Abstract:
A multiple gear driver having first and second fixed gears and first and second rotatable gears, the first fixed and rotatable gears located on a first member, and the second fixed and rotatable gears located on a second member, the first and second fixed gears having a common axis so that the first fixed gear drives the second rotatable gear and the second fixed gear drives the first rotatable gears when the first and second member are moved relative to each other.

Description:
BACKGROUND OF THE INVENTION 
     This invention has to do with a measuring tool for use in the construction profession with particular applicability to finish carpentry, framing carpentry, wall layout, drywall installation, fitting countertops, piping layouts, floor and ceiling installations and cabinetry. It also has direct applications in the graphic arts field, the engineering and drafting fields and other manufacturing situations where angle measurements are performed. This invention has direct applications in virtually every situation requiring an angle measurement, and it has a multitude of professional and household applications, providing precise angle readings for any carpentry project and any other project that requires angle measurement, angle copying, angle transferring, and/or angle projection. Such projection of an angle may be accomplished with a laser, scope or other means of projecting or sighting to a distant point, line, plane or planes. 
     This invention is used in the fitting of trim and decorative pieces, or any material, to the surface of wall surfaces, or any surfaces, which meet at an angular junction. This angular junction is commonly referred to as a miter joint. A miter saw/miter box is used to cut the trim and decorative pieces, or any material, in a precise manner so that a clean and accurate miter joint is established. 
     The invention is also used for fitting single pieces of trim, or any material, into any angle that is encountered. A miter saw/miter box is used to cut the material in a precise manner so that a clean and accurate fit is established between the freshly cut piece and the work surface(s). 
     In addition to the above-mentioned functions, which are specific to the angle scale that is virtually universal to the miter saw/miter box, this invention also has scales for determining the actual angle, or any interpretation of the actual angle, throughout an entire revolution (zero degrees through 360 degrees). 
     This invention has additional scales for determining, transferring and laying out the angles for common roof pitches. In the preferred embodiment, these scales are laid out in the standard “inches of rise per lineal foot.” The indicated roof pitch is simultaneously converted to a protractor or miter saw/miter box setting. 
     This invention also has scales for determining, transferring and laying out gradients. In the preferred embodiment, the slopes (grades) are presented for reading in percentages wherein 0% slope is horizontal and 100% slope is a 45° angle with respect to horizontal. 
     While a miter saw/miter box is the preferred and generally most accurate way to achieve the angled cuts determined by the invention, other means such as a hand saw, hand-held circular saw, radial arm saw, table saw, jig saw and any other means for achieving the determined cuts are contemplated by the inventor. 
     This invention has a laser/scope accessory and provision is made for said laser/scope accessory to be attached to the invention. The union of this invention with the laser/scope accessory provides a means for projecting any angle setting from a chosen point of origin along the angle chosen and out to a distance limited only by the power of the laser/scope. Such a laser/scope projection is useful in the layout of walls and construction angles, regardless of what plane they are in. Such a laser/scope projection is also useful in the electrical, plumbing, drywall and landscaping fields, as well as any trade or endeavor that requires the accurate determination, and/or projection, of any angle. It should be understood that a laser/scope, or lasers/scopes, might also be incorporated in the body of the tool as a permanent fixture(s). All such alternative means for employing a laser(s), scope(s) or other means of projecting or sighting on the measuring tool are contemplated by the inventor. 
     BRIEF SUMMARY OF THE INVENTION 
     It is an object of this invention to provide an easy to use tool to transfer angle readings from a work place surface(s) to a miter saw/miter box, to any other cutting device, or directly to any work piece, in a one-step operation. 
     It is a further object of this invention to measure and/or project with a laser, scope or other means, an angle, its complementary angle, its supplementary angle, common roof pitch angles, gradients and/or any angle measurement to which the several scales might be adapted. In the preferred embodiment all of these angle measurements are measured and projected simultaneously. 
     In the preferred embodiment of the invention an angle measurement tool is provided that in its final form has two interacting legs and a plurality of interacting gears. The first of the two legs has a fixed gear assembly at the axis of the two interacting legs. The second leg has one or more gears which are driven by the aforementioned fixed gear assembly on the first leg. One or more of these gears serve as dials for the purpose of displaying and reading a variety of angle measurements. Both of the legs and those gears employed as dials have a plurality of scale measurements scribed upon them. The tool is so constructed that the movement of the two legs relative to each other will result in an angle being formed there between that will be measured by referring to a setting on the scales so provided for the gears and the legs. 
     The tool can be utilized to measure the miter joint angle, bevel and miter settings for compound angles, the actual angle made by the legs of the tool, the complementary angle of the actual angle, the supplementary angle of the actual angle, the common roof pitch angle, gradients, and/or any angle measurement to which the several scales might be adapted. In the preferred embodiment, all of these angle measurements are measured simultaneously. The tool can also be utilized with its laser/scope accessory (or integral laser[s] and/or scope[s]) to measure, layout and project wall angles, construction angles and any angle encountered or required. This improvement is accomplished by attaching the twin-beamed laser/scope to the invention and projecting/sighting a line along a chosen angle from a known point to any other point along the laser beam(s) or sighted line(s). Said point, or points, along the projected laser beam(s), or sighted line(s), must be located in order to achieve a proper rendition of the angle required, and the laser/scope accessory achieves that purpose in a one-step operation. It should be understood by those practiced in the art that many additional deployments of lasers or scopes might be employed for a variety of angle projections that are calculated by the measuring tool. The laser, or lasers, can be used to project planes as well as points along a line. These lasers can be deployed in many useful layouts that are directly related to any of the many angle functions to which the tool can be calibrated. It should be further understood that said laser(s), or scope(s), might also be integrated into the measuring tool, in addition to, or as an alternative to the laser (or scope) accessory. 
     A first alternate embodiment is presented in which both legs are provided with a fixed gear assembly at the axis of the two interacting legs. Both legs are similarly fit with one or more gears which are driven by the aforementioned fixed gear of the respective opposite leg. This improvement provides the ability to have additional indicia bearing gears and thus the ability to provide additional angle measurements. 
     In addition, a second alternate embodiment is presented which improves on the gear trains in both the preferred embodiment and the first alternate embodiment. As will be evident in the descriptions and drawings to follow, this second alternate embodiment employs compound gears on either or both legs of the tool to provide angle measurements to a still greater degree of precision as compared to those measurements provided by a non-compound gear train. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view of all of the components of tool  10  as assembled with the legs forming an acute angle. 
         FIGS. 2A ,  2 B, and  2 C are orthographic views of bottom leg  18 . 
         FIGS. 3A ,  3 B,  3 C and  3 D are orthographic views of top leg  14 . 
         FIG. 4  is a section view of top leg  14 . 
         FIG. 5  is a section view of top leg  14 . 
         FIGS. 6A ,  6 B and  6 C are orthographic views of gear cover  22 . 
         FIGS. 7A ,  7 B,  7 C and  7 D are orthographic views of gears  26 ,  30 ,  34 ,  38  and  42 . 
         FIGS. 8A ,  8 B and  8 C are orthographic views of ‘O’ ring  46 . 
         FIGS. 9A ,  9 B and  9 C are orthographic views of bolt  50 . 
         FIG. 10  is an exploded view of tool  10 . 
         FIG. 11  is a plan view of tool  10  as assembled in a closed position. Direction of movement is shown by arrows. Gear cover  22  is not shown. 
         FIG. 12  is a section view of tool  10  as assembled in a closed position. 
         FIGS. 13A ,  13 B,  13 C and  13 D are orthographic views of the laser device  54 . 
         FIG. 14  is a perspective view of laser device  54 . 
         FIG. 15  is a perspective view of laser device  54 . 
         FIG. 16  is a perspective view of all of the components of tool  11  as assembled with the legs forming an acute angle. 
         FIGS. 17A ,  17 B,  17 C and  17 D are orthographic views of bottom leg  19 . 
         FIG. 18  is a section view of bottom leg  19 . 
         FIG. 19  is a section view of bottom leg  19 . 
         FIGS. 20A ,  20 B,  20 C and  20 D are orthographic views of top leg  15 . 
         FIG. 21  is a section view of top leg  15 . 
         FIG. 22  is a section view of top leg  15 . 
         FIGS. 23A ,  23 B and  23 C are orthographic views of gear cover  22  of tool  11 . 
         FIGS. 24A ,  24 B,  24 C and  24 D are orthographic views of fixed gear assembly  78 . 
         FIGS. 25A and 25B  are, respectively, elevation and plan views of assembly washer  70 . 
         FIGS. 26A ,  26 B,  26 C and  26 D are orthographic views of gears  86 ,  90 ,  94 ,  98  and  102 . 
         FIGS. 27A ,  27 B and  27 C are orthographic views of ‘O’ ring  47 . 
         FIGS. 28A ,  28 B and  28 C are orthographic views of bolt  51 . 
         FIG. 29  is an exploded view of tool  11 . 
         FIG. 30  is a plan view of tool  11  as assembled in a closed position. Direction of movement is shown by arrows. Gear cover  22  is not shown. 
         FIG. 31  is a section view of tool  11  as assembled in a closed position. 
         FIG. 32  is a plan view of tool  10  as assembled in a closed position. Direction of movement is shown by arrows. Gear cover  22  is not shown. 
         FIG. 33  is an exploded view of the components shown in section view  34 . Gear cover  22  is not shown. 
         FIG. 34  is a section view which applies universally to leg  14  of tool  10  and to legs  15  and  19  of tool  11 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     As can be seen in the  FIGS. 1-12  the preferred embodiment of angle measurement tool  10  is constructed from several components including top leg  14 , bottom leg  18 , bolt  50  and a plurality of interacting gears. Legs  14  and  18  are the same width and both have a circular shaped end  20 . It should be understood that circular shaped end  20  of both leg  14  and leg  18  is a semicircle of a circle having a diameter equal to the width of leg  14  and leg  18 . It should be further understood that leg  14  and leg  18  might be wider or narrower than circular shaped end  20  where the legs extend beyond the circle described by circular shaped end  20 . It should also be understood that leg  14  and leg  18  might have non-parallel edges and tool  10  will still function as intended. Leg  14  is provided with projected axis spindle  12  at the center of the circle of which circular shaped end  20  is a part. Axis spindle socket  16  of bottom leg  18  is provided at the center of the fixed gear assembly  24  which is at the center of the circle of which circular shaped end  20  is a part. In the preferred embodiment, projected axis spindle  12  is circular in shape and has a diameter equal to or less than the diameter of axis spindle socket  16 , as shown in the figures. It should be understood that projected axis spindle  12  has a diameter equal to or less than the diameter of the axis spindle socket  16  as a function of the assembly of tool  10  and thus to facilitate precisely pivoting legs  14  and  18  secured by bolt  50 . It should be further understood that projected axis spindle  12  does not have to be in the shape of a circle in order for tool  10  to operate in the fashion described. Variable friction adjustment for the pivoting legs  14  and  18  is provided when ‘O’ ring  46  is compressed by projected axis spindle  12  into axis spindle socket  16  when bolt  50  is tightened through bolt hole  32  in leg  18  and into threaded bolt hole  36  in leg  14 , as shown in the figures. Bolt hole  32  and threaded bolt hole  36  are at the center of the circle of which circular shaped end  20  is a part. With legs  14  and  18  so engaged, fixed gear assembly  24  meshes with gear  26  in a secure and rotationally precise manner. Fixed gear assembly  24  of leg  18  is housed within fixed gear cavity  53  in leg  14  in the assembled tool  10 . When the legs  14  and  18  are pivoted around their common axis as defined by projected axis spindle  12  and axis spindle socket  16 , fixed gear assembly  24  meshes with and turns gear  26 , which in turn meshes with and turns gear  30 , which meshes with and turns gear  34 , which meshes with and turns gear  38 , which meshes with and turns gear  42 . Gears  26 ,  30 ,  34 ,  38  and  42  are each precisely located for accurate meshing and rotation by axis pivots  40  located in close tolerance within gear center holes  44  as shown in the figures. Any or all of the gears may include dial indicia  43  for the purpose of measuring any angle reading throughout a full revolution of either leg  14  or leg  18 . As indicated in  FIG. 11 , each of the gears  24 ,  26 ,  30 ,  34 ,  38  and  42  is supplied with dial indicia  43  which are comprised of straight lines radiating outward from the rotational center of these gears. The purpose of these several gears is to simultaneously provide a variety of useful angle measurements on scales specifically suited to the work at hand. For example, the indicia on fixed gear assembly  24  would be marked with a protractor scale, in a 0°-180°-0° format, providing the actual angle determined by the relative positions of leg  14  and leg  18 ; in turn, gear  26  would provide the protractor scale in a 180°-0°-180° format, gear  30  would provide a scale for the miter saw setting for miter joints, gear  34  would provide a scale for the miter saw setting for butt joints, gear  38  would provide a scale for the roof pitch reading in ‘inches of rise per lineal foot’, gear  42  would provide a scale for gradients expressed as a percentage. This example is one of many configurations possible, dependent only on the angle measurements chosen for the several gears and the relative positions of these several interchangeable gears, whose interchangeability is described below. In the preferred embodiment, fixed gear assembly  24  and gears  26 ,  30 ,  34 ,  38  and  42  are the same diameter and have the same number of gear teeth, thus gears  26 ,  30 ,  34 ,  38  and  42  are interchangeable to suit the user&#39;s preference. Gears  26 ,  30 ,  34 ,  38  and  42  may also be reversible, thus providing their reverse side for additional angle measurements. Further, the interchangeable design of the gears provides the opportunity to substitute additional gears provided with specialized scales for use in any field of endeavor requiring precise measurement and layout of particular angles for particular purposes. The various gears would be so marked, or colored, as to provide immediate identification and differentiation of the various scales. It should be apparent to those practiced in the art that interchangeability and reversibility of the gears is not a necessary component of the invention and that the various gears need not be identical in shape, interchangeable or reversible for the invention to function as intended; all such non-interchangeable and non-reversible configurations are contemplated by the inventor. A means for accurately reading these several angle measurements is provided by indicator line  28  placed along the center of gear cover  22  as shown in the figures. It should be understood that many other locations for indicator line(s)  28  on gear cover  22  and/or leg  14  are possible and are contemplated by the inventor. In the preferred embodiment gear cover  22  is transparent and indicator line  28  is provided on the surface of gear cover  22  which is closest to gears  24 ,  26 ,  30 ,  34 ,  38  and  42 . In the preferred embodiment gear cover  22  is of a form that provides beveled edges  48  which securely mate with dovetail channel  52  providing a secure location for gear cover  22 . Gear cover  22  is retained by friction, ball catch, screw(s), latch(es), magnet(s) or any of the many suitable means that should be apparent to those skilled in the art. The inventor contemplates all such means of securing gear cover  22  in its assembled location within dovetail channel  52 . So located, gear cover  22  retains gears  26 ,  30 ,  34 ,  38  and  42  securely in their proper working locations with their respective gear center holes  44  engaged with their respective axis pivots  40 . Areas of the surfaces of gear cover  22  which are not necessary areas for viewing angle readings determined by indicator line  28  may be masked so as to provide a well delineated reading environment for the several angle readings so provided. It should be understood by those practiced in the art that gear cover  22  may be opaque and readings can be accomplished through openings and/or lenses in its surface; further, it should be understood that many variations of gear retention and reading means for the various scales and indicia are possible and that all such alternatives are contemplated by the inventor. It should be understood that fixed gear assembly  24  may or may not be constructed in union with leg  18 , but in its final form tool  10  comprises a bottom leg  18  that is in fixed union with fixed gear assembly  24 , such that, in operation, leg  18  is a single piece rigidly attached to, or constructed with, fixed gear assembly  24 . In operation tool  10  simultaneously provides the miter joint angle measurement, the actual angle made by the legs  14  and  18 , the complementary angle measurement of the actual angle, the supplementary angle measurement of the actual angle, roof pitch angles, gradients and/or any angle measurement to which the several scales are adapted. It should be understood by those practiced in the art that any number and any size or variety of gears can be employed in infinite configurations and that all such alternate deployments of gears driven by fixed gear assembly  24  are contemplated by the inventor. It should be further understood by those practiced in the art that, as an alternative, supplement, or addition to the preferred embodiment in which the various gears mesh directly with one another, that a gear-toothed belt drive, friction belt drive, or similar means might be employed as an alternative, supplementary or additional means of rotating all, or some, of the various gears and/or dials and that the inventor contemplates all such variations. Further, the inventor wishes it to be understood that various other friction inducing means other than ‘O’ ring  46  should be apparent to those practiced in the art and that the inventor contemplates all such friction inducing means including the substitution of a suitable magnet for ‘O’ ring  46  and bolt  50 , said magnet located in the bottom of the axis spindle socket  16  and magnetically engaging a magnetized projected axis spindle  12 . Alternate embodiments are contemplated by the inventor in which a wide variety of angle readings may be accomplished on the top surfaces, bottom surfaces and edges of, either or both of legs  14  and  18  in which leg indicia  45  and certain scales are employed at various significant intersections of legs  14  and  18  as they bypass each other while being adjusted to the work surfaces which are being measured. 
     As can be seen in  FIGS. 3A ,  3 B,  3 C and  3 D, leg  14  is provided with three peg holes  58 ,  59  and  60 . In the preferred embodiment peg holes  58 ,  59  and  60  are flush and perpendicular with the top surface of leg  14 . Peg holes  58 ,  59  and  60  are entirely contained between the bottom and top surfaces of leg  14 . Peg holes  58 ,  59  and  60  may be similarly placed in leg  18 . Peg holes  58 ,  59  and  60  may be of the same shape as each other or they may be unique shapes.  FIGS. 13A ,  13 B,  13 C,  13 D,  14  and  15  illustrate laser device  54 . Laser device  54  is intended for projecting diametrically opposed laser beams  64  and  65  in diametrically opposite directions from each other. Laser device  54  is fitted with three pegs  67 ,  68  and  69  that precisely match the shape or shapes of peg holes  58 ,  59  and  60 . Pegs  67 ,  68  and  69  may be of the same shape as each other or they may be unique shapes. Pegs  67 ,  68  and  69  are fit perpendicular to the bottom surface  62  of laser device  54 . Bottom surface  62  is in a single plane. Bottom surface  62  is parallel with laser beams  64  and  65 . The relative positions of pegs  67 ,  68  and  69  are such that they fit respectively in peg holes  58 ,  59  and  60  and in so doing they attach laser device  54  to leg  14  or leg  18  such that laser beams  64  and  65  are parallel to the angle chosen on leg  14  or leg  18 , according to the application chosen. In the preferred embodiment pegs  67 ,  68  and  69  are circular and made of steel, either magnetized or not magnetized. It should be understood that other shapes and materials are contemplated for pegs  67 ,  68  and  69 . It should also be understood that magnetic attachment is one of many means contemplated for attaching laser device  54  to leg  14  and/or leg  18 . Laser beams  64  and  65  are energized from a battery(ies) contained within laser device  54 . Laser beams  64  and  65  may be generated from a single source and redirected on diametrically opposite paths. Laser beams  64  and  65  may also be generated separately. Laser beams  64  and  65  may be generated not only as single lines, but might also be projected as planes or any number of planes. In operation laser device  54  is affixed to tool  10  by placing pegs  67 ,  68  and  69  in peg holes  58 ,  59  and  60 . It should be recognized by those practiced in the art that various other means of attaching laser device  54  to tool  10  are possible and those ways are contemplated by the inventor. Laser beams  64  and  65  are employed to project angles. In the preferred embodiment, the union of tool  10  and laser device  54  projects laser beams  64  and  65  along one side of the angle made by the legs  14  and  18 . The other side of the angle made by the legs  14  and  18  represents the base line from which the particular angle is being calculated and projected. Whichever of the legs  14  and  18  that does not have the laser device  54  mounted on it is the leg that is set parallel to the base line. Laser beams  64  and  65  are by design always parallel to one side of the angle being measured and projected. Laser beam  64  is aimed at the spring point of the angle that is to be projected. Laser beam  65  projects the chosen angle along and beyond the angle made by the legs  14  and  18 . It should be understood by those practiced in the art that there are alternate embodiments for a laser, or lasers, in which the laser function(s) are an integral part of tool  10  in addition to laser device  54 , or in place of laser device  54 . All such alternate embodiments are contemplated by the inventor. It should be understood that sighting scopes may be substituted for, or mounted in unison with, the laser beam in laser device  54 . Laser device  54  as herein described is also intended for use with tool  11 , described in the first alternate embodiment below. Additionally, laser device  54  is intended for all alternate embodiments described herein and those other embodiments contemplated by the inventor which should be apparent to those practiced in the art. 
     The following description of the first alternate embodiment of the invention utilizes the same reference numbers as those described in the preferred embodiment above in such cases where members are the same in both embodiments. New reference numerals have been assigned in cases where members are new or in some respects different when comparing the two embodiments.  FIGS. 16-31  disclose the first alternate embodiment, tool  11 , in which leg  15  is provided with a projected axis spindle  13  at the center of the circle of which circular shaped end  20  is a part. The projected axis spindle  13  is provided with threaded bolt hole  37  at the center of the circle of which circular shaped end  20  is a part, as shown in the figures. Leg  19  is provided with axis spindle socket  84  at the center of the circle of which circular shaped end  20  is a part. Leg  19  securely houses assembly washer  70  which is so constructed as to provide a secure fit in recess  71  for rotatably engaging projected axis spindle  13  with bolt  51  as bolt  51  passes through bolt hole  33  which is provided in washer  70  at the center of the circle of which circular shaped end  20  is a part. A portion of projected axis spindle  13  is provided with projected axis spindle gear teeth  74  for reasons that will become apparent below. As shown in the figures, fixed gear assembly  25  is housed within fixed gear cavity  53  in order to drive the gear train of top leg  15  in the same fashion as fixed gear assembly  24  drives the gear train of top leg  14  of tool  10  in the preferred embodiment; the latter being illustrated in  FIG. 11 . As tool  11  is assembled, bolt  51  passes through bolt hole  33  into threaded bolt hole  37 , so assembling leg  15  and leg  19  such that they rotate securely in relation to each other with an axis the center of which is located at the center of the circle of which circular shaped end  20  is a part. ‘O’ ring  47  is provided as a frictional interface between projected axis spindle  13  and washer  70 , with adjustable rotational friction for legs  15  and  19  provided as bolt  51  is tightened or loosened to the tool user&#39;s preference. In this first alternate embodiment ‘O’ ring  47  is located in ‘O’ ring channel  80  which is concentrically located on the end of projected axis spindle  13  which houses threaded bolt hole  37  at its center. Accurate rotation of legs  15  and  19  is ensured by the close-tolerance fit of projected axis spindle  13  as it revolves within axis spindle socket  84 . Projected axis spindle gear teeth  74  are fixedly engaged with fixed gear assembly  78  by meshing with the mating internal gear  82  contained at the center of fixed gear assembly  78 ; fixed gear assembly  78  then meshes with and turns gear  86 , which in turn meshes with and turns gear  90 , which meshes with and turns gear  94 , which meshes with and turns gear  98 , which meshes with and turns gear  102 . Gears  86 ,  90 ,  94 ,  98  and  102  are each precisely located for accurate meshing and rotation by axis pivots  72  located in close tolerance within gear center holes  76  as shown in the figures. Any or all of the gears may be provided with dial indicia  43  for the purpose of determining any angle reading throughout a full revolution of either leg  15  or leg  19 . As indicated in  FIG. 30  each of the gears  78 ,  86 ,  90 ,  94 ,  98  and  102  is provided with dial indicia  43  which are comprised of straight lines radiating outward from the rotational center of these gears. The purpose of these several gears is to simultaneously provide a variety of useful angle measurements on scales specifically suited to the work at hand. For example, the indicia on fixed gear assembly  78  would be marked with a protractor scale, in a 0°-180°-0° format, providing the actual angle determined by the relative positions of leg  15  and leg  19 ; in turn, gear  86  would provide the protractor scale in a 180°-0°-180° format, gear  90  would provide a scale for the explementary angle in a 0°-360° format, gear  94  would provide a scale for the explementary angle in a 360°-0° format, gear  98  would provide a scale for the miter saw settings for constructing equiangular polygons employing miter joints, gear  102  would provide a scale for the miter saw settings for constructing equiangular polygons employing butt joints. This example is one of many configurations possible, dependent only on the angle interpretations chosen for the several gears and the relative positions of these several interchangeable gears, whose interchangeability is described below. In the preferred embodiment, fixed gear assembly  78  and gears  86 ,  90 ,  94 ,  98  and  102  are the same diameter and have the same number of gear teeth, thus gears  86 ,  90 ,  94 ,  98  and  102  are interchangeable to suit the user&#39;s preference. Gears  86 ,  90 ,  94 ,  98  and  102  may also be reversible, thus providing their reverse side for additional angle measurements. Further, the interchangeable design of the gears provides the opportunity to substitute additional gears provided with specialized scales for use in any field of endeavor requiring precise measurement and layout of particular angles for particular purposes. The various gears would be so marked, or colored, as to provide immediate identification and differentiation of the various scales. It should be apparent to those practiced in the art that interchangeability and reversibility of the gears is not a necessary component of the invention and that the various gears need not be identical in shape, interchangeable or reversible for the invention to function as intended; all such non-interchangeable and non-reversible configurations are contemplated by the inventor. 
     A means for accurately reading these several angle measurements is provided by indicator line  28  which is placed along the center of gear cover  22  as shown in the figures. It should be understood that many other locations for indicator line(s)  28  on gear cover  22  and/or legs  15  and  19  are possible and are contemplated by the inventor. In this first alternate embodiment gear cover  22  is transparent and indicator line  28  is provided on the surface of gear cover  22  which is closest to gears  78 ,  86 ,  90 ,  94 ,  98  and  102 . In this first alternate embodiment gear cover  22  is of a form that provides beveled edges  48  which securely mate with dovetail channel  52  providing a secure location for gear cover  22 . Gear cover  22  is retained by friction, ball catch, screw(s), latch(es), magnet(s) or any of the many suitable means that should be apparent to those skilled in the art. The inventor contemplates all such means of securing gear cover  22  in its assembled location within dovetail channel  52 . So located, gear cover  22  retains gears  86 ,  90 ,  94 ,  98  and  102  securely in their proper working locations with their respective gear center holes  76  engaged with their respective axis pivots  72 . Areas of the surfaces of gear cover  22  which are not necessary areas for viewing angle readings determined by indicator line  28  may be masked so as to provide a well delineated reading environment for the several angle readings so provided. It should be understood by those practiced in the art that gear cover  22  may be opaque and readings can be accomplished through openings and/or lenses in its surface; further, it should be understood that many variations of gear retention and reading means for the various scales and indicia are possible and that all such alternatives are contemplated by the inventor. It should be understood that fixed gear assembly  25  may or may not be constructed in union with leg  19 , but in its final form tool  11  comprises a bottom leg  19  that is in fixed union with fixed gear assembly  25 . In operation tool  11  simultaneously provides the miter joint angle measurement, the actual angle made by the legs  15  and  19 , the complementary angle measurement of the actual angle, the supplementary angle measurement of the actual angle, the explementary angle measurement of the actual angle, roof pitch angles, gradients, miter saw settings for constructing equiangular polygons employing miter joints, miter saw settings for constructing equiangular polygons employing butt joints and/or any angle measurement to which the several scales are adapted. It should be understood by those practiced in the art that any number and any size or variety of gears can be employed in infinite configurations and that all such alternative deployments of gears driven by fixed gear assembly  25  and projected axis spindle gear teeth  74  are contemplated by the inventor. It should be further understood by those practiced in the art that, as an alternative, supplement, or addition to the preferred embodiment in which the various gears mesh directly with one another, that a gear-toothed belt drive, friction belt drive, or similar means might be employed as an alternative, supplementary or additional means of rotating all, or some, of the various gears and/or dials and that the inventor contemplates all such variations. Further, the inventor wishes it to be understood that various other friction inducing means other than ‘O’ ring  47  should be apparent to those practiced in the art and that the inventor contemplates all such friction inducing means including the substitution of a suitable magnet for ‘O’ ring  47  and bolt  51 , said magnet located in the bottom of the projected axis spindle  13  and magnetically engaging a magnetized assembly washer  70 . In this alternate embodiment there would be no bolt  51  and assembly washer  70  would have no bolt hole  33  and thus assembly washer  70  would be secured to leg  19  with screws at a point or points located around the outer edge of assembly washer  70  or by any of several other means which should be apparent to those practiced in the art. Alternate embodiments are contemplated by the inventor in which a wide variety of angle readings may be accomplished on the top surfaces, bottom surfaces and edges of either or both of legs  15  and  19  in which leg indicia  45  are employed at various significant intersections of legs  15  and  19  as they bypass each other while being adjusted to the work surfaces which are being measured. Tool  11 , so constructed in this first alternate embodiment, provides a gear train on both legs  15  and  19  for the purpose of displaying dial indicia  43  for any and all angle measurements that might be provided by the precisely pivoting legs which pivot around the center of the circle of which circular shaped end  20  is a part. It should also be understood by those practiced in the art that the first alternate embodiment here described may be so employed so as to deploy a gear train on leg  19  alone, or leg  15  alone, as might be desired for a given assembly of the inventions here described. 
     It should be understood by those practiced in the art that there are a number of arrangements of interlocking “pins”, “springs”, “cams”, “clips”, “catches”, “levers”, “latches”, “screws”, “projections”, “magnetism”, “holes”, “grooves” and “openings” that will secure projected axis spindle  12 / 13  of leg  14 / 15  in rotational union with axis spindle socket  16 / 84  of leg  18 / 19  together such that they provide tool  10 / 11  with a leg  18 / 19  that revolves securely and accurately around projected axis spindle  12 / 13  of leg  14 / 15 . The inventor contemplates all of these embodiments, including ‘snap-together’ designs and designs employing spring loaded ball catches (with or without an ‘easy release’ button) in addition to those represented in the figures. 
     The following description of the second alternate embodiment of the invention utilizes the same reference numbers as those described in the preferred embodiment and first alternate embodiment above in such cases where members are the same as those used in either or both of those embodiments as well as in this second alternate embodiment. New reference numerals have been assigned in cases where members are new or in some respects different as utilized in the second alternate embodiment. The second alternate embodiment is applicable to any of the gear trains illustrated in the preferred embodiment and first alternate embodiment described above, as detailed below.  FIGS. 32-34  disclose the second alternate embodiment which employs compound gears, the purpose of which are to employ compound gearing to rotate certain gears at a compounded rate as compared to fixed gear assembly  24  of leg  18  of the preferred embodiment, as well as fixed gear assembly  25  of leg  19  and fixed gear assembly  78  of leg  15  of the first alternate embodiment. The compounded rate of rotation of one gear relative to another provides the ability to have certain gears with accurate fractional readings of those results provided by any of the gears described in the preferred embodiment and first alternate embodiment above. It should be understood that the number of gear teeth shown on particular gears in the Figures are not necessarily indicative of the actual number of gear teeth; the depictions of the gear teeth in the Figures are in some instances abbreviated or drawn out of scale for the purpose of clear illustration. For example,  FIG. 32  is a plan view of the second alternate embodiment&#39;s compound gear train illustrating a gear assembly  110  which revolves at the same, directly proportional, rate as either of the fixed gear assemblies  24 ,  25  or  78 , just as each of the gears in the depicted embodiments of tool  10  and tool  11  revolve at the same, directly proportional, rate as fixed gear assemblies  24 ,  25  or  78 ; in every case gear assembly  110  is either directly engaged with either of the fixed gear assemblies  24 ,  25  or  78 , or is engaged by idler gears such that gear assembly  110  rotates at the same, directly proportional, rate as the fixed gear assemblies  24 ,  25  or  78 . In the second alternate embodiment, gear  114  revolves at a rate 180 times greater than that of gear assembly  110 . A full revolution of gear  114  thus provides its full dial face for depiction of fractional readings of any single whole degree increment portrayed on gear assembly  110 , in doing so a more precise reading of a specific angle is accomplished. More specifically, in this example gear assembly  110  is providing the readings for miter cuts on a miter saw, for which the entire 360° dial must be divided into 180 equally spaced dial indicia  43 . Gear  114  thus turns one full revolution for each 1/180 th  revolution of gear assembly  110 . The result is a gear  114  which displays fractional readings in tenths, hundredths, or whichever fractional reading is desired. For the purpose of this example, gear  116  is marked as a 180°-0°-180° protractor and revolves at the same rate as gear assembly  110 . The increased number of rotations for gear  114  in comparison to gear assembly  110  and gear  116  is accomplished with compound gears as described below and illustrated in the figures.  FIG. 33  is an exploded view of the second alternate embodiment&#39;s compound gear train illustrating the components shown in section view  34  and depicted in  FIG. 34 . For the purpose of this description leg  14  is the leg upon which the second alternate embodiment&#39;s compound gear train is depicted. It should be understood that the second alternate embodiment&#39;s compound gear train is suitable for any and all of the legs  14 ,  15 , and  19  and that the inventor contemplates all such embodiments.  FIG. 34  is a section view of the second alternate embodiment depicted in plan in  FIG. 32 . As assembled, gear assembly  110  is located on axis pivot  122 ; idler gear  118  is located on axis pivot  124 ; compound gear  112  is located on top of idler gear  118  on axis pivot  124 ; idler gear  120  is located on axis pivot  126 ; gear  114  is located on top of idler gear  120  on axis pivot  126 ; and gear  116  is located on axis pivot  128 . Gear assembly  110 , while manufactured or assembled as a single piece, comprises two gears, the lower of those two gears, lower gear  106  is closest to leg  14  and engages idler gear  118 , while the upper gear, upper gear  108 , engages the upper gear  113  of compound gear  112 . Compound gear  112  is manufactured or assembled as a single piece and comprises two gears, the lower of those two gears, lower gear  111  is closest to gear  118  and engages gear  114 , while the upper gear, upper gear  113 , engages gear  108 . Idler gear  118 , being thus engaged with lower gear  106 , in turn engages idler gear  120 , which in turn engages gear  116 . This train of gears  106 ,  118 ,  120  and  116  is driven by a fixed gear assembly, either  24  or  25  or  78 , directly or through idler gear(s), the result being gears  106  and  116  which revolve at the same, directly proportional, rate as the fixed gear assemblies  24  or  25  or  78 . Upper gear  108  of gear assembly  110  contains 120 teeth around its circumference and is engaged with the 6 toothed upper gear  113  of compound gear  112 . The lower gear  111  of compound gear  112  has 45 teeth around its circumference and is engaged with 5 toothed gear  114 . In this second alternate embodiment, compound action of the upper level gears causes the compounded increase in the number of revolutions of gear  114 , providing the fractional readings desired by providing a gear  114  which turns 180 full revolutions for each single revolution of gear assembly  110 . It should be understood by those practiced in the art that infinite deployments of gear ratios may be employed in such a compound gear train and the inventor contemplates them all. It should be further understood that the second alternate embodiment&#39;s compound gear train may comprise as few or as many compound gears as desired, in any number of layers and ratios, and that the inventor contemplates all such combinations of gears. Further, it should be understood that the second alternate embodiment&#39;s compound gear train herein described is driven by either fixed gear assembly  24  or fixed gear assembly  25  or fixed gear assembly  78 , just as the fixed gear assemblies  24  and  25  and  78  drive the gear trains previously described and depicted in the preferred embodiment and first alternate embodiment denoted respectively as tool  10  and tool  11  above and in the figures. It should be further understood by those practiced in the art that, as an alternative, supplement, or addition to the second alternate embodiment in which the various gears mesh directly with one another, that gear-toothed belt drives, friction belt drives, or similar means might be employed as an alternative, supplementary or additional means of rotating all, or some, of the various gears and/or dials and that the inventor contemplates all such variations. It should be further understood that the compounding of the gear action might be accomplished with epicyclic or planetary gearing or by other gearing means and the inventor contemplates all such variations. 
     It should be further understood that any number of different scales and indicia can be deployed on any of the gears, leg surfaces or leg edges of the invention, throughout an infinite number of conceivable angle layouts. The inventor contemplates all such variations of the layout of the scales and indicia. 
     It should be understood by those practiced in the art that all of the above described gears, and those parts in contact or close proximity with those gears, as assembled, may include any of a number of common friction reduction means such as, but not limited to, low-friction materials employed in the construction of the several legs, gears, and gear covers; low-friction washers, bushings, lubricants, or bearings at points of contact between a gear face and another gear face or a gear face and either of the legs  14 ,  15  and  19  and/or gear cover  22 . Such a friction reduction means might be a separate part or might be molded, or affixed, directly onto the gear or the contact area of legs  14 ,  15 , and  19  and/or gear cover  22 . Similarly placed ball-bearings, roller bearings or other means might be used to reduce friction and might be a part of, or intermediary for, any of the gears, axis pivots, legs, or gear covers. The inventor contemplates all such friction reduction means. 
     Although specific embodiments of the invention have been described it should be recognized that additional modification and other alternate embodiments may be apparent to those skilled in the art.