Statics of Partial Dentures










Statics of Partial
Dentures
2 11
Basic Terms in Mechanics
This section outlines the basic terms in statics and dynamics that are used in dental tech-
nology. Statics is the study of the equilibrium of forces acting on a rigid body. In statics,
rigid bodies are structures that deform so little when loaded by forces that the points of
application of force undergo minimal displacement. Equilibrium refers to the state when
a rigid body is at rest or in uniform motion.
There are seven variables fundamental to physics and engineering: length, time, mass,
temperature, current intensity, amount of substance, and light intensity. Other variables
are derived from these, including velocity, work, and density. Quantities are either scalar
or vector. Scalar quantities are represented by a numeric value and a unit—for example,
time (t), temperature (T), mass (m), and electric charge (Q). Vector (or vectorial) quanti-
ties are represented by a numeric value, a unit, and a direction—for example, velocity
(v = m/s), electric  eld strength, and force. The character of a vector quantity is deter-
mined by the directional dependence of its action.
Forces are bound, aligned vectors that can be displaced along their line of action. They
can be depicted as arrows in a diagram. The of cial unit of force is the Newton (1 N =
1 kg × 1 m/s
2
), and force is characterized by the following:
• Magnitude, number, and unit (eg, 30 N)
Direction, represented by the vector arrow, in which the tip points the direction and the
length represents the measure of force
• Position of the line of action on which the force can be moved
In equilibrium, any force (action force or input force) causes a counterforce (reaction
force or output force) that is equal and in the opposite direction (Newton’s third law).
If, for example, a body rests on a solid support, its weight presses on that support; the
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212
Statics of Partial Dentures
action force (G) is absorbed by the support by an
equivalently sized reaction force (F), or else the
body is not in the resting state (action force =
reaction force).
Forces that act on a body are combined by geo-
metric addition to form a resultant force. This is
done with a parallelogram of forces for two forc-
es or with a polygon of forces for several forces.
Single forces (components) on a common line
of action can be added together or subtracted; the
sum or difference is the resultant (Fig 7-1). Single
forces on different lines of action are combined
to form a polygon of forces, and the resultant is
determined from the diagram.
In a parallelogram of forces, two forces with dif-
ferent directions but the same point of force ap-
plication are combined in the diagram to produce
a resultant. This resultant is obtained by drawing a
straight line from the origin to the intersection of
the parallel forces (Fig 7-2). If there are more than
two forces, a polygon of forces is constructed, and
the resultant is drawn from the origin of the rst
vector to the tip of the last vector (Fig 7-3).
Where there are different points of force appli-
cation, the forces are moved along their lines of
action to a common point of intersection to form
a polygon of forces (Fig 7-4). Now the line of ac-
tion and magnitude of the resultant are known
but not its point of force application.
Forces can also be resolved into two compo-
nents with the parallelogram of forces, provided
the direction or magnitude of the components is
known. If the direction is known, the lines of ac-
tion are placed through the point of force applica-
tion, and the parallelogram of forces is construct-
ed. If the magnitude of the components is known,
Fig 7-1 Forces that have a common line of action can be combined by simple
addition or subtraction. The resultant force lies on this same line of action.
Line of
action
F
1
F
2
F
3
(F
1
+ F
2
– F
3
)
= F
res
Fig 7-2 If two forces are not parallel but have
a common point of application, the resultant
force is determined by means of a parallelo-
gram of forces. A parallelogram is formed, the
diagonal is plotted, and the resultant is deter-
mined based on magnitude and direction.
F
1
F
2
F
res
α
F
2
F
1
F
3
F
2
F
1
F
3
(F
2
)
F
res
(F
3
)
Fig 7-3 The resultant of several nonparallel forces is determined by
means of a polygon of forces. The force vectors are moved parallel
to each other and strung together so that the resultant can be plot-
ted from the origin of the rst vector to the tip of the last vector.
F
1
F
2
F
res
F
1
F
2
(F
2
)
Fig 7-4 Force vectors that are not acting at one point can
be extended on their lines of action until they intersect.
The resultant can then be determined from a polygon of
forces.
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213
Basic Terms in Mechanics
one arc of a circle is drawn at the origin of the
force being resolved and another arc at the tip;
the magnitude of the force forms the radius of the
arc. The point of intersection of the arcs provides
the corners of the parallelogram (Fig 7-5).
A force couple comprises two equal and paral-
lel but oppositely directed forces. A force couple
exerts a static moment; if rotation takes place, it
is known as the turning moment (torque). Torque
is produced by a force that acts on a rigid body
when the line of action runs at some distance
from the fulcrum (Figs 7-6 and 7-7). Torque is the
product of force and the perpendicular distance
of its line of action from the fulcrum:
Moment (M) = Force (F) × Distance of action (X)
F
F
1
F
2
Draw the arcs of a circle
F
1
F
2
F
(F
1
)
F
Fig 7-5 A given force can be resolved if the magnitudes of the single forces
are known. To do this, a polygon of forces is constructed by drawing arcs of
circles at the origin and at the tip of the force being resolved, along with the
radius of the components. The intersection of the arcs establishes the apices
of the components. If the angle between the given force and the unknown
forces is known, the forces are drawn in the corresponding angle without the
magnitude; they are moved parallel to the polygon of forces until they enclose
the given force as a diagonal.
L
F
M
L
M
F
Fig 7-6 Torque is an axial vector. Such vectors
can be classied as free vectors, which are not
bound to any lines of action but can be moved
in parallel. Counterclockwise moments are
identied with a negative sign, and clockwise
moments are identied with a positive sign. If
a force acting on a tooth is not in the direction
of the tooth axis or runs at a distance from the
axis, a torque acts on the tooth. The torques
countering the acting forces have to be applied
by the periodontium.
F F
F
L
L
F
S
F
H
F
S
F
H
F
S
L
H
L
H
L
S
M
M
L
S
M
Fig 7-7 The periodon-
tium is the least protect-
ed against eccentric
forces (not acting axial-
ly). In multiple-rooted
teeth, eccentric forces
can be absorbed to a
certain degree. In the
case of tilted teeth, forc-
es encountered have di-
sastrous effects when
they produce torques
that tip the tooth.
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214
Statics of Partial Dentures
Newtons Laws of Motion
The forces acting on a rigid body can produce
either a progressive motion (translation) or a
circular motion (rotation). Newton’s rst law of
motion states that a rigid body is in equilibrium
if the resultant of all the forces and the sum of
all the torques equal zero. Without any additional
external force being exerted, the body continues
in a state of rest or in uniform motion in a straight
line. This property of a body can also be referred
to as inertia. From this, it may naturally be de-
duced that any change in the state of a motion or
rest is based on the action of forces. Furthermore,
the degree of force can actually be determined by
measuring the strength of the change in the state
of motion.
According to Newton’s second law of motion,
the acting force and the acceleration achieved be-
have in proportion to each other based on the fol-
lowing equation:
Force (F) = Mass (m) × Acceleration (a)
Here a new term is introduced: mass. Based on
what was outlined earlier, mass is bound to have
something to do with inertia. The mass of a body
depends on the speed at which it moves. Thus,
if a body moves very quickly, inertia will be very
great, or a great deal of force needs to be applied
to brake the motion of the body or make it move
even faster.
The unit of force is dened on the basis of this
equation: F = m × a. According to this, 1 N is the
force required to accelerate a mass of 1 kg by 1 m
per second squared:
1 N = 1 kg × 1 m/s
2
Newton’s third law of motion states that forces
always occur in pairs in the nature of an action
and reaction force. If a body exerts a force on an-
other body, it is reacted to with an equal and op-
posite force. This is also known as Newton’s law
of reaction. These interactive forces include:
Gravitational forces or forces of attraction be-
tween two bodies
Attraction and repulsion forces between electri-
cally charged bodies or magnets
• Intermolecular forces
Forces between the nucleons in the nucleus of
an atom
Volume is the spatial extent of the mass. Bodies
that have the same volume but are made of dif-
ferent materials therefore have a different mass.
Density denes the ratio of the mass of a body
to its volume:
Density =
Mass
Volume
or ρ =
m
v
where ρ stands for density, m stands for mass,
and v stands for volume.
The term density is initially hard to grasp be-
cause, based on the experience of our senses,
wood seems just as dense as metal: Both are
solid and both are opaque; wood is simply lighter
than metal. This property should be referred to as
density, namely, how much mass of a substance
is accommodated in a specic spatial volume.
The dimension of density is g/cm
3
(kg/dm
3
or kg/
m
3
). The atoms are most densely packed together
in metal because this is the only way the metallic
bond can function; thus, metal is very dense and
heavy, certainly heavier than wood. In the casting
technique, the amount of metal required can be
calculated from the mass of the wax pattern, the
density of the wax, and the density of the metal.
The density of solid and liquid bodies depends
on temperature; that is, density decreases with
rising temperature. In gaseous bodies, density
is also dependent on pressure, which is why the
term condensing is used when gaseous bodies
are compressed.
Principles of Mechanical
Systems
When partial and complete dentures are being
constructed, the aim is always to achieve a com-
promise that combines the esthetic concerns with
secure seating of the denture under functional
conditions. Secure seating is determined not only
by the possibilities of anchorage to the residual
dentition or mucosa but also by the forms of
functional loading and the static relationships of
dentures on the dental arches. For this purpose,
it is necessary to work on the basic terms in stat-
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215
Principles of Mechanical Systems
ics that can be applied to a rigid body that rests
on a base and is supported by what are known
as bearings. These bearings are meant to absorb
all the forces acting on the rigid body. Depending
on the type of bearing, different support reactions
occur; bearings can be classied as ranging from
single-value to six-value bearings (Fig 7-8).
A single-value bearing can only absorb com-
pressive forces from one direction in space; this
is known as a oating or movable bearing. A
oating bearing does not offer stability because
a body whose bearing can only absorb compres-
sive forces threatens to tip when external forces
are applied. A xed bearing absorbs forces but no
moments from three directions in space; this is a
three-value bearing. A xed clamp is a six-value
bearing that can absorb all forces and moments.
Support reactions are determined by means of
the equilibrium conditions that apply to the static
system. There are two types of static systems:
statically determinate and statically indeterminate
systems. The notion of statically determinate or
indeterminate systems becomes clear when one
looks at a three-legged and a four-legged table.
A three-legged table will always stand stably; a
four-legged table will wobble unless one of the ta-
ble legs is variable in length and adjusted to allow
for the base on which it stands. If a four-legged
table does not wobble, even without a variable
fourth leg, this is because the table is adapting
to the support by distorting slightly. Similarly, a
statically indeterminate system wobbles and will
only reach a state of equilibrium if it deforms. In
a statically indeterminate system, the equilibrium
conditions are insufcient to calculate support re-
actions; here the deformation conditions provide
the equations that are lacking.
In a statically determinate system, the support
reactions can be ascertained from its equilibrium
conditions alone. Adding the term equilibrium
further broadens our insight into static systems.
There are three static states in relation to the
equilibrium position (Fig 7-9):
1. Stable equilibrium exists when a body seeks to
return to its initial position if displaced by ex-
ternal forces.
2. Unstable equilibrium exists when a body tries
to leave its original position.
3. Neutral equilibrium exists when any displace-
ment brings the body into a new equilibrium
position.
Floating bearing
Fixed bearing
Radial bearing
Sliding bearing
Fixed joint
Clamp
F
x
F
z
F
z
F
z
F
x
F
y
F
z
F
x
F
y
M
z
M
x
M
y
2
1
3
6
Fig 7-8 This chart shows different types of
bearings, the structure and symbols for the
bearings, and the corresponding reaction
sizes and bearing values. Note that only a
xed clamp is able to absorb all the acting
forces and moments.
Structure Symbol Reaction size Value
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216
Statics of Partial Dentures
The static states become clear from the follow-
ing system: A bar rests on two bearings without
being xed and protrudes beyond the bearing
points on one side. A load can be applied at three
different points on the bar (Fig 7-10):
1. The load lies between the two bearing points
so that all the compressive forces are placed on
the bearings, and the bar rests in stable equi-
librium.
Fig 7-9 The three static states: (a) In the stable equilibrium position, the body returns to its initial position when it is displaced by
external forces. (b) In the neutral equilibrium position, any displacement of the body produces a new equilibrium position. (c) In the
unstable equilibrium position, the body tries to leave its original position.
a b c
Fig 7-10 The static states, when transferred to a real case, demonstrate the special features of a static system: (a) A bar is placed
on two bearings and loaded in the middle; both bearings must absorb equal forces, namely ½F. (b) If the bar is not loaded in the
middle but over bearing A, bearing A has to absorb the entire force. While a stable state existed in the rst case, a neutral state now
exists because bearing B remains fully unloaded; this support reaction cannot be calculated at all. (c) If the same bar is now loaded
outside the bearings, an unstable state exists whereby bearing B is unable to compensate for the torque that arises. If bearing B
is a oating bearing, the bar will be levered off.
a b c
F
A
F
B
F
BA BA
F
A
F
F
A
F
M
BA
–F
B
Fig 7-11 A lever is a rigid body that can turn around an axis. In a class 2 lever, the fulcrum lies at one end and forces can act on the
lever at different distances from the fulcrum. In a class 1 lever, the fulcrum lies between the forces applied. For both types, the law
of levers applies: Force × Force arm = Load × Load arm (F
1
× L
1
= F
2
× L
2
). In this condition, the lever is in equilibrium (ie, it does
not move). Torques of equal size are acting on the lever in opposite directions, so the lever stays in the resting state.
L
1
L
2
F
1
F
2
L
1
L
2
F
1
F
2
L
1
L
2
F
1
F
2
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217
Forces Acting on the Residual Dentition
2. The load is located outside the bearing points
so that the compressive force can no longer be
absorbed by the bearing and the bar will tip; the
bar is in unstable equilibrium.
3. The load lies on one bearing point so that all
the compressive forces rest on that one bear-
ing, and the bar is in neutral equilibrium.
Unstable equilibrium can be converted into a
stable state if the bar is xed in a bearing. That
bearing now absorbs the forces that arise from
the torque of load and load arm up to the rst
bearing. Two terms now emerge that are taken
from the description of the rst law of levers. This
law expresses special equilibrium conditions per-
taining to a lever.
A lever is a rigid body that can be turned around
an axis (Fig 7-11). In a class 2 lever, the fulcrum
lies at one end, and in a class 1 lever, the fulcrum
lies in the middle. When equilibrium exists, the
following law of levers applies:
Force × Force arm = Load × Load arm
Forces Acting on the
Residual Dentition
Centric occlusion is dened as the hinge position
(maximal intercuspation) in which the teeth are
loaded axially (ie, centrically to their periodonti-
um). Eccentric loads during dynamic occlusion
are compensated for in a closed dental arch by
the approximal contacts, tissue coupling, and
anatomical double interlocking. In a partially
edentulous dentition, this functional interaction is
disrupted; the essential approximal support is in-
terrupted. Horizontally acting forces lead to tip-
ping and twisting of the remaining teeth.
On a solitary tooth, a horizontal action of force
occurs on the sloping surfaces of the cusps. If a
vertical force acts on a sloping surface, this load
is split into vertically and horizontally acting com-
ponents. The horizontally acting force component
will tip the tooth. The more sloping the surface, the
larger the horizontal force component becomes
in relation to the vertical component. Where tooth
surfaces slope by about 45 degrees, the vertical
and horizontal actions of force are equal. With
more pronounced tipping, the horizontal as well
as the vertical action becomes smaller in relation
to the perpendicular force being exerted. The geo-
metric and mathematic illustrations in Figs 7-12
to 7-14 show the relationship between the force
loading the tooth and the horizontally and verti-
cally acting forces.
The mathematic depiction of the actions of
force demonstrates the basic relationships. How-
ever, this view needs to be qualied. In normal
punctiform occlusal contact in a healthy denti-
tion, the slopes of the cusps will ensure that all of
the teeth are loaded centrically to their periodon-
tal tissues.
In a partially edentulous dentition with soli-
tary teeth, the horizontal force action cannot be
absorbed; the tooth is tipped and becomes dis-
placed. As a result, the loading conditions be-
come pathologic. A tooth that is already tilted will
be extremely stressed in its tipping by a vertically
acting force because the vertical force compo-
nent no longer loads the tooth exactly axially. The
pressure on the tilt becomes even greater.
Forces acting at a distance from the central
axis of the tooth act like lever forces, where the
distance from the central axis equates to the le-
ver arm. The vertical force component can work
with a lever arm that roughly corresponds to two-
thirds of the tooth length. If a tooth is already dis-
placed, horizontal and vertical force components
with different lever arms will act in the direction
of tipping.
When constructing partial dentures, it is impor-
tant to ensure that the remaining teeth are not
exposed to any eccentric action of force by the
retainers. Tipping of an abutment tooth by occlu-
sal rests must be prevented. In particular, a tooth
that is already tipped should not be engaged in its
sloping position.
Sagittal forces should run so that an abutment
tooth can brace itself via existing approximal con-
tacts. Therefore, in a shortened dental arch, sagit-
tal thrusts can be compensated for mesially if the
dental arch is closed mesially.
Transverse forces in a vestibular direction can
be prevented by contouring the articial occlusal
eld of the denture so that no effect arises from
transverse thrusts. Therefore, the articial teeth on
the partial denture must be placed as far lingually
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218
Statics of Partial Dentures
as possible so that the masticatory forces run
roughly through the middle of the alveolar ridge
of the edentulous segments of the dental arch.
Vertical masticatory forces should be absorbed
by occlusal rests in a supported denture. The
splinting parts of the retainers must absorb the
horizontally acting forces. The support points cre-
ated by the occlusal rests are assumed to be rigid.
The rigid anchorage of free-end saddles to the
residual dentition is the method of choice for
achieving statically determinate systems and
controllable loading on abutment teeth. Statically
indeterminate systems are outside the area of
statics analysis. If a free-end saddle has mixed
support, the mechanical system is no longer at
rest and can no longer be calculated by statics
methods. For this purpose, kinetics analysis crite-
ria should be used, and because this is the sphere
of anatomy and biology, the approaches of bioki-
netics should be adopted. Kinetics is the study of
movements and deformations in response to
forces and stresses (Fig 7-15).
Fig 7-12 When calculating the force components, the size of normal force is rst
established, which is perpendicular to the sloping surface: F
N
= F
S
× cos α, where F
N
is the normal force, F
S
is the force impacting on the tooth, and α is the angle of inclina-
tion of the tooth surface. Normal force is now broken down into horizontally and verti-
cally acting forces. The angle of inclination of the tooth surface occurs again between
the vertical force component and normal force, so that it can be used for calculation.
α
α
F
S
F
N
F
S
F
N
F
V
F
H
α
α
F
S
F
N
F
V
F
H
Fig 7-13 The horizontal force is then
dened as follows: F
H
= F
S
× sin α = F
S
× cos α × sin α. The vertical component
F
V
is then calculated: F
V
= F
N
× cos α =
F
S
× cos
2
α. If the tooth surface slopes
by 45 degrees, the vertical component
is as large as the horizontal component.
F
S
F
V
F
H
F
N
Fig 7-14 If the ratio of vertical to horizontal force component
is to be calculated, the result is
The more the angle of the slope of the tooth surface in-
creases beyond 45 degrees, the larger the horizontal force
component on the tooth becomes in relation to the vertical
force. Having said that, the horizontal force action becomes
smaller in relation to the vertical masticatory force striking
the tooth surface (F
S
); that is, the horizontal force compo-
nent is largest when the cusp inclination is 45 degrees.
Mathematic deduction of the function yields a maximum at
α = 45 degrees; it thus becomes clear that the tipping force
for a tooth will not exceed half of the vertically striking force
if the tooth stands perpendicular.
F
H
=
F
N
· sin α
F
V
F
N
· cos α
= tan α, where F
H
= F
V
× tan α (tan 45° = 1).
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Statics of Partial Dentures2 11Basic Terms in MechanicsThis section outlines the basic terms in statics and dynamics that are used in dental tech-nology. Statics is the study of the equilibrium of forces acting on a rigid body. In statics, rigid bodies are structures that deform so little when loaded by forces that the points of application of force undergo minimal displacement. Equilibrium refers to the state when a rigid body is at rest or in uniform motion. There are seven variables fundamental to physics and engineering: length, time, mass, temperature, current intensity, amount of substance, and light intensity. Other variables are derived from these, including velocity, work, and density. Quantities are either scalar or vector. Scalar quantities are represented by a numeric value and a unit—for example, time (t), temperature (T), mass (m), and electric charge (Q). Vector (or vectorial) quanti-ties are represented by a numeric value, a unit, and a direction—for example, velocity (v = m/s), electric  eld strength, and force. The character of a vector quantity is deter-mined by the directional dependence of its action. Forces are bound, aligned vectors that can be displaced along their line of action. They can be depicted as arrows in a diagram. The of cial unit of force is the Newton (1 N = 1 kg × 1 m/s2), and force is characterized by the following:• Magnitude, number, and unit (eg, 30 N) • Direction, represented by the vector arrow, in which the tip points the direction and the length represents the measure of force• Position of the line of action on which the force can be movedIn equilibrium, any force (action force or input force) causes a counterforce (reaction force or output force) that is equal and in the opposite direction (Newton’s third law). If, for example, a body rests on a solid support, its weight presses on that support; the http://dentalebooks.com 212Statics of Partial Denturesaction force (G) is absorbed by the support by an equivalently sized reaction force (F), or else the body is not in the resting state (action force = reaction force).Forces that act on a body are combined by geo-metric addition to form a resultant force. This is done with a parallelogram of forces for two forc-es or with a polygon of forces for several forces.Single forces (components) on a common line of action can be added together or subtracted; the sum or difference is the resultant (Fig 7-1). Single forces on different lines of action are combined to form a polygon of forces, and the resultant is determined from the diagram.In a parallelogram of forces, two forces with dif-ferent directions but the same point of force ap-plication are combined in the diagram to produce a resultant. This resultant is obtained by drawing a straight line from the origin to the intersection of the parallel forces (Fig 7-2). If there are more than two forces, a polygon of forces is constructed, and the resultant is drawn from the origin of the rst vector to the tip of the last vector (Fig 7-3).Where there are different points of force appli-cation, the forces are moved along their lines of action to a common point of intersection to form a polygon of forces (Fig 7-4). Now the line of ac-tion and magnitude of the resultant are known but not its point of force application. Forces can also be resolved into two compo-nents with the parallelogram of forces, provided the direction or magnitude of the components is known. If the direction is known, the lines of ac-tion are placed through the point of force applica-tion, and the parallelogram of forces is construct-ed. If the magnitude of the components is known, Fig 7-1 Forces that have a common line of action can be combined by simple addition or subtraction. The resultant force lies on this same line of action.Line of actionF1F2F3(F1 + F2 – F3) = FresFig 7-2 If two forces are not parallel but have a common point of application, the resultant force is determined by means of a parallelo-gram of forces. A parallelogram is formed, the diagonal is plotted, and the resultant is deter-mined based on magnitude and direction.F1F2FresαF2F1F3F2F1F3(F2)Fres(F3)Fig 7-3 The resultant of several nonparallel forces is determined by means of a polygon of forces. The force vectors are moved parallel to each other and strung together so that the resultant can be plot-ted from the origin of the rst vector to the tip of the last vector.F1F2FresF1F2(F2)Fig 7-4 Force vectors that are not acting at one point can be extended on their lines of action until they intersect. The resultant can then be determined from a polygon of forces.http://dentalebooks.com 213Basic Terms in Mechanicsone arc of a circle is drawn at the origin of the force being resolved and another arc at the tip; the magnitude of the force forms the radius of the arc. The point of intersection of the arcs provides the corners of the parallelogram (Fig 7-5).A force couple comprises two equal and paral-lel but oppositely directed forces. A force couple exerts a static moment; if rotation takes place, it is known as the turning moment (torque). Torque is produced by a force that acts on a rigid body when the line of action runs at some distance from the fulcrum (Figs 7-6 and 7-7). Torque is the product of force and the perpendicular distance of its line of action from the fulcrum:Moment (M) = Force (F) × Distance of action (X)FF1F2Draw the arcs of a circleF1F2F(F1)FFig 7-5 A given force can be resolved if the magnitudes of the single forces are known. To do this, a polygon of forces is constructed by drawing arcs of circles at the origin and at the tip of the force being resolved, along with the radius of the components. The intersection of the arcs establishes the apices of the components. If the angle between the given force and the unknown forces is known, the forces are drawn in the corresponding angle without the magnitude; they are moved parallel to the polygon of forces until they enclose the given force as a diagonal.LFMLMFFig 7-6 Torque is an axial vector. Such vectors can be classied as free vectors, which are not bound to any lines of action but can be moved in parallel. Counterclockwise moments are identied with a negative sign, and clockwise moments are identied with a positive sign. If a force acting on a tooth is not in the direction of the tooth axis or runs at a distance from the axis, a torque acts on the tooth. The torques countering the acting forces have to be applied by the periodontium.F FFLLFSFHFSFHFSLHLHLSMMLSMFig 7-7 The periodon-tium is the least protect-ed against eccentric forces (not acting axial-ly). In multiple-rooted teeth, eccentric forces can be absorbed to a certain degree. In the case of tilted teeth, forc-es encountered have di-sastrous effects when they produce torques that tip the tooth.http://dentalebooks.com 214Statics of Partial DenturesNewton’s Laws of MotionThe forces acting on a rigid body can produce either a progressive motion (translation) or a circular motion (rotation). Newton’s rst law of motion states that a rigid body is in equilibrium if the resultant of all the forces and the sum of all the torques equal zero. Without any additional external force being exerted, the body continues in a state of rest or in uniform motion in a straight line. This property of a body can also be referred to as inertia. From this, it may naturally be de-duced that any change in the state of a motion or rest is based on the action of forces. Furthermore, the degree of force can actually be determined by measuring the strength of the change in the state of motion.According to Newton’s second law of motion, the acting force and the acceleration achieved be-have in proportion to each other based on the fol-lowing equation:Force (F) = Mass (m) × Acceleration (a)Here a new term is introduced: mass. Based on what was outlined earlier, mass is bound to have something to do with inertia. The mass of a body depends on the speed at which it moves. Thus, if a body moves very quickly, inertia will be very great, or a great deal of force needs to be applied to brake the motion of the body or make it move even faster.The unit of force is dened on the basis of this equation: F = m × a. According to this, 1 N is the force required to accelerate a mass of 1 kg by 1 m per second squared:1 N = 1 kg × 1 m/s2Newton’s third law of motion states that forces always occur in pairs in the nature of an action and reaction force. If a body exerts a force on an-other body, it is reacted to with an equal and op-posite force. This is also known as Newton’s law of reaction. These interactive forces include:• Gravitational forces or forces of attraction be-tween two bodies• Attraction and repulsion forces between electri-cally charged bodies or magnets• Intermolecular forces• Forces between the nucleons in the nucleus of an atomVolume is the spatial extent of the mass. Bodies that have the same volume but are made of dif-ferent materials therefore have a different mass.Density denes the ratio of the mass of a body to its volume:Density = MassVolume or ρ = mvwhere ρ stands for density, m stands for mass, and v stands for volume.The term density is initially hard to grasp be-cause, based on the experience of our senses, wood seems just as dense as metal: Both are solid and both are opaque; wood is simply lighter than metal. This property should be referred to as density, namely, how much mass of a substance is accommodated in a specic spatial volume. The dimension of density is g/cm3 (kg/dm3 or kg/m3). The atoms are most densely packed together in metal because this is the only way the metallic bond can function; thus, metal is very dense and heavy, certainly heavier than wood. In the casting technique, the amount of metal required can be calculated from the mass of the wax pattern, the density of the wax, and the density of the metal.The density of solid and liquid bodies depends on temperature; that is, density decreases with rising temperature. In gaseous bodies, density is also dependent on pressure, which is why the term condensing is used when gaseous bodies are compressed.Principles of Mechanical SystemsWhen partial and complete dentures are being constructed, the aim is always to achieve a com-promise that combines the esthetic concerns with secure seating of the denture under functional conditions. Secure seating is determined not only by the possibilities of anchorage to the residual dentition or mucosa but also by the forms of functional loading and the static relationships of dentures on the dental arches. For this purpose, it is necessary to work on the basic terms in stat-http://dentalebooks.com 215Principles of Mechanical Systemsics that can be applied to a rigid body that rests on a base and is supported by what are known as bearings. These bearings are meant to absorb all the forces acting on the rigid body. Depending on the type of bearing, different support reactions occur; bearings can be classied as ranging from single-value to six-value bearings (Fig 7-8).A single-value bearing can only absorb com-pressive forces from one direction in space; this is known as a oating or movable bearing. A oating bearing does not offer stability because a body whose bearing can only absorb compres-sive forces threatens to tip when external forces are applied. A xed bearing absorbs forces but no moments from three directions in space; this is a three-value bearing. A xed clamp is a six-value bearing that can absorb all forces and moments.Support reactions are determined by means of the equilibrium conditions that apply to the static system. There are two types of static systems: statically determinate and statically indeterminate systems. The notion of statically determinate or indeterminate systems becomes clear when one looks at a three-legged and a four-legged table. A three-legged table will always stand stably; a four-legged table will wobble unless one of the ta-ble legs is variable in length and adjusted to allow for the base on which it stands. If a four-legged table does not wobble, even without a variable fourth leg, this is because the table is adapting to the support by distorting slightly. Similarly, a statically indeterminate system wobbles and will only reach a state of equilibrium if it deforms. In a statically indeterminate system, the equilibrium conditions are insufcient to calculate support re-actions; here the deformation conditions provide the equations that are lacking.In a statically determinate system, the support reactions can be ascertained from its equilibrium conditions alone. Adding the term equilibrium further broadens our insight into static systems. There are three static states in relation to the equilibrium position (Fig 7-9):1. Stable equilibrium exists when a body seeks to return to its initial position if displaced by ex-ternal forces.2. Unstable equilibrium exists when a body tries to leave its original position.3. Neutral equilibrium exists when any displace-ment brings the body into a new equilibrium position.Floating bearingFixed bearingRadial bearingSliding bearingFixed jointClampFxFzFzFzFxFyFzFxFyMzMxMy2136Fig 7-8 This chart shows different types of bearings, the structure and symbols for the bearings, and the corresponding reaction sizes and bearing values. Note that only a xed clamp is able to absorb all the acting forces and moments.Structure Symbol Reaction size Valuehttp://dentalebooks.com 216Statics of Partial DenturesThe static states become clear from the follow-ing system: A bar rests on two bearings without being xed and protrudes beyond the bearing points on one side. A load can be applied at three different points on the bar (Fig 7-10):1. The load lies between the two bearing points so that all the compressive forces are placed on the bearings, and the bar rests in stable equi-librium.Fig 7-9 The three static states: (a) In the stable equilibrium position, the body returns to its initial position when it is displaced by external forces. (b) In the neutral equilibrium position, any displacement of the body produces a new equilibrium position. (c) In the unstable equilibrium position, the body tries to leave its original position.a b cFig 7-10 The static states, when transferred to a real case, demonstrate the special features of a static system: (a) A bar is placed on two bearings and loaded in the middle; both bearings must absorb equal forces, namely ½F. (b) If the bar is not loaded in the middle but over bearing A, bearing A has to absorb the entire force. While a stable state existed in the rst case, a neutral state now exists because bearing B remains fully unloaded; this support reaction cannot be calculated at all. (c) If the same bar is now loaded outside the bearings, an unstable state exists whereby bearing B is unable to compensate for the torque that arises. If bearing B is a oating bearing, the bar will be levered off.a b cFAFBFBA BAFAFFAFMBA–FBFig 7-11 A lever is a rigid body that can turn around an axis. In a class 2 lever, the fulcrum lies at one end and forces can act on the lever at different distances from the fulcrum. In a class 1 lever, the fulcrum lies between the forces applied. For both types, the law of levers applies: Force × Force arm = Load × Load arm (F1 × L1 = F2 × L2). In this condition, the lever is in equilibrium (ie, it does not move). Torques of equal size are acting on the lever in opposite directions, so the lever stays in the resting state.L1L2F1F2L1L2F1F2L1L2F1F2http://dentalebooks.com 217Forces Acting on the Residual Dentition2. The load is located outside the bearing points so that the compressive force can no longer be absorbed by the bearing and the bar will tip; the bar is in unstable equilibrium.3. The load lies on one bearing point so that all the compressive forces rest on that one bear-ing, and the bar is in neutral equilibrium.Unstable equilibrium can be converted into a stable state if the bar is xed in a bearing. That bearing now absorbs the forces that arise from the torque of load and load arm up to the rst bearing. Two terms now emerge that are taken from the description of the rst law of levers. This law expresses special equilibrium conditions per-taining to a lever.A lever is a rigid body that can be turned around an axis (Fig 7-11). In a class 2 lever, the fulcrum lies at one end, and in a class 1 lever, the fulcrum lies in the middle. When equilibrium exists, the following law of levers applies:Force × Force arm = Load × Load armForces Acting on the Residual DentitionCentric occlusion is dened as the hinge position (maximal intercuspation) in which the teeth are loaded axially (ie, centrically to their periodonti-um). Eccentric loads during dynamic occlusion are compensated for in a closed dental arch by the approximal contacts, tissue coupling, and anatomical double interlocking. In a partially edentulous dentition, this functional interaction is disrupted; the essential approximal support is in-terrupted. Horizontally acting forces lead to tip-ping and twisting of the remaining teeth.On a solitary tooth, a horizontal action of force occurs on the sloping surfaces of the cusps. If a vertical force acts on a sloping surface, this load is split into vertically and horizontally acting com-ponents. The horizontally acting force component will tip the tooth. The more sloping the surface, the larger the horizontal force component becomes in relation to the vertical component. Where tooth surfaces slope by about 45 degrees, the vertical and horizontal actions of force are equal. With more pronounced tipping, the horizontal as well as the vertical action becomes smaller in relation to the perpendicular force being exerted. The geo-metric and mathematic illustrations in Figs 7-12 to 7-14 show the relationship between the force loading the tooth and the horizontally and verti-cally acting forces.The mathematic depiction of the actions of force demonstrates the basic relationships. How-ever, this view needs to be qualied. In normal punctiform occlusal contact in a healthy denti-tion, the slopes of the cusps will ensure that all of the teeth are loaded centrically to their periodon-tal tissues.In a partially edentulous dentition with soli-tary teeth, the horizontal force action cannot be absorbed; the tooth is tipped and becomes dis-placed. As a result, the loading conditions be-come pathologic. A tooth that is already tilted will be extremely stressed in its tipping by a vertically acting force because the vertical force compo-nent no longer loads the tooth exactly axially. The pressure on the tilt becomes even greater. Forces acting at a distance from the central axis of the tooth act like lever forces, where the distance from the central axis equates to the le-ver arm. The vertical force component can work with a lever arm that roughly corresponds to two-thirds of the tooth length. If a tooth is already dis-placed, horizontal and vertical force components with different lever arms will act in the direction of tipping.When constructing partial dentures, it is impor-tant to ensure that the remaining teeth are not exposed to any eccentric action of force by the retainers. Tipping of an abutment tooth by occlu-sal rests must be prevented. In particular, a tooth that is already tipped should not be engaged in its sloping position. Sagittal forces should run so that an abutment tooth can brace itself via existing approximal con-tacts. Therefore, in a shortened dental arch, sagit-tal thrusts can be compensated for mesially if the dental arch is closed mesially.Transverse forces in a vestibular direction can be prevented by contouring the articial occlusal eld of the denture so that no effect arises from transverse thrusts. Therefore, the articial teeth on the partial denture must be placed as far lingually http://dentalebooks.com 218Statics of Partial Denturesas possible so that the masticatory forces run roughly through the middle of the alveolar ridge of the edentulous segments of the dental arch.Vertical masticatory forces should be absorbed by occlusal rests in a supported denture. The splinting parts of the retainers must absorb the horizontally acting forces. The support points cre-ated by the occlusal rests are assumed to be rigid.The rigid anchorage of free-end saddles to the residual dentition is the method of choice for achieving statically determinate systems and controllable loading on abutment teeth. Statically indeterminate systems are outside the area of statics analysis. If a free-end saddle has mixed support, the mechanical system is no longer at rest and can no longer be calculated by statics methods. For this purpose, kinetics analysis crite-ria should be used, and because this is the sphere of anatomy and biology, the approaches of bioki-netics should be adopted. Kinetics is the study of movements and deformations in response to forces and stresses (Fig 7-15).Fig 7-12 When calculating the force components, the size of normal force is rst established, which is perpendicular to the sloping surface: FN = FS × cos α, where FN is the normal force, FS is the force impacting on the tooth, and α is the angle of inclina-tion of the tooth surface. Normal force is now broken down into horizontally and verti-cally acting forces. The angle of inclination of the tooth surface occurs again between the vertical force component and normal force, so that it can be used for calculation.ααFSFNFSFNFVFHααFSFNFVFHFig 7-13 The horizontal force is then dened as follows: FH = FS × sin α = FS × cos α × sin α. The vertical component FV is then calculated: FV = FN × cos α = FS × cos2 α. If the tooth surface slopes by 45 degrees, the vertical component is as large as the horizontal component.FSFVFHFNFig 7-14 If the ratio of vertical to horizontal force component is to be calculated, the result isThe more the angle of the slope of the tooth surface in-creases beyond 45 degrees, the larger the horizontal force component on the tooth becomes in relation to the vertical force. Having said that, the horizontal force action becomes smaller in relation to the vertical masticatory force striking the tooth surface (FS); that is, the horizontal force compo-nent is largest when the cusp inclination is 45 degrees. Mathematic deduction of the function yields a maximum at α = 45 degrees; it thus becomes clear that the tipping force for a tooth will not exceed half of the vertically striking force if the tooth stands perpendicular.FH = FN · sin αFV FN · cos α= tan α, where FH = FV × tan α (tan 45° = 1).http://dentalebooks.com 219Spring Force and FrictionSpring Force and FrictionAccording to Newton’s rst and second laws of motion, forces cause changes in the movement of a rigid body. In the case of a nonrigid body, however, forces can also produce changes of shape; for instance, compressive forces can press together and tensile force can pull apart. There is actually no absolutely rigid body; every material has a certain elasticity.Metals display the property of returning to their original state after deformation. Although metals are not as elastic as rubber, within certain lim-its they can be bent or pulled by the application of force and then afterward spring back to their original state. Only when metals are exposed to excessive force can they deform permanently.In the elastic range of a material (whether rub-ber or metal), deformation is proportional to the application of force so that a proportionality fac-tor is introduced, which, in the case of springs, is known as the spring constant. This yields the following formula:Spring force = Spring constant × Spring deection or F = c × sSpring force is the cause of a change in the shape of a body, here specically a spring. The spring constant is the key value that is dependent on the material and on the shape of the spring body. The spring deection is the magnitude of the change of shape, here specically the change in length of a spring or the bending of a clasp arm. In dental technology, spring clip ttings are used mainly in the form of clasps as retainers.The proportionality of spring force and spring deection can be represented in a diagram illus-trating Hooke’s law, according to which deforma-tion is linear within the elastic range (Fig 7-16). Diagrams depicting the behavior of elastic bodies are known as spring characteristics; the area un-der the spring characteristic curve is the spring work. The steeper the spring characteristic curve, or the straight line according to Hooke’s law, the harder a spring is; this means the spring constant is very large.MechanicsBiokineticsBiologyAnatomyKinematics: Study of movements and deformationsDynamics: Study of forces, movements, and stressesStatics: Study of forces in a state of equilibriumKinetics: Study of movements under the inuence of forcesPhysiologyFig 7-15 Analysis of denture construction encompasses the following: (1) statics of the rigid denture body, where the retentive forces of the anchoring elements and the support reactions are examined; (2) science of the strength of materials, whereby the dimensions of denture frameworks for removable and xed dentures are determined to compensate for deformation caused by masticatory forces or thermal stresses; and (3) kinetics (biokinetics) to determine movements and support reactions of dentures with mixed support.http://dentalebooks.com 220Statics of Partial DenturesFriction is an energy-consuming form of resis-tance that impedes the relative motion of two bodies being moved against each other with their surfaces in contact. Friction force always acts in parallel to the contact surface; it is consistently smaller than the normal force with which the bodies press against each other, and it opposes movement. Following is the formula for calculat-ing friction force:Friction force = Friction coefcient × Normal force or F = µ × FnThe friction coefcient µ is a reference value that depends on several factors: (1) the material from which the friction bodies are composed; (2) the surface properties of the bodies; and (3) the nature of the movement in which the bodies slide past each other. The following distinctions are made.Static friction occurs when a body at rest on a supporting surface is being set in motion by ex-ternal forces. In this arrangement, static friction is as great as the acting force when the body starts to move. In this case, the friction is entirely in-dependent of the size of the contact area. Static friction only arises due to vertically acting normal force and the friction coefcient. The coefcient of static friction is denoted as µ0.The coefcient of static friction can be experi-mentally determined by inclining a plane until the body lying on it is set in motion. Equilibrium between static friction force and slope force then prevails. The geometric relationship can be ex-pressed as follows:µ0 = tan α0 (α0 = Angle of static friction)Sliding (or dynamic) friction occurs when a body in motion rubs on its supporting surface; when a body slides down an inclined plane at constant speed, this is known as sliding friction. The coefcient of sliding friction is calculated as:µ = tan α (α = Angle of sliding friction)Figure 7-17 lists the values of static and slid-ing friction coefcients for various material pairs. Rolling friction occurs when a body rolls on the supporting surface. Rolling friction is much small-er than sliding friction. It is dependent on the ma-terial and radius of the rolling wheel.FSS0SmaxS0F (N)SmaxS (mm)Fig 7-16 A spring is described by several terms. Spring force (F) is the force with which a spring is compressed, pulled, or bent. Spring deection (S) is the amount by which the spring force compresses, lengthens, or bends a spring. The variable S0 characterizes the original spring length before application of force; Smax denotes the maximum spring deection. In the dia-gram, the spring characteristic curve, which indicates spring deection over spring force, is an ascending straight line. The area under the spring characteristic curve represents the amount of spring work.Material pairing Static frictionSliding frictionDry LubricatedSteel/steel 0.15 0.1 0.01Steel/cast steel 0.19 0.18 0.01Cast iron/cast iron 0.25 0.2 0.1Fig 7-17 Static and sliding friction coefcients µ and µ0.http://dentalebooks.com 221Mixed SupportMixed SupportThis section applies the terms previously dis-cussed to concrete prosthodontic situations. This includes considering the static relationships in the case of a removable denture that is replacing a free-end segment of the dental arch. The statics of the support of a cantilever prosthesis are also examined.Edentulous segments of a dental arch are less suitable than the residual teeth for absorbing masticatory forces because of the resilience of the mucosa. If the mucosa is also compressed by denture movements, the alveolar ridge or the denture-bearing area will quickly shrink. If a removable denture is attached to the remaining teeth, masticatory forces should be absorbed via that support, and movements or embedding of the denture should be prevented.Mucosa-borne dentures can be interpreted as rigid bodies that rest on oating bearings or springs; all compressive, tensile, shearing, and tipping forces will tilt, twist, displace, or tip the rigid body. This is a statically indeterminate sys-tem. Mucosa-borne complete dentures have in-determinate static support; the acting forces have to be directed so that the denture remains in the mouth. Attempts are made to achieve this by spe-cial tooth positioning and specic contouring of the denture base. The system of a semirigid canti-lever denture or a free-end prosthesis with hinged anchorage is also statically indeterminate. The semirigid and hinged coupling between the resid-ual dentition and the prosthesis produces mixed support of the restoration, as described earlier. It arises in dentures that have clasps with rests, regular joints, or resilient connectors.True load distribution between the supports (periodontium and mucosa) is not achieved. Ex-tremely uneven loading on the mucosal support may even occur, causing a triangular impression in the mucosa. If the rigid body is tipped around the periodontal support with the semirigid or hinged coupling because no moments can be absorbed, the rigid body and the support are twisted and displaced in the horizontal plane in a totally uncontrolled way. This type of loading is extremely damaging to a periodontal support (tooth) because the tooth is not protected against transverse thrusts.Support on the mucosa can only be assumed to act as a spring bearing to a limited extent. In fact, mucosal resilience is not merely a matter of tis-sue compressibility (as in the case of an air-lled container) but involves squeezing tissue uid as well as compressing and displacing the tissue. Therefore, the resilient behavior of the mucosa is dependent on the body’s constitution; the tissue’s uid content; and the underlying layers, compris-ing connective tissue, glandular, or fat accumula-tions. The compressibility of the mucosa is also inuenced by the shape of the support: Parts that are subject to punctiform loading will sink more deeply (up to 3 mm) than edges with linear load-ing (up to 2 mm), while extensive saddle areas undergo relatively little sinking (up to 0.5 mm). Therefore, viscoelastic bedding of the denture should be assumed (Fig 7-18).Sinking of a mucosa-borne denture is great-est at the point of load application as the denture base is shifted and twisted. In the case of mixed support on the residual dentition and mucosa, displacements of the statically indeterminate sys-tem always occur (Fig 7-19). Even extensive den-ture saddles fail to bring about uniform mucosal loading but always exhibit triangular embedding facing away from the rest area (see Figs 7-23 and 7-24). Any observed and measured sinking of a saddle will provide information about the maxi-mum amount to which the mucosa is squeezed. Resorption of the mucosa results in alternating, intermittent, and uneven loading and sinking of the saddle. In the process, this will jiggle the abut-ment tooth to and fro so that it is soon lost as well.Based on observations of static relationships, the most practical support is a rigid coupling of free-end saddles to the residual dentition. A xed bearing is statically determinate and able to transfer all masticatory forces to the abutment teeth. Vertical and horizontal forces and moments do not load the mucosa but are absorbed by the periodontium. The more residual teeth that are connected by the rigid anchorage—in other words, the more extensive the xed bearing is—the more secure the support.http://dentalebooks.com 222Statics of Partial DenturesaLToothSaddle2/3 LFKFGFZFKFZFGFHFHFZXFig 7-18 When calculating movements and support reactions of a supported free-end saddle in a mixed-support situation, visco-elastic bedding of the denture on the mucosa may be assumed. A free-end saddle is loaded with masticatory force (FK), which is absorbed by bearing force (FZ) and mucosal loading (FG) on the active length of the free-end saddle. To solve the mechanical prob-lem, the saddle is cut free in order to isolate the effective forces. It becomes clear that the bearing force of the mucosa is always perpendicular to the saddle; as a result, a distally directed force (FH) almost parallel to the saddle becomes effective and will tip the abutment tooth distally. In the bearing forces of the tooth, this tipping force is called FHZ. The right-hand diagram shows a model of the viscoelastic behavior of the mucosa, which is not equivalent to that of a rubber base but is determined by tissue elasticity and uid displacement.Pressure- freeF3F2F1FK+–Fig 7-19 A clasp denture for restoring a free-end saddle is always a statically indeterminate system because it has mixed support. When loaded by masticatory forces, the free-end saddle will sink, and the denture will tip around the rests on the terminal abutments. Resistance leverage can only become active once the denture has been tipped by a certain amount, at least equivalent to the retention depth of the clasp arms. Only when the clasps are tilted during denture movement will resistance leverage im-mediately take effect. This situation is illustrated in a three-dimensional model: Only when the long load arm is affected by masticatory force (FK) can the resistance levers F1, F2, and F3 become active because they require a certain stroke to achieve maximum spring force.Maximum spring forcehttp://dentalebooks.com 223Periodontal Support of Free-End SaddlesPeriodontal Support of Free-End SaddlesAnchorage with cast clasps produces statically indeterminate systems because these anchor-ing and supporting elements create semirigid or articulated couplings between the denture and the residual dentition. Anchorage of interdental saddles running straight between the abutments bordering the gap is relatively unproblematic if the abutments bordering the gap are support-ed. Special considerations come into play when constructing free-end dentures and large, arch-shaped bounded or interdental dentures.The occlusal rests of clasps act in cantilever dentures as pivot points about which the free-end saddles can rotate. To ascertain how the denture is turned around the rests under loading from masticatory pressure, the statics can be analyzed by constructing support lines. The support lines connect the rest points on the abutment teeth tangentially to the dental arch. In relation to situ-ations with partially edentulous arches, the sup-port lines follow different paths so that different periodontal support areas are formed (Figs 7-20 to 7-22):• Polygonal support areas for alternating edentu-lous spaces• Square (trapezoidal) support areas• Triangular support areas• Linear supports• Punctiform supportsThe positional stability of a denture is secured if the denture saddles are located inside the peri-odontal support area. When a support line inter-sects the denture, this creates an axis of rotation around which the dentures will tip, resulting in settling of the denture saddles (see Fig 7-21).The law of clasp lines describes a situation where the support lines are tangential to the den-ture. The support line indicates the axis around which the denture tips, or the active lever arm of a free-end saddle is measured from the support line.A free-end saddle that lies outside the periodon-tal support area acts like a lever arm. Such den-ture saddles may tip the whole prosthesis around the support line on masticatory loading. The lon-ger the denture saddle and hence the lever arm, the more pronounced the tipping. To shorten the lever arm, the support line must be placed as far as possible on the eccentric denture saddle. Sup-port lines run through the occlusal rests of the clasps. With regard to the position of the occlusal Fig 7-20 Supporting a partial denture periodontally is a basic principle of denture constructions. Because the mucosa is more yielding than the periodontium, a denture supported by occlusal rests and simultaneously mucosa borne can be tipped around the occlusal rests. If all of the available rests of a denture are joined together, the results are support lines around which the denture can be rotated. Depending on the available residual dentition, different arrangements of support lines can be constructed. If a denture is supported on only one remaining tooth, this is by far the least satisfactory form because the denture can be rotated around all the spatial axes. A support line between two rests always represents an axis of rotation.http://dentalebooks.com 224Statics of Partial Denturesrest, there are three forms of support: (1) support close to the saddle, (2) support remote from the saddle, and (3) support on the residual dentition remote from the saddle.Support close to the saddle is provided on the saddle-facing approximal marginal ridge of the abutment bordering the gap. The result is severe rotation around the rest with triangular sinking of the denture base and the following effects (Fig 7-23):• The saddle presses onto the marginal periodon-tium bordering the gap if the border area has not been relieved.• The abutment tooth is pulled distally, depending on the amount of rotation; the more the saddle is tipped toward the horizontal, the greater the horizontally acting force components that pull the saddle from the rest point.• The distribution of load is balanced between the abutment and the mucosal base. The two sup-port areas distribute the load from masticatory pressure, assuming that the point of force ap-plication is in the middle of the denture saddle.Support remote from the saddle is support on the marginal ridge of the abutment tooth border-ing the gap, on the side that faces away from the saddle. This also results in a rotational movement with sinking of the denture saddle and the follow-ing effects (Fig 7-24):• The marginal periodontium bordering the eden-tulous gap is loaded.• The saddle sinks uniformly; mucosal areas close to abutments also absorb masticatory forces.• The abutment tooth is pulled distally, depending on the sinking (Fig 7-25).Fig 7-21 An axis of rotation also arises when the support line divides the denture body. The support lines should always be tan-gential to the dental arch and thereby encompass an area. Even a triangular support area can provide stable support for a denture. In the case of a triangular area, however, if a denture saddle lies outside the support area, one support line of the construction will depict the axis of rotation, namely the line that divides the denture body. Only a square area, where the denture saddles lie within that area, is stably supported.Fig 7-22 Punctiform or linear support will arise, depending on the arrangement of the support lines. A support area is formed when spanned by three or more support lines: (a) a triangular support area by three support lines, (b) a square support area by four support lines, and (c) a polygonal support area by at least ve support lines.Triangular support area Square support area Polygonal support areaa b chttp://dentalebooks.com 225Periodontal Support of Free-End Saddles• Because the lever arm of the eccentric saddle is longer, the mucosa has to absorb more load; the periodontal support is relieved of loading.Support on the residual dentition remote from the saddle involves an abutment tooth remote from the saddle. The rotational movements around such a rest lead to almost-parallel movement of the denture saddle relative to the mucosa with the following effects (Fig 7-26):• The sinking is more uniform the longer and larg-er the saddle is.• The periodontium bordering the edentulous gap is not loaded (Fig 7-27).• The abutment tooth is not pulled to the saddle.• The periodontal support decreases rapidly; the masticatory load is absorbed almost entirely by the mucosal support.Fig 7-23 If a free-end saddle is supported on the abutment bordering the edentulous gap, there is pronounced rotational movement around this rest with substantial triangular sinking of the base and pressure on the marginal periodontium. The greater the mucosal loading, the shorter the free-end saddle.Fig 7-24 A rest remote from the saddle is created on the side that is turned away or on the marginal ridge on the same abut-ment tooth. As a result, the lever arm is lengthened mesially; this leads to roughly parallel sinking of the base and reduced loading of the interface. However, distribution of the load shifts to the detriment of mucosal loading.Fig 7-25 Depending on the amount of sinking, the mastica-tory load becomes a distal pull on the saddle and will therefore act on the abutment tooth. A vertical force on an inclined plane produces a slope force dependent on the angle of inclination α; this slope force produces the pull on the abutment tooth directed distally. Depending on the degree to which the saddle sinks, the sublingual bar will move toward the alveolar ridge and settle.Fig 7-26 Almost-parallel sinking of the base occurs where support on the residual dentition is remote from the saddle. The longer and more extensive the base, the more uniform the sinking of the base. The function of the periodontal support is lost, and the mucosa is overloaded.Fig 7-27 If a bounded saddle is loaded centrally, the abut-ments bordering the gap absorb this load in equal parts. Mov-ing further away from the distal abutment, its load is applied to the mucosal support and the saddle may sink, as described earlier. The mesial abutment continues to absorb its force com-ponent.http://dentalebooks.com 226Statics of Partial DenturesAction and Resistance LeversA clasp denture does not offer rigid anchorage, and the statically indeterminate system of mixed support will always result with free-end dentures, in which the mucosa is subject to nonphysiologic stress from masticatory pressure. A decrease in mucosal loading can be achieved if a free-end saddle covers the mucosa extensively, as the load is transferred to a large area based on the snow-shoe principle and hence the degree of sinking is reduced. A free-end saddle should be shaped as an extension saddle that embraces the maxillary tuberosity in the maxilla and the retromolar pad in the mandible. In addition, the last third of the denture saddle is not loaded by masticatory pres-sure. The terminal molars are placed out of occlu-sal contact, thereby shortening the lever arm to the support line. The lever arm to the support line can be further shortened if a rest is placed close to the saddle, giving rise to uniform load distri-bution between the periodontal support and the mucosa.In the case of large, arch-shaped bounded sad-dles, the following considerations are important: If a denture is to be supported on two terminal molars, masticatory pressure will be absorbed almost entirely by the underlying mucosal sup-port. This kind of denture must be designed like a complete prosthesis. The terminal molars merely secure the horizontal position and serve as reten-tion. Occlusal support is necessary to prevent the denture from embedding at the molars and to prevent the development of occlusal interfer-ences and sinking of the clasps.Sinking of the free-end saddle can most suc-cessfully be prevented by opposing the load arm (free-end saddle) and the load (masticatory force) with a force on one force arm. For this purpose, another clasp is placed in the dental arch ahead of the abutment tooth bordering the edentulous gap; this clasp is withdrawn when the saddle sinks. This gives rise to a system of levers com-prising an action lever (free-end saddle) and a re-sistance lever to the additional clasp.The maximum retentive force of a clasp is 10 N, which would be too low to resist sinking. How-ever, because the clasp is not pulled in the path of insertion but in a circular movement from the tooth, it tilts and offers adequate resistance. The result is quasi-rigid anchorage of the free-end saddle.The resistance lever arm should be at least as long as or longer than the action lever. Clasping of the resistance lever arm subjects the abutment Fig 7-28 In response to horizontal thrusts, the clasped teeth are loaded by the enclosing parts of the clasps. Denture design must take this fact into account by supporting the denture saddles with clasps so that the denture is not twisted on the underlying mucosa in response to horizontal thrusts. The clasp line is obtained by connecting opposing open clasps on different halves of the jaw. A clasp line must traverse the denture body. It must be possible to draw at least two clasp lines for denture construction. Only then is the denture denitely secured against twisting in response to horizontal thrusts. An important point is that the clasp line connects two opposing open clasps.http://dentalebooks.com 227Action and Resistance Leverstooth to traction, which has to be compensated for by the splinting effects of the whole group of clasps. Therefore, as many residual teeth as pos-sible are enclosed in the groups of clasps: one anchoring and supporting element for each tooth being replaced.The construction involving action and resis-tance levers also counteracts the tipping of den-ture saddles by pull-off forces (eg, sticky food or the appliance’s weight). In the case of normal clasping, the saddle acts like a beam suspended from one side, which can tip downward. This movement is prevented by the resistance lever, which acts to prevent tipping.Horizontal positional stability is determined not only by the position of the support points but also by the position of the splinting parts. If all of the rigid clasp parts lie mesially in the maxilla (all the clasps being open distally), the denture can be displaced mesially on the mucosal support. If all of the clasps are open mesially in the maxilla, the denture moves on the underlying support when the mandible is retracted. The same applies to a mandibular denture. If clasps open in the opposite direction are mounted on each half of the jaw, the denture is secured against horizontal shifts and twisting. For statics analysis, connecting lines can be drawn between such clasps (Fig 7-28). These lines are re-ferred to as clasp lines or traction lines. According to the law of clasp lines, these lines should di-vide the denture. The clasp or traction line shows whether a denture can be twisted by horizontal shearing and tractive forces. If such twisting is possible, the clasps are altered so that the splint-ing parts will counteract this twisting.Based on the analysis of static relationships, the following design principles apply to free-end saddles:• They ensure support close to the saddle.• They make use of a resistance lever to construct tilting elements.• They shape the extension saddle.• The terminal molar is positioned outside occlu-sal contact.Figures 7-29 to 7-39 illustrate various lever ef-fects with dentures.Fig 7-29 Mandibular movement and denture movement inter-act as follows: When the mandible is moved forward, the den-tures can be shifted relative to the dental arch being restored. A mandibular prosthesis is held by the antagonists and there-fore moves distally relative to the underlying support, which means the clasped tooth tips distally. A maxillary denture is moved forward by its antagonists on protrusive movement of the mandible, and the clasped teeth are tipped mesially. Gener-ally speaking, on protrusion of the mandible, a maxillary den-ture will be pushed mesially and a mandibular denture distally.http://dentalebooks.com 228Statics of Partial DenturesRLALAL RLRL1RL2ALFig 7-32 Effective reduction of mucosal loading is achieved by means of several resistance lever arms (RL1 and RL2). In addition to the normal double-arm clasp, another double-arm clasp is mounted mesially on the residual dentition. With the distance from the pivot, this clasp acts as a resistance lever and to prevent tipping.RL1RL2ALFig 7-33 If a free-end denture and an anterior interdental sad-dle are supported on the abutments bordering the gap, the resistance lever lifts the clasp off the abutment tooth on load-ing. Because the clasp is not lifted off in the path of insertion, it tilts, and a semirigid coupling ensues between the denture and the residual dentition.Fig 7-30 Resistance lever arms (RL) can be used to reduce mucosal loading with free-end saddles. The free-end saddle as the action lever (AL) rotates around the occlusal rest on load-ing by masticatory pressure; in the process, the clasp arm of a normal double-arm clasp counteracts this twisting movement.Fig 7-31 If a Bonwill clasp with a rest remote from the saddle is used, the action lever arm (AL) becomes longer while the resistance lever arm (RL) remains the same length. The clasp part opened distally acts to prevent tipping against withdrawal forces acting on the free-end saddle. The mucosal loading is not reduced in this case but actually increases; the abutment teeth absorb less load.ALRLALRLFig 7-34 A free-end denture is constrained on the terminal abutments with occlusal rests. All of the clasps mounted mesially from the free-end saddle act as resistance lever arms; they reduce mucosal loading and prevent tipping. Both solutions bear two resistance lever arms, but in the second case the clasps on the canine tilt more effectively, leading to better bracing of the residual dentition and better vertical positional stability. However, the second solution may still have to be rejected because this clasp posi-tion is esthetically less satisfactory in patients with a short lower lip; in addition, the minor connectors to the Bonwill clasps lie more distally, where self-cleaning is not as effective as mesially.http://dentalebooks.com 229Action and Resistance LeversALRLFig 7-37 If the teeth on a denture are set up slightly outside the alveolar ridge on the vestibular side, lever effects may occur, and the denture may be tipped off. The distance from the point of force application to the center of the alveolar ridge is regarded as the action lever arm. Clasping the denture on the opposite side of the jaw counteracts the tipping as a resistance lever arm.Fig 7-35 In the case of an anterior interdental saddle, which follows an arched course, support similar to that achieved with a free-end saddle should be constructed. With four Bonwill clasps, this denture is oversized, but the problem becomes clear: The action lever arm is far shorter than the resistance lever arm. As a result, the pull on the resistance abutment tooth is very low. An attempt should be made to achieve these conditions when constructing resistance levers.Fig 7-36 The principle of a tipping preventer is clearly illustrated by a bar suspended on one side. The bar will tip downward as a result of its own weight. If coun-terbearing is applied by lengthening the bar beyond the suspension mounting, the beam supports itself and does not tip. This principle of a tipping preventer becomes effective because of the application of resis-tance levers.http://dentalebooks.com 230Statics of Partial DenturesDesign-Planning CriteriaThe planning and design of tooth replacements is the dentist’s responsibility. The dental technician carries out the prosthodontic work based on the dentist’s instructions and relevant working docu-ments. However, the dental technician shares a great deal of responsibility for fabricating a pros-thesis, and this includes not only the technical production but also the planning and design.Dening the criteria for design planning of par-tial dentures simply involves applying and sum-marizing the facts previously outlined. These criteria are primarily intended to enable dental technicians to understand dentists’ design plan-ning and instructions properly and implement them productively in order to fabricate a func-tional restoration. Only then will dental techni-cians be capable of presenting technically sound design proposals to complement the treatment provision offered by the dentist.A pragmatic approach to handling design plan-ning involves deducing objectively established criteria for error analysis as a systematic element of treatment optimization. Error analysis leads to reection about one’s own actions, assessment of one’s own work outcomes, and optimization of one’s technical material-processing methods and ⇒ Fig 7-38 If clasp structures are dispensed within the visible anterior area, free-end saddles may result. These structures clearly re-veal the disadvantage of free-end dentures: The free-end saddle embeds mesially to the detriment of the tooth-prosthesis interface and forces the adjacent tooth out of the dental arch. This tooth will be the rst one to be lost.Fig 7-39 To prevent overloading of the mucosa in the case of free-end saddles, the last third of the free-end saddle can be relieved (ie, the terminal molar should be placed outside oc-clusal contact if necessary). The free-end saddle may only be shaped in extended form (ie, as generously as possible to dis-tribute masticatory force according to the snowshoe principle).http://dentalebooks.com 231Design-Planning Criteriaorganizational structures. Error analysis means anticipating and eliminating possible mistakes in planning and carrying out prosthodontic work. The purpose of error analysis is hence to identify the correct procedure and to optimize processes and products; it also helps technicians develop planning expertise and technical skills. Error analysis is a dynamic process that should lead to maturity in technical and manual expertise; it is documentary evidence of a dental technician’s current level of professionalism and represents a never-ending process. Dening the targets for a working process, a product, or use of a material is the rst step to-ward formal implementation of error analysis. An extensive collection of facts can be derived from this, in order to draw up a list of criteria for qual-ity control. The analysis criteria should be practi-cal, clearly understandable, and appropriate; they provide a basis for assessment and pointers for optimizing the object of the analysis.The criteria of design planning or error analysis outlined here relate solely to the technical realiza-tion of dental restorations. However, because the restoration is intended to merge into a functional unit with the residual dentition, any design plan-ning must incorporate the physiologic environ-ment. Medical indications will not be discussed in this context.For a denture that is expected to be durable, re-liable, and practical, the following areas must be analyzed from the technical point of view:• Static relationships• Physiologic conditions• Cost-effectivenessAnalysis of static relationshipsAnalysis criteria are derived from observations of the statics of the partial denture and the functional principles governing anchoring elements. Based on a statics diagram in which tipping lines, action levers, and resistance levers are plotted, horizon-tal and vertical positional stability is checked:• An effort should be made to achieve complete periodontal support in which denture movements are stopped, mucosal overloading is prevented, and there is uniform distribution of forces to as many residual teeth as possible.• Anchoring elements should have dened reten-tive forces so that abutment teeth are not over-loaded on denture removal and a secure and rm seating of the denture is guaranteed in the mouth during functioning and in the resting phase.• For clasp dentures, there should be one clasp with support close to the saddle for each tooth being replaced.• The denture design must actively support the residual dentition through splinting.Analysis of physiologic conditionsThis area of analysis concerns the structural de-tails of the anchoring and supporting elements, the denture frameworks, and the saddles, from which the practical value of the denture is directly determined:• Observe the principles of periodontal hygiene:– Shape details should facilitate the self-cleaning function and normal oral hygiene measures.– Plaque accumulation or mechanical wear of the tooth surface by prosthodontic compo-nents should be avoided.– The xed prosthodontic components should not cover the mucosa.– Intracoronal integration of retaining compo-nents should be established to relieve the in-terface.• Design denture frameworks to be stable, slim, and clear of the periodontium and tongue.• Make handling and cleaning easy for the patient.• Allow for the possibility of periodontal treatment.• Avoid using a diversity of materials.• Use biocompatible materials.• Relate esthetic concerns to the patient’s needs in order to create the psychologic effect that the patient has regained a complete dentition that re-ects health, vitality, and physical attractiveness.Unsightly retaining elements or the wrong tooth color must not constantly remind the patient of the mutilation of his or her dentition. Neverthe-less, the form of a tooth replacement is not pri-marily a matter of esthetics but an expression of its placement in the functioning organic system. The optimum functional form of a tooth—based on the anatomical model—will always be the per-fect esthetic form as well.http://dentalebooks.com 232Statics of Partial DenturesObservations on the supposed optimization of esthetic detail can only be made via analysis of the anatomical functional value. If esthetic con-cerns beyond the psychologic and functional value of prosthodontic work are subordinated to ideas of beauty endorsed by fashion, this will have a negative effect on functional suitability.Cost-effectiveness analysisThe technical effort involved in fabricating the tooth replacement and anchoring elements should be kept to a level that does not jeopardize func-tional suitability through process and system er-rors.• Choose simple and effective anchoring ele-ments; that means rigid, prefabricated structural components.• Technical effort should be in reasonable propor-tion to achievable functional value.• The risk-benet calculation requires systematic comparison of alternative solutions, bearing the following in mind:– The technical effort should be cost-effective.– Clasp dentures are inexpensive but have a lower functional value.– Prefabricated structural components are cheap-er than manually fabricated components.– Precious metal alloys are more costly than tried-and-tested alternative alloys.– Aftercare, reparability, and extension possibili-ties must be disclosed. One aspect that may be assessed is whether the restoration loads the residual dentition during wearing to such an extent that later restorative work can no longer be done or can be done only at considerable cost.A life-span calculation establishes which pros-thodontic design offers the longest life span based on medical, materials science, and static considerations and which has the greatest func-tional value at the lowest cost.Residual Dentition Situations and Design DescriptionsDesign 1This example concerns a mandibular arch short-ened on one side that is broken up by an anterior edentulous gap. The dentition is further weak-ened by a posterior edentulous space. The re-sidual dentition situation includes usable anchor-ing abutments for the prosthodontic restoration. Both canines and rst premolars are still present, as well as the right second premolar and the left second molar as a terminal abutment bordering the gap (Fig 7-40).A design with rigid anchoring and supporting elements is the rst to be planned (Fig 7-41). It is advisable to place veneered full crowns on the remaining teeth; only the molar is tted with a full-cast crown. Teeth that are close together are primarily splinted. Secondary splinting of all the teeth is achieved via the denture framework if the anterior edentulous gap is tted with two rod-type attachments, and the free-end gap at the terminal abutment as well as the posterior eden-tulous gap at the molar and premolar are each t-ted with a T-attachment. The left rst premolar and right second premolar are given circular notches for shear distribution arms. The free-end saddle is shaped to allow for the possibility of extension and the need for reduction; the denture frame-work comprises a semi–drop-shaped sublingual bar that meets the requirements for periodontal hygiene, hence maintaining minimum distances from the cervical margins, the alveolar ridge, and the oor of the mouth.Statics of the designIn this case, secondary full splinting awlessly sat-ises the demand for a rigid connection between the denture and the residual dentition. Primary splinting by bar connectors within the edentulous gaps can be dispensed with because horizontal thrusts and rotations, which would be absorbed by the bar, are adequately compensated for here by the rigid intracoronally placed attachments http://dentalebooks.com 233Residual Dentition Situations and Design Descriptionsfor the anterior edentulous gap and the terminal abutments. For large edentulous gaps, bar con-nectors should in any case always be checked for their suitability in terms of periodontal hygiene; if other solutions offer comparable quality, they should be used instead.The tipping line, around which the free-end saddle might be tipped, runs through the T- attachments on the mandibular right second pre-molar and the mandibular left second molar. Via the sublingual bar, four resistance levers of differ-ing length and position then counteract distal tip-ping. The T-attachment close to the saddle with a shear distributor on the free-end part also resists distal sinking, so that sinking of the saddle is only possible by means of periodontal resilience, the elasticity of the bar, and the extremely small t tolerance of the attachments.The relationship of the residual dentition to the replacement teeth is shifted to the detriment of the abutment teeth, yet stresses on the inter-dental saddles caused by masticatory forces are readily absorbed.By means of rigid coupling with the resistance levers, in interaction with the necessary full splint-ing, the free-end stresses should also be trans-ferred to the periodontium. Although the denti-tion is considerably reduced, the impediment can still be remedied by prosthodontic means. The static relationships suggest that no impairment of masticatory function may be expected (Fig 7-42).Fig 7-40 A mandibular arch shortened on one side combined with anterior and posterior edentulous gaps is a common situ-ation requiring prosthodontic treatment. The asymmetry of the arrangement of gaps will produce uneven loading of the re-maining teeth. Fig 7-41 The rst proposed solution involves a removable par-tial denture with rigid anchoring and supporting elements. All of the remaining teeth undergo coronal restoration, and teeth that are close together are subject to primary splinting. The edentulous gaps are tted with closed, intracoronal parallel at-tachments, and the free-end gap is tted with a T-attachment and a double-arch shear distributor. As a result, secondary splinting of the abutment teeth is achieved.Fig 7-42 The statics of a partial denture that is combined with rigid anchoring and supporting elements are balanced. The free-end saddle may only sink by means of the periodontal re-silience of the abutment teeth. All of the masticatory forces are transferred to the periodontium. The denture sits absolutely rmly, the periodontal hygiene conditions are favorable, and the result is a reliable long-term restoration.http://dentalebooks.com 234Statics of Partial DenturesAdvantages of the designDespite the mutilation of the dentition, a rigidly anchored, periodontally supported denture is created. The secondary full splinting ensures uni-form distribution of masticatory forces to all the periodontal tissues of the abutment teeth. All the attributes of a reliable denture are met:• Secure, rm seating in the mouth• Rigid denture–residual dentition connection• No mucosal loading• Worn parts can be replaced• Excellent esthetic quality• Favorable conditions for periodontal hygiene due to intracoronal placement of attachmentsDisadvantages of the designWhen the relationship of the residual dentition to the replacement teeth is unbalanced, there is a risk of permanent overloading of the abutments. This partially edentulous situation is a borderline case. The available remaining teeth are excellent abutments and lend themselves to full splinting via a rigid denture connector. The secure seating of the denture, however, misleads people into de-manding too much from the restoration. In addi-tion, handling of this construction is problematic, and only manually dexterous patients will likely be able to cope. This denture is not a good value for the money.Design 2: Model cast-clasp dentureThe same residual dentition situation is to be treated with a model cast-clasp denture. First, all of the abutments bordering the gap are provided with occlusal rests close to the saddle. The pre-molars on the right are tted with a Bonwill clasp, while saddle-guided double-arm clasps are tted around both canines and the left rst premolar and second molar.The esthetics in the anterior region can be im-proved by placing Bonwill clasps around the ca-nines and the rst premolar. However, clasp parts guided approximally over the dental arch are more visible in the mandible than in the maxilla. The mandibular canine is usually concealed by the substantial lower lip.The sublingual bar joins the saddles and bears the minor connector to the Bonwill clasp. The den-ture saddles must be kept in extended form be-cause masticatory forces also have to be brought to bear on the mucosa. Statics of the designThe clasp lines, drawn according to the law of clasp lines, result in a polygonal support area that contains the two interdental saddles within its borders. In shortened dental arches, an eccentric free-end saddle will always arise. The tipping line through the rests on the right second premolar and left second molar indicates the tipping line of the action lever and establishes the length and position of the resistance levers (Fig 7-43).Full clasping provides several effective resis-tance levers comprising the Bonwill clasps and double-arm clasps around the canines and the rst premolar (Fig 7-44). These clasps can only prevent distal tipping of the free-end saddle by tilting toward the path of insertion. The bodily enclosure by clasps is not as effective as paral-lel guidance; thus, denture movements affect the free-end saddle. This gives rise to a denture with mixed support in which only the interdental sad-dles are supported periodontally.Advantages and disadvantages of the designThis denture is the most cost-effective; it is easy to handle and causes no cleaning difculties. However, mechanical loading of the enamel of the abutments as well as plaque buildup due to full clasping affect every remaining tooth—rst because of the preparation of the rests required and the approximal connection to the Bonwill clasp, and second because the lingual surfaces of the abutment teeth may have to be prepared parallel for the guide arms.Full clasping requires framework connections that jeopardize periodontal hygiene in the inter-face to the denture saddles and put under pres-sure the marginal area of the free-end abutment bordering the gap. The esthetic issues concerning full clasping are in any case indisputable. Elastic connection between the denture and the resid-ual dentition places high stress on the severely reduced partially edentulous dental arch, which http://dentalebooks.com 235Residual Dentition Situations and Design Descriptionshastens decay of the dentition after a short func-tioning period. If the mandibular rst premolar is omitted from the clasping, the static relationships deteriorate and loading on the individual abut-ments is increased.Alternative solutionsTwo extravagant solutions emerge: (1) The eden-tulous gaps can be closed with veneered partial denture pontics, and the shortening of the dental arch can be remedied by an interlocked monore-ducer; or (2) a removable partial denture can be constructed that embraces all of the remaining teeth and is secured by a lock attachment on the right second premolar. The remaining teeth should be prepared for telescopic anchoring crowns, for which support cones with a large convergence angle are suitable because a lock attachment ap-plies the retentive force.ALRL2RL3RL4RL5Fig 7-43 The tipping line through the rests on the left second molar and the right second premolar establishes the action lever (AL) and ve active resistance levers (RL). The clasp shoulders on the canines are tilted on loading of the free-end saddle so that horizontal positional stability of the free-end saddle is effectively ensured. The interdental saddles are supported close to the saddle and are able to bear the full masticatory load. Full clasping distributes the masticatory load to the entire residual dentition and splints all the remaining teeth into an effective resistance block. Stress on the residual dentition results from mechanical wear of the abutment teeth and deciencies in periodontal hygiene caused by cast clasps; the esthetic demands cannot be satised. This prosthesis is cost-effective as a long-term replacement (ie, for about 5 years).Fig 7-44 For esthetic reasons, the canines and rst premolars on both sides are tted with Bonwill clasps. The static relation-ships are comparable if the anterior rests close to the saddle are placed so they can tilt when the free-end saddle is loaded.RL1http://dentalebooks.com 236Statics of Partial DenturesConical crowns can be designed to be cosmeti-cally more favorable, and no marginal gaps are formed. As sturdy secondary parts nd space on the relatively delicate conical subcrowns, the par-tial denture framework functioning as a denture framework can be made stable enough.All of the replacement teeth are periodontally supported and rigidly coupled by an interlocking mechanism. Therefore, sinking of the free end only occurs via the elasticity of the partial den-ture framework and the periodontal resilience of the abutments.The removable partial denture has all of the positive wearing properties of a xed restoration and is therefore seen as an elegant solution (Fig 7-45). The real advantage, however, lies in the ex-cellent periodontal hygiene conditions that allow all possible means of periodontal prophylaxis, which is more than a xed replacement can offer. Handling is simple once the patient has learned to unlock the restoration. The cleaning possibilities and esthetic quality are outstanding. A removable partial denture is very cost-intensive, however, and requires considerable technical effort.Design 3This symmetric residual dentition situation has canines and premolars as solid abutment teeth; it is a symmetric partially edentulous dentition (Fig 7-46). Two types of denture framework are avail-able for this common situation:• A sectioned horseshoe connector or a broad an-terior palatal strap• A skeleton plate made of a narrow anterior and broad posterior palatal strapThe skeleton plate will leave the pressure and fricative eld largely clear, while the sectioned plate fully covers the plicae palatinae, which can mean phonetic interference and impaired taste. Therefore, a model cast skeleton is chosen.Full clasping becomes necessary because of the ratio of remaining teeth to articial teeth. Two Bonwill clasps are placed around the canines and rst premolars, and the anterior interdental sad-dle is supported with two additional rests close to the saddle. The second premolars are tted with mesially open double-arm clasps with support close to the saddle (Fig 7-47).Clearance from the periodontium of clasped teeth must be guaranteed by guiding the frame-work at a minimum distance of 4 mm from the periodontal margin and by running the minor connectors to the Bonwill clasps at the minimum distance. The denture base has an extended shape that encompasses the maxillary tuberosities.Statics of the designTo lengthen the resistance levers, all of the den-ture saddles are supported on the marginal ridges of the teeth bordering the edentulous gap. These rests close to the saddle form the axis points of the tipping lines. If the second molars on the free-end saddle are placed outside occlusal contact, the resistance levers to the canines are longer than the action levers, which creates favorable load relationships. For the anterior interdental saddle, the resistance levers to the double-arm clasps pull on the second premolars. Horizontal positional stability is adequately secured by the full clasping.This straightforward solution can be achieved with minimal technical effort and without elabo-rate preparations. This solution is an inexpen-sive and seemingly up-to-date construction that is frequently used today. If the clasped teeth are correctly surveyed, a relatively reliable denture is obtained that is easy to handle and keep clean.Fig 7-45 Far better wearing comfort and better esthetic effect are achieved with a xed partial denture to which a double-arch circular notch at the free-end saddle is created for the shear distribution arm of a monoreducer. However, this solution is disproportionately more expensive.http://dentalebooks.com 237Residual Dentition Situations and Design DescriptionsThe connection between the denture and the residual dentition is not rigid. Stresses on the free-end saddle lead to appreciable tipping and intermittent movements of the denture, which means the enamel of the clasped teeth is subject to mechanical wear.Clasp structures are unfavorable in terms of periodontal hygiene and cosmetic appearance. They cannot be activated and require the prepa-ration of rest surfaces.Alternative solutionThe remaining teeth are tted with veneer crowns and splinted together. Bordering the anterior in-terdental gap, two rod-type attachments are integrated to secure the secondary full splint-ing by means of the denture framework. Two T-attachments are placed intracoronally on the second premolars and supported by shear distri-bution arms (Fig 7-48).The denture framework consists of a skeleton plate that joins together the four attachment parts. The extended denture saddles make allow-ance for dental arch reduction needs. The require-ments for denture framework and denture base design in terms of periodontal hygiene must be fullled.The arrangement comprising shear distribu-tors and parallel attachments provides an abso-lutely rigid connection to the residual dentition. All masticatory forces and transverse stresses are absorbed as a result of rigid coupling and full splinting of the residual dentition. This is the ad-vantage of a high degree of coupling. The static Fig 7-46 The symmetric residual dentition situation shown here comprises an anterior edentulous gap and two free-end gaps due to missing molars. Symmetric partially edentulous situations produce symmetric stresses on the remaining teeth. This situation is very common in prosthodontic care and lends itself to various possible solutions.Fig 7-47 The rst proposed solution to the situation in Fig 7-46 shows a removable partial denture with two double-arm clasps and two Bonwill clasps for complete splinting of the residual dentition. An anterior and posterior tipping line is formed. By means of full clasping, the saddles are adequately secured against sinking under masticatory pressure. The additional rests on the canines can tilt on free-end loading and provide positional stability.Fig 7-48 The alternative solution to the situation in Fig 7-46 involves closed parallel attachments together with double-arch circular notches with shear distributors at the free-end saddles. This anchorage provides rigid coupling to the residual dentition to secure the horizontal and vertical position and to achieve secondary splinting of the abutment teeth.http://dentalebooks.com 238Statics of Partial Denturesrelationships of this structure are physiologically entirely positive.No intermittent denture movements occur; hence, the harmful suction and compressive ef-fects on the mucosa are absent. Resorptive atro-phy of dental arch segments is curbed.This solution has esthetic advantages. The ac-tivatable retaining components are sunk into the abutment teeth and concealed. The shear distri-bution arms are also invisible. However, healthy residual teeth have to be pre-pared for the coronal restoration. If free-end load-ing is considerable, the remaining teeth may be overloaded despite full splinting. This solution is technically demanding and expensive.Design 4This dental arch in the maxilla is shortened on one side and interrupted by alternating edentu-lous gaps. The lateral incisor, the second premo-lar, and all the molars are missing on the left; on the right, the lateral and central incisors, the rst premolar, and the rst molar are missing (Fig 7-49).Model cast-clasp dentureThe periodontal support of a free-end saddle is a special problem because the asymmetry of the partially edentulous dentition results in uneven loading conditions. Satisfactory anchorage can only be secured via complex full clasping. The left canine and premolar are engaged with a Bonwill clasp. The premolar is given an additional rest so that the free-end saddle is supported close to the saddle to ensure periodontal transfer of forces. The central incisor is not tted with a clasp be-cause of the esthetic impression; rests have to be placed mesially and distally, and two approximal minor connectors are used for splinting (Figs 7-50 and 7-51).To secure the right anterior interdental saddle, the right canine is loaded with a mesially placed occlusal rest and tted with a mesially open double-arm clasp with rest; the second molar re-ceives a distally open double-arm clasp with rest. Four remaining teeth are now available as abut-ments for a denture to replace seven teeth. It may be practical to t the right second premolar with a double-arm clasp and rest as well.The denture framework is a metal skeleton with a broad posterior and narrow anterior pala-tal strap, which bears the interdental saddles and the free-end extension saddle. The framework is shaped according to the principles of periodontal clearance and periodontal hygiene (Fig 7-52).Statics of the designThe tipping line goes through the rests on the second molars and the left rst premolar. Various long resistance levers oppose the action lever. The periodontal support of the free-end saddle provides mixed support in which the resistance levels only act by means of tilting. The interden-tal saddles are secured periodontally. Horizontal positional stability is only approximately secured by the clasping because there are only mesially open clasps on the left side. Splinting of the re-maining teeth is ensured.This simple design may be preferred for cost reasons. It is convenient to handle and keep clean and sits relatively securely. The cosmetic impres-sion is adequate if the canine clasps can be placed cervically, which is possible if only the vestibular retentive areas are used.Fig 7-49 The asymmetric residual dentition situation shown here comprises two anterior and two posterior interdental gaps and one free-end gap. Six abutment teeth are available, of which only the left canine and rst premolar stand together; all the others are stand-alone abutments. The rst planning ap-proach envisages a removable clasp denture. The alternative is an extensive xed partial denture bearing a monoreducer for the free-end gap. Another alternative involves a 14-pontic removable partial denture with an implant supporting the gap.http://dentalebooks.com 239Residual Dentition Situations and Design DescriptionsDespite full clasping, mixed support arises, which is harmful to the underlying mucosa. Tis-sue breakdown can be expected. The abutment teeth are also excessively loaded by denture move-ments. Full clasping raises esthetic and periodon-tal hygiene concerns, quite apart from the trau-matic mechanical stress on the enamel of the abutment tooth (Fig 7-53). The anterior palatal strap may interfere with phonetics (Fig 7-54).Fig 7-50 The rst step in design plan-ning is to identify the rest points. In prin-ciple, support will be close to the saddle. One rest is enough for a single-tooth gap. Double rests are possible, as with the right canine and the left rst premolar.Fig 7-51 The rest points establish the path of the clasps. The central incisor must be incorporated into the splinting unit; if it is not, it will drift out of the den-tal arch. It is given two rests and two ap-proximal minor connectors.Fig 7-52 The shaping of the denture framework allows for periodontal hy-giene and tongue clearance. The frame-work should be delicate and stable. A wide posterior palatal strap with a skel-eton plate meets the requirements and is able to transfer masticatory forces to the palate.Fig 7-53 Full clasping of the remaining teeth offers good splinting effects, which pri-marily stabilize the central incisor, contributing to the horizontal positional stability of the free-end saddle due to tilting effects. The diagonal tipping line establishes four resistance levers, which are active against the action lever on the free-end saddle. The clasp structure offers an adequate functional replacement for medium wearing times. The esthetics are decient, and periodontal hygiene is adequate.Fig 7-54 An anterior palatal strap or a sectioned plate may be designed, but it does not meet the requirement for tongue clearance. The pressure and fricative eld is covered and may im-pede tongue function (eg, phonetics and taste); in addition, the device is less com-fortable to wear.http://dentalebooks.com 240Statics of Partial DenturesAlternative solutionA xed partial denture for the alternating inter-dental gaps bears a monoreducer (Figs 7-55 and 7-56). The anchoring function for the free-end saddle is performed by a lock attachment with a double-arch circular notch around the left canine and premolars. The free-end saddle is shaped as a functionally reduced extension saddle.The free-end saddle is rigidly joined to the re-sidual dentition. The lock attachment prevents any movement of the saddle relative to the mucosa, unless via periodontal resilience. The entire rigid partial denture framework serves as a resistance lever for any free-end loading.This design provides a secure and reliable res-toration that largely protects the residual denti-tion and the supporting tissue (Fig 7-57). The free-end saddle is supported entirely periodontally and absolutely cannot perform any intermittent relative movements.The handling, cleaning possibilities, esthetic impression, unimpeded phonetics, clear palatal area without the denture framework causing any interference, and sum of all the excellent wear-ing properties make this an excellent restoration. If all the teeth cannot be handled by extensive conservative measures because of caries lesions or other defects, coronal restoration of the entire dentition may be called into question; therein lies the weakness of this proposed solution. Convinc-ing arguments are needed to justify coronal res-torations for healthy teeth.Fig 7-55 The alternative to a clasp denture is a 14-pontic par-tial denture in which the free-end pontics are supported on at least one implant placed in the gap. The partial denture can be designed to be removable, in which case the body dimensions must be large enough. Periodontal hygiene conditions are very favorable with removable restorations; removable partial den-tures have to be so large, however, that some esthetic loss must be expected.Fig 7-56 A xed partial denture from the right second molar to the left rst premolar is supplemented by a monoreducer in the free-end area, which is secured via a lock attachment and sup-ported by a double-arch shear distributor in a circular notch. The xed partial denture offers outstanding wearing properties and esthetic benets; the monoreducer is advantageous in terms of periodontal hygiene.Fig 7-57 Static relationships for the monoreducer are satisfac-tory. The rigid coupling achieved by the lock attachment and the double-arch shear distributor secure the periodontal support of the removable restoration. The xed partial denture combines all of the remaining teeth into an effective resistance block. The ratio between residual teeth and replacement teeth is unfavor-able, so that overloading of the abutment periodontium may occur. This form of replacement may nevertheless be a practi-cal long-term solution.http://dentalebooks.com

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