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The effects of change in the incisal guide angle on cusp angulation
The effects of change on cusp angulation
in the incisal
Finn Tengs Christensen, L.D.S.* Uniuersity of Bergen, School of Dentistry,
Bergen,
guide
angle
Norway
e incisal guide on an edentulous patient is established by the dentist when lh positioning the front teeth. He must consider esthetics, ridge fullness, and ridge relation, which may influence incisal guide angle. He must also consider denture stability. A decreased incisal guide inclination reduces the horizontal forces on dentures during mastication. The stability of the denture is, therefore, influenced by the inclination of the incisal guidance. The incisal guide angle is often changed by the dentist at the try-in of the wax denture. In connection with the alteration, the cusp angulation must be changed accordingly in the articulator if balanced occlusion is to be maintained. The cusp angulation may be changed without knowledge of any theories. However, the problem and empiric formulas are discussed among dentists with advanced knowledge. Consequently, there is a certain need for more knowledge and more exact theories about this problem. The intention of this study is to express in figures the corresponding alterations of the cusp angulation necessary when the incisal guide inclination is changed and when balanced occlusion is to be maintained. THE CUSP INCLINE
FORMULAS
Most investigations concerning the ratio between incisal/condylar guide angle and cusp angulation are based on empirical considerations.l-G Most conveniently, however, the laws of articulation are expressed in Thielemann’s formula for articulation” : CG
-
IG
where : CG is the condylar guide angle, ZG is the incisal guide angle, *Prosthetic
Department.
93
94
J. I’rosth.
Christensen
Drnt.
July,
1971
CA is the cusp angulation, op is the incline of the plane of orientation, oc is the prominence of the curve of occlusion.
The relationship among the incisal guide angle, the cusp angulation, lar guide angle is expressed more accurately by Swenson’s formula : ’ cusp Incisal Fraction of incline = incline + distance incisal guidance from angle angle
p&t=
and the condy-
- gg
top), and If the condylar guide angle (CG ) , the incline of the plane of orientation formula the prominence of the curve of occlusion (oc) are fixed, ‘I’hielemann’s expresses the cusp angulation (CA) as a function of the incisal guide angle JIG’:. Swenson’s forrnula shows that the corresponding cusp angulation is equal to the incisal incline angle plus a fraction of the difference between the condylar guide angle and the incisal guide angle. This fraction depends on the distance front the incisal guide (incisal point) to the cusp in rluestion. Christensen has shown that this formula is correct.7 By using the symbols in Thiclemann’s formula, Swenson’s forlnula can be expressed in the following way : CA = IG t- d (CG - IG) Table
incisal
I. Protrusive cusp angulations guide inclinations
Condylar
guide
IO”
3rd molar distal cup 2nd molar distal cup 1st molar distal cup 2nd premolar cuspid
5.68’
4.49” 3.29” 2.10” 0.90”
(
by various
20”
/
30”
condylar
/
40”
15.39” 12.25” 9.04”
10.76” 8.48” 6.24”
3.98” 1.70”
guide
/
20.04” 16.11” 11.92” 7.65”
.5.79” 2.49”
3.30”
angles
50”
and
/
24.89” 20.13” 15.05” 9.70”
zero
60” 30.33” 24.79O 18.70” 12.15” 5.28”
4.19”
When the incisal guide angle is equal to zero degrees, the condylar guide angle is also identical with the cid angle (cid angle: condylar incisal difference angle). Consequently the figures in the table also represent the cid angle (cf. Swenson’s formula for cusp angulation) The
figures
Table
II.
concern
situations
The influence
with
distal cusp distal cusp distal cusp
2nd premolar cuspid
axis relation.
of the cid angle on the cusp aqgulation
Cid angle (Condylar guide angle minus in&al guide angle) 3rd molar 2nd molar 1st molar
an average
/ / -60
/
-50
-25 0
i
-40
-30
-20” -16” -12”
-15” -12”
/
-20
-30” -24” -18”
-20” -15”
-12”
-10”
-8”
-c;=
-5”
-4”
“_’3 0
.‘)L
values for that part of the upon the distance of the
cusp anala cusp in que:
-6”
Table II is based on Table I and shows approximate of the cid angle shown in this table. This fraction depends accuracy of the figures is 0.34” 2 0.26”.
-9”
-10” -8’ + *
4”
Volume
Number
26
Incisal
1
guide
angle
and
cusp angulation
95
where
d is the fraction of the distance from the incisal guide (incisal point) to the in question. The link (CG-IG) is also called the cid angle (condylar in&al difference angle) .’ Swenson’s formula is an empirical formula. It does not give exact values for the cusp angulations. By calculating cusp angulations at zero-degree incisal guide angle, Christensen* has found exact values for the factor d in Swenson’s formula. Factor d represents the following ratio by calculating the angle of the protrusive facets of the respective distal cusps of the posterior teeth : cusp
dMa = 5/10, dMz = 4/10, dMI = 3/10 and dPz = 2/10 With different the respective as follows7 :
condylar guide inclinations (CG) and incisal guide inclinations (IG) , cusp angulations (CA) for the distal cusps of the posterior teeth are
CA CA CA CA
for for for for
M3 Mz M1 Pz
= = = =
IG IG IG IG
t + + t
5/10 4/10 3/10 2/10
(CG (CG (CG (CC
-
These formulas may be simplified. From the formula tion (CA) of M,, we get the following ratio: CA for
Mz =
IG + 4/10
(CGIG)
=
lo/10
IG
+ 4/10
CG
IG) IG) IG) IG)
of the sagittal - 4/10
IG
=
6/10
cusp angulaZG t
4/10 CG
where IG is the incisal guide angle and CG is the condylar guide angle. By simplifying the formulas for all posterior teeth in the same way, we get the following ratios : CA CA CA CA
These formulas
are called
for for for for
Ma Mz M1 Pz
= = = =
5/10 6/10 7/10 8/10
the Cusfi Incline
IG IG IG IG
+ + + +
5/10 4/10 3/10 2/10
CG CG CG CG
Formulas.
THE CUSP ANGULATION WHEN THE INCISAL GUIDE ANGLE IS CHANGED According to Swenson’s factors. One of these factors
-10 -5” -4” -3” -2” -1”
0 0” 0” 0” 0” 0”
I 1
formula, the cusp angulations are determined by two is the incisal guide angle. The other factor is the difer-
20
20
5” 4” 3” 2” 1”
10” 8’ 6” 4” 2”
which is due to the cid angle. The cusp angulation from the incisa.l point (c.f. Swenson’s formula for
i
30 15O 12” 9” 6” 3”
/
40 20” 16” 12” 8” 4”
)
50 25” 20” 15” 10” 3LO
1
60 30” 24” 18” 12” 6”
is equal to the incisal guide angle plus the fraction cusp angulation). Compared with Table I, the
96
Christensen
Table
III. The third
0” 10” 20” 30” 40”
1
/
50"
60” 70”
’ /
molar’s
cusp incline
table
0"
10”
20”
,YO’
,1~=
0” -0 3
5” 10”
10” 15” 20” ‘:, =
20”
ii’,: ‘)-. ‘) =
30”
15” :‘O” ‘J-c ,.) 30” 35 =
3,.).- =
30"
33"
40"
30” 35”
35” 40”
40” 45”
4.i
;;I
’
.X0
i
500
60
‘0” 22 p 30” :i 5 O 40”
‘1 ,.I.- 0 :iri \ I5 10 ,> 1.3
30” :i ,r ^ -1fi’ 1 -,*
43 "
i ( Ii'
5I1 -; -1 "
50” r .- 0 J.1
i i ‘. 60“
Ml” 6.5 ’
The protrusive cusp angulation of the distal cusp of the lower third molar by conclylat guide angles from 0” to 60”, and incisal guide inclinations from 0” to 70”. The figures conccrt~ average axis relation of the casts and are calculated in accordance with the C:usp Inclinr~ Formulas and Table II. Accuracy: 0.34” 2 0.26”.
Table
IV. The second molar’s
cusp incline
tahlc -.
30”
!
40’
/
50;
60’; 24” :jc o 36’ -1-2’
40” 50” 60” 70”
i ’
24” 30” 36” 42”
“8” X4“ 40 o 46”
32” 38 = 44’ :I 0 ’
.36 o .$“” ‘18 o 5 1=
40” 46” 52”
44’ :iflC 56’
58”
62“
411” 54’ 611” 66.
The protrusive cusp angulation of the distal cusp of the lower second molar by cond& guide angles from 0” to 60”, and incisal guide inclinations from 0” to 70”. The figures concerti average axis relation of the casts and are calculated in accordance with the C:llsp Incline, Formulas and Table II. Accuracy: 0.34” i: 0.26”.
cue between the condylarjincisal guide angle, the cid angle. When the in&al ,guidt: angIe is equal to zero degrees, the condylar
Volume iTumber
In&al
26 1
Table
V. The first molar’s
;xi
@ 0”
I
0”
10” 20” 30” 40” 50” 60” 70”
’
7” 14” 21” 28” 35” 42” 49”
)
cusp incline
inclinations Tables III,
and calculated IV, and V.
THE SIGNIFICANCE
angle
and
cusp angulation
97
table
*@
2o”
3” 10” 17” 24” 31” 38” 45” 52”
6” 13” 20” 27” 34” 41” 48” 55”
The protrusive cusp angulations of guide angles from 0’ to 60”, and incisal average axis relation of the casts and Formulas and Table II. Accuracy: 0.34”
guide
;
3o”
*@
9” 16” 23” 30” 37” 44” 51” 58”
12” 19” 26” 33” 40” 47” 54” 61”
;
5o” 15” 22” 29” 36” 43” 50” 57” 64”
)
@” 18” 25’ 32 c’ 39’ 46” 53” 60” 67”
the distal cusp of the lower first molar by condylar guide inclinations from 0” to 70”. The figures concern are calculated in accordance with the Cusp Incline t 0.26”.
by means
of the Cusp Incline
Formulas,
are shown
in
OF THE TABLES
The figures in Table I refer to an average case concerning the sagittal length of the dental arch8 and an average axis relation (c.f. Bonwill’s triangle equal to 100 mm. and Balkwill’s angle equal to 26O) .g-12 Table II represents approximate figures and is a simplification of Table I. For average situations, the accuracy of Table II is within lo, which influences the cusp height less than 0.1 mm. Consequently, the Cusp Incline Formulas, as well as the Tables III, IV, and V, show the same inaccuracy as that of Table II. Compared to Table I, a statistical calculation shows a mean error of 0.34O with a standard deviation of 0.26’ (0.34O + 0.26’). HOW
TO OBTAIN
THE DESIRED
CUSP ANGULATION
In order to obtain a balanced occlusion for complete dentures, it is sufficient to have contact in the front and the last molars on either side in eccentric occlusions. If you work with 20’ cusps, for instance, and the desired cusp angulation for the second molar (Table IV) has to be 30°, you can use the occlusal curve by sloping the tooth loo which gives an effective cusp angulation of 3OO.‘” With cuspless posterior teeth, it is convenient to use a balancing ramp. If the balancing ramp occupies the place of the second molar, it may be sloped in accordance with Table IV. SUMMARY The influence on the cusp angulation when altering the incisal guide angle, has been expressed by means of simple formulas and has been gathered into three tables. The formulas and figures are accurate within 1’ in an average situation.
98
J. Prosth. Dent. July, 1971
Christensen
References 1. Boucher, C. 0.: Swenson’s Complete Dentures, ed. 5, St. Louis, 1964, The C. V, Mosby Company, p. 310. 2. Cysi, A.: Kieferbewegung und Zahnform, in Scheff and Pichler, editors: Handbucb dcr Zahnheilkunde, Band IV, Berlin und Wien, 1929, Urban und Schwarzcnberg. 3. IIanau, R.: Full Denture Prosthesis, ed. 4, Buffalo, 1930, R. Hanau. .f. Frahm, F. W.: Incisal Guidance-its Influence in Compensation and Balance. J. :\mer. Iknt. ASS. 13: 771-785,19'26. :5. Trapozzano, V. R.: Laws of Articulation, J. PROSTH. DENT. 13: 34-44,1963. 6. Thielemann, K.: Biomechanik der Pamdentose, ed. 1, Berlin, 1938, Hermann Meusser Verlag. 7. Christensen, F. T.: Cusp Angulation for Complete Dentures, J. PROSTH. DEW. 8: !+I& 923, 1958. 8. Christensen, F. T.: The Effect of Incisal Guidance on Cusp Angulation in Prosthetic Occlusion, J. PROSTH. DENT. 11: 48-54, 1961. 9. Bonwill, W. G.: The Scientific Articulation of the Human Teeth as Founded on Gometrical, Mathematical, and Mechanical Laws, D. Item. Int. 21: 617-643, 873-880, 1899, 10. Balkwill. F. H.: The Best Form and Arrangement of Artificial Teeth for Mastication, Brit. J. Dent. Sci. 9: 278-282, 1886. 11. Christensen, F. T.: Balkwill’s Angle for Complete Dentures, J. PROSTH. DEST. 10: 95-90,
1960. 12. 13.
Christensen, F. T.: The D~xT. 9: 791-796, 1959. Christensen, F. T.: The 10: 637-642, 1960. UXIVERSITY SCHOOL AR~TADv.
OF BERGEN OF DENTISTRY
17 5000 BERGEX,
NORWAY
Effect
of Bonwill’s
Compensating
Curve
Triangle for
on Complete Complete
Dentures,
Dentures,
Jo PROSTH
J. PKOSTH.
DENT
in the incisal
Finn Tengs Christensen, L.D.S.* Uniuersity of Bergen, School of Dentistry,
Bergen,
guide
angle
Norway
e incisal guide on an edentulous patient is established by the dentist when lh positioning the front teeth. He must consider esthetics, ridge fullness, and ridge relation, which may influence incisal guide angle. He must also consider denture stability. A decreased incisal guide inclination reduces the horizontal forces on dentures during mastication. The stability of the denture is, therefore, influenced by the inclination of the incisal guidance. The incisal guide angle is often changed by the dentist at the try-in of the wax denture. In connection with the alteration, the cusp angulation must be changed accordingly in the articulator if balanced occlusion is to be maintained. The cusp angulation may be changed without knowledge of any theories. However, the problem and empiric formulas are discussed among dentists with advanced knowledge. Consequently, there is a certain need for more knowledge and more exact theories about this problem. The intention of this study is to express in figures the corresponding alterations of the cusp angulation necessary when the incisal guide inclination is changed and when balanced occlusion is to be maintained. THE CUSP INCLINE
FORMULAS
Most investigations concerning the ratio between incisal/condylar guide angle and cusp angulation are based on empirical considerations.l-G Most conveniently, however, the laws of articulation are expressed in Thielemann’s formula for articulation” : CG
-
IG
where : CG is the condylar guide angle, ZG is the incisal guide angle, *Prosthetic
Department.
93
94
J. I’rosth.
Christensen
Drnt.
July,
1971
CA is the cusp angulation, op is the incline of the plane of orientation, oc is the prominence of the curve of occlusion.
The relationship among the incisal guide angle, the cusp angulation, lar guide angle is expressed more accurately by Swenson’s formula : ’ cusp Incisal Fraction of incline = incline + distance incisal guidance from angle angle
p&t=
and the condy-
- gg
top), and If the condylar guide angle (CG ) , the incline of the plane of orientation formula the prominence of the curve of occlusion (oc) are fixed, ‘I’hielemann’s expresses the cusp angulation (CA) as a function of the incisal guide angle JIG’:. Swenson’s forrnula shows that the corresponding cusp angulation is equal to the incisal incline angle plus a fraction of the difference between the condylar guide angle and the incisal guide angle. This fraction depends on the distance front the incisal guide (incisal point) to the cusp in rluestion. Christensen has shown that this formula is correct.7 By using the symbols in Thiclemann’s formula, Swenson’s forlnula can be expressed in the following way : CA = IG t- d (CG - IG) Table
incisal
I. Protrusive cusp angulations guide inclinations
Condylar
guide
IO”
3rd molar distal cup 2nd molar distal cup 1st molar distal cup 2nd premolar cuspid
5.68’
4.49” 3.29” 2.10” 0.90”
(
by various
20”
/
30”
condylar
/
40”
15.39” 12.25” 9.04”
10.76” 8.48” 6.24”
3.98” 1.70”
guide
/
20.04” 16.11” 11.92” 7.65”
.5.79” 2.49”
3.30”
angles
50”
and
/
24.89” 20.13” 15.05” 9.70”
zero
60” 30.33” 24.79O 18.70” 12.15” 5.28”
4.19”
When the incisal guide angle is equal to zero degrees, the condylar guide angle is also identical with the cid angle (cid angle: condylar incisal difference angle). Consequently the figures in the table also represent the cid angle (cf. Swenson’s formula for cusp angulation) The
figures
Table
II.
concern
situations
The influence
with
distal cusp distal cusp distal cusp
2nd premolar cuspid
axis relation.
of the cid angle on the cusp aqgulation
Cid angle (Condylar guide angle minus in&al guide angle) 3rd molar 2nd molar 1st molar
an average
/ / -60
/
-50
-25 0
i
-40
-30
-20” -16” -12”
-15” -12”
/
-20
-30” -24” -18”
-20” -15”
-12”
-10”
-8”
-c;=
-5”
-4”
“_’3 0
.‘)L
values for that part of the upon the distance of the
cusp anala cusp in que:
-6”
Table II is based on Table I and shows approximate of the cid angle shown in this table. This fraction depends accuracy of the figures is 0.34” 2 0.26”.
-9”
-10” -8’ + *
4”
Volume
Number
26
Incisal
1
guide
angle
and
cusp angulation
95
where
d is the fraction of the distance from the incisal guide (incisal point) to the in question. The link (CG-IG) is also called the cid angle (condylar in&al difference angle) .’ Swenson’s formula is an empirical formula. It does not give exact values for the cusp angulations. By calculating cusp angulations at zero-degree incisal guide angle, Christensen* has found exact values for the factor d in Swenson’s formula. Factor d represents the following ratio by calculating the angle of the protrusive facets of the respective distal cusps of the posterior teeth : cusp
dMa = 5/10, dMz = 4/10, dMI = 3/10 and dPz = 2/10 With different the respective as follows7 :
condylar guide inclinations (CG) and incisal guide inclinations (IG) , cusp angulations (CA) for the distal cusps of the posterior teeth are
CA CA CA CA
for for for for
M3 Mz M1 Pz
= = = =
IG IG IG IG
t + + t
5/10 4/10 3/10 2/10
(CG (CG (CG (CC
-
These formulas may be simplified. From the formula tion (CA) of M,, we get the following ratio: CA for
Mz =
IG + 4/10
(CGIG)
=
lo/10
IG
+ 4/10
CG
IG) IG) IG) IG)
of the sagittal - 4/10
IG
=
6/10
cusp angulaZG t
4/10 CG
where IG is the incisal guide angle and CG is the condylar guide angle. By simplifying the formulas for all posterior teeth in the same way, we get the following ratios : CA CA CA CA
These formulas
are called
for for for for
Ma Mz M1 Pz
= = = =
5/10 6/10 7/10 8/10
the Cusfi Incline
IG IG IG IG
+ + + +
5/10 4/10 3/10 2/10
CG CG CG CG
Formulas.
THE CUSP ANGULATION WHEN THE INCISAL GUIDE ANGLE IS CHANGED According to Swenson’s factors. One of these factors
-10 -5” -4” -3” -2” -1”
0 0” 0” 0” 0” 0”
I 1
formula, the cusp angulations are determined by two is the incisal guide angle. The other factor is the difer-
20
20
5” 4” 3” 2” 1”
10” 8’ 6” 4” 2”
which is due to the cid angle. The cusp angulation from the incisa.l point (c.f. Swenson’s formula for
i
30 15O 12” 9” 6” 3”
/
40 20” 16” 12” 8” 4”
)
50 25” 20” 15” 10” 3LO
1
60 30” 24” 18” 12” 6”
is equal to the incisal guide angle plus the fraction cusp angulation). Compared with Table I, the
96
Christensen
Table
III. The third
0” 10” 20” 30” 40”
1
/
50"
60” 70”
’ /
molar’s
cusp incline
table
0"
10”
20”
,YO’
,1~=
0” -0 3
5” 10”
10” 15” 20” ‘:, =
20”
ii’,: ‘)-. ‘) =
30”
15” :‘O” ‘J-c ,.) 30” 35 =
3,.).- =
30"
33"
40"
30” 35”
35” 40”
40” 45”
4.i
;;I
’
.X0
i
500
60
‘0” 22 p 30” :i 5 O 40”
‘1 ,.I.- 0 :iri \ I5 10 ,> 1.3
30” :i ,r ^ -1fi’ 1 -,*
43 "
i ( Ii'
5I1 -; -1 "
50” r .- 0 J.1
i i ‘. 60“
Ml” 6.5 ’
The protrusive cusp angulation of the distal cusp of the lower third molar by conclylat guide angles from 0” to 60”, and incisal guide inclinations from 0” to 70”. The figures conccrt~ average axis relation of the casts and are calculated in accordance with the C:usp Inclinr~ Formulas and Table II. Accuracy: 0.34” 2 0.26”.
Table
IV. The second molar’s
cusp incline
tahlc -.
30”
!
40’
/
50;
60’; 24” :jc o 36’ -1-2’
40” 50” 60” 70”
i ’
24” 30” 36” 42”
“8” X4“ 40 o 46”
32” 38 = 44’ :I 0 ’
.36 o .$“” ‘18 o 5 1=
40” 46” 52”
44’ :iflC 56’
58”
62“
411” 54’ 611” 66.
The protrusive cusp angulation of the distal cusp of the lower second molar by cond& guide angles from 0” to 60”, and incisal guide inclinations from 0” to 70”. The figures concerti average axis relation of the casts and are calculated in accordance with the C:llsp Incline, Formulas and Table II. Accuracy: 0.34” i: 0.26”.
cue between the condylarjincisal guide angle, the cid angle. When the in&al ,guidt: angIe is equal to zero degrees, the condylar
Volume iTumber
In&al
26 1
Table
V. The first molar’s
;xi
@ 0”
I
0”
10” 20” 30” 40” 50” 60” 70”
’
7” 14” 21” 28” 35” 42” 49”
)
cusp incline
inclinations Tables III,
and calculated IV, and V.
THE SIGNIFICANCE
angle
and
cusp angulation
97
table
*@
2o”
3” 10” 17” 24” 31” 38” 45” 52”
6” 13” 20” 27” 34” 41” 48” 55”
The protrusive cusp angulations of guide angles from 0’ to 60”, and incisal average axis relation of the casts and Formulas and Table II. Accuracy: 0.34”
guide
;
3o”
*@
9” 16” 23” 30” 37” 44” 51” 58”
12” 19” 26” 33” 40” 47” 54” 61”
;
5o” 15” 22” 29” 36” 43” 50” 57” 64”
)
@” 18” 25’ 32 c’ 39’ 46” 53” 60” 67”
the distal cusp of the lower first molar by condylar guide inclinations from 0” to 70”. The figures concern are calculated in accordance with the Cusp Incline t 0.26”.
by means
of the Cusp Incline
Formulas,
are shown
in
OF THE TABLES
The figures in Table I refer to an average case concerning the sagittal length of the dental arch8 and an average axis relation (c.f. Bonwill’s triangle equal to 100 mm. and Balkwill’s angle equal to 26O) .g-12 Table II represents approximate figures and is a simplification of Table I. For average situations, the accuracy of Table II is within lo, which influences the cusp height less than 0.1 mm. Consequently, the Cusp Incline Formulas, as well as the Tables III, IV, and V, show the same inaccuracy as that of Table II. Compared to Table I, a statistical calculation shows a mean error of 0.34O with a standard deviation of 0.26’ (0.34O + 0.26’). HOW
TO OBTAIN
THE DESIRED
CUSP ANGULATION
In order to obtain a balanced occlusion for complete dentures, it is sufficient to have contact in the front and the last molars on either side in eccentric occlusions. If you work with 20’ cusps, for instance, and the desired cusp angulation for the second molar (Table IV) has to be 30°, you can use the occlusal curve by sloping the tooth loo which gives an effective cusp angulation of 3OO.‘” With cuspless posterior teeth, it is convenient to use a balancing ramp. If the balancing ramp occupies the place of the second molar, it may be sloped in accordance with Table IV. SUMMARY The influence on the cusp angulation when altering the incisal guide angle, has been expressed by means of simple formulas and has been gathered into three tables. The formulas and figures are accurate within 1’ in an average situation.
98
J. Prosth. Dent. July, 1971
Christensen
References 1. Boucher, C. 0.: Swenson’s Complete Dentures, ed. 5, St. Louis, 1964, The C. V, Mosby Company, p. 310. 2. Cysi, A.: Kieferbewegung und Zahnform, in Scheff and Pichler, editors: Handbucb dcr Zahnheilkunde, Band IV, Berlin und Wien, 1929, Urban und Schwarzcnberg. 3. IIanau, R.: Full Denture Prosthesis, ed. 4, Buffalo, 1930, R. Hanau. .f. Frahm, F. W.: Incisal Guidance-its Influence in Compensation and Balance. J. :\mer. Iknt. ASS. 13: 771-785,19'26. :5. Trapozzano, V. R.: Laws of Articulation, J. PROSTH. DENT. 13: 34-44,1963. 6. Thielemann, K.: Biomechanik der Pamdentose, ed. 1, Berlin, 1938, Hermann Meusser Verlag. 7. Christensen, F. T.: Cusp Angulation for Complete Dentures, J. PROSTH. DEW. 8: !+I& 923, 1958. 8. Christensen, F. T.: The Effect of Incisal Guidance on Cusp Angulation in Prosthetic Occlusion, J. PROSTH. DENT. 11: 48-54, 1961. 9. Bonwill, W. G.: The Scientific Articulation of the Human Teeth as Founded on Gometrical, Mathematical, and Mechanical Laws, D. Item. Int. 21: 617-643, 873-880, 1899, 10. Balkwill. F. H.: The Best Form and Arrangement of Artificial Teeth for Mastication, Brit. J. Dent. Sci. 9: 278-282, 1886. 11. Christensen, F. T.: Balkwill’s Angle for Complete Dentures, J. PROSTH. DEST. 10: 95-90,
1960. 12. 13.
Christensen, F. T.: The D~xT. 9: 791-796, 1959. Christensen, F. T.: The 10: 637-642, 1960. UXIVERSITY SCHOOL AR~TADv.
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