Factors that Influence the
Gabriel R. Zuckerman, DDS
                 Mechanical Retention of                               1199 Fifth Avenue
                    the Complete Crown                                 Fast Nortbport, Nen York ¡1731
                      Retention of the complete crown is influenced by a complex
                      relationship developed between the crown preparation and
                      the adaptation of the restoration. Mechanical retention is
                      produced when the axial walls of the prepared tooth and the
                      restoration contact before the crown seats completely. The
                      force that is applied to seat the restoration completely
                      produces retention by creating compression of the tooth and
                      tension within the crown. The portion of the force that
                      produces this retention depends on the taper of the axial
                      walls of the tooth preparation, ¡nt ¡ Frosthodont 1988: 1:196-
                      200.
     he complete crown is the most frequently used                    the use of cement, it should be mechanically de-
T restoration for repairing severely damaged teeth                    veloped by appropriate tooth preparation and tech-
                                                                      nical procedures. To rely solely on the use of cement
  and as a retainer for a fixed partial denture. The
  crowns may be all cast metal, porcelain fused to a                  to retain a prosthesis that has no mechanical reten-
  cast metal coping, or cast metal with an acrylic resin              tion is to invite failure.
  veneer. Regardless of the consiruclion, the physical                   To assemble a tooth and a crown to resist sep-
  factors that influence the ability of these restorations            aration it is necessary to understand the mechanics
  to resist dislodgement remains the same.                            of the inclined plane. Figure 1 represents a model
    The literature is replete with studies that examine
 the effects of various preparations on retention.
 These studies report the effects of crown length,
 diameter and surface area, convergence of axial
 walls, auxiliary boxes, grooves and pins, and partial
 versus complete coverage on crown retention,'"^
 Some studies include the effects of cement on re-
 tent ion of the restoration as well," ^ While all of these
 studies are accurate and the results valid, none have
 defined the physical and mathematical relationship
 that exists between these factors and retention. The
 purpose of this article is to examine the fundamental
 physical phenomenon by which the complete crown
 achieves its retention so that it can be properly ap-
 plied in clinical practice.
    Retention is the ability of a restoration lo resist
 separation from a tooth when il is subjected to a
force acting along ils palh of withdrawal. Retention
is developed by appropriate tooth preparation and
adaptation of the casting. Preparation form is di-
rectly controlled by the dentist. The adaptation of
the casting is influenced by many variables, resulting
from the technical procedures employed during                                                   Fig 1 Cone and ring model
fabrication. While retention may be enhanced by                                                 inclined plane system.
                    The Inlemationaljoumai of Praitliodonticï   196    Volume I, Nun
                 Mech.initat Relertion of ttie Coniplele Crown
 inclined plane system composed of a cone and a                  is zero. Conversely, as the taper of the cone de-
 ring. Both parts are made of rigid materials and all            creases, the magnitude of the horizontal compo-
 surfaces are smooth. The taper of the cone is de-               nents increase while the magnitude of the vertical
 scribed by < Ö, the angular measurement between                 components diminishes. When < Ö approaches 0°,
 the vertical axis of the cone and its side. The hole            the retentive capacity will be greatest. When the
  in the ring is tapered to match the taper of the cone.         sides of the cone become parallel ( < Ö = 0°), there
  If the parts are assembled as illustrated until they
  make passive contact, they can be easily separated.
 When an additional load is applied to force the parts
 together, it becomes more difficult to separate them.
 The greater the load applied to force the parts to-
 gether, the more they resist separation. This rela-
 tionship can be expressed mathematically by the
 equation; R = kF, when R = resistance to sepa-
  ration; F = force or load; k = constant.
     Figure 2 illustrates the interface between the cone
 and the ring in horizontal cross-section. The load
  (F) creates stress and strain within the system, which
  is transferred to the cone and the ring across the
  interface in a direction perpendicular to its surface.
  Because the objects are circular in cross-section, the
 ring is stretched and the cone becomes com-
 pressed. The compression ofthe cone and the ten-
 sion within the ring create stress and strain (stored
 energy], which tends to expend itself with equal
 magnitude in a direction opposite the force that
 produced it.
     Figure 3 is a vector force diagram ofthe interface          Fig 2 Horizontal cross-section through cone and ring. The
                                                                 arrows represent vectors that produce the compression and
 between the cone and the ring in vertical cross-                tension in the system.
 section. The compression (O and tension (T) are
 represented by the vectors C and T, which lie mid-
 way between the top and bottom of the ring and
 perpendicular to the interface. Vectors C and T can
 be described in terms of their honzontal (C" and
 T"] and vertical ( C and T*) components. The hor-
 izontal components represent the forces that hold
the objects together; the vertical components rep-
resent the forces that push the components apart.
The difference between the horizontal and vertical
forces represents the retentive capacity of the sys-
tem (k), mathematically expressed in the following
equation:
             A- = (C" -f T") - {O- + r)
when k = retentive capacity (% of the applied force);
 C = vector producing compression; T = vector
producing tension; C" = horizontal component of
C; T" = horizontal component of T; C* = vertical
component of C; T' = vertical component of T.
   It becomes apparent by inspection that as the
taper of the cone ( < Ö) increases, the magnitude of
the horizontal componentsdiminishesand the mag-
nitude of the vertical components increases. When
< Ö is 45°, the vertical and horizontal components
are equal, and the retentive capacity of the system              Fig 3 Vertical cross-section through cone and ring.
                                                                  The Intemational Journal of Prosthodóntica
                                                   Zuckerman            Mechanical Retention of ihe Complete Crown
will be no retention, because the cone (now a cyl-                    ternal surface of the crown, no further movement
inder) will pass through the ring, creating neither                   of the parts together is possible. Loading the system
tension nor compression. This relationship can be                     at this point will not produce any increase in reten-
expressed mathematicaily:                                             tion.
                                                                         Obvio jsiy, the adaptation ofthe casting must also
lfC + T = 1 unit or the total (100%)          force applied
                                                                      be considered. If retention is to be created, the axial
to the system, then
                                                                      walls of the tooth and crown must contact before
        COS 6 = C"/C or C^'       C           cos d                   the crown seats completely.
        cos $ = T'VT or T" = T                cos 8
                                                                         The adaptation of the casting, again, is influenced
        sin 6 = eye or C^         C           sin 6
                                                                      by many variables resulting from the technical pro-
       sin d ^ V/J or T^ = T                  sin e
                                                                      cedures employed during its production. A cast res-
Since k - {C + T") •- (C^-' + T'),            it follows by
                                                                      toration may be too large or too small, or it may be
substitution and factoring that
                                                                      distorted. It is possible to analyze and predict the
  k = (C cos 6   + T co;iö) - (C sin (î + T sin                       effect of an oversized or undersized casting on re-
    = (C + T } cos 6 --      (c +    T) sin 0                         tention. Distortion can be random and its effect on
                                                                      the adaptation of the crown, and ultimately the re-
Since C + T = 1 unit of force, one concludes that                     tention, is difficult to analyze.
k = cos Ö — sin 6.
                                                                         Figure 5 illustrates a crown-tooth assembly with
 Figure 4 shows this equation plotted on a graph.                     a perfect adaptation. There is intimate contact of
    The ability of this system to resist separation de-
 pends on the magnitude of the load forcing the parts
together and the taper of the cone and matching
 ring. This relationship Is defined by the equation: R
 = f (cos e - sin e).
    Friction is another factor that influences the re-
tention of the couple, Friction is the resistance of
the parts when sliding one part against the other. It
is a function ofthe surface texture and composition
of the parts (/) and the surface area (A) in contact
between them. The force required to overcome this
resistance during assembly and separation is an ad-
ditional factor that contributes to the retention of
the couple. Mathematically this relationship is de-
scribed by the equation: R = fA, when R = reten-
tion, / = frictional resistance/unit area; A ^ area of
contact. By adding this to the original equation, a
complete mathematical definition of the retention
of the system is obtained:
                                                                      Fig 4 Graph illustrating the relationship between the taper
                                                                      of the system {d) and the portion of the seating force that
             R ^ F (cos 6 - sin 9) + fA                               produces retention {k).
   This mathematical relationship can be applied to
a crown and tooth assembly. However, to apply the
information correctly, it is necessary to recognize
the similarities and differences between the actual
clinical situation and the hypothetical analogue pre-
viously described and analyzed.
   The ring, which corresponds to the crown, is uni-
formly tapered and open on both ends. It has no
definite seat on the cone. The ring and the cone
can be assembled until the walls of the cone contact
ihe internal walls of the ring. The system can then
be loaded by force to produce retention.
   The crown has a definite seat on the prepared
tooth. Once the occlusal surface or the shoulder of
the prepared tooth contacts the corresponding in-                     Fig 5 Crown-tooth assembly with perfect adaptation.
                  The International lournal of Prosthodontics   198    Volume 1, Number 2. 1988
                    Mechanir.il Retention of the Complele Crnwn            Zuckerman
 Fig 6 Undersized casting on a tooth prepared with a feather-            Fig 7 Undersized casting on a tooth prepared with a shoul-
 edge margin.                                                            der margin.
 the crown and tooth along the entire interface. Un-                     interface between the tooth and the casting will be
 der these circumstances, there is no retention.                         open except at the shoulder, and the margins of the
    Figure 6 illustrates a tooth prepared with a feather-                casting will overhang slightly. There will be no re-
 edge margin and adapted with a casting that is too                      tention.
 small. The axial walls of the casting will bind with                       Figure 9 illustrates a tooth prepared with a feather-
 the tooth before the casting seats completely. The                      edge margin and adapted with a casting that is too
 additional force required to seat the restoration will                  large. This assembly will not be retentive, and the
 create retention. Whether the restoration will seat                     margins of the casting will overhang slightly. The
 completely at this point depends on the magnitude                       axial walls will remain out of contact if the gingivo-
 of the load, the size discrepancy between the crown                     occlusal discrepancy does not completely compen-
and the tooth, the elasticity of the casting, and the                    sate for the lateral size discrepancy.
compressibility of the dentin. Note that the margins                        By selective relief, it is possible to modify some
of the casting are closed against the tooth even if                     ofthe circumstances described. If occlusal relief were
the casting does not seat completely.                                   provided for the the crown-tooth assembly in Fig
    Figure 7 represents a tooth prepared with a shoul-                  5, the restoration would become retentive. This
der and adapted with a casting that is too small. This                  would, however, take the restoration out of occlusal
casting will be retentive. If the size discrepancy be-                  contact. By relieving the axial walls of the castings
tween the crown and the tooth is too great, the                         described in Figs 6 and 7, their retention would be
crown will not seat completely and the butt joint at                    eliminated.
the shoulder will remain open.                                             Finally, there is the unanswered question regard-
   Figure 8 depicts a tooth prepared with a shoulder                    ing the relative retention of the complete versus
and adapted with a casting that is too large. The                       partial veneer crown. Investigators'"^ have recog-
Fig 8 Oversized casting on a tooth prepared with a shoulder             Fig 9 Oversized casting on a tooth prepared with a feather-
margin.                                                                 edge margin.
                                  Volume 1, Number 2, 1988        199    The lntern¿ilíonal lournal ot' Prosthodonlics
                                                                                    al Retenlion of the Complfte Cn
nized, but could not explain, the significantlygreater                   tooth preparation. The force required to overcome
retention of the complete crown as compared with                         the frictional resistance of the contacting surfaces of
the retention of the 3/4 or 7/8 partial veneer crowns                    the tooth and restoration produces additional re-
of similiar size and configuration. It is now possible                   tention. Frictional retention is a product of the sur-
to tinderstand this phenomenon. The partial veneer                       face configuration of the parts and the size of the
crown lacks circumferential continuity. These res-                       area in contact.
torations are more easily distorted by lateral expan-
sion of their axial walls during forced seating. When
this occurs, the compression-tension effect is lost                                                References
and the retention of the restoration considerably                        1. Reisbick MH, Shillingburg HT: Effect of preparation ge-
reduced.                                                                    ometry on retention and resistance of cast sold reîtorations,
                                                                            I Calif Dent Assoc :975: 3;51.
                                                                         2. Potts RG, Shillingburg HT |r, Duncanson MC |r: Retention
                        Summary                                             and resistance of preparations for cast restorations. / Frosthet
                                                                            Denn 980; 43:303.
   Retention of the complete crown is influenced by                      3. Rosenstiel E: The retention of inlays and crowns as a func-
a complex relationship that is developed between                            tion of geometrical form, Br Dent n9S7] 103-388.
                                                                         4. Owen CP: Factors influencing the retention and resistance
the crown preparation and the adaptation of the
                                                                            of preparations for cast intracoronal restorations, / Prosthet
restoration. If mechanical retention is to be estab-                        Dent 1986; 55:674.
lished, the axial walls of the tooth preparation and                     5. Lorey RE, Myers GE: The retentive qualities of bridge re-
the restoration must contact before the crown seats                         tainers. ; Am Dent Assoc 1968; 76:568.
completely. The force that is then applied to seat                       6. Kaufman EG, Coelho DH, Colin L: Factors influencing the
the crown produces retention by creating compres-                           retention of cemented gold castings. / Prosthet Dent 1967;
sion of the tooth and tension within the crown. The                         11:487.
                                                                         7. Jorgensen KD: The relationship between retention and con-
portion of the force that produces this retention is
                                                                            vergence angle in cemented veneer crowns. Acta Odontol
determined by the taper of the axial walls of the                           Scand 1955; 13:35.
         Literature Abstract-
         In Vitro Resistance of Composite Resin Dowel and
         Cores
         The resistance of selected composite resin dowel and core systems to oblique forces was compared.
          Extracted nonrestored, noncarious human mandibular mclars were prepared to imitate endodontic
         therapy and restored with either: prefabricated dowels in conjunction with a composite resin cere
         material; all composite resin cores consisting of composite resin core material; prefabricated dowels in
         conjunction with two combined composite resin materials; ali composite resin cores consisting of two
         combined composite resin materials: or conventional cast dowel and cores. Specimens were subjected
         to a slowly increasing force from the buccal side at 45 degrees to their long axis. The mean
         resistance levels of the tour composite resin systems were significantly lower than the mean
         resistance level of the tested cast dowel and cores. Tfie introduction of a prefabricated dowel or
         composite resin combination did not have any significant infiuence on the recorded resistance ieveis of
         the composite resin core systems. Systems without a dowel showed less negative failure
         characteristics after breakdown, and restoration was considered to be possible.
         Plasmans PJM, Welle PR, Vri)lioef MMA. J Endod 19B8; 17:300-304. References: 34. Reprints: Dr PJM Plasmans,
         Department ot Occlusal Reconstruction, Dental School, Unii/ersily ot hJijmegen, Nijmegen, The Netherlands.—flic/iarö
         R. Seals. Jr, DDS, MEd, MS. The University ot Tenas Health Science Center at San Antonio
                              alional lournal of Prostliodoniic;   200    Volume 1, Numt.