes attached to the upper first molars.Points j and k serve as attachments foran elastic cervical strap which sup-Fig. 1, Plan view of 3 Kloehn extraoralmechanism. Points m and n enter buccaltubes. A cervical elastic strap is attachedto points j and X..plies the force for tooth movement.The arrows are vectors which signifythe magnitudes and directions of theapplied forces acting in the plane ofthe mechanism. The T vectors repre-sent the pull of the cervical strap and,since this strap is continuous, theforces at j and k are equal in magni-tude. Vectors FL and FR represent thereactive forces exerted by the buccaltubes against the oral bow. Since ac-tion and reaction are equal, the oralbow exerts Fr, and FR against the buc-cal tubes and through these against themolars. If the molars are tied to theother teeth of the maxillary arch, theentire arch is, of course, subjected toFL and FR.To illustrate the system of forces ac-tive in cervical traction, it becomesnecessary to write general mathematicalexpressions of the physical conditionswhich must be satisfied to producestatic equilibrium of the appliance.One of these physical conditions is thatthe sum of the forces parallel to FLand FR must be zero. This is justanother way of stating that the forcesmust be in balance. Thus from Figure1: FL +FH - 2T cos e = 0A second physical condition to be metis that the sum of the moments of theforces about any point in the planeof the forces must be zero. It may beremembered that a moment of a forceis the product of the magnitude of theforce and the perpendicular distancefrom a given point to the line of actionof the force. In symbols, taking1.201 202DrenkerOctober, 1959moments about point tn :2.FR X B + T COS 0 X A 4- Tsin e X C-TcoseX (A+B) -Tsin e x C = 0When these equations aresolvediimul-taneously for the two unknown quan-tities, FL and FR, it will be found thatFL = Fa. This result is in keepingwith the common experience that asymmetrical system of forces producesuniform force action against the buccaltubes. It may seem unnecessary toutilize equations 1 and 2 to arrive atthis simple conclusion; however, theseequations are important because theyshow which physical quantities affectthe action of the appliance.A mathematical background is notneeded to recognize the quantities inequations 1 and 2. Forces T, FL andFR are present as are dimensions A, Band C. Also of importance is the direc-tion of T with respect to the sagittalplane (forces FL and FR are assumedto be parallel to the sagittal plane). Thelocationof the joint at 0, on the otherhand, does not enter into either equa-tion. This joint is invariably soldered,welded, or banded and it must be con-sidered as being rigid. Even when thisjoint consists of a pin and tube, it re-sists bending in the plane of the ap-pliance. Since this joint is rigid, itdoes not represent a point where ex-ternal forces are applied. In otherwords the extraoral and oral bows com-prise a single unit and the location ofthe union between them has no sig-nificance as far as external force ac-tion is concerned. It is well knownin mechanics that the external effectsof a force on a body are not influencedby the shape of the body. In any forcesystem attention must be focused onthe magnitudes of the forces, on thepositions of the lines of action of theforces and on the directions of theforces along their respective lines ofFig. 2, The joint at 0 between the oraland extraoral bows has been offset to theleft from its central position shown inFig. 1.action. The performance of any ap-pliance is governed by these character-istics and not by appliance configura-tions as such.As an example of the above prin-ciples reference is made to Figure 2.Here the shape of the appliance hasbeen changed by offsetting the joint tothe left of its original central position.This is the technique commonly usedwith the intention of increasing theload against one buccal tube while de-creasing the load against the other. Inshort, unilateral action is supposed tobe established. Inspection of Fig. 2,however, will reveal that this pro-cedure has not altered any of the linesof action, directions or magnitudes ofthe applied forces. Equilibrium equa-tions for this appliance would beexactly as before with the result thatFL and FR must be equal. Thus, off-setting the soldered joint is not theroad to unilateral action because thisdoes not change the relationship be-tween the applied and the reactiveforces. An offset would work if therigid joint were replaced by a knife-edge type of connection so that notorque or bending moment could betransmitted through 0. In that case0 becomes a point at which an ex-ternal force is applied. Obviously, itwould be impossible to utilize a knife- Vol. 29, No. 4Cervical Traction203edge connection between the extraoraland oral bows in clinical orthodontics.The above principles suggest amethod by which the reactions FL andFR could be made unequal. For ex-ample, if it is desired to subject theright buccal tube to a greater forcethan the left, some way must be foundto bring the line of action of the re-sultant of the T forces closer to theright than to the left tube. The re-sultant of the T forces is the singleforce having the same external effect asthe two T forces.Fig. 3, Point k haa been displaced laterallyto the right an amount E. The angles be-tween the cervical strap and the sagittalplane are no longer equal on both sides.To displace the line of action of theresultant to the right, it is necessaryto displace the lines of action of the Tforces to the right. Because of physicallimitations it is not possible to displacej to the right, but it is feasible to do sowith k. This has been done in Figure3 where k has been moved laterally tothe right an amount E. The solutionof appropriate equilibrium equationswill show that this step will increaseFR by an amount approximately pro-portional to T X E and decrease FLby a similar amount. If E could bemadc large enough, total unilateral ac-tion could be realized by this stepalone. Unfortunately, it is seldom pos-sible to increase E beyond a value ofabout three fourths of an inch becauseof the likelihood that the applianceE0Fig. 4, The right; arm of the mechanismhas been lengthened an amount D relativeto the left arm. Point k is displaced to theright an amount E.will be dislodged during sleep. Thislimitation requires the introduction ofa second step, first used at the Univer-sity of Nebraska,' which is shown inFigure 4. Here the right arm of theface bow has been lengthened by anamount D. Such lengthening has theeffect of rotating the resultant clock-wise thereby bringing its line of ac-tion even closer to the right buccaltube. Equilibrium equations based onFigure 4 give the following:~.FR = T COS e, x (B + A + E) BT sin e, x (C + D) B- TcosexA-TsinexC+B B4. FL = T (COS e + COS e,) - FRNow, if numerical values are substi-tuted for A, B, C, D, E, T and 8, themagnitudes of FL and FR can be cal-culated. Averages of a large numberof measurements based on appliances inuse can be used for typical values ofthe above quantities. With the inch asa unit of length and letting A = 13/8,B = 254, C = 54, D = 13/4, E= 3/4, 8 = zero degrees, e! = 48degrees, and T = 1 pound, it willbe found that FR equals approximately1.4 lbs. and Fr, equals about 0.3 lbs. 204 Drenker October, 1959Thus, under these conditions the rightbuccal tube receives more than fourand one half times the load received bythe left buccal tube. Further increasesin D and E would continue to increaseFR and decrease FL. Finally a pointwill be reached where FR representsall of the distally directed force. Infact, if D and E are made too large,the appliance will be pulled out of theleft buccal tube since the left reactionmust become negative. In this case theline of action of the resultant lies to theright of the right buccal tube.If Figures 3 and 4 are re-examined,lateral forces HL and HR will be ob-served which do not appear in Figures1 and 2. These forces are introducedby the inequality of angles 0, e,, ande,. As soon as D and E appear, thecervical strap no longer makes equalangles with the sagittal plane on theright and left sides. Plainly, T sin 0does not equal T sin 0, or T sin8,. The SUE ~f HL and HE m-i-irt equalthe difference between T sin 0,and T sin e or T sin 8, and T sin8. HL and Ha are generally undesir-able except in the case where an ap-propriate crossbite is to be correctedsimultaneously.DISCUSSIONIn actual practice it is exceedinglydifficult, if not impossible, to rationallydesign an appliance so that in a givencase the total distally directed forceis placed on one or the other molar.Fortunately, it is not necessary to workwith exact forces in orthodontics and,'without this restriction, it is relativelysimple to incorporate dimensions D andE, consistent with the geometry of theface and tolerance of the patient, tocreate useful unilateral action. Ex-perience has shown that the maxillaryteeth on one side of the arch can beeffectively retracted through the useof this method.Frequently the patient will fail toverify unilateral action. There may beseveral reasons for this. One of themost common causes is that frictionbetween the elastic neck strap and theneck temporarily offsets the equality ofthe applied forces at j and k. This iseasily overcome by several movementsof the head from side to side or byrunning a finger between the strap andneck. Another cause can be traced toexcessive flexibility of the face bowwhich permits the final or seated valuesof A, C, D, and E to become differentfrom the desired or planned values.It should be emphasized that dimen-sions A, D, and E are seated dimen-sions and represent distances when theappliance is being subjected to ex-ternal forces. Usually the flexibility ofthe appliance is such that these dimen-sions are somewhat altered when theappliance is changed from the passiveto the active state. To minimize errorllUlll LlU3 DUUILC, L11G UbG VI ldlge u1-ameter wire for the extraoral bow isrecommended. Finally, binding be-tween the appliance and the buccaltubes can lead to unpredictable re-sults. Such binding adds forces notshown in Figures 1 to 4 and theseforces may either increase or decreasethe unilateral effect depending on theirdirections. It is essential that the ap-pliance fits passively into the buccaltubes to avoid the introduction of theseforces or couples.The above precautions hold also forsymmetrical cervical traction. Any oneor combination of these factors canproduce partial unilateral action whenit is not wanted. Usually the patientwill voluntarily state that he doesn'tfeel any pressure on one side or theother. A check for neck friction, lackof symmetry of the lines of action ofthe applied forces with respect to thedental arch because of excessive flex-ibility of the appliance, and bindingI.--- SL:" *L.. _.-_ -I 1 3: Vol. 29. No. 4 Cervical Traction 205within the tubes will probably locatethe reason for the non-uniform action. SUMMARYA method for establishing unilateralcervical traction with a Kloehn-type ofextraoral mechanism has been describ-ed. This involves the lateral displace-ment and lengthening of the arm ofthe face bow on the strong side relativeto the arm on the weak side. Theamount of this lateral displacementand lengthening will vary from caseto case depending on the facial dimen-sions, tolerance of the patient and theamount of unilateral action want-ed. Total or very nearly total unilateralaction can be created, in the averagecase, when the lateral displacement isabout three fourths of an inch andwhen the strong arm of the face bowis about two inches longer than theweak arm. These dimensions pertainto the active state of the appliance.Although this technique is quite ef-fective in producing unilateral distalforces, it has the disadvantage of simul-taneously subjecting the dental arch toside or lateral forces. These would beuseful only in certain crossbite cases.Study of unilateral action with theKloehn extraoral mechanism alsothrows light on some of the reasonswhy unequal forces are sometimes ex-perienced when uniform bilateral ac-tion is actually wanted. If the patientfails to vedy the type of action de-sired, a check should be made to seethat the appljance fits freely into thebuccal tubes, that the appliance is notdeformed excessively when it is seatedand that the forces provided by theneck strap are not temporarily un-balanced due to frictional forces be-tween the strap and the neck.11 1 Shoshom St., N.1.BIBLIWWHYHaagk, D. C. and Weinstein, 5.: TheMeclianics of Centrio and EccentricUervical Traction, Anter. J. of Ortho.,Vol. 44, May 1958.