NON-LANDED DRILL AND METHOD OF MAKING SUCH DRILLS
Field of the Invention
The invention relates generally to dental instruments and, more particularly,
relates to endodontic instruments for extirpating pulp tissue and dentin from a root canal before obturating the root canal.
Background of the Invention
Successful root canal therapy effectively alleviates the pain and trauma
originating from the decayed, damaged or dead circulatory and neural pulp tissue so that the
tooth need not be extracted. After the pulp chamber, and subsequently the coronal root canal
orifice(s), have been accessed during a root canal procedure, pulp tissue is extirpated from the
root canal(s) of the tooth. Some surrounding dentin is also removed in the shaping of the root
canal(s). After the root canal(s) have been sufficiently shaped and cleaned, sealant and
obturation materials are used to fill and seal the root canal(s). To conclude the procedure, the
access cavity in the coronal portion of the tooth is sealed using a restorative procedure to
prevent future infection and decay. Various endodontic instruments are employed to remove the pulp tissue and
dentin from the root canal and to enlarge and shape the root canal in preparation for
obturation. Conventional endodontic reamers or files employed for extirpation during root
canal therapy generally include a thin, flexible, metal shaft with an abrasive surface or sharp
edges, which promotes efficient cleaning of the root canal. A shank at one end of the
endodontic file is adapted for gripping by a dentist or attachment to a mechanical device such
as a dental drill. Obturation material may be packed into the prepared root canal using similar endodontic instruments. Endodontic files are normally rotated and moved into and out of the
root canal along the instrument's longitudinal axis.
Endodontic files may be categorized generally as either non-landed or landed.
Non-landed endodontic files typically have a working length that features three or more sides
and a non-aggressive scraping edge of extremely negative rake angle at the intersection
between each side pair. Although non-landed files are relatively simple to manufacture, the
instrument tends to inefficiently push or scrape pulp tissue within the root canal wall rather
than cutting the tissue. This inefficient scraping action applies additional stress to the
instrument, which increases the incidence of instrument fracture and breakage. Another
deficiency of non-landed files is that excised pulp tissue may be transported apically and
packed into the canal apex, instead of being carried in a coronal direction and removed from
the root canal.
Landed endodontic files, on the other hand, have a working length that
includes at least one tissue-removing edge defined by a lengthwise flute and one or more
curved radial lands (sometimes referred to as "margins"). Given a cross-section taken
perpendicular to the longitudinal axis, all points of each land are on the outer periphery of the
file and are equidistant radially from the file's longitudinal rotational axis. Landed
endodontic files are typically more difficult and costly to manufacture than non-landed
endodontic files because of the process of forming lands and flutes. However, landed
endodontic files may cut pulp tissue more efficiently than non-landed files, particularly if the
tissue-removing edge has a positive rake angle. In addition, the flutes provide pathways along
the instrument working length for the efficient capture and transport of excised pulp tissue in
a coronal direction out of the root canal. The working lengths of landed endodontic files tend
to have a larger cross-sectional area than the working lengths of non-landed endodontic files.
As the instrument is rotated in a curved canal, the greater cross-sectional area causes greater
cyclic fatigue, which may increase the propensity for fracture.
The radial lands on landed endodontic files represent bearing surfaces that,
when the instrument is rotated in the root canal, contact and rub against the canal wall. The
friction from the sliding contact is dissipated as heat, which induces stresses in the instrument
and may lead to unexpected fracture. In addition to a diminished product lifetime and
interruptions during root canal therapy to replace broken instruments, an instrument fracture
may result in patient discomfort and an undesirable final shape. In extreme cases an instrument fragment that cannot be retrieved may lead to infection and ultimately tooth
extraction.
Thus, there would be a need for an endodontic instrument that overcomes
these deficiencies of conventional landed and non-landed endodontic files.
Summary of the Invention
The invention overcomes the foregoing and other shortcomings and drawbacks
of conventional endodontic instruments, as described above. According to the principles of
the invention, an apparatus which may be an endodontic instrument in certain embodiments,
includes an elongated shaft having a longitudinal axis, a working length extending along the
longitudinal axis, and a plurality of longitudinal regions arranged about the longitudinal axis.
A plurality of edges extends longitudinally along the working length. Each of the edges is distanced radially from the longitudinal axis, and adjacent pairs of the edges are adjoined or joined along the working length by a corresponding one of the regions. At least one of the edges has a rake angle more negative than about -30° and at least one of the edges has a rake angle equal to or more positive than 0°. At any axial location along the working length, a cross-section may be taken perpendicular to the longitudinal axis. Each of the edges defines a maximum radius, which is measured at the axial location perpendicular to the longitudinal axis. The regions are positioned radially inside an imaginary circle centered about the longitudinal axis at the axial location and having a radius measured perpendicular to the longitudinal axis equal to the maximum radius. The edges are arranged such that each void area, bounded by each respective region and the imaginary circle, is less than half the total area of the imaginary circle.
Endodontic instruments of the invention improve upon conventional endodontic instruments as the positive attributes of landed instrument types and the positive attributes of non-landed instrument types are both present, while their significant negative attributes are either eliminated or reduced. The endodontic instruments feature a plurality of longitudinally-extending surfaces in the form of facets and curved surfaces arranged in a substantially polygonal or ovoidal cross-sectional profile and at least one longitudinally- extending flute defining an edge having a rake angle equal to or more positive than 0°. Adjacent facets meet at an edge having a rake angle more negative than about -30°. Likewise, the ovoidal longitudinally-extending surfaces leave an outermost edge having a rake angle more negative than about -30°. The endodontic instruments of the invention lack radial lands or margins between adjacent edges so that the only points of contact with the canal wall are
- the edges. In other words, the periphery of the inventive endodontic instruments lacks arcs of
constant radius, measured relative to the instrument centerline, that lie on the surface of revolution, as defined elsewhere herein.
The above and other objects and advantages of the invention shall be made
apparent from the accompanying drawings and the description thereof.
Brief Description of the Drawings
The accompanying drawings, which are incorporated in and constitute a part of
this specification, illustrate embodiments of the invention and, together with a general
description of the invention given above, and the detailed description of the embodiments
given below, serve to explain the principles of the invention. Fig. 1 is a side view of an endodontic instrument according to the invention.
Fig. 2 is a perspective view of the endodontic instrument of Fig. 1 with the tip
absent for clarity.
Fig. 3 is a cross-sectional view taken generally along line 3-3 in Fig. 2.
Fig. 3 A is an enlarged view of a portion of Fig. 3. Figs. 4A and 4B are cross-sectional views similar to Fig. 3 at stages in the
fabrication of the endodontic instrument preceding the fabrication stage of Fig. 3.
Figs. 5A-G are cross-sectional views similar to Fig. 3 of endodontic
instruments in accordance with alternative embodiments of the invention.
Fig. 6 is a side view of an endodontic instrument similar to the endodontic
instrument of Fig. 1 in accordance with an alternative embodiment of the invention.
Fig. 7 is a side view of an endodontic instrument in accordance with an
alternative embodiment of the invention.
Figs. 7A and 7B are cross-sectional views taken generally along line 7A-7A
and line 7B-7B in Fig. 7.
Figs. 8A and 8B are cross-sectional views similar to Figs. 7A and 7B of an
endodontic instrument in accordance with an alternative embodiment of the invention. Fig. 9 is a side view of an endodontic instrument in accordance with an
alternative embodiment of the invention.
Figs. 9A and 9B are cross-sectional views taken generally along line 9A-9A
and line 9B-9B in Fig. 9.
Figs. 10A and 10B are cross-sectional views similar to Figs. 9 A and 9B of an
endodontic instrument in accordance with an alternative embodiment of the invention.
Fig. 11 is a side view of an endodontic instrument in accordance with an
alternative embodiment of the invention.
Detailed Description
-The instruments of the invention may be used as reamers, files, or condensers. i all of the embodiments disclosed and described herein, the instruments are represented as
reamers or files used for cleaning and shaping root canals or for creating a space for a post
used to secure a crown or bridge. It will be appreciated by persons of ordinary skill in the art
that the instruments described herein when provided with negative helix fluting may be used
as condensers for pushing obturation materials, such as gutta percha, toward the canal apex
for filling the root canal after it has been extirpated and shaped by reamers and files.
With reference to Figs. 1 and 2, an endodontic instrument, generally indicated
by reference numeral 10, includes a shaft 11 having a base or proximal end 12, a point or
distal end 14, and an elongate working length 16 extending between ends 12 and 14 along a
longitudinal shaft axis 17 generally aligned with the centerline of the shaft 11. A shank 18
situated at the proximal end 12 and adapted for interfacing or gripping instrument 10 with a chuck or collet of a motorized rotary dental handpiece or, alternatively, of manually
manipulating the instrument 10 with a handgrip of some form. Manipulation of the instrument 10 in a cutting movement for extirpating pulp tissue and/or dentin under
conventional circumstances includes rotating the instrument 10 about the shaft axis 17 and
simultaneously reciprocating the instrument 10 longitudinally along the shaft axis 17.
The working length 16 of the instrument 10 is lengthwise tapered along axis
17 in a longitudinal direction between ends 12 and 14 with the diameter decreasing in a
direction toward distal end 14. Alternatively, the working length 16 may have a uniform
cross-sectional diameter or a zero taper, or may have a taper characterized by a slowly
increasing diameter in a direction toward distal end 14. If tapered, the taper of the
cross-sectional diameter of the working length 16 may range from about -0.02 millimeters per
millimeter to about 0.2 millimeters per millimeter when measured from the distal end 14 to
the proximal end 12. The length of the working length 16 may range, without limitation,
from about 0.5 millimeter to about 20 millimeters. The overall length of the instrument 10
may range, without limitation, from about 10 millimeters to about 60 millimeters. The
diameter of the distal end 14 may range, without limitation, from about 0.04 millimeter to
about 1.5 millimeters. With reference to Figs. 2, 3 and 3 A, extending lengthwise and linearly along
the working length 16 of endodontic instrument 10 are a plurality of cutting edges 20, 22 and
24 each defined by one of a corresponding plurality of lengthwise-extending flutes 26, 28 and
30 and a plurality of guiding edges 32 and 34. The cutting edges 20, 22 and 24, the flutes 26,
28 and 30, and the guiding edges 32 and 34 are parallel, i.e., they extend along paths that do
not intersect each other along the working length 16. The cross-sectional profile at any location along the working length 16 is
substantially identical and is shown best in Figs. 2 and 3. Each of the flutes 26, 28 and 30
includes a concave surface 26a, 28a and 30a, respectively, constructed from two planar
surfaces and a continuously curved surface joining the two planar surfaces. Each of the
concave surfaces 26a, 28a and 30a is defined or inscribed as a lengthwise groove along the
working length 16 and each extends between one of the cutting edges 20, 22 and 24 and a
corresponding one of trailing edges 36, 37 and 38. The planar surface of each of concave
surfaces 26a, 28a and 30a facing in the direction of rotation of the shaft 11, when rotating
during use, constitutes a cutting face terminated by a corresponding one of the cutting edges
20, 22 and 24. The planar surface of each of concave surfaces 26a, 28a and 30a facing in a
direction opposite to the rotation of the shaft 11, when rotating during use, constitutes a non-
cutting face terminated by a corresponding one of the trailing edges 36, 37 and 38. Each of
the flutes 26, 28 and 30 is characterized by a cross-sectional profile viewed from a perspective
parallel to the shaft axis 17, a flute depth measured radially from the shaft axis 17 to the
nearest point of the corresponding concave surface 26a, 28a and 30a, and a flute volume
given by the product of the flute cross-sectional area and working length 16, assuming the
flutes 26, 28 and 30 have a constant cross-sectional area along the working length 16. With continued reference to Figs. 2, 3 and 3A, guiding edge 32 is formed at
the intersection of two longitudinally-extending surface portions or facets 40 and 42 that
extend axially along the working length 16. At a given cross-section taken perpendicular to
the shaft axis 17 anywhere along the working length 16, cutting edges 20 and 24 and guiding
edges 32 and 34 lie on an imaginary circle 43 encircling the endodontic instrument 10: The
cutting edges 20 and 24 and the guiding edges 32 and 34 define points on the imaginary circle
43. Along the entire working length 16, a surface of revolution is generated by the infinite
series of imaginary circles defined by their respective cross-sections. Hence, this surface of
revolution intersects the outermost radial points of the working length 16. The surface of
revolution is cylindrical if the working length 16 has a zero taper or, if the working length 16
is tapered, the surface of revolution is frustoconical. Cutting edge 22 lies radially inside the
imaginary circle 43 but, nonetheless, may provide a cutting action when the endodontic
instrument 10 is rotated counterclockwise (as viewed in Fig. 3) about shaft axis 17 inside a
root canal. Flute 26 eliminates a former facet 44 (visible in Fig. 4B) and the trailing edge
36 of the concave surface 26a defining flute 26 effectively narrows the width of facet 46.
Extending axially along the working length 16 is an additional facet 48 that intersects facet 46
at guiding edge 34. Flute 28 eliminates a former facet 50 (visible in Fig. 4B) and the cutting
edge 22 of the concave surface 28a defining flute 28 effectively narrows the width of facet 48. Flute 28 also effectively narrows the width of facet 52. Concave surface 30a of flute 30
intersects the facet 52 for defining cutting edge 24 at a former location of guiding edge 64
(visible in Fig. 4B) and, due to the angle at which the curved surface 30a intersects the facet
52, transforms the former guiding edge into cutting edge 24. Flute 30 eliminates a former
facet 54 (visible in Fig. 4B) and the trailing edge 38 of the concave surface 30a defining flute
30 effectively narrows the width of facet 42.
With continued reference to Figs. 2, 3 and 3 A, each of the cutting edges 20 and
24 lie on the imaginary circle 43, although the invention is not so limited as any or all the
cutting edges 20, 22 and 24 may be positioned radially inside the imaginary circle 43. A
distinct relief angle is defined between a line tangent to the imaginary circle 43 at each of the
cutting edges 20, 22 and 24 and the corresponding adjacent one of the facets 40, 48 and 52.
The relief provides clearance and prevents rubbing against the canal wall. Each of the
guiding edges 32 and 34 lie on the imaginary circle 43. Trailing edges 36, 37 and 38 are
positioned radially inside the imaginary circle 43 unless coincident spatially with a guiding
edge. In the latter instance, the spatial coincidence does not transform a guiding edge to a
cutting edge, regardless of the angle of intersection, as each of the trailing edges 36, 37 and 38
faces a direction counter to the direction of rotation of shaft 11 and, hence, provides no
cutting action. Each of the cutting edges 20, 22 and 24 and guiding edges 32 and 34 defines a
radius measured perpendicular to the shaft axis 17 and determined at an arbitrary axial
location along the working length 16. The set of radii ranges between a maximum radius and
a minimum radius at any axial location. The facets 40, 42, 46, 48 and 52 and concave
surfaces 26a, 28a and 30a define a plurality of longitudinal regions arranged about the shaft
axis 17. Adjacent pairs of cutting edges 20 and 24 and guiding edges 32 and 34 at the
maximum radius are adjoined or joined at any arbitrary axial location by a corresponding one
of the regions, which extend about the contoured outer periphery of the working length 16.
At any arbitrary axial location, these regions are positioned radially inside the imaginary-
circle 43, which has a radius measured relative to the longitudinal axis 17 equal to the
maximum radius from among the set of radii. Each void area, or open space, is bounded by
the intervening facets and concave surfaces between an adjacent pair of edges 20, 24, 32 and
34 and the arc of the imaginary circle lying between the edge pair.
Edges 20, 24, 32 and 34, and imaginary circle 43 are arranged, when viewed in
cross section at any arbitrary axial location, such that a bounded void area is less than half of
the total area of the imaginary circle 43. Stated differently, the void area defined by any
single region cannot reduce the dynamic cross-sectional area of the working length 16 at any
axial location along the working length 16 by more than 50 percent. For example, cutting
edge 20 and guiding edge 34 are arranged such that the collective void area bounded between
concave surface 26a and facet 46, which collectively represent the region between edges 20
and 34, and the imaginary surface 43 is less than half the total area of the imaginary circle 43.
As another example, cutting edge 24 and guiding edge 34 are arranged such that the collective
void area bounded between imaginary circle 43 and the surface defined by facet 48, concave
surface 28a, and facet 52, which collectively represent the region between edges 24 and 34, is less than half the total area of the imaginary circle 43. With reference to Figs. 3 and 3 A, each of the cutting edges 20, 22 and 24 is
characterized by a positive rake angle, γ, which is measured between a line defined by the
respective cutting edge and shaft axis 17, and a line parallel to a corresponding one of
concave surfaces 26a, 28a and 30a proximate to the associated one of the cutting edges 20, 22
and 24. In alternative embodiments of the invention, the rake angle of each of the cutting
edges 20, 22 and 24 may be neutral. In other embodiments of the invention, the rake angle of
one or more of the cutting edges 20, 22 and 24 is neutral. In yet other embodiments of the
invention, the rake angle of one or more of the cutting edges 20, 22 and 24 is positive, hi yet other embodiments of the invention, each of the cutting edges 20, 22 and 24 may be
characterized without limitation by either a positive rake angle or a neutral rake angle. The efficiency or the aggressiveness of the cutting action of each of the cutting
edges 20, 22 and 24 generally increases as the rake angle is made more positive. Generally,
rake angles equal to or more positive than 0° efficiently cut dentin and pulp tissue, with the
cutting efficiency or aggressiveness increasing as the rake angle becomes more positive. The
guiding edges 32 and 34, which are characterized by rake angles more negative than about
-30°, provide some tissue scraping action, but are present primarily to guide the instrument 10 within the root canal.
With reference to Fig. 3, the concave surfaces 26a, 28a and 30a of the flutes
26, 28 and 30 are each constructed from two individual flat or planar surfaces and a
continuously curved surface joining the two planar surfaces. Alternatively, one or more of the
concave surfaces 26a, 28a and 30a may be formed from one or more flat or planar segments,
one or more continuously curved surfaces, or any combination thereof. The depth of each
flute 26, 28 and 30, which is measured radially outward from the shaft axis 17, is substantially
equal. However, the invention contemplates that the flute depths may differ among the
various flutes 26, 28 and 30. The flute volumes, which reflect the amount of material
removed from the working length 16 to introduce the flutes 26, 28 and 30, are substantially equal, although the invention is not so limited. The flutes 26, 28 and 30 are each
characterized by a substantially identical cross-sectional profile viewed parallel to the shaft
axis 17. Alternatively, the cross-sectional profiles of some or all of the flutes 26, 28 and 30
may differ. The cutting edges 20, 22 and 24 are spaced about the circumference of the
working length 16 at unequal angular intervals a, β, and θ that reflect curvilinear separations
measured about the imaginary circle 43. The invention contemplates that, alternatively, either
two or all of cutting edges 20, 22 and 24 may be spaced with equal or uniform angular
intervals. The properties of the facets 40, 42, 44, 46, 48, 50, 52 and 54 may be
characterized as though the flutes 26, 28 and 30 were absent from endodontic instrument 10
for purposes of description. With this assumption in place, the facets 40, 42, 44, 46, 48, 50,
52 and 54 have a substantially octagonal arrangement and are substantially flat or planar,
although the invention is not so limited as one or more of the facets 40, 42, 44, 46, 48, 50, 52
and 54 may be either slightly concave or slightly convex, so long as the convex shape is
inscribed within the imaginary circle 43. Alternatively, some or all facets 40, 42, 44, 46, 48,
50, 52 and 54 maybe replaced with any number of ovoidal longitudinally-extending surfaces
provided the instrument maintains its non-landed properties as exemplified in Figs. 5F and
5G. The facets 40, 42, 44, 46, 48, 50, 52 and 54 have equal widths. However, the invention contemplates that two or more of the facets 40, 42, 44, 46, 48, 50, 52 and 54 may have
unequal widths. The cross-section profile of the facets 40, 42, 44, 46, 48, 50, 52 and 54
possesses mirror symmetry about eight orthogonal planes. In alternative embodiments of the
invention, the cross-sectional profile of the facets 40, 42, 44, 46, 48, 50, 52 and 54 may have
mirror symmetry about multiple planes, only a single plane or may lack mirror symmetry.
With continued reference to Fig. 3, the guiding edges 32 and 34 and the cutting
edges 20, 22 and 24 are depicted as beveled or chamfered. However, the guiding edges 32
and 34 may alternatively be radiused or rounded, as shown for guiding edges 122, 124, and
126 (Fig. 5D), to provide a smoother contact for guiding and centering the instrument 10
within the root canal. In addition, cutting edges 20, 22, and 24 may be radiused or rounded,
as shown for cutting edges 128 and 130 (Fig. 5D).
The curved surfaces of the flutes 26, 28 and 30 define pathways that efficiently
transport excised pulp tissue and dentin in a coronal direction toward the proximal end 12 and
out of the root canal as the endodontic instrument 10 is rotated in the root canal, which
represents one benefit of conventional landed endodontic instruments. The efficient removal
of the excised pulp tissue and dentin reduces the friction acting on the working length 16,
which reduces the likelihood of fracture or breakage as torque is applied to the instrument 10.
The efficient coronal transport also reduces or eliminates transport of the excised pulp tissue
and dentin toward the canal apex, which is a positive attribute or benefit characteristic of
conventional landed endodontic instruments. The guiding edges 32 and 34 make a minor scraping contribution to the cutting action of the instrument 10, which is provided substantially exclusively by the operation of the cutting edges 20, 22 and 24. In contrast, the guiding edges 32 and 34 are designed to help guide and center the instrument 10 within the root canal.
With reference to Figs. 3, 4A and 4B, methods of manufacturing the instruments 10 of the invention are illustrated. An initial workpiece 61, which is constituted
by a single piece of a suitable material, is modified by the addition of longitudinally- extending surfaces in the form of facets 40, 42, 44, 46, 48, 50, 52 and 54 about its
circumference. Though depicted as cylindrical for the purposes of example, the invention
contemplates that workpiece 61 may initially be any shape or size without limitation.
Although eight facets are illustrated in a geometrical shape representative of Figs. 4A and 4B,
it is understood by persons of ordinary skill in the art that three or more facets are formed
with a substantially polygonal arrangement in the blank as reflected in Figs. 3 and 5A-E.
Although the facets 40, 42, 44, 46, 48, 50, 52 and 54 are depicted as planar, the invention
contemplates that these surfaces may be planar, slightly concave, slightly convex or ovoidal.
In cross-section, the polygonal arrangement of the facets 40, 42, 44, 46, 48, 50, 52 and 54
defines a boundary of a closed plane figure, which is octagonal. However, the invention
admits to other multi-sided closed plane figures for the polygon arrangement including but
not limited to triangular, quadrilateral, pentagonal, hexagonal, and heptagonal arrangements.
The closed plane figure has multiple included angles formed at the intersection of each pair of
constituent straight lines and/or curves. However, the invention contemplates that any one or
more pairs of intersecting lines or curves in the cross-sectional profile may join at a rounded
juncture, as illustrated for example in Figs. 5D, 5F and 5G.
Then, flutes 26, 28 and 30 are added to the instrument 10 to define cutting
edges. The addition of flutes 26, 28 and 30 shorten the width of certain facets and eliminate other facets in their entirety. In the illustrated embodiment, guiding edge 56 at the
intersection of facets 40 and 44 and guiding edge 64 at the intersection of facets 52 and 54 are
transformed into cutting edges 20 and 24, respectively, by the addition of the flutes 26 and 30.
Guiding edge 58 at the intersection of facets 44 and 46, guiding edge 60 at the intersection of
facets 48 and 50, guiding edge 62 at the intersection of facets 50 and 52, and guiding edge 66
at the intersection of facets 42 and 54 are removed from the blank by the addition of the flutes
26, 28 and 30. Facets 42, 46, 48 and 52 are narrowed by the addition of flutes 26, 28 and 30. With continued reference to Figs. 3, 4A and 4B, facets 40, 42, 46, 48 and 52
provide regions of clearance or relief that do not contact the canal wall during use. hi
particular, the facets 40, 42, 46, 48 and 52 do not subtend an arc of a single radius along the
imaginary circle 43 over which contact exists between the working length 16 and the root
canal wall, which contrasts with the significant contact between radial lands or margins with
the root canal wall observed in conventional landed endodontic instruments. Instead, the
facets 40, 42, 46, 48 and 52 are relieved to provide clearance with the root canal wall. Two
guiding edges 32 and 34 remain after the flutes 26, 28 and 30 are added, although the
invention is not so limited as at least one guiding edge should remain intact after an arbitrary
number of flutes are added. In alternative embodiments, the flutes 26, 28 and 30 maybe
formed before the facets 40, 42, 44, 46, 48, 50, 52 and 54 are added so that the manufacturing
stage of Fig. 4B transpires before the manufacturing stage of Fig. 4A, or all of the
aforementioned features may be formed concurrently.
The initial workpiece 61 is composed of any material having a flexibility
adequate to follow the curved path defined by the non-circular root canal without ledging or
perforating the canal wall and sufficient strength for cutting and removing pulp tissue without fracture. Suitable materials include, but are not limited to, stainless steel, nickel-titanium, or any number of plastics, composites, shape memory alloys, and the like. Persons of ordinary skill will recognize that conventional instrument-making techniques may generally be applied
to the manufacture of instruments 10 according to the invention and with various known or later-developed materials and/or methods. For example, the facets 40, 42, 44, 46, 48, 50, 52
and 54 of the instruments 10 of the invention may be formed by multi-pass grinding or
milling and the flutes 26, 28 and 30 may be formed by broaching or saw cutting.
Figs. 5A-G depict alternative embodiments of the invention in which, among
other features, the number and shape of the facets and the number and shape of the flutes are
varied. In each individual embodiment, the void area bounded by the intervening facets and
concave surfaces between adjacent pairs of guiding and cutting edges at the maximum radius,
and the imaginary circle 43, is less than half of the total area of the imaginary circle 43. With reference to Fig. 5 A in which like reference numerals refer to like
features in Fig. 3 and in accordance with an alternative embodiment of the invention, the
working length 16 of an endodontic instrument 10a is provided with a guiding edge 64 and a
pair of flutes 66 and 68 each having a corresponding continuously-curved concave surface
66a and 68a defining cutting edges 71 and 70, respectively, each having a positive rake angle.
Viewed parallel to the axis 17, the endodontic instrument 10a has a generally triangular cross-
sectional profile. The cutting edges 70 and 71 are defined at the former locations of guiding
edges, as described above. Instrument 10a includes facets 72, 74 and 76, of which the
transverse width of facets 72 and 74 are shortened by the presence of flutes 66 and 68,
respectively. Guiding edge 64 is defined at the intersection of shortened- width facet 74 and
full-width facet 76. Neglecting the presence of the flutes 66 and-68, the facets 72, 74 and 76
are substantially equal in width, are slightly convex and inscribed within the imaginary circle
43, and have mirror symmetry in cross-section about three orthogonal planes. The
dimensions and characteristics of flutes 66 and 68 may or may not be substantially equal. With reference to Fig. 5B in which like reference numerals refer to like
features in Fig. 3 and in accordance with an alternative embodiment of the invention, the
working length 16 of an endodontic instrument 10b is provided with two guiding edges 80
and 82 and two cutting edges 84 and 86 each defined by one of a pair of flutes 88 and 90,
respectively, each having a concave surface 88a and 90a formed from two intersecting planar
surfaces. Viewed parallel to the axis 17, the endodontic instrument 10b has a cross-sectional
profile generally shaped as a square. The invention contemplates that the cross-sectional
profile of endodontic instrument 10b may be any quadrilateral without limitation. Cutting
edge 84 is characterized by a neutral rake angle, while cutting edge 86 is characterized by a
negative rake angle. The flute depths, flute volumes, and cross-sectional profiles viewed
parallel to the shaft axis 17 differ for the flutes 88 and 90. Neglecting the presence of the
flutes 88 and 90, the facets 92, 94, 96 and 98 are substantially equal in width, have a slight
concave curvature, and have mirror symmetry in cross-section about four orthogonal planes.
With reference to Fig. 5C in which like reference numerals refer to like
features in Fig. 3 and in accordance with an alternative embodiment of the invention, the
working length 16 of an endodontic instrument 10c is provided with one cutting edge 100
defined by a flute 102 having a concave surface 102a constructed from one planar surface and
one continuously curved surface and four guiding edges 104, 106, 108 and 110. The rake
angle of the cutting edge 100 is neutral. Viewed parallel to the axis 17, the endodontic
instrument 10c has a generally pentagonal cross-sectional profile. Neglecting the presence of
the flute 102, facets 112, 114, 116, 118 and 120 differ in width and lack mirror symmetry.
Facets 112, 1 16 and 120 are slightly concave, facet 1 18 is slightly convex, and facet 1 14 is
substantially planar.
With reference to Fig. 5D in which like reference numerals refer to like
features in Fig. 3 and in accordance with an alternative embodiment of the invention, the
working length 16 of an instrument lOd is provided with three rounded guiding edges 122, 124, and 126 and two cutting edges 128 and 130 each defined by one of a pair of flutes 132
and 134. Cutting edge 128 has a positive rake angle and cutting edge 130 has a negative rake
angle. Viewed parallel to the axis 17, the endodontic instrument lOd has a generally
hexagonal cross-sectional profile. The flute depths, flute volumes, and cross-sectional
profiles viewed parallel to the shaft axis 17 differ for the flutes 132 and 134. Flute 132 is
formed from a concave surface 132a constructed from two planar surfaces and a continuously
curved surface and, in contrast, flute 134 has a concave surface 134a constructed from two
continuously-curved surfaces and three planar surfaces. Neglecting the presence of the flutes
132 and 134, facets 136, 138, 140, 142, 144 and 146 are substantially equal in width and have
mirror symmetry in cross-section about six orthogonal planes.
With reference to Fig. 5E in which like reference numerals refer to like
features in Fig. 3 and in accordance with an alternative embodiment of the invention, the
working length 16 of an endodontic instrument lOe is provided with five cutting edges 148,
150, 152, 154 and 156 each defined by one of five flutes 158, 160, 162, 164 and 166 and two
guiding edges 168 and 170. Cutting edges 148 and 150 have a positive rake angle, cutting
edge 154 has a neutral rake angle, and cutting edges 152 and 156 have a negative rake angle.
Viewed parallel to the axis 17, the endodontic instrument lOe has a generally heptagonal
cross-sectional profile. The flute depths, flute volumes, and cross-sectional profiles viewed
parallel to the shaft axis 17 differ among the flutes 158, 160, 162, 164 and 166. Flute 158 is
constructed with a continuously-curved concave surface 158a. Flute 160 has a concave surface 160a constructed from one continuously curved surface and one planar surface.
Flutes 162 and 166 are each formed from two intersecting planar surfaces. Flute 164 is
formed from multiple continuously curved surfaces and planar surfaces. Neglecting the
presence of the flutes 158, 160, 162, 164 and 166, facets 172, 174, 176, 178, 180, 182 and
184 differ in width, are substantially-planar, and lack mirror symmetry in any orthogonal
plane.
With reference to Fig. 5F in which like reference numerals refer to like
features in Fig. 3 and in accordance with an alternative embodiment of the invention, the
working length 16 of an endodontic instrument lOf is provided with a guiding edge 350 and a
flute 352 having a corresponding continuously-curved concave surface 352a defining cutting edge 354 with a positive rake angle. Viewed parallel to the axis 17, the endodontic
instrument 1 Of has a generally ovoidal cross-sectional profile. The cutting edge 354 is
defined at the former location of a guiding edge, as described above. Curved surface 356 is
divided by flute 352. Curved surfaces 358 and 356 are connected on one side by planar
surface 360 to define one region of the cross-section, and on the other side by curved surface
362 which, when combined with the remaining section of curved surface 356 and flute
surface 352a, define another region of the cross-section. Guiding edge 350 is defined by the
point on curved surface 358 that is most distant from the axis 17. Curved surfaces 358, 356
and 362 are substantially unequal, however, the invention contemplates that two or all of
these curves maybe substantially equal. Neglecting the presence of the flute 352, each
curved surface 356 and 358 makes contact with the imaginary circle 43 at a single point. The
cross-section shown in Fig. 5F lacks mirror symmetry in any orthogonal plane.
With reference to Fig. 5G in which like reference numerals refer to like features in Fig. 3 and in accordance with an alternative embodiment of the invention, the
working length 16 of an endodontic instrument lOg is provided with two guiding edges 370
and 372 and a flute 374 having a corresponding continuously-curved concave surface 374a
defining cutting edge 376 with a positive rake angle. Viewed parallel to the axis 17, the
endodontic instrument lOg has a generally modified ovoidal cross-sectional profile. The
cutting edge 376 is defined at the former location of a guiding edge, as described above.
Curved surface 378 is divided by flute 374. Instrument lOg includes curved surfaces 378,
380, 382, 384, 386, 388, 390 and 392, which are all connected. A section of each of curved
surfaces 378 and 382 are connected by curved surfaces 380 and 388 to define one region. Likewise, a section of each of curved surfaces 382 and 386 are connected by curved surfaces
384 and 390 to define another region. The remaining sections of curved surfaces 378 and 386
combine with curved surface 392 and flute surface 374a to define the final region of the cross-
section. Guiding edges 370 and 372 are defined by the points on curved surfaces 382 and 386, respectively, that are most distant from the axis 17. Curved surfaces 378 and 386 are
substantially equal, curved surfaces 380 and 384 are substantially equal, and curved surfaces
388, 390, and 392 are substantially equal, however, each specified group differs from the
others and they all differ from curved surface 382. Neglecting the presence of the flute 374,
each curved surface 378, 382 and 386 makes contact with the imaginary circle 43 at a single
point. Guiding edges 370 and 372, and cutting edge 376 are spaced about the circumference
of the working length 16 at unequal angular intervals ", β", and θ" and therefore the cross-
section shown in Fig. 5G lacks mirror symmetry in any orthogonal plane.
The number of flutes and, hence, the number of cutting edges maybe modified
among the various embodiments of the invention depicted in Figs. 5A-G, so long as at least
one guiding edge with a rake angle more negative than about -30° is retained. The facets and
curved surfaces only contact the root canal wall by way of a guiding edge. Therefore, the only
portions of the instrument 10 contacting the root canal wall will be the cutting edges and the
guiding edges, as the instrument 10 lacks lands. It is appreciated that instrument 10 may be used as a reamer or a file for
extirpation when rotated in a counterclockwise sense as viewed along the shaft axis 17 from
the perspective of Fig. 3, Fig. 4B and Figs. 5A-G. Instrument 10 may be configured with
negative helix fluting that is a mirror image of Figs. 6, 7 and 9 for use as a condenser for
pushing obturation materials, such as gutta percha, toward the canal apex to fill an extirpated
root canal. With reference to Fig. 6 in which like reference numerals refer to like features
in Figs. 1-4 and in accordance with- an alternative embodiment, an endodontic instrument 186
may be formed from instrument 10 by twisting the working length 16 so that the facets 40, 42,
46, 48 and 52 and flutes 26, 28 and 30 bear a helical or spiral relationship characterized by a
pitch. The pitch of helical facets and flutes may be constant or may vary, as understood by
persons of ordinary skill in the art. The instrument 186 may be manufactured by creating
straight axial facets and flutes, as depicted in Fig. 1, and then twisting, as understood by
persons of ordinary skill in the art, the instrument 10 to twist the facets 40, 42, 46, 48 and 52
and flutes 26, 28 and 30 into a helical or spiral configuration. Techniques for manufacturing
twisted endodontic instruments are disclosed in commonly-assigned U.S. Patent No.
6,315,558, the disclosure of which is hereby incorporated by reference herein in its entirety.
Subsequent to twisting, the cross-sectional profile of the endodontic instrument 186 will be
substantially identical to the cross-sectional profile of endodontic instrument 10 (Fig. 3) at
any axial position along the working length 16. Alternatively, one or both of the facets 40,
42, 46, 48 and 52 and/or flutes 26, 28 and 30 may be formed as post-twisting features. For example, flutes 26, 28 and 30 may be formed before shaft 11 is twisted and the facets 40, 42,
46, 48 and 52 may be formed after twisting. The invention contemplates that, in alternative
embodiments, the endodontic instrument 186 may have a construction based upon any of the
cross-sectional profiles shown in Figs. 5A-5G.
With reference to Figs. 7, 7A and 7B in which like reference numerals refer to
like features in Figs. 1-4 and 6 and in accordance with an alternative embodiment, an
endodontic instrument 188 includes a plurality of lengthwise-extending flutes 190, 192 and
194, similar to flutes 26, 28 and 30 (Figs. 1-3), and a plurality of facets 196, 198, 200, 202,
204, 206, 208 and 210, similar to facets 40, 42, 44, 46, 48, 50, 52 and 54 (Figs. 1-4). Each of
the flutes 190, 192 and 194 defines one of a corresponding plurality of cutting edges 212, 214,
and 216, similar to cutting edges 20, 22 and 24 (Figs. 1-3). Extending along axis 17 is a
plurality of guiding edges 218, 220, 222, 224, 226, 228, 230 and 232, similar to guiding edges
32, 34, 56, 58, 60, 62, 64 and 66 (Fig. 4B), each defined at the intersection of coextensive
adjacent facets 196, 198, 200, 202, 204, 206, 208 and 210. The invention contemplates that, in alternative embodiments, the endodontic instrument 188 may have a construction based
upon any of the cross-sectional profiles shown in Figs. 5A-5G.
The facets 196, 198, 200, 202, 204, 206, 208 and 210 and, hence, guiding
edges 218, 220, 222, 224, 226, 228, 230 and 232 have a constant zero-degree helix angle and,
hence, a constant pitch. As is best apparent in Fig. 7, the flutes 190, 192 and 194 and, hence,
cutting edges 212, 214, and 216 wind about the working length 16 with a spiral or helical
arrangement that varies in helix angle and pitch axially along the working length 16 of
endodontic instrument 188. The facets 196, 198, 200, 202, 204, 206, 208 and 210 extend
linearly along the working length 16 and are periodically interrupted by the flutes 190, 192
and 194 winding about the working length 16. This leads to discontinuities in the guiding
edges 218, 220, 222, 224, 226, 228, 230 and 232. At any axial location along the working
length 16, a specific combination of guiding edges 218, 220, 222, 224, 226, 228, 230 and 232
dependent upon the angular orientation of the flutes 190, 192 and 194 is manifested in the
cross-sectional profile of the working length 16.
The cross-sectional profile of the endodontic instrument 188 exhibits a
dependence upon axial location along the working length 16 because of the different helix
angles of flutes 190, 192 and 194 and facets 196, 198, 200, 202, 204, 206, 208 and 210. At a
first axial location shown in Fig. 7A, the cross-sectional profile of the endodontic instrument
188 has an appearance similar to that of Fig. 3. Guiding edges 220 and 230 are observed in
the cross-sectional profile for this angular orientation of the flutes 190, 192 and 194. At a second location shown in Fig. 7B, the flutes 190, 192 and 194 have effectively rotated about
axis 17 through an angle, δ. Guiding edges 226 and 232 are observed in the cross-sectional
profile for this angular orientation of the flutes 190, 192 and 194. At any arbitrary axial
location along the working length 16, however, the cutting edges 212, 214 and 216 and the
specific guiding edges 218, 220, 222, 224, 226, 228, 230 and 232 present at each axial
location are subject to the requirement of being either on or inside the imaginary circle 43.
The various cross-sectional profiles of the endodontic instrument 188 may repeat along the
working length 16. With specific reference to Fig. 7 and in an alternative embodiment, the facets
196, 198, 200, 202, 204, 206, 208 and 210 of endodontic instrument 188 may optionally
extend up shaft 11 for a greater distance in a direction toward distal end 14 than flutes 190,
192 and 194. Over this distance, the cutting edges 212, 214 and 216 are absent and only
guiding edges 218, 220, 222, 224, 226, 228, 230 and 232 are present, as indicated by the dot-
dashed lines in Fig. 7. The extent over which the facets 196, 198, 200, 202, 204, 206, 208
and 210 extend up shaft 1 1 may be less than the distance illustrated in Fig. 7 or greater than
the distance illustrated in Fig. 7. In certain specific embodiments, the facets 196, 198, 200,
202, 204, 206, 208 and 210 of endodontic instrument 188 may extend the entire length of shaft 11.
With reference to Figs. 8A and 8B in which like reference numerals refer to
like features in Figs. 1-4 and 6 and in accordance with an alternative embodiment, an
endodontic instrument 238 includes a plurality of lengthwise-extending flutes 240, 242 and
244, similar to flutes 26, 28 and 30 (Figs. 1-3), and a plurality of facets 246, 248, 250, 252,
254, 256, 258 and 260, similar to facets 40, 42, 44, 46, 48, 50, 52 and 54 (Figs. 1-4). Each of
the flutes 240, 242 and 244 defines one of a corresponding plurality of cutting edges 262, 264
and 266, similar to cutting edges 20, 22 and 24 (Figs. 1-3). Extending along axis 17 is a
plurality of guiding edges 268, 270, 272, 274, 276, 278, 280 and 282, similar to guiding edges 32, 34, 56, 58, 60, 62, 64 and 66 (Fig. 4B), each defined at the intersection of coextensive
adjacent facets 246, 248, 250, 252, 254, 256, 258 and 260. Of the guiding edges, it is
appreciated that edges 268 and 278 are transformed by the flutes 240 and 244 into cutting
edges 262 and 266, respectively, and may be observed as features in cross-sectional profiles
taken at other axial locations along the working length 16. The invention contemplates that, in alternative embodiments, the endodontic instrument 238 may have a construction based
upon any of the cross-sectional profiles shown in Figs. 5A-5G.
Flutes 240, 242 and 244 and, hence, cutting edges 262, 264 and 266 have a
constant zero-degree helix angle and, hence, a constant pitch. Facets 246, 248, 250, 252, 254,
256, 258 and 260 and, hence, guiding edges 268, 270, 272, 274, 276, 278, 280 and 282 wind
about the working length 16 with a spiral or helical arrangement that varies in helix angle and
pitch axially along the working length 16 of endodontic instrument 188. The flutes 240, 242 and 244 extend linearly along the working length 16 and are continuously altered by the facets
246, 248, 250, 252, 254, 256, 258 and 260 winding about the working length 16. At any axial
location along the working length 16, a specific combination of guiding edges 268, 270, 272,
274, 276, 278, 280 and 282 dependent upon the angular orientation of the facets 246, 248,
250, 252, 254, 256, 258 and 260 is manifested in the cross-sectional profile of the working
length 16.
The cross-sectional profile of the endodontic instrument 238 exhibits a
dependence upon axial location along the working length 16 because of the different helix
angles of flutes 240, 242 and 244, and facets 246, 248, 250, 252, 254, 256, 258 and 260. At a
first axial location shown in Fig. 8 A, the cross-sectional profile of the endodontic instrument 238 has an appearance similar to that of Fig. 3. Guiding edges 272 and 282 are observed in
the cross-sectional profile for this angular orientation of the facets 246, 248, 250, 252, 254,
256, 258 and 260 as flutes 240, 242 and 244 have eliminated the other guiding edges. At a
second location shown in Fig. 8B, the facets 246, 248, 250, 252, 254, 256, 258 and 260 have
effectively rotated about axis 17 through an angle, e. Guiding edges 268, 274 and 278 are
observed in the cross-sectional profile for this angular orientation of the facets 246, 248, 250,
252, 254, 256, 258 and 260 as the other guiding edges are not present at this axial location.
At any arbitrary axial location along the working length 16, however, the cutting edges 262,
264 and 266 and the specific guiding edges 268, 270, 272, 274, 276, 278, 280 and 282 present
at each axial location are subject to the requirement of being either on or inside the imaginary
circle 43.
With reference to Figs. 9, 9A and 9B in which like reference numerals refer to
like features in Figs. 1-4 and 6 and in accordance with an alternative embodiment, an
endodontic instrument 288 includes a plurality of lengthwise-extending flutes 290, 292 and
294, similar to flutes 26, 28 and 30 (Figs. 1-3), and a plurality of facets 296, 298, 300, 302, 304, 306, 308 and 310, similar to facets 40, 42, 44, 46, 48, 50, 52 and 54 (Figs. 1-4). Each of
the flutes 290, 292 and 294 defines one of a corresponding plurality of cutting edges 312, 314
and 316, similar to cutting edges 20, 22 and 24 (Figs. 1-3). Extending along axis 17 is a
plurality of guiding edges 318, 320, 322, 324, 326, 328, 330 and 332, similar to guiding edges
32, 34, 56, 58, 60, 62, 64 and 66 (Fig. 4B), each defined at the intersection of coextensive
adjacent facets 296, 298, 300, 302, 304, 306, 308 and 310. The invention contemplates that,
in alternative embodiments, the endodontic instrument 288 may have a construction based
upon any of the cross-sectional profiles shown in Figs. 5A-5G.
The facets 296, 298, 300, 302, 304, 306, 308 and 310 and, hence, guiding
edges 318, 320, 322, 324, 326, 328, 330 and 332 are characterized by a first helix angle and pitch. As is best apparent in Fig. 9, the flutes 290, 292 and 294 and, hence, cutting edges 312,
314, and 316 wind about the working length 16 with a spiral or helical arrangement that
varies in helix angle and pitch axially along the working length 16 of endodontic instrument
288. The facets 296, 298, 300, 302, 304, 306, 308 and 310 are characterized by a second
helix angle and pitch that differs from the first helix angle and pitch of the facets 296, 298,
300, 302, 304, 306, 308 and 310. As is again best apparent in Fig. 9, the facets 296, 298, 300,
302, 304, 306, 308 and 310 wind about the working length 16 with a spiral or helical
arrangement that varies in helix angle and pitch axially along the working length 16 of
endodontic instrument 288. In particular, the helix angle of the facets 296, 298, 300, 302,
304, 306, 308 and 310 is positive over sections of working length 16 near each of the ends 12
and 14 and is negative near the center section of the working length 16. At any axial location
along the working length 16, a specific combination of guiding edges 318, 320, 322, 324, 326,
328, 330 and 332 dependent upon the relative angular orientations of the flutes 290, 292 and
294 and the facets 296, 298, 300, 302, 304, 306, 308 and 310 is manifested in the cross-
sectional profile of the working length 16.
The cross-sectional profile of the endodontic instrument 288 exhibits a dependence upon axial location along the working length 16 because of the variable helix
angle and pitch of flutes 290, 292 and 294 and of facets 296, 298, 300, 302, 304, 306, 308 and
310. At a first axial location shown in Fig. 9A, the cross-sectional profile of the endodontic
instrument 288 has an appearance similar to that of Fig. 3. Guiding edges 320 and 330 are
observed in the cross-sectional profile for this angular orientation of the flutes 290, 292 and
294. At a second location shown in Fig. 9B, the flutes 290, 292 and 294 have effectively
rotated about axis 17 through an angle, K, and facets 296, 298, 300, 302, 304, 306, 308 and
310 have rotated through an angle, λ. Guiding edges 326 and 332 are observed in the cross-
sectional profile for this angular orientation of the flutes 290, 292 and 294. At any arbitrary
axial location along the working length 16, however, the cutting edges 312, 314 and 316 and
the specific guiding edges 318, 320, 322, 324, 326, 328, 330 and 332 present at each axial
location are subject to the requirement of being either on or inside the imaginary circle 43.
The various cross-sectional profiles of the endodontic instrument 288 may repeat along the
working length 16. With reference to Figs. 10A and 10B in which like reference numerals refer to
like features in Figs. 1-4 and 6 and in accordance with an alternative embodiment, an
endodontic instrument 360 includes cutting edges 362, 364 and 366 defined by flutes 363,
365 and 367 and multiple guiding edges, of which guiding edges 368 and 370 are visible in
Fig. 10A at a first axial location along the working length 16 and guiding edges 368 and 372
are visible in Fig. 10B at a second axial location along the working length. Other guiding
edges (not shown) may be visible in the cross-sectional profile at different locations along the
working length 16 of endodontic instrument 360. Guiding edge 368 is defined at the
intersection of facets 374 and 376, guiding edge 370 is defined at the intersection of facets
378 and 380, and guidmg edge 372 is defined at the intersection of facets 382 and 384. The cutting edges 362, 364 and 366 are spaced about the circumference of the
working length 16 at unequal angular intervals, in which the specific angular intervals are
dependent upon the axial location at which the cross-sectional profile is taken along the
working length 16. At one representative location along the working length 16 shown in Fig.
10A, the cutting edges 362, 364 and 366 are separated by angular intervals of , β, and θ. At
a different representative location defined along the working length 16 as shown in Fig. 10B,
the cutting edges 362, 364 and 366 are separated by angular intervals of α', β', and θ' that
differ from , β, and θ. These angular intervals are understood to assume an arbitrary number
of values along the working length 16. The angular variation in the circumferential location
of the cutting edges 362, 364 and 366 results from non-parallel flutes 363, 365 and 367
formed in the working length 16. The invention contemplates that, in alternative
embodiments, the endodontic instrument 360 may have a construction based upon any of the
cross-sectional profiles shown in Figs. 5A-5G.
With reference to Fig. 11, an endodontic instrument 334 includes a working
length 336 that has multiple tapered sections 338, 340 and 342 and a zero taper section 344,
respectively, between ends 12 and 14. Tapered section 338 has a positive taper and is
contiguous with tapered section 340, tapered section 340 has a less positive taper and is
contiguous with tapered section 342, and tapered section 342 has a negative taper and is
contiguous with zero taper section 344, although the invention is not so limited. Tapered
section 338 incorporates a plurality of flutes arranged about the circumference of the working
length 336, of which only flute 346 is visible. By way of example and not by way of
limitation, tapered section 338 may be given a taper of about 0.1 mm/mm, tapered section 340
may have a taper of about 0.03 mm/mm, tapered section 342 may have a taper of -0.04 mm/mm. In various different embodiments, section 338 may have any of the geometric
arrangements previously described herein, and sections 340, 342 and 344 may include only
facets and curved surfaces in any combination based upon any of the geometric arrangements
previously described herein.
While the invention has been illustrated by a description of various
embodiments and while these embodiments have been described in considerable detail, it is
not the intention of the applicant to restrict or in any way limit the scope of the appended
claims to such detail. Additional advantages and modifications will readily appear to those
skilled in the art. For example, the instruments of the invention may be utilized for non-
dental applications such as preparing bone, which has a soft internal cancellous tissue
surrounded by an outer compact/cortical tissue, for implants, or in plastic surgery. The
invention in its broader aspects is therefore not limited to the specific details, representative
apparatus and methods, and illustrative examples shown and described. Accordingly,
departures may be made from such details without departing from the spirit or scope of the
applicant's general inventive concept.