ENDODONTIC INSTRUMENT HAVING A CHISEL TIP BACKGROUND

1. Field of the Invention

This invention relates generally to the field of endodontic instruments and more particularly to reamers or files used in performing root canal procedures. These instruments are used to remove diseased tissue from the canal prior to sealing and filling the canal cavity with a suitable filler material, such as gutta-percha.

2. Description of the Related Art

One of the more technically difficult and delicate procedures in the field of dentistry is root canal therapy. The root canal of a tooth houses the circulatory and neural systems of the tooth. These enter the tooth at the terminus of each of its roots and extend through a narrow, tapered canal system to a pulp chamber adjacent the crown portion of the tooth. If this pulp tissue becomes diseased or injured, it can cause severe pain and trauma to the tooth, sometimes necessitating extraction of the tooth. Root canal therapy involves removing the diseased tissue from the canal and sealing the canal system in its entirety. If successful, root canal therapy can effectively alleviate the pain and trauma associated with the tooth so that it need not be extracted. To perform a root canal procedure, the endodontist first drills into the tooth to locate the root canal and then uses instruments of small diameter such as reamers and files to remove the decayed, injured or dead tissue from the canal. These are typically elongated instruments which are rotated and/or reciprocated within the root canal. The primary goal is to remove all of the decayed or injured nerve while leaving the integrity of the root canal walls relatively unaffected. Preserving the integrity of the root canal is important in order to allow proper filling of the root canal void in a homogenous three dimensional manner such that leakage or communication between the root canal system and the surrounding and supporting tissues of the tooth is prevented. Once as much of the diseased material as practicable is removed from the root canal, the canal is then sealed closed, typically by reciprocating and/or rotating a condenser instrument in the canal to urge a sealing material such as gutta-percha into the canal.

Root canals are not necessarily straight and are often curved or convoluted. Therefore, it is often difficult to clean the canal while preserving its natural shape. Many instruments have a tendency to straighten out the canal or to proceed straight into the root canal wall, altering the natural shape of the canal and sometimes transporting completely through the canal wall. Also, the openings of many root canals are small, particularly in older patients, due to calcified deposits on the root canal inner walls. Thus the files or reamers must be able to withstand the torsional load necessary to penetrate and enlarge the canal opening without breaking the instrument. To preserve the natural shape of the root canal and to facilitate insertion of the tip of the instrument into small root canal openings, traditional reamers or files have an elongated working portion having a uniform taper such that the diameter of the working portion increases uniformly from a small diameter at the tip of the instrument to a larger diameter at the base of the working portion. The taper rate may vary from instrument to instrument and commonly ranges from about 0.02 mm/mm to about 0.08 mm/mm. Helical flutes defining cutting edges are typically provided along the tapered working portion to promote tissue removal and desired shaping of the root canal and

advancement of dental chips and debris up the expanding diameter of the instrument along the helical flutes and away from the tip of the instrument.

One problem with traditional endodontic instruments used for extirpating and filling a root canal is that the torsional limitations of the instrument are often exceeded, resulting in breakage of the instrument in the canal. Breakage of the instrument can occur as a result of inadequate removal of dental chips which are cut from the wall of the root canal. These dental chips often become engaged between the instrument and the root canal wall resulting in increased friction and excessive torque on the instrument. Inadequate chip removal may occur particularly at or near the tip of the instrument where the flutes are relatively shallow. Build up of debris between the flutes and the canal wall can cause damage to the canal walls and/or inadequate or uneven tissue removal and can also lead to failure of the instrument.

Another problem that can occur is transportation or penetration through the canal wall. This can occur when a straight file or reamer is used to prepare a curved canal. The file often will tend to maintain a straight path into the root canal wall instead of following the natural path of the canal. In some extreme cases, the file can actually perforate or penetrate the wall of the root canal causing injury to the supporting tissues of the tooth. One prior attempt to solve this problem was to provide a dental file or reamer having a smooth-walled, non-cutting pilot tip for guiding the file or reamer into the curved root canal. See, for instance, U.S. Patent 4,299,571 to McSpadden, incorporated herein by reference. While the provision of such a smooth-walled pilot tip represented a significant improvement in the art at the time, the design has several significant drawbacks in certain cases.

One drawback is that the pilot tip, being blunt and smooth, has little or no cutting ability. While the blunt tip can fairly easily wedge its way into the soft, fleshy nerve, there is often difficulty encountered in a calcified root canal which has layers of calcified accretion built up along the inner wall of the canal. It is often difficult in these highly calcified root canals to penetrate through the calcified material to a depth sufficient to allow cutting to begin. When using such files having a blunt tip, the file must essentially burnish or grind its way into the calcified material before entering the canal. This generates significant heat and friction as the tip attempts to burnish its way through the hard calcified material. This can cause pain and heating of the tooth which is undesirable. It can also cause increased torsional loads on the file or reamer which can increase the risk of breakage in the canal and decrease the life of the tool.

SUMMARY OF THE INVENTION The present invention is directed to an improved endodontic instrument design for use in an endodontic root canal procedure. The instrument generally comprises an elongated working portion having a length of from about 3 to about 18 millimeters, a peripheral diameter ranging from about 0.08 millimeters to about 1.9 millimeters, at least one helical flute, at least one helical land and at least one tissue-removing edge. Each flute and land has a pitch ranging from about 1 spiral per 16 millimeters to about 1 spiral per millimeter.

In accordance with one preferred embodiment, the above-described working portion has a chisel tip adjacent the distal end of the working portion. The chisel tip comprises plural facets which intersect along a substantially linear chisel edge that is substantially orthogonal to a longitudinal axis of the elongate working portion. The facets

integrate with the flutes to define additional tissue-removing edges at the tip of the instrument. When rotated in a root canal the chisel edge loosens decayed or diseased tissue and the tissue-removing edges at the tip of the instrument cuts the tissue and as the file progresses down the root canal. In another preferred embodiment, the chisel tip has asymmetric proportions such that the tip will tend to wobble or wonder as it progresses down the root canal.

In accordance with another preferred embodiment at least a portion of the working portion is tapered either in diameter, web thickness, or both, and terminates at a chisel tip. The rate of taper adjacent the tip is greater than the rate of taper in the remainder of the working portion so as to define a region of locally enhanced compliance adjacent the tip. The enhanced compliance adjacent the tip allows the instrument to more readily follow the central axis of a curved root canal with less tendency to transport through the canal wall. The region of locally enhanced compliance can also be achieved in a number of other ways such as by providing additional flutes, recesses and/or by annealing or treating the region chemically or thermally so as to produce enhanced compliance characteristics.

In accordance with another preferred embodiment the working portion is divided into at least two regions, including a first region extending from a first point adjacent the proximal end portion to a second point intermediate the proximal and distal end portions and a second region adjacent the first region and extending from the second point to a third point adjacent the distal end portion of the working portion. The working portion has a stiffness in the first region which decreases substantially continuously along a first curve progressively from the first point to the second point. The stiffness of the working portion in the second region decreases substantially continuously along a second curve, steeper than the first curve, progressively from the second point to the third point. These and other features and advantages will become readily apparent to those skilled in the art, having reference to the following detailed description and accompanying drawings, the invention not being limited, however, to any particular preferred embodiment disclosed or shown.

BRIEF DESCRIPTION OF THE DRAWINGS The figures shown and described below illustrate particular preferred embodiments of endodontic instruments having various working portion and tip configurations. The particular instruments shown are illustrated as reamers or files. However, it should be understood that these instruments can also be configured for use as condensers or compactors by reversing the direction of twist of the helical flutes and lands and/or reversing the direction of rotation of the instrument as will be readily apparent from the detailed description having reference to the appended figures, of which: FIGURE 1 is a representational partial schematic drawing of a typical calcified root canal;

FIGURE 2A is an elevational view of a reamer instrument including a chisel tip; FIGURE 2B is a detailed side elevational view of the distal end portion of the endodontic reamer of FIGURE 2A;

FIGURE 2C is a detail end view of the chisel tip of the reamer of FIGURE 2A; FIGURE 20 is a transverse cross-section view of the reamer of FIGURE 2A through a point adjacent the chisel tip;

FIGURE 2E is a detail side elevational view of the working portion of the reamer instrument shown in FIGURE 2A;

FIGURE 3 is a schematic free body diagram illustrating the effects of asymmetric forces exerted on the chisel tip of an endodontic instrument having features as disclosed herein; FIGURE 4A is an SEM photograph (magnification 25x) of the distal end portion of an endodontic reamer including a chisel tip having features as disclosed herein;

FIGURE 4B is an SEM photograph (magnification 250x) of the distal end portion of an endodontic reamer including a chisel tip having features as disclosed herein;

FIGURE 5A is an elevational view of another embodiment an endodontic reamer instrument having an accelerated web taper;

FIGURE 5B is a detail side elevational view of the distal end portion of the endodontic reamer of FIGURE 5A illustrating the accelerated web taper adjacent the tip of the instrument;

FIGURE 5C is a detail end view of the tip of the endodontic reamer instrument of FIGURE 5A; FIGURE 5D is a transverse cross-section view of the reamer instrument of FIGURE 5A through a point adjacent the tip;

FIGURE 5E is a detail side elevational view of the working portion of the reamer instrument of FIGURE 5A; FIGURE 6A is a graph of bending stiffness along the working portion of a conventional reamer instrument (shown as a solid line) as compared to the bending stiffness of a reamer instrument having features of the present invention (shown as a dashed line); FIGURE 6B is a representational schematic drawing illustrating the bending response characteristics of a conventional reamer instrument (shown in solid lines) as compared to a reamer instrument having features of the present invention (shown in dashed) when subjected to a bending force F applied at the tip;

FIGURE 7A is an SEM photograph (magnification 250x) of the distal end portion of an endodontic reamer having features as disclosed herein; and FIGURE 7B is an SEM photograph (magnification 250x) of the tip of an endodontic reamer having features as disclosed herein.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

As noted above, a significant drawback of conventional endodontic files or reamers is that the tip is typically blunt or smooth and, therefore, has little or no cutting ability. While a blunt tip can easily wedge its way into the soft, fleshy nerve, there is often difficulty encountered in root canals, particularly in older patients, which have become built up with layers of calcified accretion along the inner wall of the canal. This is illustrated in

FIGURE 1. The opening of the root canal 12 would normally be of diameter "D." But as shown in FIGURE 1 the opening of a calcified root canal may be reduced to a much smaller diameter "d." Again, this is due to the build up of layers of calcified accretion 14 within the root canal 12 of the root structure 10. For these small root canal openings it is difficult to enter the canal with a conventional file having a blunt or rounded tip because the tip of the instrument has little or no cutting or abrading ability. Rather, the instrument

must grind or burnish its way into the canal before any cutting action takes place. Even then, the cutting action only occurs at the periphery of the instrument and not at the tip of the instrument which continues to grind or burnish its way down the canal. This increases the wear and tear on the instrument, increases the risk of breakage and, in addition, can cause heating in the canal and resulting damage to surrounding tissues. Also, the root canal procedure takes longer to complete, resulting in increased cost and discomfort to the patient.

One possible solution would be to make the tip of the instrument smaller than the reduced diameter "d" of the calcified canal 12. But there is a practical limit to how small the tip can be made on a conventional uniformly tapered endodontic file without compromising the integrity of the instrument. Conventional tapered files have tip diameters that are as small as .06 mm corresponding to a size "06" file. But even these small instruments have difficulty penetrating into root canal openings having significant calcium build up. Moreover, making such conventional instruments any smaller could lead to failure of the instrument in the canal.

The present invention solves these and other problems by providing, in one embodiment, a tip having improved cutting ability. It was heretofore widely believed that the use of a cutting tip would lead to an increased likelihood of canal wall transportation. To the contrary, the present invention, in one embodiment, involves the discovery that providing at least some cutting ability on the tip can increase the overall cutting efficiency and clinical efficacy of the instrument without significantly increasing the likelihood of canal wall transportation. As will be explained in more detail below, the particular file configurations and tip geometries disclosed and described herein reduce the cutting friction between the instrument and the tooth canal, improve cutting efficiency and performance of the instrument, while reducing the tendency of the instrument to fail under torsional stress. FIGURES 2A-E illustrate one preferred embodiment of an endodontic file or reamer 100. In particular, the file 100 is provided with a chisel tip 150, as shown in FIGURES 2B and 2C. The chisel tip 150 provides cutting ability at the tip of the instrument 100, which dramatically improves the ability of the instrument to penetrate the small opening of a calcified root canal.

The file 100 generally comprises a shaft 102 having a shank portion 104 and an elongated working portion 106. The working portion 106 extends from a proximal end 107 adjacent the base of the shank 104 to a distal end 108 terminating in a chisel tip 150. The shank portion 104 may include an optional fitting portion 109 for mating with the chuck of a dental handpiece (not shown). Alternatively, or in addition to the fitting portion 109, the shank portion 104 may include a knurled or otherwise treated surface (not shown) or handle to facilitate hand manipulation of the file 100. Those skilled in the art will appreciate that each of the endodontic instruments shown and described herein may be used by manipulating the instrument manually in a rotating or reciprocating action, or the instruments may be manipulated by attaching the shank portion of the instrument to a motorized handpiece for effecting more rapid removal of tissue from the root canal, as desired.

In the particular preferred embodiment shown, the endodontic file 100 includes two helical flutes 124 and 126 formed in the working portion 106 extending from the distal end 108 adjacent the tip 150 and exiting at the proximal end 107 (sometimes called the "flute exit" or "exit"), as shown in FIGURES 2A and 2D. Those skilled in

the art will readily appreciate that a similar instrument could also be configured with one flute or with three or more flutes, as desired.

Helical lands 116 and 118 are provided generally extending between adjacent flutes 124 and 126. The helical flutes 124, 126 and helical lands 116, 118 intersect one another to define leading edges 128, 132 and trailing edges 130, 134 with respect to clockwise rotation of the instrument. The leading edges 124, 126 are preferably sharp so as to remove tissue from the root canal as the instrument is rotated or reciprocated. Accordingly, these may sometimes be referred to herein as "tissue-removing" edges. The trailing edges 130, 134 may be sharp or not, depending upon the particular file geometries and manufacturing convenience.

The rake angles of the tissue-removing edges 128, 132 may be positive, negative, or neutral, as desired. Satisfactory results have been obtained with rake angles ranging from about -12 degrees to about -36 degrees measured with respect to a radial line passing through the tissue-removing edge perpendicular to a line tangent to the periphery of the working portion. The rake angles of the tissue-removing edges 128, 132 may be equal to one another or they may be different such that, for example, one may be substantially positive and another may be substantially neutral or negative. The rake angle of one or more tissue-removing edges may also vary along the length of the working portion 106, as desired, or as may be convenient for purposes of manufacturing the instruments.

Helical flutes 124, 126 may be equally sized and spaced about the periphery of the working portion 106 or, more preferably, they may be unequally sized and/or spaced about the periphery such that the curvilinear distance between tissue-removing edge 128 and tissue-removing edge 132 is different in the clockwise direction than in the counter-clockwise direction. The tissue-removing edges 128, 132 are preferably unequally spaced about the periphery of the working portion 106 by an offset angle or "clocking" angle a as shown in FIGURE 2D. Unequal spacing of flutes and/or tissue-removing edges provides asymmetries in the file 100 which, according to clinical studies, significantly improve the ability of the file 100 to remove tissue evenly from the walls of a curved root canal and to more readily maintain the central axis of the canal. The precise mechanism for the clinical improvements realized is not entirely understood at this time. But, it is believed that asymmetries in the instrument cause it, when rotated, to wander or wobble away from its rotational center, thereby more effectively contacting and cleaning out all portions of the root canal wall. Also, it is believed that due to the resulting imbalance of forces created, an asymmetric instrument will tend to cut equally aggressively on all portions of a surrounding tissue in a curved root canal than a conventional symmetric file, countering the natural tendency of a file to cut more aggressively on the inner wall at the pressure point of a file bent to conform to the shape of a curved root canal.

As shown in FIGURES 2D and 2E the helical lands 117, 118 are preferably formed so as to define outer peripheral land portions 116, 120 having width w, (sometimes referred to herein as "margin width") and recessed land portions 112, 114 having width w ₂ (sometimes referred to herein as "relief width"), respectively. The combined width w„ w ₂ is sometimes referred to herein as "land width." The recessed land portions 112, 1 14 are at a first predetermined radial distance R, from the cross-sectional center of the working portion 106. The outer land portions

116, 120 lie at the outer periphery of the working portion 106 at a second predetermined radial distance R ₂ from the center of the working portion 106, which is preferably about 4 to 30 percent greater than the radial distance R,. The disclosed combination of outer and recessed land portions reduces frictional forces exerted on the instrument 100 as it is rotated within the root canal, thereby reducing overall torsional loads on the instrument. The working portion 106 of the instrument 100 has a length ranging from about 3 mm to about 18 mm.

A preferred length is about 16 mm. The working portion 106 may have a constant cross-sectional diameter or, more preferably, it is tapered from the proximal end 107 to the distal end 108, as shown. In the particular preferred embodiment shown, the taper is uniform ^•• that is, the rate of taper is constant along the working portion 106. This taper may range from about 0.01 mm/mm to about 0.08 mm/mm and, more preferably, from about 0.02 mm/mm to about 0.06 mm/mm. The web thickness "t _w " - that is the thickness of the "web" of material between opposed flutes 124, 126 -- is also preferably tapered from the proximal end 107 of the working portion to the distal end 108. The web taper may be the same as or different from the diameter taper of the instrument. In the preferred embodiment shown the web taper may be about -.01 mm/mm to about 0.08 mm/mm and, more preferably, is about 0.03 mm/mm. As used herein, the term "taper" or "taper rate" may refer to either the web taper rate or the diameter taper rate.

As noted above, an important feature of the instrument 100 shown in FIGURES 2A-E is the chisel tip 150, shown in more detail in FIGURES 2B and 2C. The chisel tip 150 generally comprises two or more facets 151, 153 which intersect to define a chisel edge 154. The chisel edge 154 is preferably substantially linear and substantially orthogonal to a longitudinal axis of the working portion 106, although such configuration is not necessary. Additional sharp tissue-removing edges 155, 157 are formed at the tip 150 by the intersection of the facets 151, 153 with the flutes 124, 126. Upon rotation of the instrument in a root canal the chisel edge 154 loosens diseased or decayed tissue while the tissue-removing edges 155, 157 cut away and remove the tissue as the file is inserted into the canal.

The chisel tip 150 may be formed by grinding flats or facets 151, 153 into the tip of the instrument 100, as shown, forming the chisel edge 154. The facets 151, 153 define an included point angle β of between about 45 degrees and 100 degrees, and more preferably about 60 degrees or 90 degrees, as shown in FIGURE 2B. The chisel edge 154 is preferably canted from center by a primary angle y of between about 5 and 25 degrees, and, more preferably, about 15 degrees, as shown in FIGURE 2C. While a two-facet chisel tip 150 is shown and described, those skilled in the art will readily appreciate that any one of a number of multifaceted chisel tip designs may be used while enjoying the benefits and advantages of the invention as disclosed herein. For example, a four- faceted chisel tip may provide a suitable compromise for many endodontic applications.

An inherent feature of the structure shown and described above is that the facets 151 , 153 of the chisel tip 150 will have apices defined by the tissue-removing edges 128, 132 and additional tissue-removing edges 155, 157 which are unequally spaced about the center of rotation of the instrument. This asymmetrical structure, in addition to providing the benefits of more even canal cutting, as described above, also creates desirable asymmetries in the chisel tip 150 of the file, giving the tip 150 a tendency to "wander" or "wobble" as the instrument is rotated

in the root canal. This is particularly advantageous for extirpating a curved or convoluted root canal because the tip 150 will tend to probe around and follow the path of least resistance down the root canal, rather than make a straight path possibly through the canal wall. This feature is explained in more detail below.

FIGURE 4 is a schematic free body diagram illustrating the effects of asymmetric forces exerted on the chisel tip 150. In operation, the tip is subjected to a rotational driving force represented as the moment "M". This moment produces certain reaction forces at the tip of the instrument represented by forces F, and F ₂ . Those skilled in the art will appreciate that the forces F, and F ₂ are schematic representations of the actual forces exerted on the tip of the file which are distributed throughout the facets and edges comprising the tip 150. The simplified schematic representation of these forces is useful to illustrate the wandering dynamics of the chisel tip portion 150. Assuming mean equilibrium conditions at the tip, the moment created by forces F, and F ₂ acting about the rotational centerline of the file will counterbalance the moment "M" such that the two moments cancel out and the rotational speed of the tip is constant. On the other hand, due to the aforementioned asymmetries in the tip geometry, the forces F, and F ₂ , although equal in mean absolute magnitude, will not cancel out. This is because the force F, has a negative Y component that is equal to the magnitude of the force F„ while the force F ₂ has both positive X and Y components that are equal to the magnitude of the force F ₂ multiplied by the sine and cosine of the clocking angle a, respectively. Thus, assuming the magnitudes of the forces F, and F ₂ are equal, the net resultant force R on the tip will have an X component equal to F ₂ -(sine a) and a Y component equal to -F ₂ -(1 - cos σ). Of course, the magnitude and direction of the resultant force R will change with the rotation of the instrument in the root canal, thus producing the above-described wandering effect. Desirable tip asymmetries can also be achieved in other ways, as will be readily appreciated by those skilled in the art, such as by making the rake angles of the removing edges 128, 132 different from one another and/or by dulling one of the tissue-removing edges adjacent the tip 150. The wandering chisel tip 150 combined with the ability to cut or abrade calcified material more efficiently produces an endodontic file that is faster and more efficient at cutting, while still minimizing the risk of canal transportation. FIGURES 4A and 4B are SEM photographs which illustrate in more detail one particular preferred embodiment of an endodontic file having a chisel tip as shown and described above. FIGURE 4A is an SEM photograph of the distal end portion of an endodontic file having a chisel tip viewed at a magnification of 25x. FIGURE 4B is an SEM photograph of the distal end portion of an endodontic file having a chisel tip viewed at a magnification of 250x. FIGURES 5A-E illustrate another preferred embodiment of an endodontic file or reamer 200. This instrument is generally similar to that shown and described above in connection with FIGURES 2A-E, except that the distal end of the instrument adjacent the tip 250 has been modified to provide a region of enhanced compliance as will be described in more detail below. For convenience like reference numerals have been used to designate like structures and/or features. The file 200 generally comprises a shaft 202 having a shank portion 204 and an elongated working portion

206. The working portion 206 has an overall length of about 3-18 mm, and, more preferably about 16 mm, and

extends from a proximal end 207 adjacent the base of the shank 204 to a distal end 208 terminating in a chisel tip 250. The shank portion 204 may include an optional fitting portion 209 for mating with the chuck of a dental handpiece (not shown). Alternatively, or in addition to the fitting portion 209, the shank portion 204 may include a knurled or otherwise treated surface (not shown) or handle to facilitate hand manipulation of the file 200. In the particular preferred embodiment shown, the endodontic file 200 includes two helical flutes 224 and

226 and helical lands 216 and 218, as shown in FIGURE 5D. The helical flutes 224, 226 and helical lands 216, 218 intersect one another to define leading edges 228, 232 and trailing edges 230, 234 with respect to clockwise rotation of the instrument. The leading edges 224, 226 are sharp so as to remove tissue from the root canal as the instrument is rotated or reciprocated. The trailing edges 230, 234 may be sharp or not, depending upon the particular design and manufacturing convenience.

The rake angles of the tissue-removing edges 228, 232 may be positive, negative, or neutral, as desired. Satisfactory results have been obtained with rake angles ranging from about -12 degrees to about -36 degrees measured with respect to a radial line passing through the tissue-removing edge perpendicular to a line tangent to the periphery of the working portion. The rake angles of the tissue-removing edges 228, 232 may be equal to one another or they may be different such that, for example, one may be substantially positive and another may be substantially neutral or negative. The rake angle of one or more tissue-removing edges may also vary along the length of the working portion 206, as desired, or as may be convenient for purposes of manufacturing the instruments.

Helical flutes 224, 226 may be equally sized and spaced about the periphery of the working portion 206 or, more preferably, they may be unequally sized and/or spaced about the periphery such that the curvilinear distance between tissue-removing edge 228 and tissue-removing edge 232 is different in the clockwise direction than in the counter-clockwise direction. The tissue-removing edges 228, 232 are preferably unequally spaced about the periphery of the working portion 206 by an offset angle or "clocking" angle a as shown in FIGURE 5C. As noted above, unequal spacing of flutes and/or tissue-removing edges provides asymmetries in the file 200 which improve the ability of the file 200 to remove tissue evenly from the walls of a curved root canal and to more readily maintain the central axis of the canal.

The helical lands 217, 218 are preferably formed so as to define outer peripheral land portions 216, 220 having width w, and recessed land portions 212, 214 having width w ₂ , respectively, as shown in FIGURES 5D and 5E. The recessed land portions 212, 214 are at a first predetermined radial distance R, from the cross-sectional center of the working portion 206. The outer land portions 216, 220 lie at the outer periphery of the working portion 206 at a second predetermined radial distance R ₂ from the center of the working portion 206, which is preferably about 4 to 30 percent greater than the radial distance R _v The disclosed combination of outer and recessed land portions reduces frictional forces exerted on the instrument 200 as it is rotated within the root canal, reducing overall torsional loads on the instrument. The instrument 200 preferably has a chisel tip 250, as shown in more detail in FIGURES 5B and 5C. The chisel tip 250 generally comprises two or more facets 251, 253 which intersect to define a chisel edge 254. The

chisel edge 254 is preferably substantially linear and substantially orthogonal to a longitudinal axis of the elongated working portion 206, although such configuration is not necessary. Additional sharp tissue-removing edges 255, 257 are defined at the tip by the intersection of each facet with the flutes 224, 226. Upon rotation of the instrument in a root canal the chisel edge 254 loosens the diseased or decayed tissue while the tissue-removing edges 255, 257 cut away and remove the tissue as the file is inserted into the canal.

The chisel tip 250 may be formed by grinding flats or facets 251, 253 into the tip of the instrument 200, as shown, forming the chisel edge 254. The facets 251, 253 define an included point angle β of between about 45 degrees and 100 degrees, and more preferably about 60 degrees, as shown in FIGURE 5B. The chisel edge 254 is preferably canted from center by a primary angle y of between about 5 and 25 degrees, and, more preferably, about 15 degrees, as shown in FIGURE 5C. Again, while a two-facet chisel tip 250 is shown and described, those skilled in the art will readily appreciate that any one of a number of multifaceted chisel tip designs may be used while enjoying the benefits and advantages as disclosed herein.

The working portion 206 is preferably tapered from the proximal end 207 to the distal end 208, as shown. In the particular preferred embodiment shown the rate of taper is nonuniform - that is, the rate of taper (either the web taper, diameter taper or both) changes along the length of the working portion 206. In the particular embodiment shown in FIGURES 5A-E the web taper rate from a point approximately 0.02 inches (0.5 mm) from the tip 250 accelerates or increases towards the tip 250, thereby forming a region of enhanced compliance 264 adjacent the tip 250. Advantageously, this enhanced compliance region 264 enables the instrument to extirpate and enlarge a root canal more quickly and efficiently and with less tendency to transport through the canal wall than a conventional instrument of uniform taper.

In part, the performance improvements can be attributed to the enhanced compliance in the region 264 adjacent the tip 250, which improves the ability of the file to follow a curved root canal while simultaneously decreasing the tendency of the file to define its own path possibly through the canal wall. FIGURES 6A and 6B illustrate desired compliance characteristics of a file having the above-described features. FIGURE 6A is a graph of stiffness (resistance to bending) along the working portion of a conventional file of uniform taper (shown as a solid line) as compared to the stiffness of a file constructed in accordance with the present invention and having an accelerating taper defining an enhanced compliance region adjacent the tip. The conventional tapered file will have a stiffness which decreases substantially smoothly and continuously from the proximal end of the working portion to the distal end along a single curve 270 traversing both regions A and B. In contrast, a file constructed in accordance with the present invention and having an accelerated rate of taper in the region B, as described above, will have a stiffness which decreases along a first curve 272 in the region A and then decreases along a second curve 274, which is steeper than the first curve 272, in the region B.

FIGURE 6B is a representational schematic drawing illustrating the bending response characteristics of a conventional file of uniform taper (shown in solid lines) as compared to a file having an accelerated taper as described above (shown in dashed lines), subjected to a bending force F. Note that when each of the instruments is subjected to a bending force F applied at the tip of the instrument, the instrument having an accelerated taper

in the region B (shown in dashed lines) will have a tip deflection d ₂ which is greater than the tip deflection d, achieved by a conventional tapered instrument. Thus, a file constructed in accordance with the present invention will have enhanced compliance in the region 264 adjacent the tip of the instrument, resulting in the aforenoted performance improvements. Moreover, those skilled in the art will appreciate that the compliance of such a file having an enhanced compliance region 264 in accordance with the present invention is greater than can be achieved with a conventional uniformly tapered file. To achieve the same degree of compliance adjacent the tip of a conventional tapered instrument would render the instrument unusable because it would become too compliant in the other regions of the working portion which need to be more stiff in order to withstand the torsional loads exerted on the file. The present invention, therefore, provides a unique solution by providing desired compliance characteristics adjacent the tip of an endodontic instrument without affecting desired compliance characteristics throughout the remaining portions of the instrument.

The accelerated web taper in the region 264 as shown and described above also produces a thinner web thickness two at the tip 250 and, accordingly, a shorter chisel edge 254, as illustrated in FIGURE 5C (compare, eg. FIGURE 2C). Advantageously, this structure results in more cutting taking place at the sharp tissue-removing edges 255, 257, rather than at the more negatively raked chisel edge 254. The tissue-removing edges 255, 257 are sharper and more efficient at cutting than the chisel edge 254. Another advantage of such structure is that the depth of the flutes 224, 226 in the region 264 are deeper, allowing more efficient removal of tissue and less friction in this region. It should be noted that the invention as disclosed and described herein is not limited to files having an accelerated web taper. Similar enhanced compliance regions can be achieved by other means such as by providing an accelerated diameter taper in the region 264 and/or by annealing or other heat and/or chemical treating of the region 264 to produce desired localized compliance characteristics. For example, rather than accelerating the rate of web taper in the region 264 one could instead (or in addition) accelerate the rate of the diameter taper in the region 264 to achieve desired localized compliance characteristics adjacent the tip of the instrument. Providing an endodontic file with an accelerated diameter taper could also have additional advantages, such as reducing the tip diameter of the instrument so as to allow it to more easily enter and enlarge small root canal openings. Alternatively, a combination of these techniques would be used.

It should also be noted that while the preferred embodiments shown and described in connection with FIGURES 5A-E illustrate the particular desirability of providing an accelerated taper in the region 264 adjacent the tip of the instrument, a wide variety of other configurations are also possible. The accelerating taper can be either a localized effect or it can extend the entire length of the working portion of the instrument, if desired. Moreover, the change in taper rate can be either graduated or substantially instantaneous, as desired. These and other embodiments of the present invention will be readily apparent to those persons skilled in the art. FIGURES 7A and 7B are SEM photographs which illustrate in more detail one particular preferred embodiment of an endodontic file having an accelerated web taper in a region adjacent the tip as shown and

described above. FIGURE 7A is an SEM photograph of the distal end portion of such an endodontic file viewed at a magnification of 25x. FIGURE 7B is an SEM photograph of the distal end portion of such an endodontic file viewed at a magnification of 250x.

The endodontic instruments in accordance with the preferred embodiments described above are preferably made from a strong, highly elastic material such as nickel-titanium, Nitinol™ or other suitable alloy. They can also be made from surgical stainless steel, if desired. A particularly preferred material is titanium 13-13 or a nickel- titanium alloy comprising about 56% nickel and about 44% titanium, such as SE508 nickel-titanium wire available from Nitinol Devices and Components, Inc. of Fremont, California.

Those skilled in the art will recognize that any one of a variety of well known techniques for making conventional instruments may generally be applied to the manufacture of instruments as disclosed herein with various known or later developed improvements in materials or processing. For example, the instruments may be ground from a straight or tapered rod, twisted, and/or drawn to a taper with or without grinding. Suitable grinding techniques which may be used are described in standard metallurgical texts for grinding various metals.

The following examples provide preferred specifications, dimensions and fabrication techniques for producing various preferred embodiments of endodontic files having features and advantages as disclosed herein. All dimensions are in millimeters unless otherwise noted.

EXAMPLE 1:

The following instrument was formed from a tapered blank of SE508 nickel-titanium wire having a substantially uniformly tapered outer diameter and a substantially uniform web taper. This particular instrument has two helical flutes (denoted flute "A" and flute "B") of unequal size and spaced unevenly around the periphery of the instrument. The flutes were formed by grinding the blank with a 320 grit CBN grinding wheel at a grinding speed of about 9,000 SFPM (2,750 m/min.) and an axial feed rate of about 2 inches/min. (5 cm/min.).

NOMINAL PLUS MINUS

DIAMETER AT TIP 0.25 0.01 0.01 DIAMETER TAPER RATE 0.050 SHANK DIAMETER 1.05 0.008 0.008

FLUTE LENGTH 16.0 0.25 0.25 RELIEF LENGTH 16.0 0.25 0.25 HELIX ANGLE (Ψ) @ TIP 30° 1° 1° HELIX ANGLE (Ψ) @ EXIT 45° 1° 1° WEB THICKNESS (3 TIP 0.074 0.015 0.015

LAND WIDTH § TIP 0.13 0.01 0.01 LAND WIDTH @ EXIT 0.70 0.01 0.01 RELIEF DIAMETER @ TIP 0.20 0.02 0.02 MARGIN WIDTH @ TIP 0.05 0.01 0.01 MARGIN WIDTH <ά> EXIT 0.33 0.01 0.01

WEB TAPER RATE @ TIP 0.0300 0.0040 0.0040 WEB TAPER RATE @ EXIT 0.0300 0.0040 0.0040 POINT ANGLE [β] 90° 2° 2° PRIMARY ANGLE [y) 15° 1° 1° CLOCKING ANGLE (σ) 175° 1° 1°

OVERALL LENGTH 30.5 0.025 0.025

REFERENCE DIMENSIONS ONLY RAKE ANGLE FLUTE A @ TIP 14°

RAKE ANGLE FLUTE B @ TIP -10° RAKE ANGLE FLUTE A @ EXIT -34°

RAKE ANGLE FLUTE B § EXIT -35°

EXAMPLE 2:

The following instrument was formed from a tapered blank of SE508 nickel-titanium wire having a substantially uniformly tapered outer diameter and a non-uniformly tapered web. This particular instrument has two helical flutes of approximately equal size and shape and which are unequally spaced around the periphery of the instrument. The flutes were formed by grinding the blank with a 600 grit diamond grinding wheel at a grinding speed of 6,31 1 SFPM (1,924 m/min.) and an axial feed rate of 1.95 inches/min. (4.95 cm/min.).

NOMINAL PLUS MINUS

DIAMETER AT TIP 0.40 0.008 0.008

DIAMETER TAPER RATE 0.020 0.001 0.001

SHANK DIAMETER 0.72 0.008 0.008

FLUTE LENGTH 16.0 0.3 0.3

RELIEF LENGTH 16.0 0.3 0.3

HELIX ANGLE (Ψ) @ TIP 30° 1 ° 1°

HELIX ANGLE (Ψ) @ EXIT 45° 1 ° 1°

NUMBER OF FLUTES IN .630 13

WEB THICKNESS (3 TIP 0.07 0.03 0.03

RELIEF DIAMETER @ TIP 0.31 0.03 0.03

LAND WIDTH 1 @ TIP 0.206 0.02 0.02

LAND WIDTH 2 @ TIP 0.25 0.02 0.02

LAND WIDTH 1 @ EXIT 0.38 0.02 0.02

LAND WIDTH 2 @ EXIT 0.45 0.02 0.02

MARGIN WIDTH 1 @ TIP 0.09 0.02 0.02

MARGIN WIDTH 2 @ TIP 0.079 0.02 0.02

MARGIN WIDTH 1 @ EXIT 0.2 0.02 0.02

MARGIN WIDTH 2 @ EXIT 0.19 0.02 0.02

WEB THICKNESS @ .02 FROM TIP 0.13 0.003 0.002

WEB TAPER RATE (TIP TO .02) 0.110 0.002 0.002

WEB TAPER RATE (.02 TO EXIT) 0.020 0.002 0.002

POINT ANGLE (β) 60° 2° 2°

PRIMARY ANGLE (y) 15° 2° 2°

CLOCKING ANGLE (σ) 170° 2° 2°

OVERALL LENGTH 38.1 0.08 0.08

REFERENCE DIMENSIONS ONLY

RAKE ANGLE @ TIP -12° 2° 2°

RAKE ANGLE @ EXIT > -15°

EXAMPLE 3:

The following instrument was formed from a tapered blank of SE508 nickel-titanium wire having a substantially uniformly tapered outer diameter and a non-uniformly tapered web. This particular instrument has two helical flutes of approximately equal size and shape and which are unequally spaced around the periphery of the instrument. The flutes were formed by grinding the blank with a 320/400 grit CBN grinding wheel at a grinding speed of 9,579 SFPM (2,920 m/min.) and an axial feed rate of 1.70 inches/min. (4.3 cm/min.)

NOMINAL PLUS MINUS

DIAMETER AT TIP 0.45 0.0076 0.0076

DIAMETER TAPER RATE 0.020 0.001 0.001

SHANK DIAMETER 0.76 0.0076 0.0076

FLUTE LENGTH 16.0 0.25 0.25

RELIEF LENGTH 16.0 0.25 0.25

HELIX ANGLE (Ψ) @ TIP 30° 1° 1°

HELIX ANGLE (Ψ) § EXIT 45° 1° 1°

NUMBER OF FLUTES IN .630 12

WEB THICKNESS § TIP 0.084 0.025 0.025

RELIEF DIAMETER @ TIP 0.36 0.025 0.025

LAND WIDTH 1 @ TIP 0.26 0.020 0.020

LAND WIDTH 2 @ TIP 0.25 0.020 0.0020

LAND WIDTH 1 |8 EXIT 0.45 0.020 0.020

LAND WIDTH 2 @ EXIT 0.50 0.020 0.020

MARGIN WIDTH 1 @ TIP 0.14 0.020 0.020

MARGIN WIDTH 2 @ TIP 0.14 0.020 0.020

MARGIN WIDTH 1 @ EXIT 0.26 0.020 0.020

MARGIN WIDTH 2 @ EXIT 0.26 0.020 0.020

WEB THICKNESS § .02 FROM TIP 0.14 0.025 0.025

WEB TAPER RATE (TIP TO .02) 0.121 0.002 0.002

WEB TAPER RATE (.02 TO EXIT) 0.020 0.002 0.002

POINT ANGLE \β) 60° 2° 2°

PRIMARY ANGLE (y) 15° 2° 2°

CLOCKING ANGLE (a) 170° 2° 2°

OVERALL LENGTH 38.1 0.076 0.076

REFERENCE DIMENSIONS ONLY

RAKE ANGLE @ TIP ^■ 12° 2° 2°

RAKE ANGLE § EXIT >v15°

EXAMPLE 4:

The following instrument was formed from a tapered blank of SE508 nickel-titanium wire having a substantially uniformly tapered outer diameter and a non-uniformly tapered web. This particular instrument has two helical flutes of approximately equal size and shape and which are unequally spaced around the periphery of the instrument. The flutes were formed by grinding the blank with a 600 grit diamond grinding wheel at a grinding speed of about 9,000 SFPM (2750 m/min.) and an axial feed rate of 1.70 iπches/min. (4.3 cm/min.)

NOMINAL PLUS MINUS

DIAMETER AT TIP 0.25 0.0076 0.0076

DIAMETER TAPER RATE 0.030 0.001 0.001

SHANK DIAMETER 0.72 0.0076 0.0076

FLUTE LENGTH 16.0 0.25 0.25

RELIEF LENGTH 16.0 0.25 0.25

HELIX ANGLE (Ψ) @ TIP 30° 1° 1°

HELIX ANGLE (Ψ) @ EXIT 45° 1° 1°

NUMBER OF FLUTES IN .630 16

WEB THICKNESS @ TIP 0.046 0.025 0.025

RELIEF DIAMETER @ TIP 0.18 0.025 0.025

LAND WIDTH 1 @ TIP 0.15 0.020 0.020

LAND WIDTH 2 @ TIP 0.16 0.020 0.020

LAND WIDTH 1 @ EXIT 0.38 0.020 0.020

LAND WIDTH 2 § EXIT 0.42 0.020 0.020

MARGIN WIDTH 1 @ TIP 0.48 0.020 0.020

MARGIN WIDTH 2 @ TIP 0.064 0.020 0.020

MARGIN WIDTH 1 @ EXIT 0.18 0.020 0.020

MARGIN WIDTH 2 @ EXIT 0.17 0.020 0.020

WEB THICKNESS @ FROM TIP 0.13 0.025 0.025

WEB TAPER RATE (TIP TO .02) 0.16 0.002 0.002

WEB TAPER RATE (.02 TO EXIT) 0.03 0.002 0.002

POINT ANGLE (/?) 60° 2° 2°

PRIMARY ANGLE (y) 15° 2° 2°

CLOCKING ANGLE (σ) 170° 2° 2°

OVERALL LENGTH 38.1 0.076 0.076

REFERENCE DIMENSIONS ONLY RAKE ANGLE @ TIP -16° 2° 2°

RAKE ANGLE @ EXIT >-15°

EXAMPLE 5:

The following instrument was formed from a tapered blank of SE508 nickel-titanium wire having a substantially uniformly tapered outer diameter and a -non-uniformly tapered web. This particular instrument has two helical flutes of approximately equal size and shape and which are unequally spaced around the periphery of the instrument. The flutes were formed by grinding the blank with a 600 grit diamond grinding wheel at a grinding speed of 9,078 SFPM (2,767 m/min.) and an axial feed rate of 2.17 inches/mm. (5.5 cm/mm.).

NOMINAL PLUS MINUS

DIAMETER AT TIP 0.25 0.0076 0.0076

DIAMETER TAPER RATE 0.040 0.001 0.001 SHANK DIAMETER 0.89 0.0076 0.0076

FLUTE LENGTH 16.0 0.25 0.25

RELIEF LENGTH 16.0 0.25 0.25

HELIX ANGLE (Ψ) @ TIP 30° 1° 1°

HELIX ANGLE (Ψ) @ EXIT 45° 1° 1° NUMBER OF FLUTES IN .630 15

WEB THICKNESS @ TIP 0.046 0.025 0.025

RELIEF DIAMETER @ TIP 0.18 0.025 0.025

LAND WIDTH 1 @ TIP 0.14 0.020 0.020

LAND WIDTH 2 @ TIP 0.19 0.020 0.020 LAND WIDTH 1 (3 EXIT 0.52 0.020 0.020

LAND WIDTH 2 @ EXIT 0.54 0.020 0.020

MARGIN WIDTH 1 @ TIP 0.079 0.020 0.020

MARGIN WIDTH 2 § TIP 0.094 0.020 0.020

MARGIN WIDTH 1 @ EXIT 0.34 0.020 0.020 MARGIN WIDTH 2 @ EXIT 0.31 0.020 0.020

WEB THICKNESS @ .02 FROM TIP 0.12 0.025 0.025

WEB TAPER RATE (TIP TO .02) 0.150 0.002 0.002

WEB TAPER RATE (.02 TO EXIT) 0.02 0.002 0.002

POINT ANGLE lβ) 60° 2° 2° PRIMARY ANGLE iy) 15° 2° 2°

CLOCKING ANGLE (σ) 170° 2° 2°

OVERALL LENGTH 38.1 0.076 0.076

REFERENCE DIMENSIONS ONLY RAKE ANGLE @ TIP -16° RAKE ANGLE @ EXIT __.15°

EXAMPLE 6:

The following instrument was formed from a tapered blank of SE508 nickel-titanium wire having a substantially uniformly tapered outer diameter and a non-uniformly tapered web. This particular instrument has two helical flutes of approximately equal size and shape and which are unequally spaced around the periphery of the instrument. The flutes were formed by grinding the blank with a 320 grit CBN grinding wheel at a grinding speed of 8,963 SFPM (2,732) and an axial feed rate of 1.95 inches/min. (4.95 cm/min.).

NOMINAL PLUS MINUS

DIAMETER AT TIP 0.25 0.0076 0.0076 DIAMETER TAPER RATE 0.050 0.001 0.001 SHANK DIAMETER 1.04 0.0076 0.0076

FLUTE LENGTH 16.0 0.25 0.25 RELIEF LENGTH 16.0 0.25 0.25 HELIX ANGLE (Ψ) @ TIP 30° 1° 1° HELIX ANGLE (Ψ) @ EXIT 45° 1° 1 ° NUMBER OF FLUTES IN .630 13

WEB THICKNESS @ TIP 0.046 0.025 0.025 RELIEF DIAMETER @ TIP 0.18 0.025 0.025 LAND WIDTH 1 @ TIP 0.15 0.020 0.020 LAND WIDTH 2 § TIP 0.20 0.020 0.020 LAND WIDTH 1 @ EXIT 0.62 0.020 0.020

LAND WIDTH 2 @ EXIT 0.68 0.020 0.020 MARGIN WIDTH 1 @ TIP 0.074 0.020 0.020 MARGIN WIDTH 2 @ TIP 0.10 0.020 0.020 MARGIN WIDTH 1 @ EXIT 0.39 0.020 0.020 MARGIN WIDTH 2 @ EXIT 0.37 0.020 0.020

WEB THICKNESS @ .02 FROM TIP 0.13 0.005 0.005 WEB TAPER RATE (TIP TO .02) 0.170 0.002 0.002 WEB TAPER RATE (.02 TO EXIT) 0.04 0.002 0.002 POINT ANGLE </?) 60° 2° 2° PRIMARY ANGLE iy) 15° 2° 2°

CLOCKING ANGLE (a) 170° 2° 2° OVERALL LENGTH 38.1 0.076 0.076

REFERENCE DIMENSIONS ONLY RAKE ANGLE @ TIP -16° 2° RAKE ANGLE @ EXIT >-15°

EXAMPLE 7:

The following instrument was formed from a tapered blank of SE508 nickel-titanium wire having a substantially uniformly tapered outer diameter and a non-uniformly tapered web. This particular instrument has two helical flutes of approximately equal size and shape and which are unequally spaced around the periphery of the instrument. The flutes were formed by grinding the blank with a 600 grit diamond grinding wheel at a grinding speed of 8,898 SFPM (2,712 m/min.) and an axial feed rate of 1.70 inches/min. (4.3 cm/min.)

NOMINAL PLUS MINUS

DIAMETER AT TIP 0.25 0.0076 0.0076 DIAMETER TAPER RATE 0.060 0.001 0.001 SHANK DIAMETER 1.22 0.0076 0.0076

FLUTE LENGTH 16.0 0.25 0.25 RELIEF LENGTH 16.0 0.25 0.25 HELIX ANGLE (Ψ) @ TIP 30° 1° 1° HELIX ANGLE (Ψ) § EXIT 45° 1° 1° NUMBER OF FLUTES IN .630 12

WEB THICKNESS @ TIP 0.046 0.025 0.025 RELIEF DIAMETER @ TIP 0.17 0.025 0.025 LAND WIDTH 1 @ TIP 0.14 0.020 0.020 LAND WIDTH 2 @ TIP 0.16 0.020 0.020 LAND WIDTH 1 @ EXIT 0.43 0.020 0.020

LAND WIDTH 2 @ EXIT 0.53 0.020 0.020 MARGIN WIDTH 1 @ TIP 0.086 0.020 0.020 MARGIN WIDTH 2 @ TIP 0.10 0.020 0.020 MARGIN WIDTH 1 @ EXIT 0.19 0.020 0.020 MARGIN WIDTH 2 @ EXIT 0.20 0.020 0.020

WEB THICKNESS @ .02 FROM TIP 0.10 0.005 0.005 WEB TAPER RATE (TIP TO .02) 0.105 0.002 0.002 WEB TAPER RATE (.02 TO EXIT) 0.024 0.002 0.002 POINT ANGLE \β) 60° 2° 2° PRIMARY ANGLE (y) 15° 2° 2°

CLOCKING ANGLE (σ) 170° 2° 2° OVERALL LENGTH 38.1 0.076 0.076

REFERENCE DIMENSIONS ONLY RAKE ANGLE (gl TIP -16° 2° 2° RAKE ANGLE @ EXIT ≥- 15°

EXAMPLE 8:

The following instrument was formed from a tapered blank of SE508 nickel-titanium wire having a substantially uniformly tapered outer diameter and a non-uniformly tapered web. This particular instrument has two helical flutes of approximately equal size and shape and which are unequally spaced around the periphery of the instrument. The flutes were formed by grinding the blank with a 600 grit diamond grinding wheel at a grinding speed of 8,980 SFPM (2,737 m/min.) and an axial feed rate of 1.30 inches/min. (3.3 cm/min.).

NOMINAL PLUS MINUS

DIAMETER AT TIP 0.15 0.0076 0.0076 DIAMETER TAPER RATE 0.020 0.001 0.001 SHANK DIAMETER 0.50 0.0076 0.0076 FLUTE LENGTH 16.0 0.25 0.25 RELIEF LENGTH 16.0 0.25 0.25 HELIX ANGLE (Ψ) § TIP 30° 1° 1° HELIX ANGLE (Ψ) @ EXIT 45° 1° 1° NUMBER OF FLUTES IN .630 27 WEB THICKNESS @ TIP 0.028 0.025 0.025 RELIEF DIAMETER @ TIP 0.11 0.025 0.025 LAND WIDTH 1 @ TIP 0.081 0.020 0.020 LAND WIDTH 2 @ TIP 0.10 0.020 0.020 LAND WIDTH 1 @ EXIT 0.25 0.020 0.020 LAND WIDTH 2 § EXIT 0.30 0.020 0.020 MARGIN WIDTH 1 @ TIP 0.036 0.020 0.020 MARGIN WIDTH 2 @ TIP 0.043 0.020 0.020 MARGIN WIDTH 1 @ EXIT 0.010 0.020 0.020 MARGIN WIDTH 2 @ EXIT 0.010 0.020 0.020 WEB THICKNESS @ .02 FROM TIP 0.010 0.025 0.025 WEB TAPER RATE (TIP TO .02) 0.141 0.002 0.002 WEB TAPER RATE (.02 TO EXIT) 0.019 0.002 0.002 POINT ANGLE \β) 60° 2° 2° PRIMARY ANGLE (y) 15° 2° 2° CLOCKING ANGLE a 170° 2° 2° OVERALL LENGTH 38.1 0.076 0.076

REFERENCE DIMENSIONS ONLY RAKE ANGLE @ TIP -12°

RAKE ANGLE (3 EXIT 2_-15°

EXAMPLE 9:

The following instrument was formed from a tapered blank of SE508 nickel-titanium wire having a substantially uniformly tapered outer diameter and a non-uniformly tapered web. This particular instrument has two helical flutes of approximately equal size and shape and which are unequally spaced around the periphery of the instrument. The flutes were formed by grinding the blank with a 600 grit diamond grinding wheel at a grinding speed of 8,909 SFPM (2715 m/min.) and an axial feed rate of 1.70 inches/min. (4.3 cm/min.).

NOMINAL PLUS MINUS

DIAMETER AT TIP 0.20 0.0076 0.0076

DIAMETER TAPER RATE 0.020 0.001 0.001 SHANK DIAMETER 0.52 0.0076 0.0076

FLUTE LENGTH 16.0 0.25 0.25

RELIEF LENGTH 16.0 0.25 0.25

HELIX ANGLE (Ψ) @ TIP 30° 1° 1°

HELIX ANGLE (Ψ) @ EXIT 45° 1° r NUMBER OF FLUTES IN .630 22

WEB THICKNESS (3 TIP 0.038 0.025 0.025

RELIEF DIAMETER @ TIP 0.17 0.025 0.025

LAND WIDTH 1 @ TIP 0.081 0.020 0.020

LAND WIDTH 2 @ TIP 0.27 0.020 0.020 LAND WIDTH 1 @ EXIT 0.27 0.020 0.020

LAND WIDTH 2 @ EXIT 0.32 0.020 0.020

MARGIN WIDTH 1 @ TIP 0.028 0.020 0.020

MARGIN WIDTH 2 @ TIP 0.028 0.020 0.020

MARGIN WIDTH 1 § EXIT 0.17 0.020 0.020 MARGIN WIDTH 2 @ EXIT 0.17 0.020 0.020

WEB THICKNESS @ .02 TIP 0.13 0.005 0.005

WEB TAPER RATE (TIP TO .02) 0.182 0.002 0.002

WEB TAPER RATE (.02 TO EXIT) 0.019 0.002 0.002

POINT ANGLE iβ) 60° 2° 2° PRIMARY ANGLE iy) 15° 2° 2°

CLOCKING ANGLE (σ) 170° 2° 2°

OVERALL LENGTH 38.1 0.076 0.076

REFERENCE DIMENSIONS ONLY RAKE ANGLE @ TIP -12° RAKE ANGLE @ EXIT ≥A 5"

EXAMPLE 10:

The following instrument was formed from a tapered blank of SE508 nickel-titanium wire having a substantially uniformly tapered outer diameter and a non-uniformly tapered web. This particular instrument has two helical flutes of approximately equal size and shape and which are unequally spaced around the periphery of the instrument. The flutes were formed by grinding the blank with a 600 grit diamond grinding wheel at a grinding speed of 8,963 SFPM (2,732 m/min.) and an axial feed rate of 1.56 inches/min. (3.96 cm/min.).

NOMINAL PLUS MINUS

DIAMETER AT TIP 0.25 0.0076 0.0076

DIAMETER TAPER RATE 0.020 0.001 0.001

SHANK DIAMETER 0.57 0.0076 0.0076

FLUTE LENGTH 16.0 0.25 0.25

RELIEF LENGTH 16.0 0.25 0.25

HELIX ANGLE (Ψ) @ TIP 30° 1° 1°

HELIX ANGLE (Ψ) @ EXIT 45° 1° 1°

NUMBER OF FLUTES IN .630 20

WEB THICKNESS § TIP 0.046 0.025 0.025

RELIEF DIAMETER @ TIP 0.16 0.025 0.025

LAND WIDTH 1 @ TIP 0.11 0.020 0.020

LAND WIDTH 2 @ TIP 0.13 0.020 0.020

LAND WIDTH 1 @ EXIT 0.22 0.020 0.020

LAND WIDTH 2 @ EXIT 0.27 0.020 0.020

MARGIN WIDTH 1 @ TIP 0.050 0.020 0.020

MARGIN WIDTH 2 @ TIP 0.048 0.020 0.020

MARGIN WIDTH 1 @ EXIT 0.14 0.020 0.020

MARGIN WIDTH 2 @ EXIT 0.14 0.020 0.020

WEB THICKNESS @ .02 FROM TIP 0.12 0.005 0.005

WEB TAPER RATE (TIP TO .02) 0.149 0.002 0.002

WEB TAPER RATE (.02 TO EXIT) 0.019 0.002 0.002

POINT ANGLE \β) 60° 2° 2°

PRIMARY ANGLE iy) 15° 2° 2°

CLOCKING ANGLE (σ) 170° 2° 2°

OVERALL LENGTH 38.1 0.076 0.076

REFERENCE DIMENSIONS ONLY RAKE ANGLE @ TIP -16° 2° 2° RAKE ANGLE @ EXIT ≥-15°

This invention has been disclosed and described in the context of various preferred embodiments. It will be understood by those skilled in the art that the present invention extends beyond the specific disclosed embodiments to other alternative possible embodiments, as will be readily apparent to those skilled in the art. Thus, it is intended that the scope of the present invention herein disclosed should not be limited by the disclosure herein, except as encompassed by a fair reading of the claims which follow.