Abstract:
A tool for measuring an object having a circularly curved surface provides a generally rectilinear body defining a V notch having two converging sides meeting at an apex and an angulated wedge track. A wedge movable along the wedge track and across the V notch intersects a bisector of the V notch at an angle other than perpendicular. Sides of the V notch and a measuring edge of the wedge simultaneously contact the circular curve at three equally spaced apart positions along the circumference of the circular curve. Measuring indicia on the body adjacent the wedge track allows determination of the lateral movement of the wedge along the wedge track. The distance the wedge moves on the wedge track is equal to the radius of the circular curve.

Description:
BACKGROUND OF INVENTION 
       [0001]    A. Related Applications 
         [0002]    There are no applications related hereto heretofore filed in this or in any foreign country. 
         [0003]    B. Field of Invention 
         [0004]    This invention relates to geometrical instruments, and more particularly to tools for measuring the radius of a circular curve. 
         [0005]    C. Background and Description of Prior Art 
         [0006]    The radius of curvature of an article is commonly measured by direct measurement of the article&#39;s diameter, using a micrometer or similar device. Such devices typically measure the distance between two components contacting the article on diametrically opposing sides, using either mechanical or electronic means. The measured distance is then divided in half to provide the radius of the article. 
         [0007]    While this method can be accurate, it requires simultaneous access to opposing sides of the article which may not always be accessible. For example, partially buried pipes do not normally permit access to opposing sides of the pipe, and measuring an inventory of tubular stock is often hampered by the lack of access to opposing sides of the tubular stock. Further, not all curves are completely cylindrical in cross-section, but rather may be partial curves such as at the intersection of two planar surfaces. 
         [0008]    Various diameter and radius measuring tools are available, but they are generally complex, difficult to use and require conversion tables or calculations to generate a useable measurement. The majority of such tools are “Y” shaped devices that have a base and a yoke formed by two angularly diverging legs that have a 60 degree angle therebetween. A movable probe bisects the angle and extends outwardly from the base into the area defined by the yoke. A curve to be measured is positioned in the yoke so the legs simultaneously contact the curve at two spaced apart positions. Thereafter the probe is moved outwardly from the base until it contacts the curved surface between the two contact points. The distance the probe moves between the base and the curved surface, plus the radius being measured is the hypotenuse of a right triangle. Because the angles are known, the radius and diameter of the curve can be calculated using known trigonometric formulas. 
         [0009]    Yoke type radius measuring devices have disadvantages as well. First, such devices are almost universally constructed using a 60 degree angle because the sine of 30 degrees is 0.5 which leads to simple mathematical calculations. Unfortunately, such devices are unable to measure many articles because the curve to be measured will not fit within the yoke. Yoke type devices defining notches greater than about 60 degrees are not conducive to probe movement and when the probe movement is minimal, an accurate measurement may not be possible. Such minimal probe travel from the base to the curve requires that any delineations between measuring indicia on the probe be closely spaced leading to difficult reading and interpretation. Such minimal movement also necessitates frequent recalibration of the probe position relative to the base to maintain device accuracy. Further, yoke type devices often require an operator to perform mathematical calculations to convert the distance the probe moves into a usable measurement. 
         [0010]    What is needed is a device for measuring a circular curve without requiring access to diametrically opposite sides of the article or the article&#39;s cross-section, a device with sufficient probe movement to provide an accurate measurement and a device that provides a usable measurement without resorting to conversion tables or calculators. 
         [0011]    The present invention provides such a device and resolves various of the aforementioned drawbacks. 
         [0012]    My radius measuring tool provides a user friendly device that directly measures the radius of circular curves without accessing diametrically opposed sides of the article, without a need for conversation tables, without calculations and without needing frequent recalibrations. My radius measuring tool has improved accuracy because the probe moves across the V notch rather than bisecting the notch which leads to increased travel and increased accuracy. Further, my radius measuring tool operates on the principle that actual movement of the probe relative to a fixed zero point is equal to the radius of the measured circular curve. 
         [0013]    My invention does not reside in any one of the identified features individually but rather in the synergistic combination of all of its structures, which give rise to the functions necessarily flowing therefrom as hereinafter specified and claimed. 
       SUMMARY 
       [0014]    A tool for measuring the radius of a circularly curved surface provides a generally rectilinear body defining a V notch having an apex and an angulated wedge track spacedly adjacent the apex. A wedge movable along the wedge track and across the V notch intersects a bisector of the V notch at an angle. Opposing angulated sides of the V notch and a measuring edge of the wedge simultaneously contact the circumference of the circular curve at three equally spaced apart positions. Measuring indicia on the body adjacent the wedge track allows determination of the movement of the wedge along the wedge track. The distance the wedge moves is equal to the radius of the circular curve. 
         [0015]    In providing such an apparatus it is: 
         [0016]    a principal object to provide a radius measuring tool wherein movement of a wedge from a fixed point is equal to the radius of the measured circular curve. 
         [0017]    a further object to provide a radius measuring tool wherein movement of a wedge from a fixed point correlates to the radius of the measured circular curve. 
         [0018]    a further object to provide a radius measuring tool that provides precise and accurate measurement of the radius of a curve. 
         [0019]    a further object to provide a radius measuring tool that does not require calculations or use of conversion tables to obtain a radial measurement. 
         [0020]    a further object to provide such a radius measuring tool that assists in replication of curvilinear bends. 
         [0021]    a further object to provide such a radius measuring tool that does not need to be recalibrated after each measurement. 
         [0022]    a further object to provide such a radius measuring tool that is user friendly. 
         [0023]    a further object to provide such a radius measuring tool that is capable of measuring the radius of rounded corners. 
         [0024]    a further object to provide such a radius measuring tool the accuracy of which can be increased with the increasing of the angle of the V notch. 
         [0025]    a still further object to provide such a radius measuring tool that is of new and novel design, of rugged and durable nature, of simple and economic manufacture and one that is otherwise well suited to the uses and purposes for which it is intended. 
         [0026]    Other and further objects of my invention will appear from the following specification and accompanying drawings which form a part hereof. In carrying out the objects of my invention it is to be understood that its structures and features are susceptible to change in design and arrangement with only one preferred and practical embodiment of the best known mode being illustrated in the accompanying drawings and specified as is required. 
     
    
     
       BRIEF DESCRIPTIONS OF DRAWINGS 
         [0027]    In the accompanying drawings which form a part hereof and wherein like numbers refer to similar parts throughout: 
           [0028]      FIG. 1  is an isometric front, bottom and first end view of my radius measuring tool. 
           [0029]      FIG. 2  is an isometric back, bottom and a second end view of the radius measuring tool of  FIG. 1 . 
           [0030]      FIG. 3  is an orthographic front view of the radius measuring tool of  FIG. 1  measuring the radius “r” of a circularly curved object within the V notch. 
           [0031]      FIG. 4  is an enlarged orthographic back view of the radius measuring tool of  FIG. 1 . 
           [0032]      FIG. 5  is an orthographic bottom view of the radius measuring tool of  FIG. 4 . 
           [0033]      FIG. 6  is an orthographic top view of the radius measuring tool of  FIG. 4 . 
           [0034]      FIG. 7  is an orthographic partial cross sectional view of the first end of the radius measuring tool of  FIG. 4  showing the threaded stud and the threaded fastener engaged therewith. 
           [0035]      FIG. 8  is an orthographic partial cross sectional view of the second end of the radius measuring tool of  FIG. 4  showing the threaded stud and the threaded fastener engaged therewith. 
           [0036]      FIG. 9  is an orthographic front view of the front plate. 
           [0037]      FIG. 10  is an orthographic front view of the back plate. 
           [0038]      FIG. 11  is an orthographic front view of the wedge. 
           [0039]      FIG. 12  is a diagrammatic illustration of a curve being measured in the V notch having angle α and right triangle ABC that is used to calculate distance H which is a function of R. 
           [0040]      FIG. 13  is a diagrammatic illustration of right triangle DEA, angle β and triangle legs to calculate the lateral movement of the wedge to create the desired relationship between the radius of the circular curve and movement of the wedge. 
       
    
    
     DESCRIPTION OF PREFERRED EMBODIMENT 
       [0041]    As used herein, the term “front”, its derivatives, and grammatical equivalents refers to the planar portion of my radius measuring tool that is generally closest to a user. The term “back”, its derivatives, and grammatical equivalents refers to the planar portion of my radius measuring tool that is generally opposite the user. The term “outer”, its derivatives, and grammatical equivalents refers to an elongate end portion of the radius measuring tool as opposed to a laterally medial portion of the radius measuring tool. The term “radius” is intended in its broadest sense to be in a straight line from a center of a circular curve to the curvature thereabout. 
         [0042]    My radius measuring tool provides a body  10  defining a V notch  21  and an angulated guide track  40  carrying a wedge  50  movable across the V notch  21 . 
         [0043]    The body  10  is preferably made of a rigid durable material, such as steel, and is generally rectilinear having an upper edge portion  11 , a lower edge portion  12 , a first elongate end portion  13  proximate to the V notch  21  and a second elongate end portion  14  distal from the V notch  21 . The body  10  has a back plate  20  and a front plate  30  that are structurally connected to one another with plural spacedly arrayed spot welds  62 . 
         [0044]    As shown in  FIG. 10 , the back plate  20  defines the V notch  21  that opens to the upper edge portion  11  spacedly adjacent the first elongate end portion  13 . The V notch  21  has a first angulated edge  21   a  and a second angulated edge  21   b  that converge to intersect at apex  23 . The back plate  20  also defines an elongate angulated through slot  24  that has one end portion spacedly adjacent the second angulated edge  21   b  and an opposing end portion spacedly adjacent the second elongate end portion  14 . The V notch  21  defines an angle α that is between approximately 40 degrees and 170 degrees but is preferably 120 degrees. 
         [0045]    As shown in  FIG. 9 , the front plate  30  defines a “cut out”  31  at a corner portion adjoining the upper edge portion  11  and the first elongate end portion  13 . An elongate rectilinear notch  32  communicates with edge  31   b  of the cutout  31  and extends angularly through medial portion of the front plate  30  terminating at a base  32   b  spacedly adjacent the second elongate end portion  14  and the lower edge portion  12 . The elongate rectilinear notch  32  has upper edge portion  32   a  and a spaced apart parallel lower wedge track  40 . Base  32   b  is perpendicular to the upper edge portion  32   a  and perpendicular to the wedge track  40 . 
         [0046]    Angle  52  of the elongate rectilinear notch  32  relative to the lower edge  12  of the body  10  and relative to an imaginary line  25  that bisects the V notch  21  is dependent upon the angle α of the V notch  21  and the desired use of the radius measuring tool. For example a tool that is used to measure smaller articles, such as hand tools, may use a one-to-one ratio between wedge  50  movement and radius measured, while a tool used to measure larger articles having radii measured in meters may use a multiple-to-one ratio between wedge  50  movement and radius measured. As angle α changes so too must the angle  52  of the rectilinear notch  32  relative to the lower edge portion  12  to maintain the desired wedge  50  movement to radius relationship. 
         [0047]    As shown in  FIG. 3 , the front plate  30  is aligned with, and structurally fastened to, the back plate  20  so that the upper edges  11 , the lower edges  12 , the second elongate end portions  14  and the first elongate end portions  13  are aligned and adjacent. The cutout portion  31  in the front plate  30  overlays the V notch  21  defined in the back plate  20 , edge  31   b  is adjacent second angulated edge  21   b  and the elongated rectilinear notch  32  forms a spacedly adjacent perimeter about the elongated angulated slot  24 . In the preferred embodiment, the wedge track  40  is an indented ledge in the body  10  for the wedge  50  to frictionally move therealong. (See  FIGS. 1 and 3 ). In an alternative embodiment the wedge track  40  may protrude from the body  10  forming a “lip” upon which the wedge  50  may movably slide. 
         [0048]    The wedge  50  ( FIG. 11 ) has a base end portion  50   a  and an opposing tapered end portion  50   b . A track edge portion  50   d  is perpendicular to the base end portion  50   c  and frictionally slides upon and along the wedge track  40 . An anti-pivot portion  50   e  and measuring edge portion  50   c  are end-to-end and cooperatively form the upper edges of the wedge  50 . The anti-pivot portion  50   e  is parallel to the track edge portion  50   d  and is adjacent to and perpendicular to the base end portion  50   a . The measuring edge portion  50   c  is proximate to the tapered end portion  50   b  and angle  51  of the measuring edge portion  50   c  relative to the track edge portion  50   d  is the same as the angle  52  of the wedge track  40  relative to the lower edge portion  12  of the body  10  so that the measuring edge portion  50   c  is perpendicular to imaginary line  25  bisecting the angle α of the V notch  21 . ( FIG. 3 ). A threaded stud  60  ( FIGS. 7 and 8 ) is structurally carried by the wedge  50  spacedly adjacent the base end portion  50   a . The threaded stud  60  extends through the elongated slot  24  and moves therein so that the wedge  50  moves along the wedge track  40 . A threaded fastener  61  carried by the threaded stud  60  maintains the wedge  50  on the wedge track  40  and allows a user to positionally secure the wedge  50  on the wedge track  40  as desired. 
         [0049]    Measuring indicia  63  having numbered gradations beginning at zero adjacent the base  32   c , to a desired maximum measurement distance and subdivided equally, is preferably engraved in the front plate  30  adjacent below the wedge track  40  so that change in position of the wedge  50  along the wedge track  40  can be measured. The base end portion  50   a  of the wedge  50  is the preferred fixed point of measurement, so that when the base end portion  50   a  is immediately adjacent the base  32   b  of the elongated rectilinear notch  32  the measuring indicia  63  indicates zero and the tapered end  50   b  of the wedge  50  is immediately adjacent the apex  23  of the V notch  21 . Although this is the preferred fixed measuring point, any point along the wedge track  40  and on the wedge  50  may also be a fixed measuring point. 
         [0050]    The geometric relationship of the angles of the V notch  21 , the wedge  50  and the wedge track  40  are interdependent. The angle α of the V notch  21  may be varied depending upon the intended use of the radius measuring tool and the sought-after accuracy. In general, as the V notch  21  angle α increases and the angle  51  of the of the measuring edge  50   a  relative to the track edge  50   d  decreases, the accuracy of the radius measuring tool increases because the distance the wedge  50  must move across the V notch  21  before contacting the curve  64  being measured is increased. The increased travel distance allows more widely spaced and therefore more precise measuring indicia  63 . For example a radius measuring device that is used to measure small hand tools such as sockets may use a one-to-one ratio between wedge movement and radius measured, while a radius measuring device used to measure items that have radii measured in meters may use a one-to-multiple ratio between wedge movement and radius measured. 
         [0051]    In the preferred embodiment, the angle α of the V notch  21  is 120°, and the angle  51  of the measuring edge portion  50   a  relative to the track edge portion  50   d  of the wedge  50  is approximately 8.8994 degrees. ( FIG. 11 ). The angle  52  of the guide track  40  relative to the lower edge  12  of the body  10  is similarly approximately 8.8994 degrees. ( FIG. 9 ). These preferred angle measurements provide a one-to-one ratio between the movement of the wedge  50  and the radius of the curve  64  being measured. 
         [0052]    The measuring edge portion  50   a  of the wedge  50  moves across the V notch  21  perpendicular to the imaginary line  25  that bisects the V notch  21  ( FIG. 3 ). This perpendicular intersection necessitates that the angle  52  of the wedge track  40 , relative to the lower edge  12  of the body  10  is the same as the angle  51  of the of the measuring edge  50   a  relative to the track edge portion  50   d  of the wedge  50 , so that in unison, the two angles  52 , and  51  form a straight horizontal line. 
         [0053]    As shown in  FIG. 12 , α is the angle between the first angulated edge  21   a  and the second angulated edge  21   b . R is the radius of the circular curve  64  and is equal to leg CB of right triangle ABC. AB is the adjacent leg of the right triangle ABC where angle CAB is α/2. In the preferred embodiment angle α is 120 degrees meaning angle CAB is 60 degrees, and angle ACB is 30 degrees. H is the distance between the apex  23  and point E which is the lowest portion of the circular curve  64 . Hypotenuse AC of triangle ABC is equal to R+H. Radius R of the circular curve  64  is determined using the following equation: 
         [0000]        R =( R+H )sin α/2 
         [0054]    H which is the distance between the apex  23  (point A) and point E is determined using the following equation: 
         [0000]        H=R[ 1/sin(α/2)−1] 
         [0055]    Values for R and for H are not required to calculate the needed angle  51  ( FIG. 11 ) of the measuring edge  50   c  of the wedge  50  and the angle  52  ( FIG. 9 ) of the wedge track  40  to generate a one-to-one relationship between wedge  50  movement and radius measured. 
         [0056]    As shown in  FIG. 13 , right triangle DEA represents the portion of the wedge  50  that has crossed the bisector  25  of the V notch  21  when the measuring edge portion  50   c  of the wedge  50  contacts the curve  64  at point E which is the lowest portion of the circular curve  64 . X is the hypotenuse AD of the right triangle DEA and represents the positional change of the wedge  50  on the wedge track  40  away from the base  32   b . ( FIG. 3 ). H is side AE of the right triangle DEA and as previously indicated H=R[1/sin(α/2)−1]. Angle EDA is represented by β. It follows that: 
         [0000]        X  Sine β= R[ 1/sin(α/2)−1] 
         [0057]    In the desired case where X=R the following equation provides the calculation to determine β for a one-to-one relationship between wedge  50  movement and radius R: 
         [0000]      Sine β=[1/sin(α/2)−1] 
         [0058]    Upon solving, β=(sin −1 )[1/sin(α/2)−1]. Where α/2=60 degrees, the following solution is provided: 
         [0000]      β=(sin −1 )[1/0.8660254−1]. β≈8.8994 degrees. 
         [0059]    Similar calculations can be made for other angles α which also provide a one-to-one relationship between the radius R of the circular curve  64  and the movement of the wedge  50 . For example, a V notch  21  defining an angle α of 90 degrees requires a β angle of approximately 24.4698 degrees. A V notch  21  defining an angle α of 150 degrees requires a β angle of approximately 2.0216 degrees. A V notch  21  defining the ratio of R/X=10 has an angle α of 130.76004 degrees requires a β angle of approximately 5.7392 degrees. Other α angles can likewise be associated with corresponding β angles based upon the desired ratio between R and X. 
         [0060]    Having described the structure of my radius measuring tool, its operation may be understood. 
         [0061]    To measure the radius R of a curve, the wedge  50  is moved to its extreme limit distal from the V notch  21  so that the base end portion  50   a  is immediately adjacent the base  32   b  of the elongate rectilinear notch  32 . This position is known as the “zero” position where the tapered end portion  50   b  of the wedge  50  is immediately adjacent the apex  23  of the V notch  21 . The circular curve  64  to be measured is positioned in the V notch  21  so that the circumferential surfaces of the circular curve  64  simultaneously contacts the first angulated edge  21   a  and the second angulated edge  21   b  on either side of the apex  23 . (See  FIG. 3 ). To obtain optimal accuracy in measuring the radius, the body  10  must be perpendicular to the axis of the circular curve  64 . The wedge  50  is moved along the wedge track  40  and across apex  23  until the measuring edge portion  50   c  touches the bottom most portion of the circular curve  64  within the V notch  21 . 
         [0062]    The threaded fastener  61  on the threaded stud  60  is tightened to secure the wedge  50  in this position, or the user may hold the wedge  50  in this position. 
         [0063]    The user compares the base end portion  50   a  of the wedge  50  with the measuring indicia  63  engraved in the front plate  30 . The distance shown by the measuring indicia  63  is the radius of the circular curve  64 . Alternatively, a known type of measuring caliper (not shown) may be used to measure the distance between the base end portion  50   a  of the wedge  50  and the base  32   b  of the rectilinear notch  32 . The distance between the base portion  50   a  and base  32   b  of the rectilinear notch  32  is the radius of the curve  64 . 
         [0064]    In an alternative embodiment (not shown) the radius measuring tool will incorporate a mechanical or electrical measuring apparatus that is interconnected to the wedge  50  and the body  10  that automatically calculates the travel of the wedge  50  along the wedge track  40  to provide the measurement to the user. 
         [0065]    Having thusly described my invention, what I desire to protect by Letters Patent, and 
         [0066]    What I claim is: