Abstract:
A system for modeling a recessed or protruding angle formed by convergent surfaces and transferring that modeled angle directly to a miter saw for facilitating the cutting of workpieces in conformance with the bisection of that modeled angle. This system may be manufactured with, or retrofitted onto a standard miter saw or used with a hand miter saw designed to accommodate the system.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a system for miter cutting, and more particularly, to a system for miter cutting that includes a device for modeling the angle of convergent surfaces and transposing the modeled angle to a miter saw for miter cutting through a slot defined on the miter saw. 
   2. Background of the Related Art 
   The primary function of a miter saw is to cut a piece of material (hereinafter also referred to as a “workpiece”) at a defined angle. Miter saws are most often used to prepare moldings or decorative trim to fit adjacent to surfaces that converge to form an angle, such as an inside or outside corner, so that the moldings or trim appear to follow along the surfaces continuously. 
   For practical reasons as well as aesthetics, the workpieces are fit to the convergent surfaces by cutting each of the workpieces at an angle which equals, as nearly as possible, one half of the angle formed at the convergence. 
   Most, if not all, miter saws have preset locking positions for various angles and setting the cutting angle is easily accomplished if the convergence angle corresponds with one of these positions. For example, virtually all miter saws have a preset position for 45 degrees to facilitate cutting workpieces to fit a 90 degree convergence angle. 
   However, the process becomes more difficult if the convergence angle does not correspond to an angle having a preset cutting position on the miter saw. This circumstance is encountered more often than not, especially throughout existing structures, such as residential homes and apartments. 
   In these circumstances, half the convergence angle must be measured and transferred to the miter saw in a way that enables the miter saw to be positioned for cutting each workpiece accordingly. Moreover, most moldings or trim are not of equidimensional design, in that they have a planar surface which opposes an ornamental surface and top and bottom edges which may differ in width. For such applications, the miter saw can be set so that a first workpiece is cut to half the convergent angle for the workpiece to be placed along a first convergent surface, but the miter saw must then be set to the inverse or mirror image of the first angle before cutting the second workpiece so that the second workpiece can be positioned along the second convergent surface with the correct orientation. Thus, the measured angle of convergence must be measured and/or transferred to the miter saw twice. 
   Some devices exist which can measure both internal and external existing angles in degrees, enabling the operator to set the miter saw to one half of that angle by using the saw&#39;s miter scale. Other devices duplicate the existing angle and provide a means for transferring one half of that angle to the workpiece by pencil, or scribe, enabling the operator to set the miter saw by visual reference to that line. 
   The primary problems associated with using such devices are that they are prone to inaccuracies, because, among other things, they involve one or more intermediate steps between the measurement of the existing angle and the setting of the miter saw, each of which is capable of introducing error. 
   U.S. Pat. No. 5,473,821 to DeMarco discloses a device that can model a convergence angle and transfer one half of that angle to a power miter saw, but only if the miter saw is manufactured to resemble the miter saw described by DeMarco (hereinafter also referred to as the “DeMarco miter saw”). The Demarco miter saw, as described in the &#39;821 patent, deviates from standard power miter saws so much that it would be impossible to use the DeMarco angle-modeling device on miter saws which have not been specifically manufactured in accordance therewith. DeMarco does not demonstrate flaws in the standard power miter saw design or provide justification for changing manufacturing practices to produce miter saws as those shown in the &#39;821 patent, and his design introduces a variety of problems not presented by the standard design. 
   For example, a workpiece placed on the DeMarco miter saw is held against a guide fence on only one side of the cut rather than both sides as it is with standard designs. This configuration decreases support for the workpiece and increases the possibility that it will move during the cutting process, thereby compromising accuracy, since the cutting action of the blade tends to move or bend the workpiece. The configuration also reduces the operator&#39;s options with regard to stabilizing the workpiece against the fence, thus creating safety issues which are not found in the standard design. 
   Another problem with the DeMarco design relates to the need to move the fences to duplicate the angel of convergence. This configuration increases the complexity and difficulty associated with using the DeMarco miter saw because it requires the reorientation of the workpiece, and any workpiece support system, for different angles and for mitering separate pieces to frame the same angle. In contrast, with the standard design the workpiece is always cut along the same axis, which generally corresponds to a workbench or other support system for the workpiece. 
   The DeMarco miter saw presents further difficulty in using it to frame an interior angle because each fence blocks the path of a workpiece placed against the other, thus eliminating the operators ability to make one cut for both dimension and angle. 
   Thus, there is a need for a device which overcomes the problems associated with the prior art as described above. In particular, what is needed is a system or device for modeling an angle formed by convergent surfaces and transferring one half of that angle directly to a miter saw, which can be employed with power miter saws of standard design and hand miter saws designed to accommodate it. Clearly, a device such as this would increase the speed, accuracy and efficiency of the miter saw and miter cutting process. 
   SUMMARY OF THE INVENTION 
   The present invention solves the problems of the prior art by, among other things, providing a device for modeling an angle formed by two convergent surfaces and a system for transferring one half of that modeled angle directly to a miter saw to facilitate the cutting of workpieces to border the convergent surfaces, which can be manufactured with or retrofitted onto a standard power miter saw and can also be used with a hand miter saw which is designed to accommodate it. 
   The present invention consists of a tool and miter saw having a slot defined thereon. The miter saw is configured so that the slot remains parallel to the cutting plane of the miter saw as it is rotated relative to a fixed fence or other device for aligning the workpiece. The tool models the angle of convergence via pivotally connected angle framing arms which are then fixed in position; bisects that angle by support links which are pivotally connected to each other and to each of the framing arms; and transfers the appropriate cutting angle to the miter saw. In this embodiment, the transfer is accomplished by one or more positioning members, which are used to align the bisecting line of the convergence angle with the longitudinal axis of the slot. 
   The tool is configured so that one framing arm may be placed against and adjacent to each of the convergent sides of an interior angle, with the pivotal coupling of the framing arms being equidistant from the outside edge of each. The pivotal couplings of the framing arms to the support links are equidistant from the outside edge of each framing arm and from the pivotal coupling of the framing arms. The pivotal coupling of the support links is equidistant from the pivotal coupling of each support link to a framing arm. 
   The present invention is also directed to a system for facilitating miter cutting which includes a tool for modeling a convergence of two surfaces having a first elongate framing arm pivotally coupled with a second elongate framing arm. The first and second framing arms are interconnected by two support links. The first and second framing arms are each pivotally coupled to a support link, which support links, in turn, are pivotally coupled to each other. 
   This embodiment of a tool constructed in accordance with the present invention also includes a pair of miter positioning members that extend in the same general direction, substantially perpendicularly with respect to the plane of the tool. The miter positioning members are centered on a line between the pivotal coupling of the framing arms and the pivotal coupling of the support links. Preferably, one positioning member is aligned with and directly below the pivotal coupling of the framing arms and the other is aligned with and directly below the coupling of the support links. 
   A fastener is also provided for adjusting the rigidity of the tool to control the pivotal movement of the first and second framing arms. The fastener may be associated with one or more of the pivotal couplings. 
   In one embodiment, the tool includes an elongate central arm which shares the pivotal coupling between the first and second framing arms and includes a longitudinal slot defined therein along which the pivotal coupling of the support links is slidably mounted. In this embodiment, the position of the framing arms may be locked by restricting slidable movement of this pivotal coupling along the longitudinal slot. 
   A tool constructed in accordance with the present invention can also include a setting or support structure which permits modeling external angles. This may include extending the length of the first and second framing arms along their respective longitudinal axes, such as by attaching extension arms of adjustable length to the first and second framing arms. 
   The present invention is also directed to a miter saw which includes a base having a rotatably mounted carriage disposed thereon that supports a planar work surface, a fence for aligning and affixing the workpiece thereto, which may be in two or more linearly aligned fence segments, is perpendicular to the working surface and is mounted on the base or in such other manner that it remains stationary as the work surface rotates; a knob or other assembly for directing the rotation of the rotatably mounted carriage and work surface disposed thereon and locking the carriage and work surface in a desired position; and a pivoting arm or other means for bringing a saw blade to the work surface which is mounted on the carriage and rotates with the work surface. 
   This embodiment of a system constructed in accordance with the present invention includes a substantially planar kerf plate for being mounted in, and substantially flush with, the rotatably mounted work surface of a miter saw either as original equipment on a miter saw designed to be utilized with the present invention or as a replacement for the kerf plate on an existing miter saw. The kerf plate of this embodiment has a central slot which is substantially parallel to the cutting plane and configured and dimensioned for engaging the miter positioning members of the tool constructed in accordance with the present invention and receiving the saw blade. Preferably, the kerf plate is fabricated from a non-ferrous material. 
   The system constructed in accordance with the present invention is generally intended for use as described herein. For an interior angle formed by the convergence of two surfaces, the angle is modeled and one half of that angle transposed to the miter saw by placing each framing arm adjacent to one of the surfaces, locking the tool in that position, engaging the miter positioning members in the miter saw kerf plate slot, rotating the work surface until a framing arm is adjacent to the fixed fence and then locking the work surface in that position. 
   For an exterior angle formed by the convergence of two surfaces, the angle is modeled and one half of that angle transposed to the miter saw by extending the framing arms of the tool, placing each extended arm adjacent to one of the surfaces, locking the tool in that position, releasing or removing the extending portions of the framing arms, engaging the miter positioning members in the kerf plate slot, rotating the work surface until a framing arm is adjacent to the fixed fence and then locking the work surface in that position. 
   To cut framing pieces for the angle, the saw is set twice. The first piece is cut after the working surface has been rotated to one side, bringing one framing arm to a position adjacent to the fence, and the second piece is cut after the working surface has been rotated to the other side, bringing the other framing arm to a position adjacent to the fence. 
   In a preferred embodiment constructed in accordance with the present invention, the miter saw includes a base having a rotatably mounted carriage disposed thereon which supports a planar work surface and a locking knob assembly for directing and locking its rotational movement; a fence for aligning and holding the work piece consisting of two fence segments, one on each side of the cutting plane, which are perpendicular to the work surface, linearly aligned and mounted on the base in such a manner that they remain stationary as the work surface rotates; and a spring loaded pivot joint and pivotal arm which supports a housing for a circular blade and electric drive motor. The pivot joint and pivotal arm are configured and mounted to rotate with the work surface, thereby maintaining a fixed position relative to the work surface, and establish a cutting plane which is perpendicular to the work surface and intersects the rotational center of the carriage and work surface. 
   The miter saw also includes a substantially planar slotted kerf plate mounted in, and substantially flush with, the work surface. The kerf plate slot is disposed over an aperture in the work surface, parallel with respect to, and centered on, the cutting plane. The slot is configured and dimensioned to receive the circular saw blade and engage the miter positioning members of an angle modeling device constructed in accordance with the present invention. 
   The modeling device includes a first elongate framing arm pivotally coupled with a second elongate framing arm about an elongate central arm. The elongate central arm includes a longitudinal slot defined therein. Two support links are interconnected with the first and second framing arms by pivotal couplings. The pivotal coupling connecting the support links to each other is mounted on the central arm to slide along the longitudinal slot, and includes a fitting, such as a threaded shaft and wing nut or threaded knob, configured to compress the linking arms and the central arm, thereby locking the device in position. 
   In accordance with this preferred embodiment, the angle modeling device includes two miter positioning members extending in the same direction, perpendicularly with respect to the plane of the tool. One such positioning member is aligned with and directly below the pivotal coupling of the framing arms while the other positioning member is aligned with and directly below the coupling of the support links. 
   In addition, the device of this preferred embodiment includes detachable extension arms of variable lengths, which extend the length of the first and second framing arms along their respective longitudinal axes, thereby providing a tool to model exterior angles. 
   In a second preferred embodiment constructed in accordance with the present invention, the miter saw includes a base having a rotatably mounted carriage disposed thereon which supports a planar work surface and a locking knob assembly for directing and locking its rotational movement; a fence for aligning and holding the workpiece consisting of two fence segments, one on each side of the cutting plane, which are perpendicular to the work surface, linearly aligned and mounted on the base in such a manner that they remain stationary as the work surface rotates; two slotted guides mounted at the front and back of the rotatably mounted carriage in such a manner that they rotate with the work surface, thereby maintaining a fixed position relative to it. The slots in the guides are perpendicular to the work surface and configured to engage and guide a hand saw. The guides are mounted in a manner to establish a cutting plane which is perpendicular to the work surface and intersects the rotational center of the carriage and work surface. 
   The miter saw also includes a substantially planar kerf plate mounted in and substantially flush with, the work surface. The kerf plate slot is disposed over an aperture in the work surface, is parallel to the cutting plane, centered on it, and configured and dimensioned to receive the hand saw blade and to engage the miter positioning members of an angle modeling device as described above. 
   The present invention is also directed to a method for mitering two pieces of material to frame converging surfaces. The method includes the step of applying a tool at the convergence of the converging surfaces to model the angle of convergence. The tool may include first and second elongate framing arms pivotally coupled to each other at an end thereof, first and second support links, each pivotally coupled to a framing arm at a point which is equidistant from the pivotal coupling of the framing arms. The support links can be pivotally coupled to each other at a point equidistant from their respective pivotal couplings with the framing arms. The tool may further include fastening means for temporarily setting the first and second framing arms in a desired angular relationship facilitated by the pivotal coupling of the first and second framing arms, pivotal couplings of the first and second support links to the first and second framing arms, and the pivotal coupling of the first and second support links to each other, and at least two positioning members extending substantially perpendicular to the plane of the tool and coaxial with the pivotal coupling of the framing arms and the pivotal coupling of the first and second support links to each other, whereby the axis formed between the positioning members bisects the angle formed by the coupling of the first and second framing arms. 
   The method also includes the steps of locking the tool to maintain the first and second framing arms in a position corresponding to the angle of convergence, and affixing the tool to a miter cutting system. 
   The miter cutting system may include a rotatable planar work surface and stationary guide fence for supporting a work piece and positioning the work piece in an angular relationship for cutting with a saw, receiving means for the at least two positioning members in the rotatable work surface, whereby alternate rotation of the work surface such that the first and second framing arms abut alternate sides of the guide fence positions the work surface for cutting a work piece along the axis formed between the positioning members. 
   The positioning members of the tool being received by the receiving means, the method further includes the steps of rotating the work surface until one of the framing arms contacts the guide fence, positioning a first work piece on the work surface in alignment with the guide fence and cutting the work piece with a saw, and removing the cut work piece. With the positioning members of the tool being received by the receiving means, the method further includes rotating the work surface until the other one of the framing arms contacts the guide fence, positioning a second work piece on the work surface in alignment and with the guide fence, cutting the work piece with a saw; and removing the cut workpiece. 
   Other objects and advantages of the invention will be apparent from the following description, the accompanying drawings and the appended claims. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     So that those having ordinary skill in the art to which the present invention appertains will more readily understand how to make and use the same, reference may be had to the drawings wherein: 
       FIG. 1  is a top plan view of a tool for modeling angles constructed in accordance with the present invention; 
       FIG. 2  is a side elevational view of the tool illustrated in  FIG. 1 ; 
       FIG. 3  is a top plan view of the tool shown in  FIG. 1 , illustrating extensions to the framing arms and attachment points for extensions; 
       FIG. 4  is a perspective view of a power miter saw of generally standard design; 
       FIG. 5  is a front view of the miter saw shown in  FIG. 4 , illustrating the rotational movement of the working surface and pivotal arm provided by the rotatably mounted carriage; 
       FIG. 6  is a perspective view of a miter saw shown in  FIG. 4 , illustrating the downward or cutting pivotal movement of the arm used to cut a workpiece placed on the worksurface; 
       FIG. 7  is a top view of the tool shown in  FIG. 1  positioned in an inside corner formed by two convergent surfaces and configured to model the angle of convergence; 
       FIG. 8  is a top view of the tool taken from the inside corner as shown in  FIG. 7 , wherein the tool is positioned on the kerf plate of a miter saw work surface in accordance with the present invention; 
       FIG. 9  is a top view of the tool positioned on the kerf plate of a miter saw as shown in  FIG. 8 , wherein the miter saw work surface has been rotated so that a first arm of the tool contacts the fixed fence; 
       FIG. 10  is a top view of the miter saw work surface rotated as shown in  FIG. 9  with a workpiece positioned on the work surface for cutting with the miter saw; 
       FIG. 11  is a top view of the inside corner of  FIG. 7 , wherein the workpiece cut by the miter saw as shown in  FIG. 10  in accordance with the present invention is positioned to border one of the two converging surfaces forming the inside corner; 
       FIG. 12  is a top view of the tool configured to model the inside corner as shown in FIG.  7  and positioned on the kerf plate of a miter saw work surface in accordance with the present invention, wherein the miter saw work surface has been rotated so that the second arm of the tool abuts the fixed fence; 
       FIG. 13  is a top view of the miter saw work surface rotated as shown in  FIG. 12  with a workpiece positioned on the work surface for cutting with the miter saw; 
       FIG. 14  is a top view of the inside corner of  FIG. 11 , wherein the workpiece cut by the miter saw as shown in  FIG. 13  in accordance with the present invention is positioned to border the second of the two converging surfaces forming the inside corner; 
       FIG. 15  is a top view of the tool shown in  FIG. 1  with arm extensions, such as those depicted in  FIG. 3 , wherein the tool is positioned in an outside corner formed by two convergent surfaces and configured to model the angle of convergence; 
       FIG. 16  is a top view of the tool taken from the outside corner as shown in  FIG. 15 , wherein the tool is positioned on the kerf plate of a miter saw work surface without arm extensions in accordance with the present invention; 
       FIG. 17  is a top view of the tool positioned on the kerf plate of a miter saw as shown in  FIG. 16 , wherein the miter saw work surface has been rotated so that a first arm of the tool contacts the fixed fence; 
       FIG. 18  is a top view of the miter saw work surface rotated as shown in  FIG. 17  with a workpiece positioned on the work surface for cutting with the miter saw; 
       FIG. 19  is a top view of the outside corner of  FIG. 15 , wherein the workpiece cut by the miter saw as shown in  FIG. 18  in accordance with the present invention is positioned to border one of the two converging surfaces forming the outside corner; 
       FIG. 20  is a top view of the tool configured to model the outside corner as shown in  FIG. 15 , wherein the tool is positioned on the kerf plate of a miter saw work surface without arm extensions in accordance with the present invention and the miter saw work surface has been rotated so that the second arm of the tool abuts the fixed fence; 
       FIG. 21  is a top view of the miter saw work surface rotated as shown in  FIG. 20  with a workpiece positioned on the work surface for cutting with the miter saw; 
       FIG. 22  is a top view of the outside corner of  FIG. 19 , wherein the workpiece cut by the miter saw as shown in  FIG. 21  in accordance with the present invention is positioned to border the second of the two converging surfaces forming the outside corner; 
       FIG. 23  is a top plan view of a miter saw work surface with a kerf plate constructed in accordance with the present invention secured thereon. 
       FIG. 24  is a top plan view of a hand miter saw designed to accommodate a tool for modeling angles constructed in accordance with the present invention; and 
       FIG. 25  is a front elevational view of the saw shown in FIG.  24 . 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The advantages of a system for perfecting miter cuts constructed or retrofitted on a miter saw in accordance with the present invention will become more readily apparent to those having ordinary skill in the art from the following detailed description of certain preferred embodiments taken in conjunction with the drawings which set forth representative embodiments thereof. Unless otherwise apparent, or stated, directional references, such as “right,” “left,” “upper,” “below,” “horizontal” “vertical,” “upward” and “downward”, are intended to be relative to the orientation of a particular embodiment of the invention as shown in the first numbered view of that embodiment. In addition, a given reference numeral indicates the same or similar structure when it appears in different figures and like reference numerals identify similar structural elements and/or features of the subject invention. 
   Referring now to  FIG. 1 , in which there is illustrated a preferred embodiment of a miter angle modeling and transferring tool constructed in accordance with the present invention and generally designated by the reference numeral  10 . Tool  10  is substantially planar and includes a left elongate framing arm  12  and a right elongate framing arm  14 . This preferred embodiment also includes an elongate central arm  16 . The left arm  12  and right arm  14  are pivotally connected adjacent to a first end of each, respectively, by coupling  18 , and are configured so that one framing arm may be placed against and adjacent to each of the convergent sides of an interior angle. Left and right arms  12  and  14  can be pivoted via coupling  18  to define an angle between arms  12  and  14 . As can be best viewed in  FIG. 2 , coupling  18  includes a miter positioning member  20  which extends perpendicularly with respect to the plane of tool  10 . In this embodiment, miter positioning member  20  is essentially a protrusion, referred to hereinafter as locator pin  20 . Locator pin  20  is positioned equidistant from the outer edges of left and right arms  12  and  14 , respectively. 
   A left support link  22  is pivotally interconnected adjacent to a first end thereof, with left arm  12  at a coupling  24 . Similarly, a right support link  26  is pivotally interconnected adjacent to a first end thereof, with right arm  14  at a coupling  28 . 
   Left and right support links  22  and  26  are pivotally connected to central arm  16  by a coupling  30 . Preferably, coupling  30  is disposed adjacent the second ends of each of the support links  22  and  26 . Pivotal connections  24  and  28  are equidistant from pivotal connection  18 , pivotal connection  30  and from the outside edges of framing arms  12  and  14 . 
   In this embodiment, coupling  30  includes another protruding miter positioning member  32 , which is also referred to hereinafter as locator pin  32 . Locator pin  32  is substantially centered on and extends from coupling  30  substantially perpendicularly with respect to the plane of tool  10 , and in the same general direction as locator pin  20 . 
   In the embodiment of the present invention depicted in the figures, coupling  30  is slidably mounted on central arm  16  for movement within a central slot  34  defined longitudinally in central arm  16 . Locator pin  32  is substantially centered on coupling  30  and also is slidably engaged within central slot  34  by virtue of its connection with coupling  30 . Preferably, coupling  30  may be tightened, by a threaded shaft and knob or similar device, so that coupling  30  remains in its position, thus preventing pivotal movement by tool  10 . 
   An independent fastening assembly may also be used with the present invention, such as a wing-nut and threaded bolt, which can be tightened to lock coupling  30  in position along central slot  34 . Other fastening assemblies which prohibit pivotal movement of left and right arms  12  and  14  may also be utilized. 
   Left elongate arm  12  and right elongate arm  14  are expandable along the longitudinal axis towards coupling  18 . For example, this may be accomplished by including additional members of the same width as the arms  12  and  14 , respectively, which are slidably attached thereto, or by including arms  12  and  14  which are telescoping or contain telescoping sections. 
   In this embodiment of the present invention, as shown in  FIG. 3 , extension members  36  having substantially the same width as arms  12  and  14 , respectively, but greater longitudinal length, are attached to arms  12  and  14  via fasteners  38  to facilitate the modeling of exterior angles. Fasteners  38  may include bolts and wingnuts, hook and latch, or any other suitable fastening devices. It should be readily apparent to those skilled in the art that it is within the purview of the present invention to provide extension members  36  of various lengths, or extension members  36  which are adjustable, to accommodate a variety of exterior angles and surrounding conditions. 
   Referring now to  FIG. 4 , in which there is illustrated a preferred embodiment of a miter saw orientated for operation thereof, which employs a system constructed in accordance with the present invention designated generally by a reference numeral  40 . Miter saw  40  is powered by an electrical connection to a home outlet, however, the source of power is not critical for the operation of the present invention. 
   Miter saw  40  includes a base  42  having a generally planar and circular work surface  44 . A fence, consisting of a linearly aligned right side segment  46  and left side segment  48 , is disposed perpendicularly with respect to work surface  44 , is supported by base  42  so that it remains stationary as work surface  44  is rotated and is used to position and support a work piece against surface  44  for cutting. A kerf plate  50  with a longitudinal slot  52  is seated in surface  44  between right side fence segment  46  and left side fence segment  48 . Kerf plate  50  is recessed so that it is substantially evenly aligned with surface  44 . Slot  52  is located over an aperture in the work surface  44  (not shown) and sufficiently sized to receive a saw blade. Furthermore, slot  52  is sufficiently configured to engage pins  20  and  32  therein and may further include keyed notches, indents or the like for matching corresponding keyed elements in pins  20  and  32 . Preferably, for safety reasons, among other things, kerf plate  50  is constructed of a resilient but non-ferrous material, such as plastic. 
   Work surface  44  is disposed over a carriage  54  mounted on base  42  and configured for rotational movement in the horizontal plane. A locking clamp and knob assembly  56  is disposed on carriage  54  to facilitate movement of the carriage  54  along with work surface  44 . An arm  58  is supported by a spring loaded pivot assembly  60  connected with carriage  54 , which provides for pivotal movement of arm  58  thereby causing the circular blade  62  mounted on its upper portion to move through a vertical plane which is perpendicular to working surface  44 , and passes through and is aligned with the rotational center of carriage  54  and with slot  52 .  FIG. 6  best illustrates the manner in which this pivotal movement is utilized to cut material. Pivot assembly  60  and clamp and knob assembly  56  are positioned in substantially opposed, radially outer portions of the carriage  54 . 
   Carriage  54  facilitates rotational movement of work surface  44  in excess of 45 degrees to the left and right relative to the center alignment (i.e., with slot  52  being set in a substantially perpendicular relationship with respect to base  42 ).  FIG. 5  depicts miter saw  40  with carriage  54  rotated to the right and illustrates the manner in which work surface  44 , slot  52  and arm  58  rotate with carriage  54  and maintain their respective positions relative to each other. 
   A circular blade  62 , which is driven by an onboard motor  64  and covered by a retractable guard  66 , is mounted for rotational motion on the upper portion of arm  58 . A trigger switch  68  in electrical communication with motor  64  is positioned adjacent a handle  70  defined on arm  58  to facilitate activation of blade  62  while moving arm  58  to cut a workpiece on surface  44 , as shown in FIG.  6 . 
   The system in accordance with the present invention may be used in a variety of ways to produce highly accurate miter angle cuts.  FIGS. 7-14  illustrate a preferred method for using tool  10  to model/measure an inside angle (i.e., formed by two recessing convergent surfaces) and transfer that angle to miter saw  40  for cutting a workpiece to fit within the inside angle accordingly. 
   As shown in  FIG. 7 , tool  10  is fit onto inside corner  80  by using right and left framing arms  12  and  14  to form a surrounding border about the convergence, thus matching the angle of inside corner  80 , as defined by a left side surface  82  and right side surface  84 , with arms  12  and  14 . Once the convergence is modeled by tool  10 , the fastener associated with coupling  30  is tightened to ensure that the “framed” position of arms  12  and  14  is maintained. In  FIG. 8 , tool  10  is placed on work surface  44  so that pins  20  and  32  are engaged in slot  52  of kerf plate  50 . Using locking clamp and knob assembly  56 , carriage  54  is rotated to move work surface  44 , along with tool  10  while still engaged in slot  52 , so that left arm  12  abuts left side fence segment  48  as shown in FIG.  9 . After positioning work surface  44 , tool  10  is then removed from kerf plate  50 . As shown in  FIG. 10 , the workpiece is placed on surface  44  abutting right side and left side fence segments  46  and  48  before being cut by the saw. As shown in  FIG. 1 , one end of the cut workpiece matches half the angle of inside corner  80  and can be positioned to border left side convergent surface  82 . 
     FIGS. 12-14  illustrate the same process for cutting another workpiece so that one end includes an angle matching the right side half of interior corner  80 . The tool  10  is placed back into slot  52 , and work surface  44  is rotated so that right arm  14  abuts right side fence segment  46 . Tool  10  is removed and the workpiece is positioned against the right side and left side fence segments  46  and  48  before being cut. As shown in  FIG. 14 , the workpiece can be positioned against right side surface  84  so that the two workpieces fit together and form a border about inside corner  80 . 
     FIGS. 15-22  illustrate the method for using tool  10  to model/measure the angle of an outside corner  86  formed by two projecting convergent surfaces, a left side surface  88  and a right side surface  90 , and transfer that modeled angle to the miter saw  40  for cutting workpieces to border the outside corner  86 . 
   As shown in  FIG. 15 , extension members  36  are attached to right and left arms  12  and  14 , respectively, to frame outside corner  86 . Once the convergence is modeled, arms  12  and  14  are held in position by tightening the fastener associated with coupling  30 . Extension members  36  are removed and tool  10  is fit into slot  52  of kerf plate  50 , as shown in FIG.  16 . In  FIG. 17 , work surface  44  is rotated so that left arm  12  abuts left side fence segment  48 . Tool  10  is removed and the workpiece is placed on surface  44  for cutting with miter saw  40 , as shown in FIG.  18 . For an outside corner such as corner  86 , the workpiece cut with the tool  10  abutting left side fence segment  48  will provide the border for right side surface  90 , as shown in FIG.  19 . 
   As depicted by  FIGS. 20-22 , the process is similar for producing a workpiece that can border left side surface  88  and fit with the right side surface workpiece about outside corner  86 . 
   The present invention is advantageously adapted to existing miter saws without redesigning or reconfiguring existing equipment, or changing the design of the present invention. As shown in  FIG. 23 , any existing kerf plate on a miter saw can be removed by screws  92  and replaced by a kerf plate in accordance with the present invention. The kerf plate may also consist of two parts, each of which defines one half of the central slot. 
     FIGS. 24 and 25  illustrate the manner in which a tool  10  constructed in accordance with the present invention, as described above, may be used in conjunction with a hand miter saw which is generally designated by the reference numeral  140 . 
   Hand miter saw  140  includes a base  142  having a rotatably mounted carriage  154  which is configured for rotational movement in the horizontal plane and which supports a generally planar and circular work surface  144 . A fence, consisting of linearly aligned right side and left side segments  146  and  148  is used to position and support a workpiece against surface  144  for cutting. The fence is perpendicular to work surface  144  and is supported by base  142  so that it remains stationary as work surface  144  rotates. 
   A substantially planar kerf plate  150  with a longitudinal slot  152  is seated in surface  144  between right side fence segment  146  and left side fence segment  148 . Kerf plate  150  is recessed so that it is substantially evenly aligned with surface  144 . Slot  152  is sufficiently sized to receive a saw blade, is located over an aperture in work surface  144  and is configured to engage locator pins  20  and  32  from tool  10  therein. Slot  152  may further include keyed notches, indents or the like for matching corresponding keyed elements in pins  20  and  32 . Preferably, kerf plate  150  is constructed of a resilient but non-ferrous material such as plastic. 
   A locking clamp and knob assembly  156  is disposed on carriage  154  to facilitate movement of carriage  154  along with work surface  144 . Braces  194  and  196  are supported by carriage  154  for rotational movement therewith. Braces  194  and  196  project above work surface  144  in a spaced relationship at either end of slot  152 . Both braces  194  and  196  contain a slot  198  disposed in the same place, perpendicularly with respect to work surface  144 . Slots  198  are configured and dimensioned to receive a hand saw without restraining the movement in slots  198  associated with cutting. Preferably, the hand saw is of the type commonly known as a back saw. Braces  194  and  198  with slots  198  are mounted and configured to align a hand saw positioned therein with slot  152  in kerf plate  150 . 
   Tool  10  would be used to model/measure an angle formed by either exterior or interior convergent surfaces in the same manner as in the previous embodiment. The angle is transferred to miter saw  140  in substantially the same manner as described above and illustrated in  FIGS. 7 through 22 , except the workpiece is cut with a hand saw. 
   While the systems and methods for using the system contained herein constitute preferred embodiments of the invention, it is to be understood that the invention is not limited to these precise systems and methods of use, and that changes may be made thereto without departing from the scope of the invention which is defined in the appended claims.