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O R I G I N A L A R T I C L E

On b r acket slo t he igh t : A m ethodo log ic s tu dy

Tors t e in R . Me l ing , M D , a J a n ~ d e g a a r d , B D S , M S , D r o d o n t , b a n dD i e t m a r S e q n e r , D M D , P h D cOslo and Stavanger, Norway, and H amburg, G ermany

Effec t ive bracket s lo t he ight i s es t imated by us ing a formula tha t descr ibes the re la t ionship be tweenbracket s lo t he ight , wi re d imens ions , wi re edge bevel , and tors iona l p lay ( th i rd-order c learance) .With a torque measur ing ins t rument , the tors iona l p lay was es t ima ted for 10 d i ffe rent brackets(0 .018- inch s ta ted s lo t ) of the same manufac turer and type . One arch wire wi th known d imens ionsand edge bevel was used for a l l the me asureme nts . Wi th known tors iona l p lay, wi re d imen s ionsand edg e bevel , the bracket s lo t he ight could be ca lcu la ted . This was pe r formed f ive t ime s for eachbracket and the m ethod er ror for es t imat ion of tors iona l p lay for a s ingle me asurem ent was 0 .04 ~correspon ding to 0 .36 mm in s lo t he ight . The b rackets tes ted had a mean s lo t he ight of 0 .476 _+

0.003 mm, with a range of 0.470 to 0.481 mm (0.0187 -+ 0.0001 inches, range 0.0185 to 0.0189).The var ia t ion in bracket s lo t he ight was much grea ter than the method er ror. The method used tomeasu re bracket s lo t he ight seems to have a h igh degree of accuracy and i s eas ie r to im plem entthan convent iona l methods . (Am J Or thod Dentofac ia l Or thop 1998;113:387-93 . )

M a n u f a c t u r e r s d o n o t d e cl ar e w h a tm e t h o d t h e y u s e w h e n m e a s u r i n g b r a c k e t s l o t h e i g h t( v e r t ic a l d i m e n s i o n ) , o r d o t h e y s t a te t h e t o l e r a n c e so f b r a c k e t s l o t d i m e n s i o n s i n t h e i r p r o d u c t c a t a -l o g u e s o r o n p r o d u c t l a b e l s . T h e e x a c t b r a c k e t s l o th e i g h t i s d i ff i cu l t t o m e a s u r e . O p t i c a l c o m p a r a t o r s

a r e u s e d t o c o n t r o l t h e t o l er a n c e s w h e n p r o d u c i n gc e r a m i c b r a c k e ts , a n d a s im i la r m e t h o d c a n b e u s e df o r m e t a l b r a c k e ts ? A n o t h e r m e a s u r e m e n t m e t h o di s t h e u s e o f g a u g e b l o c k s to e x a m i n e t h e d e g r e e o ff it b e t w e e n t h e b r a c k e t s l o t a n d t h e b l o c k . T h e s e c a nb e d e l iv e r e d i n in c r e m e n t s o f 0 .0 1 m m ( M i t u t o y oC o r p . , s e r i e s 5 1 6 ) . T h e p r o b l e m w i t h m e a s u r i n gb r a c k e t s l o t h e i g h t i s th a t i ts s iz e m a y v a r y f r o m t h ee n t r a n c e t o t h e m i d d l e o f th e s l o t in a h o r i z o n t a ld i r e c t i o n ?

I t is o f i n t e r e s t t o o r t h o d o n t i s t s t o h a v e t h ek n o w l e d g e a b o u t t h e a c c u r a c y o f b r a c k e t s lo ts ,a ll o w in g d e l i v er y o f m o r e c o r r e c t m o m e n t s o ft o r q u e . I t is a ls o o f i n t e r e s t t o g e t a n i d e a o f t h ea c c u r a c y o f t h e v a r io u s m e t h o d s u s e d i n t h e p r o d u c -t i o n o f o r t h o d o n t i c b r a c k e ts . T h e p u r p o s e o f th i ss t u d y i s t o d e v e l o p a m e t h o d w h e r e b y e f f e c t i v eb r a c k e t s l o t h e i g h t c a n b e m e a s u r e d m o r e a c c u -ra t e ly.

This s tudy was suppor ted by R esearch Forum, Ul levaa l Hospi ta l , FUS.aDep artmen t of Maxil lofacial Surgery, Ullevaal Ho spital , Oslo, Norway.bVisi ting Professor, De par tmen t of Or thodont ics , Univers i ty of Ham burg ,Germ any and in private practice, Stavanger, Norway.CProfessor, Depar tm ent of O r thodont ics , Univers i ty of Hamb urg .Reprint requests to: Dr. Torstein R. Meting, Madlaveien 9B, 4008Stavanger, Norway.Copyr igh t 9 1998 by the A mer ican Assoc ia tion of Or thodont i s ts .0889-5406/98/$5.00 + 0 8/1/77490

R E V I E W O F L I T E R AT U R E

A c c u r a t e m e a s u r e m e n t s o f b r a c k e t sl o t h e i g h th a v e n o t r e c e i v e d m u c h a t t e n ti o n , e v e n t h o u g h c l o s es l o t t o l e r a n c e s i s e s s e n t i a l f o r a c c u r a t e t o r s i o n a lc o n t r o l. C r e e k m o r e 3 q u o t e d b r a c k e t t o l e r a n c e s,b a s e d o n d a t a f r o m U n i t e k C o r p o r a t i o n , f o r an o m i n a l 0 . 0 1 8 - i n c h b r a c k e t b e i n g w i t h i n 0 . 0 1 8 2a n d0 . 0 18 7 i n c h e s . I n a l a t e r a r t ic l e , b a s e d o n d a t a f r o m3 M / U n i t e k , C r e e k m o r e a n d K u n i k 4 g a v e a r a n g ef r o m 0 . 0 1 8 2 t o 0 . 0 1 9 2 i n ch e s , w i th a m i d r a n g e v a l u eo f 0 .0 1 8 7 i n ch e s . H o w e v e r , n o i n f o r m a t i o n w a s g i v e na s t o t h e m e t h o d u s e d t o o b t a i n t h e s e d a t a .

M e l i n g e t a l. 2 u s e d a m e t a ll u rg ic m e t h o d f o r m e a -sur ing bracket s lo t height in s ta in less s tee l brackets ,p repa r ing c ross - sec t iona l cu t s t h rou gh th e b rack e t s lo t.T h e s l o t h e i g h t c o u l d b e m e a s u r e d t o t h e n e a r e s t 0 . 0 1m m w i t h a Z e i s s A x i o s c o p e ( C a r e Z e i s s ) w i t h at ravel ing s tage . I t was vi r tual ly impossible to achieveany g rea te r accuracy, because p l ac ing the in t e rna lpos i t ion ing c ross accura t e ly on the s lo t edg e wasd i ff icu lt . Fu r the r mo re , t he m e th od was ve ry t ime-consum ing . As the b ra cke t s lo t t ape red s l igh t ly f romen t ran ce to ward the s lo t base , t he e ff ec t ive he igh t w i l lbe s l ight ly d i fferen t for a 0 .016 0 .016- inch wire th anfo r a 0.018 x 0 .025- inch wi re . Th us a m e th od tom e a s u r e t h e s l o t h e ig h t a t t h e a c t u a l p o i n t o f c o n t a c tb e t w e e n t h e w i r e a n d b r a c k e t w o u l d b e p r e f e r a b l e .

O d e g a a r d e t a l. 5 d e sc r i b e d a n i n s t r u m e n t t om e a s u r e t h e t o r s i o n a l t w i st w i t h a h ig h d e g r e e o fe x a c t n e s s . T h e r o t a t i o n a l d e f l e c t i o n c o u l d b e r e -c o r d e d w i t h t o t h e n e a r e s t 1 / 5 0 ~ M e l i n g e t a l. 6p r e s e n t e d a n e w f o r m u l a t h a t d e s c r ib e s t h e r e l a ti o n -

38 7

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T1

F i g . 1 . R e c t a n g u l a r a r c h w i r e w i t h r o u n d e d corners( b e v e l e d e d g e s ) h a s b e e n t w i s t e d w i t h b r a c k e t s l ot .A n g l e o f t w i s t o r p l a y is % a n d is d i ff e r e n c e b e t w e e na n g l e s ~ a n d 13. H = b r a c k e t s l o t h e i g h t , h = w i r e h e i g h t ,w = w i r e w i d t h , d = d i s t a n c e b e t w e e n c e n t e r s o fr o u n d i n g a n d r = r a d i u s o f w i r e ro u n d i n g .

s h i p b e t w e e n b r a c k e t s l o t h ei g h t , w i r e d i a m e t e r , a n dw i r e e d g e b e v e l , w i t h r e s p e c t t o t o r s i o n a l p l a y( t h i r d - o r d e r c le a r a n ce ) . T h e y d e m o n s t r a t e d h o wd e v i a t i o n s f r o m s t a t e d w i r e d i m e n s i o n s , e d g e b e v e l ,a n d b r a c k e t s l o t h e i g h t c a n s t r o n g l y i n f lu e n c e t o r -s i o n a l p l a y. 6,7 L a t e r M e l i n g e t a l . 8 s h o w e d t h a t t h en e w f o r m u l a , i n c l u d i n g t h e e ff e c t o f a n e d g e b e v e lo n t h e t o r s i o n a l p l a y, ga v e a fa r m o r e a c c u r a t ee s t i m a t e o f t h e t o r s i o n a l p l ay t h a n t h e f o r m u l ap r e v i o u s l y u s e d b y o t h e r i n v e s t ig a t o r s .

M AT E R I A LS A N D M E T H O D ST h e o r e t i c a l C o n s i d e r a t i o n s

I n F i g . 1, a r e c t a n g u l a r a r c h w i r e w i t h r o u n d e d c o r n e r s( b e v e l e d e d g e ) h a s b e e n t w i s t e d w i t h i n a b r a c k e t s l o t . T h ea n g l e o f t w i s t o r p l a y is y a n d i s t h e d i f f e r e n c e b e t w e e n t h eangles ~x and 13. Th e d iago na l d i s the d i s tanc e be tw een thec e n t e r s o f r o u n d i n g , a n d i s g iv e n b y f o r m u l a ( 1 ) . I n t h etwo t r i ang le s used for c a lcu la t in g a and 13, d i s the

h y p o t e n u s e . We t h e n h a v e t h e f o l l o w i n g :

d = ~ - 2 r) 2 + ( h - 2r ) 2 ( 1)

wh ere w i s wi re wid th a nd h i s wi re h e igh t , whi le r i s ther a d i u s o f r o u n d i n g .

T h e a n g l e y c a n t h e n b e f o u n d b y t h e f o l l o w i n gf o r m u l a :

H - 2r h - 2ry = a r c s i n ~ a r c s i n ~ ( 2 )

W h e n t h e a n g l e o f p l a y, w i r e h e i g h t , w i d t h , a n d e d g eb e v e l a r e k n o w n , t h e b r a c k e t s l o t h e i g h t H c a n b e c a l c u -l a t e d . S o l v i n g t h e e q u a t i o n f o r H , w e t h e n h a v e t h ef o l l o w i n g :

H = d .( h - 2 r ]

+ cos -

+ 2r (3 )

B r a c k e t s

Te n b r a c k e t s o f t h e s a m e l o t w e re o b t a i n e d t h r o u g hn o r m a l s u p p l y c h a n n e l s ( O r m c o , m e d i u m t w in , s t a n d a r de d g e w i s e 0 . 0 1 8 i n c h , 0 ~ o r q u e a n d a n g u l a t i o n ) .

Te s t Wi r e

A rec tang ula r Dentaur um 0 .018 x 0 .025- inch Spr ingH ard s ta in less s tee l wi re com mon ly used in the 0 .018- inchedgewise t echnique was used as t es t wi re . Th is wi re waschosen on the bas i s o f p rev ious f ind ings regard ing i t s cross -sec t iona l accuracy and s tab il i ty. ,s M ajor empha s i s was pu t

on the amount o f an edge beve l and i t s s tandard dev ia t ion .I n i t i a l ly, o n e w i r e l e n g t h w a s r a n d o m l y c h o s e n f r o m

t h e t u b e a n d i t s d i m e n s i o n s m e a s u r e d o n 1 0 d i f f e r e n ts e g m e n t s. T h e d i m e n s i o n s w e r e m e a s u r e d t o t h e n e a r e s t0 .0 0 01 m m w i t h a d i g i t a l m i c r o m e t e r ( m o d e l 2 9 3 - 5 21 )a c c u r a t e t o - + l l x m ( M i t u t o y o C o r p . , To k y o , J a p a n ) . S u b -s e q u e n t l y, t w o p i e c e s , 5 c m i n l e n g t h , w e r e c u t f r o m t h i sw i r e l e n g t h a s t e s t p i e ce s .

F o r m e a s u r e m e n t o f a n e d g e b e v e l , 10 p i e ce s , 1 c m i nl e n g t h , c u t f r o m v a r i o u s p l a c e s o n t h e i n i t i a l w i r e l e n g t hw e r e p l a c e d o n a w a x p l a t e i n a v e r t i c a l p o s i t i o n a n d w e r ee m b e d d e d i n c o l d c u r e a cr y l ic . T h e s p e c i m e n s w e r ep r e p a r e d b y u si n g s t a n d a r d m e t a l lu r g i c a l m e t h o d s t o

o b t a i n a c r o s s - s e c t io n a l c u t p e r p e n d i c u l a r t o t h e i r l o n ga x is a n d m a g n i f i e d x 7 2 0 u n d e r a m e t a l l u rg i c a l m i c r o -s c o p e . T h e r a d i u s o f c o r n e r r o u n d i n g w a s m e a s u r e d f o r a l lf o u r c o r n e r s , a n d t h e a r i t h m e t i c m e a n u s e d i n t h e s u b s e -q u e n t c a l c u l a t i o n s . T h e m e t h o d f o r m e a s u r i n g a n e d g eb e v e l s e e m s b o t h v a l i d a n d h a s a l o w i n t r a i n d i v i d u a l a n di n t e r i n d i v i d u a l e r r o r. T h e i n t r a i n d i v i d u a l m e t h o d e r r o r,b a s e d o n 1 2 0 d o u b l e m e a s u r e m e n t s , w a s 2 . 9 I x m , a na v e r a g e o f 4 % o f t h e m e a n r e s u l t. T h e i n t e r i n d i v i d u a lm e t h o d e r r o r , b a s e d o n 8 0 d o u b l e m e a s u r e m e n t s , w a s 2 .0I xm , an a v e r a g e o f 3 % o f t h e m e a n r e s u l t . 7

Te s t M e t h o d

T h e b r a c k e t s w e r e t e s t e d i n a p r e v i o u s l y d e s c r i b e dt o r q u e m e a s u r i n g i n s t r u m e n t w i t h a n i n t e r b r a c k e t d i s -t a n c e o f 4 r a m . 5 T h e p r i n c i p l e o f t h e i n s t r u m e n t d e s i g n( F i g . 2 , A ) i s t h a t t h e t e s t p i e c e i s h e l d i n p o s i t i o n b y t h r e eb r a c k e t s . T h e c e n t e r b r a c k e t ( A ) i s s t a t i o n a r y, m o u n t e do n a p e d e s t a l . Tw o s u p p o r t i n g b r a c k e t s ( B ) a l i g n e d w i t ht h e c e n t e r b r a c k e t , a r e f i x e d t o a c r o s s b a r ( C ) t h a t c a nr o t a t e a r o u n d i t s l o n g a xi s. W h e n m o u n t e d , t h e b r a c k e ts l o t s a r e o r i e n t e d s u c h t h a t a n o r t h o d o n t i c w i r e p a s s i n gt h r o u g h t h e b r a c k e t s w i l l h a v e i t s c e n t r a l a x i s c o i n c i d i n gw i t h t h e c e n t r a l a x is o f t h e c r o s s b a r.

To r q u e i s a p p l i e d t o t h e c r o s s b a r b y a d d i n g w e i g h t s t oa b a s k e t a t t a c h e d t o a p u l l e y ( E ) f i x e d t o t h e c r o s s b a r.We i g h t s a r e a d d e d t o i n c r e m e n t s c o r r e s p o n d i n g t o i n -

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American Journal of Orthodontics and Dentofacial Orthopedics Meling, Odegaard, and Segne r3 8 9Volume 113, No. 4

Centralaxis

A

E ] Cross-bar Pulley La :

Laser dot ~ - -

\ \ 6 mm.\

\

B Laser

Fig . 2 . A, Schemat ic d iagram of tes t appara tus . B , Pos i t ion of tes t ing appara tus ins idemeasur ing sca le . Dis tance f rom axis -ce nter to m i l l imeter gr id pa per on ins ide of a rc i s 716m m .

creases in applied torque of 5.0 Nmm, up to a maximumof 30 Nmm.

Onto the ends of the crossbar are mounted twomirrors (F) that rotate with the crossbar. The degree oftorsional twist can be measured with laser lamps (G)projecting thin beams of light through the mirrors onto ameasuring scale (Fig. 2, B). The scale is a full half arc ofa circle, and its inside is covered with millimeter paper,consti tuting the scale. The l ong axis of the crossbarcoincides with the c enter of the m easuri ng scale. The scalecan be read accurately to 1/50 ~

The inst rument has been tested for method error in avery comprehensive manner. The overall method error forthe torsional measurements, based on 400 double mea-surem ents at 10 Nmm, was 0.106~ 5 The meth od error forDe nta uru m Har d 0.018 0.025-inch wires was 0.054 ~ At test for systematic error bet ween the first and the secondmeasurements indicated that no permanent deformationof the wires or brackets occurred during the experiment(t = 0.02).

Torsional play can be estimated in two different ways.

We can fit a linear regression line to the linear portion ofthe torque-twist curves. The interception of this line withthe abscissa represents the amount of torsional playbetween wire and bracket going from a central position toone extreme. If the bracket slot height, wire dimensions,and wire edge bevel are known, we can also calculate thetorsional play by using the formula. We have previouslydemonstrated that there is no statistically significant dif-ference between the estimate of torsional play using thelinear regression method when compared with the meth odusing the formula if the bracket slot height is known, s'9 Aregression analysis has revea led a correla tion factor of r =0.99 between the two estimates. Thus the formula isapparently both valid and reasonably accurate.

The two supporting brackets (Ormco standard edge-wise, different from a test lot) were not changed duringthe e ntire testing. To estimate the contributio n of the sidebrackets to the total torsional play, one of the test pieceswas used. Its height and width were measured 10 times attwo different places, corresponding to the areas whereside bracket-wire interaction take place. The difference

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T a b l e I . M e a s u r e m e n t s o f b r a c k e t s lo t h e i g h t s . Te n O r m c o 0 . 0 1 8 - i n c h b r a c k e t s w e r e t e s t e d f iv e t i m e s . T h e t o r s i o n a l p l a y w a sc a l c u l a t e d b y f it t in g a r e g r e s s i o n l i n e t o t h e l i n e a r p o r t i o n o f t h e t o r q u e - t w i s t d i a g r a m a n d f i n d i n g i ts in t e r c e p t w i t h t h e t w i st - ax i s . T h es l ot h e i g h t w a s e s t i m a t e d u s i n g t h e f o r m u l a p r e s e n t e d

Bracket No.

Torsional play

in degrees

Mean SD

Calculated slot height

in mm

Mean SD

Calculated slot height

in inches

Mean SD

1 5 1 .09 0 . 05 0 .47 0 4 0 . 0 005 0 .0 1852 0 . 0 00022 5 2 . 68 0 . 03 0 .47 7 5 0 . 0 003 0 . 0 1880 0 . 0 00013 5 2 . 40 0 . 03 0 .47 4 9 0 . 0 003 0 . 0 1870 0 . 0 00014 5 2 . 71 0 . 04 0 .47 78 0 . 0004 0 . 0 1881 0 . 0 0 0 0 25 5 2 . 6 0 0 . 09 0 .47 6 8 0 . 0 008 0 .0 1877 0 . 0 00036 5 3 . 0 6 0 . 04 0 .48 1 0 0 . 0 004 0 .0 1894 0 . 0 00027 5 2 . 9 3 0 . 03 0 .47 9 8 0 . 0 003 0 .0 1889 0 . 0 00018 5 2 . 1 3 0 . 02 0 .47 2 4 0 . 0 002 0 .0 1860 0 . 0 00019 5 2 . 38 0 . 03 0 .47 4 7 0 . 0 003 0 .0 1869 0 . 0 0001

10 5 2 . 44 0 . 0 5 0 .4753 0 . 000 5 0 .018 71 0 . 0 0 0 02

between the two segments was la te r sub jec ted to a s ta t i s -t i c a l a n a l y s i s . T h e m e a n d i m e n s i o n s w e r e u s e d i n t h esubsequent ana lys i s . The tes t p iece was then l iga ted in thec e n t e r b r a c k e t a n d e m b e d d e d w i t h li g h t -c u r e c o m p o s i t e t of i rmly secure i ts pos i t ion in the bracke t s lo t. Torq ue w asappl ied an d the to rs ion a l p lay ca lcu la ted wi th the l inearr e g r e s s i o n m e t h o d , b a s e d o n t o r q u e - t w i s t d i a g r a m s . Tonegate the e ffec t o f s l igh t incor rec tness in s ide bracke to r i e n t a t io n , t h e c e n t e r b r a c k e t w i th t h e w i r e w a s r o t a t e d180~ a n d t h e w i r e l o a d e d a g a in . T h e m e a n o f t h e s e t w oes t imates was used in the subsequent ana lys i s . Tes t ing int h i s m a n n e r w a s c a r r i e d o u t 1 0 s e p a r a t e t i m e s a n d t h em e a n t o r s i o n a l p l a y p r e s e n t i n t h e t w o s i d e b r a c k e t sca lcu la ted .

T h e b r a c k e t s t o b e t e s te d w e r e a t t a c h e d t o t h ec e n t r a l p e d e s t a l . C o l d c u r e a c r y li c w a s u s e d t o b o n d t h eb r a c k e t s. T h e i n t e r b r a c k e t d i s t a n c e w a s c h e c k e d f o re a c h b r a c k e t w i th a f ix e d g a u g e a n d k e p t a t 4 m m . T h es e c o n d t e s t w ir e w a s u s e d f o r m e a s u r e m e n t o f s lo th e i g h t. I t s d i m e n s i o n s w e r e m e a s u r e d 1 0 t i m e s a t t h r e ed i f f e r e n t p l a c e s , n a m e l y, w h e r e b r a c k e t - w i r e i n t e r a c -t i o n s ta k e p l a c e . T h e d i f fe r e n c e a m o n g t h e t h r e e s e g -m e n t s w a s l a t e r s u b j e c t e d t o a s t a t i s t i c a l a n a l y s i s . T h ea r i t h m e t i c m e a n w a s s u b s e q u e n t l y u s e d i n a l l t h ec a l c u la t io n s . To r q u e w a s t h e n a p p l i e d a n d t h e t o r s i o n a lp l a y e s t i m a t e d . A g a i n , t o n e g a t e t h e e f f e c t o f s li g h ti n c o r r e c t n e s s i n b r a c k e t o r i e n t a ti o n , e a c h b r a c k e t w a st e s t e d i n o n e p o s i t io n , r o t a t e d 1 8 0 ~ a n d l o a d e d a g a in .To e s t i m a t e t h e a c c u r a c y, t h i s p r o c e d u r e w a s c a r r i e do u t f i v e t i m e s f o r e a c h b r a c k e t . T h e m e a n t o r s i o n a lp l a y f o r e a c h b r a c k e t w a s u s e d i n t h e s u b s e q u e n tc a l c u l a t i o n .

To es t imate the to rs iona l p lay presen t so le ly in thec e n t e r b r a c k e t , t h e m e a n e s t i m a t e d p l a y in t h e s i d ebracke ts was subt rac ted f rom the to ta l p lay. In th i scontex t ,play i s d e f i n e d a s t h e a n g u l a r r o t a t i o n o f t h e w i r ef rom i ts pass ive pos i t ion (wi re c ross -sec t ion para l le l to s lo twai l s ) to the pos i t ion where two d iagonalcorners m a k econtac t to the oppos ing s lo t wal l s .

Statistical Analysis

T h e m e t h o d e r r o r w a s e s t i m a t e d f r o m d o u b l e m e a -s u r e m e n t s o f 1 0 b r a ck e t s w i t h t h e D a h l b e rg f o r m u l a . 1 ~T h e t o t a l t o r s io n a l p l a y f o r e a c h b r a c k e t w a s e s t i m a t e df ive t imes , and the resu l t s subm i t ted to ana lys is o f var iancef o r r e p e a t e d m e a s u r e m e n t s .

R E S U L T S

T h e o r i g i n a l w i r e l e n g t h u s e d h a d a h e i g h t o f0 . 4 5 3 +_ 0 . 0 0 0 4 m m , a w i d t h o f 0 . 6 3 8 ___ 0 . 0 0 0 7 m m ,a n d a n e d g e b e v e l r a d i u s o f 0 . 04 6 ___ 0 . 0 0 2 7 m m . T h et e s t p i e c e u s e d f o r e s t i m a t i n g t o r s i o n a l p l a y i n th e s i d eb r a c k e t s w a s n o t s i g ni f ic a n t ly d i ff e r e n t f r o m t h e t e s tp i e c e u s e d f o r m e a s u r i n g t h e t o t a l to r s i o n a l p l a y. T h el a t t e r h a d d i m e n s i o n s H = 0 . 4 5 2 _+ 0 . 0 0 0 5 a n d W - -0 . 6 3 8 ___ 0 . 0 0 0 4 f o r c e n t e r b r a c k e t c o n t a c t . T o c a l c u l a t et h e s l o t h e i g h t , t h e f o l l o w i n g v a l u e s w e r e t h e r e f o r eu s e d : h e i g h t 0 .4 5 2 m m , w i d t h 0 . 6 3 8 m m , a n d e d g eb e v e l 0 . 0 4 6 m m .

T h e e s t i m a t e d t o r s i o n a l p l a y i n t h e s i d e b r a c k e t sw a s 4 . 5 5 ~ ___ 0 . 0 5 ~ T h i s c o r r e s p o n d s t o a s l o t h e i g h to f 0. 4 9 5 m m i n t h e s i d e b r a c k e t s, w i t h t h e f o r m u l ad e s c r i b e d i n e q u a t i o n ( 3) .

T h e e s t i m a t e d b r a c k e t s l o t h e i g h t s a r e g i v e n i nTa b l e I a n d p r e s e n t e d g r a p h i c a l l y i n F ig . 3 . T h em e t h o d e r r o r f o r e s t im a t i n g t h e t o r s io n a l p l a y w i t ht h e D a h l b e r g f o r m u l a w a s 0 . 04 ~ B e c a u s e t h e m e a no f f iv e d i f f e re n t m e a s u r e m e n t s w e r e u s e d i n th es u b s e q u e n t a n al y si s, th e m e a n ' s a c t u a l m e t h o d e r r o rw i ll b e t h e c a l c u l a t e d m e t h o d e r r o r d i v i d e d b y~/5.11

F i g . 4 d e m o n s t r a t e s t h e r e l a t i o n s h i p b e t w e e na n g l e o f to r s i o n a l p l a y a n d b r a c k e t s l o t h e i g h t , b a s e do n t h e c r o s s - s e c t i o n a l d i m e n s i o n s o f t h e w i r e u s e d i nt h is e x p e r i m e n t . T h e r e l a t i o n s h i p s b a s e d o n t h ew o r s t p o s s i b l e c o m b i n a t i o n s i n b o t h d i r e c t i o n( M e a n + 2 S D f o r h e ig h t a nd w i dt h a n d - 2 S D f o r

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F i g . 4 . R e l a ti o n s h i p b e t w e e n a n g l e o f t o r s io n a l p l a y a n d b r a c k e t s l o t h e i g h t, b a s e d o nm e a n c r o s s - s e c t io n a l d i m e n s i o n s o f w i re u s e d in t h is e x p e r i m e n t . T h i s r e la t io n s h i p b a s e do n w o r s t p o s s ib l e c o m b i n a t i o n s in b o t h d i r e ct io n ( M e a n + 2 S D f o r h e ig h t a n d w i d t h a n d- 2 S D f o r e d g e b e v e l , o r M e a n - 2 S D f o r h e i g h t a n d w i d t h a n d + 2 S D f o r e d g e b e v e l ) h a v ea l s o b e e n p l o t t e d .

e d g e b e v el , o r M e a n - 2 S D f o r h e i g h t a n d w i d t h a n d+2 SD fo r edge beve l ) have a l so been p lo t t ed .

A o n e - w a y a n al ys is o f va r ia n c e ( A N O VA ) d e m -onst ra ted a s igni f icant d i fference betw een the brack-ets ( F = 3 1 2 f o r D F 9 ,4 0). T h e A N O V Afo rr epea t ed measu remen t s r evea l ed no d i f f e r encesamong the f ive tes t ser ies .

D I S C U S S I O N

M o d e r n o r t h o d o n t i c te c h n i q u e o f t e n u s e s p r e -to rqued b racke t s . Deba te s have a r i s en on the co r-r ec t to rque ang le , and o r thodon t i s t s may d i scussva r i a t ion in t o rqued s lo t s o f a f ew deg rees . Th i s can

be co r r ec t f rom a theo re t i ca l po in t o f v iew, bu t i fsuch f ine d i fferences are to make sense , i t i s impor-t an t t ha t manufac tu re r s g ive add i t i ona l i n fo rma t ionabou t t he i r p roduc t s t o a l l ow the o r thodon t i s t t omake co r r ec t ion fo r dev ia t ion f rom nomina l va lues .

Th i s r a i s e s t he impor t an t ques t ion o f qua l i t ycon t ro l . B racke t s a r e deno ted in 1 /1000 inch , bu tdev ia t ions f rom s t a t ed va lues a r e no t g iven . Manu-fac tu re r s do no t s t a t e t he i r t o l e r ances fo r b racke t swi th r e spec t t o s lo t he igh t i n t he i r p roduc t ca t a -logues o r on the p roduc t l abe ls , t he word be ing tha tthey usua l ly a r e w i th in + 0 .0007 inches o f t he nom -ina l va lue . Th i s i s i n ag reem en t w i th t he v a lues g iven

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F i g . 5 . F i g u r e s h o w s d i f f e re n c e b e t w e e n c i rc u l a r a n d o c t a g o n a l c r o s s - s e c t io n f o r g i v e nr a d i u s , r. A t 7 ~ o f t o r s io n a l p l a y, c o r r e s p o n d i n g t o b r a c k e t s l o t h e i g h t o f 0 . 5 1 6 m m ,d i f fe r e n c e b e t w e e n t w o e s t i m a t e s is 0 . 7 t x m .

b y C r e e k m o r e , 3 w h e r e a s t h e v a l u e s g i v e n i n a l a t e ra r t i c le b y t h e s a m e a u t h o r 4 i n d i c a t e l a rg e r t o l e r -a n c e s .

O r t h o d o n t i c w i r e s s h o w d e v i a t i o n s f r o m t h es t a t e d v a l u e s . 7 T h i s i n v e s t i g a t i o n r e v e a l s t h a t v a r i a -t i o n a l s o e x i s ts i n b r a c k e t s l o t d i m e n s i o n s . 1 W e h a v ep r e v i o u s l y d e m o n s t r a t e d t h e e f f e c t o f d e v i a t i o n s i nb r a c k e t s l o t h e i g h t o n t h e t o r s i o n a l p l a y. 6 A s a ne x a m p l e , c o n s i d e r a 0. 0 1 6 x 0 . 0 2 2 - i n c h w i r e w i t hd i m e n s i o n s a s s ta t e d a n d p e r f e c t l y s h a r p c or n e r s .T h e t o r s i o n a l p la y t h a t h a s t o b e n e g a t e d w i ll b e t h ep l a y fr o m a c en t r a l p o s i t io n t o o n e e x t r e m e i n t w ob r a c k e t s w h e n a p p l y i n g t o r q u e t o a t o o t h . T h et o r s i o n a l p l a y w i l l i n c r e a s e f r o m 1 0 . 8 ~ t o 1 6 . 6 ~ o ra l m o s t 5 4 % , i f t h e b r a c k e t s l o t h e i g h t i s 0 . 0 1 9 i n c h e sa n d n o t t h e s t a t ed 0 . 0 1 8 i n c h e s . I f t h e w i r e h a s t h em e a n h e i g h t , w i d t h , a n d e d g e b e v e l d i m e n s i o n sf o r m e r l y r e p o r t e d , 7 t h e i n c r e a s e i n p l a y w i l l b e f r o m1 3 .6 ~ t o 20 .8 ~

I n a p r e v i o u s i n v e s t i g a t i o n , M e l i n g e t a l . 2 n o t e d

t h a t t h e b r a c k e ts u s e d h a d b r a c k e t s l o t s t h a t w e r et o o h ig h . T h e y s h o w e d t h a t O r m c o m e d i u m s ta n -d a r d e d g e w i s e 0 . 0 1 8 - i n c h b r a c k e t s h a d a b r a c k e t s l o th e i g h t o f 0 . 4 7 5 m m ( 0 . 0 1 8 7 i n c h e s ) a t a d i s t a n c e o f0 . 03 m m f r o m t h e s l o t b a s e . F u r t h e r m o r e , a s l ig h tt a p e r o f 1 . 8 5 ~ w a s o b s e r v e d . T h e e s t i m a t e d b r a c k e ts l o t i n t h i s in v e s t i g a t i o n w a s 0 . 4 7 6 _+ 0 . 0 0 3 2 m m(0 .0 18 7 _ + 0 .0 001 3 i nch e s ) .

T h e r e i s s o m e i n t r as a m p l e v a r i a t io n i n b r ac k e ts l o t h e i g h t , t h e r a n g e b e i n g 0 . 4 7 0 t o 0 . 4 8 1 m m( 0 . 0 1 8 5 t o 0 . 0 1 8 9 i n c h e s ) . T h i s c o r r e s p o n d s t o av a r i a t i o n i n t h e t o r s i o n a l p l a y o f 1 ~ f o r a 0 . 0 1 8 0 . 0 2 5 - in c h w i r e a n d w o u l d b e e v e n h i g h e r f o r a0 . 0 1 6 0 . 0 2 2 - i n c h w i r e . T h i s i n v e s t i g a t i o n d o e s n o tg i v e a n y i n d i c a t i o n a b o u t t h e v a r i a t i o n t h a t m a y e x i s ta m o n g m a n u f a c t u r e r s o r a m o n g p r o d u c t i o n l ot s . I tm i g h t b e a s s u m e d t h a t t h i s v a r i a t i o n i n b r a c k e t s l o th e i g h t i s h i g h e r , e s p e c i a l l y b e t w e e n d i f f er e n t m a n u -f a c t u r e r s a n d p r o d u c t l i n e s .

T h e m e t h o d e r r o r w a s 0 . 3 6 I x m . T h e c o e f fi c ie n t

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Amer i can Jou rna l o f Or th odo n t i c s an d De n to f ac i a l Or tho ped i c s Meling, Odegaard, and Segn er3 9 3Vo l u m e 113, N o . 4

o f r e l i a b i l it y 12 w a s 0 . 97 4 , i n d i c a t i n g t h a t t h e m e t h o de r r o r i n r e l a t i o n t o t h e v a r i a b i l i t y i s s m a l l . F ig . 4s h o w s t h a t 0 .1 ~ o f c h a n g e i n t o r s i o n a l p l a y c o r r e -s p o n d s t o 0 . 9 I x m c h a n g e i n s l o t h e i g h t . A s t h em e t h o d e r r o r w a s l e s s t h a n 0 .1 ~ i t f o ll o w s t h a t t h eb r a c k e t s l o t h e i g h t c a n b e c a l c u l a t e d w i t h a h i g hd e g r e e o f a c c u ra c y. I f w e c o m b i n e t h e w o r s t p o s s i b l ec o m b i n a t i o n s ( 2 S D o f w i r e h e i g h t, w i d th , a n d e d g eb e v e l ), t h e e x p e c t e d d e v i a t i o n a r o u n d t h e m e a nc a l c u l a t e d s l o t h e i g h t w o u l d b e o n l y _ __0 .0 02 m m a t2 .5 ~ o f t o r s i o n a l p l a y, w h i c h i s s i m i l a r t o t h e r e s u l t sa c h i e v a b l e w i t h e l e c t r o n ic m i c r o m e t e r s f o r m e a s u r e -m e n t s o f w i r e d i a m e t e r s .

T h e f o r m u l a a s s u m e s t h e e d g e b e v e l t o b e ap e r f e c t l y c i rc u l a r s e c t i o n ( 9 0 ~ o f a n a r c h ) . W e h a v ep r e v i o u s l y s h o w n t h a t t h i s i s n o t a l w a y s t h e c a s e . 5T h e o t h e r e x t r e m e w o u l d b e a n o c t a g o n a l c ro s s-s e c t i o n , o r " f i a t b e v e l . " T h e a c t u a l e d g e b e v e l isp r o b a b l y s o m e w h e r e i n b e t w e e n t h e s e t w o e x t re m e s ,b u t s l i g h t d e v i a t i o n f r o m a p e r f e c t l y c i r c u l a r s e c t i o nw i l l n o t s u b s t a n t i a l l y a l t e r t h e c a l c u l a t i o n s ( F i g . 5 ) .

T h e m e t h o d d o e s n o t d i r e ct l y a d d r e s s t h e e f fe c to f a sl o t t a p e r . T h e c a l c u l a t e d s l o t h e i g h t o b t a i n e db y t h is m e t h o d i s a n e s t i m a t e o f th e e f f e c t i v e s l o th e i g h t. A s t h e l a t t e r a r e a c o m b i n a t i o n o f b r a c k e ts l o t h e i g h t a n d s l o t t a p e r , i t i s i n d i r e c t l y t a k e n i n t oa c c o u n t .

T h i s a r t ic l e e s t a b l is h e s a m e t h o d f o r e s t im a t i n gb r a c k e t s l o t h e i g h t s , a n d t h e m e a s u r e m e n t s c a n b er e p e a t e d w i t h o u t a n y s ig n i fi c an t d i f fe r e n c e b e t w e e ns e r ie s o f m e a s u r e m e n t s . L a s t l y, t h e m e t h o d s e e m sv a l i d . S u b s e q u e n t i n v e s t i g a t i o n s w i l l e v a l u a t e d i f f e r-e n c e s b e t w e e n p r o d u c t i o n b a t c h e s, p r o d u c t i o nm e t h o d s , a n d m a n u f a c t u r e r s .

C O N C L U S I O N S

1. We have es tabl i shed a novel method to es t imatebracket s lo t he ight . With a formula descr ib ing there la t ionship be tween bracket s lo t he ight , wireheight and width , wire edge bevel , and tors ional

p lay ( th i rd-order c learance) , the effec t ive brack et

s lo t he ight can be es t imated to a h igh degree ofaccuracy, i f the o ther fac tors a re known.

2 . Becau se bracket s lo ts have a s l ight taper ing tow ardthe base, 2 the effective slot heigh t w ill be sl ightly

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0.016-inch wire than for a0 .018 0 .025-inch wire . The m etho d measu res thes lo t he ight a t the poin t where the wire ac tua l lymakes co n t ac t w i th t he b r acke t , wh ich s eem s p re f -erable .

3 . The measured brackets had a s lo t he ight of0.476m m (ran ge o f 0.470 to 0.481) o r 0.0187 inches(range 0.0185 to 0.0189). This range is outside theone m os t commonly quo ted fo r t h is t ype o fbracket .

4 . Be t t e r i n fo rma t ion f rom the manufac tu re r s con -cerning devia t ions f rom s ta ted va lues i s a prereq-uis i te for correc t force appl ica t ions .

The ass is tance of Mr. Alf Skar tve i t of the StavangerTekn. Fagskole , Norway, in prepar ing the wire andbracket spec imens for c ross-sec t ional photography i sgrea t ly apprec ia ted .

REFERENCES

1. Sebanc J, Brantley WA, Pincsak J J, Conover JP. Variability of effective root torqueas a function of edge bevel on orthodontic arch wires. Am J Ort hod 1984;86:43-50.

2. Meling T, Odegaard J, Holt e K, Meling E, Segner D. A formula fo r the deflectionof an arch wire when subjected to a second-order moment. Am J Ort hod DentofacOrthop 1997 [in press].

3. Creekmore TD. On torque. J Cli n Ortho d 1979;13:305-10.4. Creekmore TD , Kunik RL. Straight wire: the next generation. A m J Orthod

Dentofac Orthop 1993;104:8-20.

5. Odegaard J, Meling T, Meling E, Segner D. A new instrument to measure torsionalmoments in orthodontic appliances. Kieferorthop Mittl g 1993;6:53-61.

6. Meling T, Odegaard J, Meling E. A theoretical evaluation of the influence ofvariation in bracket slot height and wire rounding on the amount of torsional playbetween bracket and wire. Kieferorthop Mittl g 1993;7:41-8.

7. Meling T, Odegaard J, Meling E. Cross-sectional stability of square and rectangularstainless steel wires. Kieferorthop Mittl g 1994;8:41-54.

8. Meling T, Odegaard J. On the mechanical properties of square and rectangularstainless steel wires tested in torsion. Am J Orthod Dentofac Ortho p 1997;111:310-20.

9. Meling T, Odegaard J, Meling E. The effect of cross-sectional dimensionalvariation of square and rectangular chrome-cobalt wires on torsion. Angle Orthod[in press].

10. Dalhberg G. Statistical methods for medical and biological students. New York:Interscience Publications; 1940.

11. Odegaard J. The skeletal profile of Norwegian children from age 4 to 10 years. [Dr.odont, thesis.] Bergen: University of Bergen, 1970.

12. Houston WJB. The analysis of errors in orthodontic measurements. Am J Orthod

1983;83:382-90.