Abstract:
A method for cutting a chamfer on an edge of a concrete slab, the method comprising the steps of: making a generally planar cut, beginning a distance from the edge, with a generally circular, generally laminar concrete saw blade rotatably powered by a right-angle grinder motor, the generally planar cut being made at a desired angle and creating a cantilevered ledge above the generally planar cut; fracturing and removing at least a portion of the cantilevered ledge from the slab whenever an edge of the cantilevered ledge is proximate the hub; and continuing the generally planar cut until the cantilevered ledge is severed from the slab.

Description:
[0001]     This is a continuation of Application No. 11/358,548, filed on Feb. 21, 2006, titled APPARATUS FOR REMOVING TRIP HAZARDS IN CONCRETE SIDEWALKS, now U.S. Pat. No. 7,???,???, which was a continuation of Application No. 10/975,677, filed on Oct. 28, 2004, titled Method and Apparatus for Removing Trip Hazards in Concrete Sidewalks, now U.S. Pat. No. 7,000,606, which was a continuation of Application No. 10/155,663, filed on May 24, 2002, titled Method and Apparatus for Removing Trip Hazards in Concrete Sidewalks, now U.S. Pat. No. 6,827,074 B2. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     Signed into law as Section 12181 of Title 42 of the United States Code on Jul. 26 1990, the Americans with Disabilities Act (ADA) is a wide-ranging legislation intended to make American society more accessible to people with disabilities. The legislation, which took effect on Jul. 26, 1992, mandates, among other things, standards for access to public facilities, including public sidewalks. The law not only requires that curb cuts be made at intersections and crosswalks to facilitate wheelchair access, but also mandates specifications for slopes and transitions between two surfaces of different levels. Some of the relevant provisions of the law are as follows:  
         [0003]     4.5.2 Changes in Level. Changes in level up to ¾ inch (6 mm) may be vertical and without edge treatment. Changes in level between ¼ inch and ½ inch (6 mm and 13 mm) shall be beveled with a slope no greater than 1:2. Changes in level greater than ½ inch (13 mm) shall be accomplished by means of a ramp that complies with 4.7 or 4.8.  
         [0004]     4.72 Slope. Slopes of curb ramps shall comply with 4.8.2. Transitions from ramps to walks, gutters, or streets shall be flush and free of abrupt changes. Maximum slopes of adjoining gutters, road surface immediately adjacent to the curb ramp, or accessible route shall not exceed 1:20.  
         [0005]     4.8.2 Slope and Rise. The least possible slope shall be used for any ramp. The maximum slope of a ramp in new construction shall be 1:12. The maximum rise for any run shall be 30 inches (760 mm). Curb ramps and ramps to be constructed on existing sites or in existing building or facilities may have slopes and rises as allowed in 4.1.6(3)(a) if space limitations prohibit the use of a 1:12 slope or less.  
         [0006]     3-a-1. A slope between 1:10 and 1:12 is allowed for a maximum rise of 6 inches.  
         [0007]     3-a-1. A slope between 1:8 and 1:10 is allowed for a maximum rise of 3 inches. A slope steeper than 1:8 is not allowed.  
         [0008]     Public sidewalks and private sidewalks open to the public must comply with the foregoing provisions of the ADA. Tree roots are the single most significant cause of unlevel conditions of sidewalks. Because sidewalks are generally made of contiguous concrete slabs, unevenness typically occurs at the joints between the slabs. Unstable and inadequately compacted soils can also lead to differential settling of adjacent slabs.  
         [0009]     Historically, trip hazards caused by uneven lifting and settling of contiguous sidewalk sections have been eliminated either by tearing out the old concrete and replacing it with new slabs having no abrupt transitions between joints, by forming a transition ramp on the lowermost section with macadam, or by creating a chamfer on the edge of the uppermost section. The first method represents the most expensive fix. The second method, which uses dark-colored macadam on a light-colored sidewalk, is unsightly. If the chamfer is made using a surface cutter or grinder, the second method is slow, given that all material removed through grinding must be pulverized. In addition, if the process is performed with a drum cutter, the equipment is relatively expensive and leaves a rough surface. In addition, most equipment used heretofore is incapable of removing the trip hazard over the entire width of a sidewalk. Furthermore, if two adjacent sidewalk slabs have twisted in opposite directions as they have settled or raised, it may be necessary to create a ramp across a portion of the width of the sidewalk on both sides of the joint.  
         [0010]     What is needed is a new method and apparatus that will reduce the time required to form chamfers, that is capable of removing a trip hazard over the entire width of a sidewalk, and that is capable of chamfering portions of two intersecting slabs at a common joint. Ideally, the equipment and expendables required will be relatively simple and inexpensive, and will not require pulverization of all material removed during a chamfer operation.  
       SUMMARY OF THE INVENTION  
       [0011]     The present invention provides both a method and apparatus for cutting a chamfer on an upper edge of a concrete slab. First and second embodiment apparatuses include a hub having a threaded aperture designed for installation on the threaded output spindle of an angle grinder, and a specially-modified diamond-grit-edged rotary blade which mounts on the hub. For a presently preferred embodiment of the hub, an attachment collar is unitary and concentric with both a blade mounting flange and a blade centering shoulder on the flange. The attachment collar is machined for a minimum clearance, self-centering fit on the output spindle to minimize imbalance conditions. The collar has at least one pair of flattened parallel sides for receiving a wrench used to tighten the hub on the output spindle. The side of the blade mounting flange opposite the collar is equipped with at least two, and preferably three or more, countersunk holes, by means of which the blade may be attached. The holes may be blind, or may penetrate the flange. In the former case, the holes are threaded. In the latter case, the holes are unthreaded and the screws are secured with self-locking nuts on the side of the collar side of the blade mounting flange. The rotary blade is equipped with a central positioning aperture sized to fit over the blade centering shoulder with a generally minimum amount of clearance required for a non-interference fit. The blade is equipped with countersunk holes which align with those on the blade mounting flange. Countersinking screws are employed to affix the blade to the blade mounting flange. When fully tightened in the countersunk holes in the flange, the head of each of the screws is flush with the surface of the blade. As the blade rotates and cuts into concrete, the lower surface of the blade may remain in contact with the lower cut surface. Because the hub will contact the concrete above the cut, that concrete must be periodically broken and removed to provide adequate clearance for the hub as the cut is continued.  
         [0012]     Third and fourth embodiment apparatuses employ a hub having a central aperture machined for close tolerance mounting on the output spindle of the right-angle grinder. The blade has a core with a central recess. A nut, which engages the end of the output spindle, secures the blade to the hub and spindle. The nut may be separate from the blade assembly, in which case, the hub incorporates a blade centering shoulder which mates with a central positioning aperture in the blade core. Alternatively, the nut may be incorporated in the blade assembly. For example, the nut may be swaged within a central blade aperture. As will be hereinafter shown, certain modifications are made to the hub to accommodate the swaged nut.  
         [0013]     A trip hazard typically occurs when the upper surface of one of two abutting concrete slabs is at a higher elevation than the upper surface of the other. Using the heretofore described hub and blade in combination with a right-angle grinder motor, the trip hazard can be removed by cutting a chamfer on the abutting upper edge of the higher- elevated slab. The method of cutting the chamfer involves the following steps: providing a right-angle grinder motor having an output shaft with a first axis of rotation; providing a generally circular, generally laminar concrete saw blade rotatable about a second axis of rotation; coupling said concrete saw blade to said output shaft with said first and second axes of rotation being coincident; making a generally planar cut at a desired angle beginning a distance from said edge, the generally planar cut creating a cantilevered ledge above the generally planar cut; fracturing and removing at least a portion of the cantilevered ledge from the slab whenever an edge of the cantilevered ledge is proximate the hub; and continuing the generally planar cut until the cantilevered ledge is severed from the slab.  
         [0014]     With training, a skilled worker can make an angled chamfer cut into the edge of a raised concrete slab, so that a smooth transition between a lower slab and the raised slab may be formed. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0015]     Drawing  FIGS. 1-10  show a first embodiment apparatus;  FIGS. 11-14 , a second embodiment apparatus;  FIG. 14 , a blade guard;  FIGS. 16-21 , a third embodiment apparatus; and  FIGS. 22-24  a fourth embodiment apparatus.  
         [0016]      FIG. 1  is a side elevational view of a typical electric right-angle grinder;  
         [0017]      FIG. 2  is a top plan view of a first embodiment hub;  
         [0018]      FIG. 3  is side elevational view of the first embodiment hub, taken parallel to the wrench flats;  
         [0019]      FIG. 4  is side-elevational see-through view of the first embodiment hub, taken perpendicular to the wrench flats;  
         [0020]      FIG. 5  is an isometric top view of the first embodiment hub;  
         [0021]      FIG. 6  is an isometric bottom view of the first embodiment hub;  
         [0022]      FIG. 7  is a top plan view of the blade;  
         [0023]      FIG. 8  is an exploded side elevational view of the right-angled grinder of  FIG. 1 , the hub of  FIGS. 2-6 , the blade of  FIG. 7 , and multiple countersinking screws, positioned for assembly;  
         [0024]      FIG. 9  is a side elevational view of the right-angled grinder of  FIG. 1 , having installed thereon the hub of  FIGS. 2-6  and the blade of  FIG. 7 ;  
         [0025]      FIG. 10  is an enlarged cross-sectional view of the portion of  FIG. 9  within the ellipse  10 , taken through the central axis and a pair of blade-securing holes;  
         [0026]      FIG. 11  is an isometric top view of a second embodiment hub having blind holes for blade retaining screws;  
         [0027]      FIG. 12  is an isometric top view of the second embodiment hub;  
         [0028]      FIG. 13  is an exploded side elevational view of a portion of the right-angled grinder of  FIG. 1 , the hub of  FIGS. 12-13 , the blade of  FIG. 7 , and multiple countersinking screws, positioned for assembly;  
         [0029]      FIG. 14  an enlarged cross-sectional view of a portion of the assembled components of  FIG. 13 , the view being comparable to that of  FIG. 10 ;  
         [0030]      FIG. 15  is a side elevational view of the right-angled grinder of  FIG. 1 , having installed thereon the hub of  FIGS. 2-6 , the blade of  FIG. 7 , and a blade guard trimmed to function with the blade and hub of the present invention;  
         [0031]      FIG. 16  is an isometric top view of a third embodiment hub having an unthreaded central aperture;  
         [0032]      FIG. 17  is an isometric top view of the third embodiment hub;  
         [0033]      FIG. 18  is an exploded side elevational view of a portion of the right-angled grinder of  FIG. 1 , the hub of  FIGS. 16-17 , a specially designed blade having a core with a concave center region, and a retaining nut, all positioned for assembly;  
         [0034]      FIG. 19  is an isometric view of the retaining nut first shown in  FIG. 18 ;  
         [0035]      FIG. 20  is a cross-sectional view of the assembled components of  FIG. 18 ;  
         [0036]      FIG. 21  is an isometric top view of a fourth embodiment hub having an unthreaded central aperture;  
         [0037]      FIG. 22  is an isometric top view of the fourth embodiment hub;  
         [0038]      FIG. 23  is an exploded side elevational view of a portion of the right-angled grinder of  FIG. 1 , the hub of  FIGS. 21-22 , a specially designed blade having a core with a concave center region, and an integral swaged retaining nut, all positioned for assembly;  
         [0039]      FIG. 24  is a cross-sectional view of the assembled components of  FIG. 23 ;  
         [0040]      FIG. 25  is a side elevational view of the mounted blade making a first chamfer cut on the edge of a raised concrete slab;  
         [0041]      FIG. 26  is a side elevational view of the concrete slab, with the cutting equipment removed following the first cutting pass;  
         [0042]      FIG. 27  is a side elevational view of the cut concrete slab of  FIG. 26 , following the fracturing of the first overhanging ledge;  
         [0043]      FIG. 28  is a side elevational view of the mounted blade making a second chamfer cut on the edge of the raised concrete slab shown in  FIG. 25 ;  
         [0044]      FIG. 29  is a side elevational view of the concrete slab, with the cutting equipment removed following the second cutting pass;  
         [0045]      FIG. 30  is a side elevational view of the cut concrete slab of  FIG. 29 , following the fracturing of the second overhanging ledge;  
         [0046]      FIG. 31  is a side elevational view of the mounted blade making a third chamfer cut on the edge of the raised concrete slab shown in  FIG. 25 ; and  
         [0047]      FIG. 32  is the concrete slab shown in  FIG. 25  following completion of the chamfer cut, and removal of the cutting equipment and debris. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0048]     Various embodiments of an apparatus for cutting a chamfer on an upper edge of a concrete slab will now be described with reference to drawing  FIGS. 1 through 24 . Description of a method for cutting the chamfer will reference drawing  FIGS. 25-32 .  
         [0049]     Referring now to  FIG. 1 , a typical right-angle grinder motor  100  is shown. The grinder motor  100  has a body  101 , which encloses an electric drive motor, a cooling fan and a right-angle gear train (none of which are visible in this drawing). The grinder motor  100  has a rotatably powered threaded output spindle  102 , a handle  103 , a power switch  104 , motor brush caps  105 , cooling vents  106 , and an electrical power cord  107 . Although the invention will be shown in combination with an electrically-powered right-angle grinder, it will be obvious to those of ordinary skill in the art of grinding equipment that a compressed-air-powered right-angle grinder may be used in combination with the invention with equally satisfactory results.  
         [0050]     Referring now to  FIGS. 2 through 6 , the apparatus of the invention comprises a hub  200  at is designed for installation on the threaded output spindle  102  of an angle grinder, such as the electric grinder motor  100  shown in  FIG. 1 . For a first and preferred embodiment of the hub  200 , an attachment collar  201  is unitary and concentric with both a blade mounting flange  202  and a blade centering shoulder  203  on the flange  202 . A central mounting aperture  204  passes through the collar  201 , the flange  202 , and the shoulder  203 . The mounting aperture  204  is threaded to receive and engage the threaded output spindle  102  of the right-angle grinder motor  100 . The attachment collar  201  has at least one pair of flattened parallel sides  205  for receiving a wrench used to tighten the hub  200  on the output spindle  102 . The side  206  of the blade mounting flange  202  opposite the collar  201  is equipped with at least two, and preferably three or more, countersunk holes  207 , by means of which a generally circular, diamond-grit-edged rotary blade may be attached with countersinking screws and self-locking nuts (not shown in this drawing figure).  
         [0051]     Referring now to  FIG. 7 , the rotary blade  700  is equipped with a central positioning aperture  701  sized to fit over the blade centering shoulder  203  with a generally minimum amount of clearance required for a non-interference fit. The blade is equipped with non-threaded countersunk holes  702  which align with the threaded countersunk holes  202  on the blade mounting flange  202 . Countersinking screws (shown in  FIG. 8 ) are employed to affix the blade  700  to the blade mounting flange  202 . When fully tightened in the countersunk threaded holes  202  in the flange  202 , the heads of each of the screws is flush with the surface of the blade  700 . Although it is possible to countersink only the holes  702  of the saw blade  700  and use specially designed screws having a very shallow countersinking head, conventional countersinking screws have greater structural integrity. The edge  703  of blade  700  is formed from a metal matrix which incorporates diamond grit throughout, which enables the blade, when rotating, to cut through “green” or seasoned concrete. For a presently preferred embodiment of the blade, the new diameter is 8 inches (about 203 mm), and the blade core has a thickness of about 0.55 inch. The height of the blade centering shoulder  203  is preferably also about 0.055 inch. If the blade centering shoulder were to protrude through the blade, the edges thereof would become peened over the edges of the blade centering aperture  701 , thereby making removal of the blade difficult.  
         [0052]     Referring now to the exploded assembly  800  of  FIG. 8 , an electrically-powered right-angle grinder motor  100  is shown together with the hub  200 , the blade  700 , multiple countersinking blade-attachment screws  801  and multiple self-locking nuts  802 , all positioned for assembly as a unit. It will be noted that each of the self-locking nuts has a deformable polymeric insert  1005 , which provides the self-locking function. It will be further noted that the right-angle grinder motor  100  has an output shaft  102  with a first axis of rotation  803 , that the generally circular, generally laminar concrete saw blade  700  is rotatable about a second axis of rotation  804  and that, when the concrete saw blade  700  is coupled to the output shaft  102 , the first and second axes of rotation  803  and  804 , respectively, are coincident.  
         [0053]     Referring now to assembled unit  900  of  FIG. 9 , the hub  200  has been installed on the output spindle  102  of the right-angled grinder motor  100 , and the blade  700  has been secured to the hub  200  with the countersinking screws  801  and the self-locking nuts  802 . It will be noted that the lower surface  901  of the blade  700  is completely flat, with no attachment hardware protruding below its surface.  
         [0054]     Referring now to  FIG. 10 , the portion of  FIG. 9  within the ellipse  10  is shown in cross-sectional format. In this detailed view, it is clearly seen that the attachment collar  201  is unitary and concentric with the blade mounting flange  202  and the blade centering shoulder  203  on the flange  202 . The threads  1001  within the central mounting aperture  204 , which have spirally engaged the threads  1002  on the output spindle  102 , are clearly visible in this view. It will be noted that the head  1003  of each countersinking blade attachment screw  801  has a socket  1004 . The blade attachment screws  801  are inserted through the countersunk holes  702  in the blade  700 , through the holes  207  in the blade mounting flange  202  and secured with the self-locking nuts  802 . Using an allen-type wrench which engages the sockets  1004 , the screws  801  may be kept from rotating while the self-locking nuts  802  are tightened against the upper surface of the blade mounting flange  202 , thereby securing the blade  700  to the hub  200 . It will also be noted that the central positioning aperture  701  in the blade  700  is sized to fit over the blade centering shoulder  203  with a generally minimum amount of clearance required for a non-interference fit.  
         [0055]     Referring now to  FIGS. 11 through 14 , a second embodiment of the hub  1100  is shown. Identical numbers are used for identical items of the first and second embodiments. The only difference between the first embodiment hub  200  and the second embodiment hub  1100  is that the latter has countersunk and threaded blade attachment holes  1201  in place of the self-locking nuts  802 . Shorter screws  1301  may therefore be employed with this arrangement. It has been determined that the dust from the cutting process tends to cause the blade attachment screws  1301  to seize within the threaded holes, making it difficult to remove a blade  700  when it must be replaced. This problem may be solved by using blue Loctite® thread-locking and anti-seizing compound, or a similar product, when installing the blade. The thread-locking and anti-seizing compound seals the threads on both the screws  1301  and within the blade attachment holes  1201  from dust.  
         [0056]     It should be mentioned that right-angle grinders are sold with a guard that shields the rear half of a grinding wheel. As grinding wheels are of generally greater thickness than a concrete cutting blade, the guard must be trimmed so that it does not extend beyond the lower surface of the concrete cutting blade. In this way, flush cuts are possible, even with the blade guard installed on the grinder motor. Referring now to  FIG. 15 , a guard  1501  is shown. The guard has been trimmed along the lower edge thereof so that it does not extend below the lower surface of the concrete cutting blade  700  when it is mounted on the hub  200 , which is installed on the threaded output spindle  102  of the right-angle grinder  100 .  
         [0057]     Referring now to  FIGS. 16 and 17 , a third embodiment hub  1600  has an axis of rotation  1601 , a central aperture  1602  coincident with the axis of rotation  1601 , the aperture sized for close tolerance mounting on the output spindle  102  of the right-angle grinder  100 , thereby minimizing rotational imbalances. It will be noted that the lower surface  1603  of the hub  1600  is recessed, and that the recessed lower surface  1603  incorporates a blade centering shoulder  203 . The recessed lower surface  1603  acts as a backing surface to which the blade is mated.  
         [0058]     Referring now to  FIG. 18 , a generally circular blade  1800  has an axis of rotation  1801 , a generally laminar metal core  1802 , and a metal matrix edge  703  affixed to a circumferential edge of the core  1802 , the metal matrix edge being embedded with diamond grit. The laminar metal core  1802 , which is preferably stamped from sheet steel, includes a center portion  1803  with a raised upper surface  1804  and an indented lower surface  1805 , said core having a planar flange portion  1806  extending radially from the center portion  1803 , said flange portion having an outer circular circumferential edge  1807 , to which metal matrix edge  703  is affixed. At the very center of the center portion  1803  is a central mounting hole  1808  sized to snugly fit over the blade centering shoulder  203  of the hub  1600 . When the blade  1800  is mounted to the hub, at least a portion of the raised upper surface  1804  mates with the lower surface  1603  of the hub  1600 . Also shown in this exploded view is a nut  1900 , which engages the threads on the end of the output spindle  102 . The nut  1900  may be employed to secure the blade  1800  and the hub  1600  to the output spindle  102 . For a preferred embodiment of the blade, the center portion  1803  of the core  1802  is bell shaped, having a circular central disk portion  1809 , which incorporates the central mounting hole  1808 , the central disk portion  1809  being coupled to a conical-shaped skirt portion  1810  that is, in turn, coupled to the flange portion  1806 . For this particular embodiment of the blade  1800 , the nut  1900  is biased against the lower surface of the circular central disk portion  1809  when the blade  1800  and hub  1600  are secured to the output spindle  102 .  
         [0059]     Referring now to  FIG. 19 , the nut  1900  is seen in more detail. The female threads  1901  are sized to spirally engage the male threads of the output spindle  102 .  
         [0060]     Referring now to  FIG. 20 , the individual components of  FIG. 18  have been assembled into a single unit, with the nut  1900  securing both the hub  1600  and the blade  1800  to the output spindle  102 . It will be noted that the indented lower surface  1805  provides a recess  2001  in which the nut  1900  is positioned when the hub  1600  and blade  1800  are secured to the output spindle  102 , such that a straight edge may be placed in contact with any two segments of the metal matrix edge  703  on the lower surface  2002  of the blade without encountering an intervening obstruction. Thus, the blade  1800  is enabled to cut through concrete, unimpeded by blade attachment projections on the blade&#39;s lower surface  2002 .  
         [0061]     Referring now to  FIGS. 21 and 22 , a fourth embodiment hub  2100  is similar to that of  FIGS. 16 and 17 , with the exception that the blade centering shoulder  203  is replaced by a circular recess  2201 .  
         [0062]     Referring now to  FIG. 23 , the blade assembly  2300  also has a core  2301  that, for all practical purposes, is identical to the core  1802  of  FIGS. 18 and 20 . However, the top edge  2303  of the blade retaining nut  2302  is swaged around the central mounting hole  1808 , so that the nut  2302  is integrated into the blade assembly  2300 .  
         [0063]     Referring now to  FIG. 24 , the individual components of  FIG. 23  have been assembled into a single unit. It will be noted that the upper portion of the swaged blade retaining nut  2302  fits into the circular recess  2201  within the hub  2100 . It will also be noted that as with the assembly of  FIG. 20 , the blade securing nut  2302  fits completely with the central recess  2401  of the blade assembly  2300 , thereby allowing the bottom surface  2402  of the blade assembly  2300  to cut concrete unimpeded by blade attachment projections on that surface.  
         [0064]     Referring now to  FIG. 25 , it will be noted that, at the junction of a first concrete slab  2501  and a second concrete slab  2502 , there is a trip hazard  2503  that has been caused by the first slab  2501  being raised with respect to the second slab  2502 . Removal of the trip hazard, by making a dry chamfer cut on the first concrete slab  2501 , will now be described in detail with reference to the remaining drawing figures. The chamfer, when complete, will have a 1:8 rise. Both slabs  2501  and  2502  rest on a substrate  2504  of gravel, sand or soil. Using the right-angle grinder motor  100  with the hub  200  and blade  700  mounted thereon, a first chamfer cut  2505  is made on the edge of concrete slab  2501 , which has raised with respect to the second concrete slab  2502 . It will be noted that the bottom surface of the blade  901  is in close proximity to the lower cut surface  2506 . However, as heads  1003  of the blade-attachment screws  801  are flush with the lower surface of the blade  700 , they are shielded from abrasive action of the concrete within the cut  2505 . In order to protect the hub  200  from abrasion by the concrete, the cut must stop before the rotating hub  200  contacts the upper edge  2507  of the cut concrete. Using a blade having a diameter of about 8 inches (about 203 mm), a 2.375 inch deep cut may be made without endangering the hub.  
         [0065]     Referring now to  FIG. 26 , the blade has been removed from the cut  2505 . It will be noted that a first cantilevered ledge  2601  extends over the cut  2505 .  
         [0066]     Referring now to  FIG. 27 , the cantilevered ledge  2601  has been fractured by hitting it with a hammer or other similar instrument.  
         [0067]     Referring now to  FIG. 28 , a second chamfer cut  2801  is made, which is a continuation of the first chamfer cut  2505 . Once again, in order to protect the hub  200  from abrasion by the concrete, the cut must stop before the rotating hub  200  contacts the upper edge  2802  of the cut concrete. It will be noted that while making the second chamfer cut  2801 , which is a continuation of the first chamfer cut  2505 , a center portion  2803  of the blade  700  is superjacent regions of the slab which were cut during the first chamfer cut  2505 .  
         [0068]     Referring now to  FIG. 29 , the blade has been removed from the cut  2801 . It will be noted that a second cantilevered ledge  2901  extends over the cut  2801 .  
         [0069]     Referring now to  FIG. 30 , the second cantilevered ledge  2901  has been fractured by hitting it with a hammer or other similar instrument.  
         [0070]     Referring now to  FIG. 31 , a third chamber cut has been made which removes the remainder  3101  of the trip hazard  2503 .  
         [0071]     Referring now to  FIG. 32 , the first concrete slab  2501  is shown with the a completed chamfer cut  3201 . The cutting equipment, which consists of the right-angle grinder motor  100 , the attached hub  200  and blade  700 , have been removed, as have been the trip hazard debris pieces  2601 ,  2801  and  3101 .  
         [0072]     With training, a skilled worker can make an angled chamfer cut into the edge of a raised concrete slab, so that a smooth transition between a lower slab and the raised slab may be formed. Trip hazards of slightly more than 2.54 cm height can be removed in using three cuts with an eight-inch blade. Trip hazards of nearly two inches in height can be removed with additional cuts, using the invention as heretofore described.  
         [0073]     Although only several embodiments of the apparatus and a single embodiment of the cutting method have been heretofore described, it will be obvious to those having ordinary skill in the art that changes and modifications may be made thereto without departing from the scope and the spirit of the invention as hereinafter claimed.