Patent Publication Number: US-2006000957-A1

Title: Universally positionable mounting apparatus

Description:
FIELD OF THE INVENTION  
      The present invention relates to a universally positionable mounting apparatus, and in particular to a ball-and-socket structured for clamping one or more resiliently deformable ball mounts within a bifurcated clamping device.  
     BACKGROUND OF THE INVENTION  
      A universally positionable ball-and-socket mounting apparatus of the type disclosed by Carnevali in U.S. Pat. No. 5,845,885, entitled “U NIVERSALLY  P OSITIONABLE  M OUNTING  D EVICE ,” issued to Jeffrey D. Carnevali on Dec. 8, 1998, which is incorporated herein by reference, is generally well known and is known to be very effective for universally positioning and immoveably supporting an otherwise relatively movable object in a substantially infinite variety of combinations of fixed angular and spatial relations to a relatively stationary object or mounting surface, with the ball-and-socket mounting apparatus oriented at variable angular orientations with respect to either or both of the supported and relatively stationary objects.  
       FIG. 1  is an exploded view of the ball-and-socket mounting device  1  of the prior art as disclosed by Carnevali in U.S. Pat. No. 5,845,885;  FIG. 2  is a detail view of one portion of the mounting device  1 ; and  FIG. 3  is a detail view taken from  FIG. 2 . The mounting device  1  is formed of a split arm assembly  3  formed of a pair of elongated, relatively rigid arm sections  7  and  9 , a clamping mechanism  5  for squeezing together the pair of arm sections  7  and  9 , a compression coil spring  11  for biasing apart the pair of arm sections  7 ,  9 , and a pair of resiliently deformable ball-end mounts or “couplers”  13  and  15  with part-spherical heads  17  and  19  formed thereon, respectively, to which the split arm assembly  3  is clamped by the clamping mechanism  5  when the device  1  is put to use in mounting a relatively movable supported object on a support platform surface P in relation to a relatively stationary object or support surface S. The respective arm sections  7 ,  9  are identical, and are in operatively juxtaposed arrangement to one another along a line of juncture  21  extending therebetween. The respective arm sections  7 ,  9  have inner faces  23  thereon which are operatively opposed to one another across a plane  25  (shown in  FIG. 2 ) coincident with the line of juncture  21 ; and also pairs of corresponding first and second head or “end” portions  27  and  29  thereof that are operatively opposed to one another across the plane  25 . Pairs of recesses in the faces of the respective arm sections  7 ,  9  form pairs of operatively opposing first and second sockets  31  and  33  in the pairs of first and second heads or end portions  27 ,  29  of the arm sections  7 ,  9 , respectively. The respective pairs of sockets  31 ,  33  have part spherical surfaces at the inner peripheries thereof, and rims  35  formed thereabout on the faces  23  of the respective arm sections. The respective rims  35  are cut away by indentations  37  and  39  formed therein. The respective pairs of sockets  31 ,  33  have cruciate grooves  41  formed therein at the inner peripheries thereof.  
      The faces  23  of the respective arm sections  7 ,  9  are hollowed-out by elongated lengthwise recesses  43  formed therein between the first and second sockets  31 ,  33  of the first and second heads or end portions  27 ,  29 . Rounded bosses  45  are formed in the hollowed-out recesses  43  for retaining the compression coil spring  11  between the arm sections  7 ,  9 .  
      Apertures  47  are formed through the respective arm sections  7 ,  9  at the center of bosses or lands  49  positioned midway between the first and second sockets  31 ,  33 . Hexagonal counter-bores  51  are formed at the mouths of the apertures  47  on the outer surfaces of the arm sections  7 ,  9 . When the pair of arm sections  7 ,  9  is operatively juxtaposed to one another to form the split arm assembly  3 , the apertures  47  are arranged in a substantially coaxial relationship with one another and the compression coil spring  11  is interposed between the pair of rounded bosses  45  in the hollowed-out recesses  43  of the arm sections  7 ,  9  so as to be caged lengthwise between the pair of arm sections  7 ,  9  when the pair of arm sections is squeezed together by the clamping mechanism  5 . The compression spring  11  yieldably biases the arm sections  7 ,  9  to relatively separate from one another when the clamping mechanism  5  is relaxed, and compresses between the pair of arm sections  7 ,  9  when the arm sections are squeezed together by the clamping mechanism  5 .  
      The clamping mechanism  5  operates between the pair of arm sections  7 ,  9  along the axis  53  of the apertures  47 .  
      The clamping mechanism  5  is formed of a bolt  55  with an elongated shank  57  that is inserted through the apertures  47  of arm sections  7 ,  9 . A hexagonal head  59  at one end of the shank  57  is seated in the hexagonal counter-bore  51  of one arm section  7 , which retains the bolt  55  against rotation. A threaded end portion  61  of the shank  57  extends through the aperture  47  in the second arm section  9  and is engaged by a washer  63  and an internally threaded knob  65  with diametrically opposing wings  67  for operation as a wing nut. The knob  65  and the bolt  55  function as the clamping mechanism  5 , in that the pair of arm sections  7 ,  9  are squeezed together along the longitudinal axis  53  of the bolt  55  against the bias of the compression spring  11  by threading the knob  65  relatively inwardly along the length of the threaded end portion  61  of the shank  57  in the direction of the bolt head  59 . The pair of arm sections  7 ,  9  are allowed to separate from one another by unthreading the knob  65  along the shank  57  of the bolt in the opposite direction, to allow the bias of the compression spring  11  to separate the pair of arm sections  7 ,  9  from one another. In both cases, because of the eccentricity of the spring  11  with respect to the axis  53  of the bolt  55 , there is a differential in the reaction of the respective pairs of first and second head or end portions  27 ,  29  of the arm sections  7 ,  9  to the clamping forces generated by the clamping mechanism  5 .  
      The ball-end mounts or couplers  13  and  15  are identical and each includes a disc-shaped base  69  and  71 , respectively, with a reduced diameter stem or “neck”  73  relatively upstanding thereon, and a ball-shaped head  17 ,  19 , respectively, upstanding in turn on the neck  73 . Each ball-shaped head  17 ,  19  has a part spherical surface  75  (shown in  FIG. 2 ) about the outer periphery thereof, and a relatively resiliently pressure deformable elastomeric material in the body thereof, which renders the head relatively radially compressible. The material is relatively resilient so that, when the compressive forces are released, the body of the ball-shaped heads  17 ,  19  resumes its original ball shaped configuration at the surfaces  75  thereof. The respective ball-shaped heads  17 ,  19  are sized so that the radii thereof are approximately equal to those of the inner peripheral surfaces of the sockets  31 ,  33 , and in the operation of the device  1 , the sockets  25  in the end portions  3  of the arm sections  7 ,  9 , are engaged about the ball-shaped head  17  of the coupler  13  so as to form a ball-and-socket joint  77  (shown in  FIG. 2 ) therebetween. That is, the inner peripheral surfaces of the sockets  25  and the part spherical surfaces  75  of the first ball-shaped head  17  are caused to substantially coincide with a first circle of revolution  83  (shown in  FIG. 3 ) having its center at a first locus  79  of the head  17 .  
      The inner peripheral surfaces of the sockets  26  and the part spherical surfaces  75  of the second ball-shaped head  19  are caused to substantially coincide with a second circle of revolution (not shown) having its center at a second locus  81  of the head  19 .  
      Later in the operation of the device, the inner peripheral surfaces of the sockets  26  in the end portions  4  of the arm sections  7 ,  9  are caused to engage about the surfaces  75  of the ball-shaped head  19  of the coupler  15  to form a similar joint therebetween, but only that between the ball-shaped head  17  and the sockets  25  is shown in the drawings. In each case, the pressure deformable material in the body of the head  17 ,  19  enables the head to be squeezed between the surfaces  75  thereof to less than the diameter of the circle of revolution  83  with which the respective surfaces of the sockets  31 ,  33  and the ball-shaped head  17 ,  19  coincide. Moreover, the resiliency of the material in the body of the ball-shaped head  17 ,  19  enables the surfaces  75  thereof to resume coincidence with that circle when the compression on the head is released in a subsequent stage in the operation of the device.  
      The base  69 ,  71  of each respective coupler  13 ,  15  has multiple clearance holes  85  therein for screws (not shown) for fastening the coupler  13  to an object to be supported, hereinafter “object” (not shown), and for fastening the coupler  15  in like manner to the support surface S.  
      The mounting device  1  has two principal stages of operation: a first stage in which the split arm assembly  3  and the clamping mechanism  5  make a loose connection between the object and the support surface S; and a second stage in which that connection is rigidified so as to support one the object on the support surface S. Between the two stages, there is an intermediate stage in which the angular orientation of the line of juncture  21  between the pair of arm sections  7 ,  9  is variable with respect to either or both of the object and the support surface S, so as to vary the angular orientation of object with respect to the support surface S. The connection may be made to have sufficient rigidity at one end thereof,  3 ,  13 ,  3 , moreover, that the adjustment can be made at the other end thereof,  4 ,  15 ,  4  while the rigidity of the one end  3 ,  13 ,  3  is relied on to maintain the angular orientation of the line of juncture  21  with respect to the object at the one end of the connection.  
      To carry out the operation, initially, the two couplers  13 ,  15  are secured to the object and the support surface S, respectively. The two couplers  13 ,  15  are also arranged so that the first and second ball-shaped heads  17 ,  19  are spaced apart from one another at the first and second loci  77 ,  81 , respectively, adjacent the opposite ends of a line of juncture  21  along which the mounting device  1  is to be interposed between the object and the support surface S. This leaves part spherical surfaces  75  of the first ball-shaped head  17  disposed on opposite sides of the plane  25  (shown in  FIG. 2 ) of the line of juncture  21 , and substantially in coincidence with a first circle of revolution  83  (shown in  FIG. 3 ) having its center at the first locus  79  of the first ball-shaped head  17 . Either simultaneously with or subsequent to securing the couplers to the object relative to the support surface S, the split arm assembly  3  is arranged about the line of juncture  21  so that the pair of arm sections  7 ,  9  is operatively juxtaposed to one another along the line of juncture  21  between the spaced first and second loci  21  and  23  of the first and second ball-shaped heads  17 ,  19 ; and the pairs of corresponding first and second end portions  3  and  4  of the arm sections  7 ,  9  are operatively opposed to one another across the plane  25  of the line of juncture  21 . The faces  23  of the arm sections  7 ,  9  are likewise operatively opposed to one another across the plane  25  of the line of juncture  21 .  
      The compression coil spring  11  and the clamping mechanism  5  are engaged between the arm sections  7 ,  9  so as to hold the pair of arm sections  7 ,  9  together, and the knob  65  is threaded onto the threaded end portion  61  of the shank  57  of the bolt  55  and engaged sufficiently to apply initial clamping forces to the pair of arm sections  7 ,  9  and thereby squeeze the arm sections  7 ,  9  together relatively crosswise the plane  25  of the line of juncture  21 . As the arm sections  7 ,  9  are squeezed together, the compression spring  11  produces a differential in the reaction of the respective pairs of first and second end portions  3  and  4  of the arm sections  7 ,  9 , so that the arm sections  7 ,  9  assume a relatively transversely contracted disposition thereof about the first ball-shaped head  17  in which the pair of first sockets  25  is operatively engaged about the peripheral surfaces  75  of the first ball-shaped head  17  in substantial coincidence with the first circle of revolution  83 . At this point in the operation, the pair of second end portions  4  of the arm sections  7 ,  9  is spaced apart from one another about the second ball-shaped head  19  to the extent that although the arm sections  7 ,  9  forms a connection between the first and second ball-shaped heads  17 ,  19 , at the second ball-shaped head  19  the connection allows the arm sections  7 ,  9  to be squeezed further together about the second ball-shaped head  19 . This completes the first stage in the operation of the device and inasmuch as at the conclusion of it, the pair of first sockets  25  forms a first ball and socket joint  77  (shown in  FIG. 2 ) with the outer peripheral surfaces  75  of the first ball-shaped head  17 . The first ball-shaped head  17  and the arm sections  7 ,  9  may be pivoted in relation to one another at the first joint  77  to position the line of juncture  21  at any angular orientation desired with respect to either or both of the object  6  and the support surface S while the first and second ball-shaped heads  17 ,  19  remain connected by the device  1 . However, because of the differential in the reaction of the pairs of end portions  3  and  4  of the arm sections  7 ,  9 , the connection may be made tighter at the end thereof coupled to the first head  17 ; and an adjustment may be made more readily at the end of the connection at the second head  19 . An adjustment may be made at either end, however, and while such adjustment is being made, the connection remains intact, so that only limited assistance from an operator is needed to support the object during this intermediate stage.  
      When an angular orientation for the line of juncture  21  has been selected, the device  1  is put through the second stage in the operation thereof to rigidify the connection between the object and the support surface S. Accordingly, the knob  65  is further engaged with the threads  61  on the bolt shank  57  to apply additional clamping forces to the arm sections  7 ,  9 , and to apply those forces to the extent necessary to rigidify the connection between the first and second ball-shaped heads  17 ,  19  at the selected angular orientation of the line of juncture  21  with respect to the object and support surface S. When the clamping mechanism  5  has completely overcome the biasing forces of the compression spring  11 , then the sockets  26  in the end portions  4  of the arm sections  7 ,  9  are squeezed further together about the second ball-shaped head  19  at the second locus  81 .  
      The inherent resiliency in the body of the first head  17  permits the first joint  77  to be restored if desired to enable a further adjustment to be made in the orientation of the line of juncture  21 , by releasing the clamping mechanism  5  relatively crosswise the plane  25  of the line of juncture  21  until the arm sections  7 ,  9  and the first head  17  can be pivoted in relation to one another to a new location at which the line of juncture  21  is repositioned at a different angular orientation with respect to the object and the support surface S.  
      Alternatively, while the clamping mechanism is being released, the arm sections  7 ,  9  may be retracted in relation to one another to a “third” position of the bifurcated arm assembly  3  in which the faces  23  of the arm sections  7 ,  9  are sufficiently spaced apart from one another about the head  19  of the coupler  15 , that the head  19  is detachable from the bifurcated arm assembly  3  and vice versa. In addition, the space between the first and second loci  77 ,  81  of the pair of couplers  13 ,  15  may be of such length, due to the length of the split arm assembly  3 , that when the second head  19  is detached from the bifurcated arm assembly  3  and vice versa, the end portions  4  of the arm sections can be pinched together against the bias of the compression spring  11  to separate the pair of sockets  25  from one another to the extent that the first head  17  can be detached from the arm sections  7 ,  9  and vice versa.  
      When operatively opposed to one another, the indentations  37 , formed in the rims  35  of the sockets  31 ,  33  form slots therebetween that are greater in width than the necks  73  of the couplers  13 ,  15 , so that the angular orientation of the line of juncture  21  can be made to extend at right angles to the neck of either coupler, if desired, for example, by rotating the bifurcated arm assembly  3  about the head  17 ,  19  of the respective coupler  13 ,  15  until the neck  73  engages in the slot formed by the indentations. Similarly, the indentations  39  formed in the rims  35  of the sockets  31 ,  33  at the ends of the arm sections form “fish mouths” therebetween that are sufficiently wider than the necks  73  of the couplers  13 ,  15 , that the bifurcated arm assembly can be rotated about a head, for example, the head  17  of the coupler  13 , to an angular orientation in which the plane  25  of the line of juncture  21  extends at an oblique angle to the head.  
      The indentations  37 ,  39  and the cruciate grooves  41  in the sockets  31 ,  33  also provide recesses into which the bodies of the respective heads  17 ,  19  can deform when they are subjected to compression by the pairs of sockets  31 ,  33  corresponding thereto.  
      The respective heads  17 ,  19  are formed of nitrile rubber material at the surfaces  75  thereof. Other materials, including other hardened rubber and elastomer materials, may be employed. The materials are commonly given a Shore A durometer of between about 30-100 and preferably between about 60-100. Most preferable is a Shore A durometer of about between 85-90. In some versions, the heads  17 ,  19  have a Shore D hardness of between 40 and 70.  
      While supporting the object on the support surface S, the mounting device  1  operates to attenuate or “damp” transmission of mechanical vibrations between the object and support surface S, and in fact to function as a shock absorber between the two. Furthermore, the heads  17 ,  19  act as electrically insulative media in the combination, so that any stray current will not travel between the object and support surface S.  
      Another universally positionable ball-and-socket mounting apparatus of the type described by Carnevali in U.S. Pat. No. 6,561,476, “P OSITIVELY -P OSITIONABLE  M OUNTING  A PPARATUS ,” issued to Jeffrey D. Camevali on May 13, 2003, which is incorporated herein by reference, is also generally well known and is known to be very effective for universally positioning and immoveably supporting an otherwise relatively movable object in a substantially infinite variety of combinations of fixed angular and spatial relations to a relatively stationary object or mounting surface, with the ball-and-socket mounting apparatus oriented at variable angular orientations with respect to either one or the other of the supported and relatively stationary objects.  
       FIG. 4  is a detailed side view illustration of a positively-positionable positionable wheel-and-axle mounting apparatus  101  of the prior art as disclosed by Carnevali in U.S. Pat. No. 6,561,476 as substantially rigid positively-positionable wheel-and-axle mounting coupler  102  having a substantially rigid multisided stem or axle portion  103  with a substantially rigid disc-shaped button or wheel portion  105  mounted at one end. The axle portion  103  projects from a surface base  107  fixed to the support surface S. The support base  107  and the positively-positionable wheel-and-axle mounting coupler  102  projecting from it are formed of a relatively rigid material, such as a metal or hard plastic.  
      According to one embodiment of the invention, the axle portion  103  is formed with a convex polygon shape, having multiple flat or planar surfaces  109   a ,  109   b ,  109   c  through  109   n . The axle portion  103  is long enough to ensure that a portion of each of a pair of arm sections  111  and  113  (shown in  FIG. 7 ) of another split-arm assembly  114  (described below) can obtain a suitable grip between the wheel portion  105  which is sufficiently thick to support at least a minimum predetermined load applied to the split-arm assembly  114 .  
       FIG. 5  is a cross-section view taken through the multisided axle portion  103  of the positively-positionable mounting apparatus  101  illustrated in  FIG. 4 . Each of the multiple surfaces  109   a  through  109   n  is rotated at substantially the same angle relative to the adjacent surfaces on either side, the angles summing to 360 degrees. According to the exemplary embodiment illustrated, the axle portion  103  has a convex polygon-shape that includes eight adjacent surfaces  109   a - h . Other equivalent embodiments of the invention optionally include more or less adjacent surfaces  109   a - n . However, the adjacent surfaces  109   a - n  are sufficiently small in number to ensure positive positioning without slipping relative to the portions of the operatively juxtaposed convex polygon-shaped socket sections of the arm sections  111 ,  113  which are structured to fit around the convex polygon-shaped axle portion  103 . Such positive positioning is ensured primarily by a length of each of the surfaces  109   a - n  that is significant relative to the thickness of the multisided axle portion  103 . Accordingly, the number of adjacent surfaces  109   a - n  is in the range of about three or four to as many as about a dozen or more.  
       FIG. 5  also shows an underside  115  of the disc-shaped wheel portion  105  in relation to the axle portion  103 . The wheel portion  105  is formed substantially concentric with the axle portion  103 , such that the two portions  103  and  105  share a common longitudinal axis A. The disc-shaped wheel portion  105  has a sufficiently large diameter relative to the thickness of the axle portion  103  to ensure that a portion of each of the arm sections  111 ,  113  of the split-arm assembly  114  can obtain a suitable grip to support a minimum predetermined load applied to the split-arm assembly  114 .  
       FIG. 6  illustrates one embodiment of one of two relatively rigid arm sections  111 ,  113  of which the split-arm assembly  114  is formed, as disclosed in U.S. Pat. No. 6,561,476. The other arm section  113  is formed similarly to the described arm section  111 . The arm sections  111 ,  113  are formed of a relatively rigid material, such as a metal or hard plastic. The arm section  111  is formed as a short rod which is optionally hollow except for its functional features. One functional feature is a convex polygon-shaped aperture  117  formed in an end face  119  of the arm section  111 . The convex polygon-shaped aperture  117  is provided by multiple substantially planar interior wall surfaces  121   a  through  121   n  that are formed substantially perpendicularly to the end face  119 . The wall surfaces  121   a  through  121   n  are formed to mate with the planar surfaces  109   a  through  109   n  of the axle portion  103  of the positively-positionable wheel-and-axle mounting platform P. Thus, each wall surface  121   a  through  121   n  is rotated from the adjacent wall surfaces at an angle substantially equal to that of the angles between the planar surfaces  109   a  through  109   n  of the axle portion  103 .  
      The end portion  178  of the arm section  111  is formed with a thickness that is at least slightly less than the length of the planar surfaces  109   a  through  109   n  of the axle portion  103 , both of which are formed with sufficient length or thickness to ensure that the end face  119  of each of the arm sections  111 ,  113  can support a minimum predetermined load applied to the split-arm assembly  114 . An interior portion  122  of the arm section  111  is recessed or hollowed out under the end face  119  to provide a space large enough to accept the disc-shaped wheel portion  105  of the wheel-and-axle assembly  14 . Thus, the end face  119  fits in the gap between the mounting base  107  and the disc-shaped wheel portion  105  of the wheel-and-axle assembly  14 . The matching sizes, shapes, and angles between the interior wall surfaces  121   a  through  121   n  exterior axle surfaces  109   a  through  109   n  permit the axle portion  103  to nest within the shaped aperture  117  of the arm section  111  in each of several consecutive positively locking positions.  
      Another functional feature is a socket-shaped cavity  123  formed at the other end of the arm section  111  distal from the end face  119 . The socket-shaped cavity  123  is formed with a substantially smooth, part hemispherical inner peripheral surface approximately the same diameter as the pressure deformable ball mount or part-spherical head  17  of the type disclosed by Carnevali in U.S. Pat. No. 5,845,885, which is incorporated herein by reference. A sector or portion of the part hemispherical socket-shaped cavity  123  at the end face of the arm section  111  is removed, for example, in a plane cutting perpendicular to the length of the arm section  111 . The arm section  111  thus has the indentation  39  formed as a generally hemicircular opening in the end face opposite from the end face  119 . The diameter of the hemicircular opening  39  is large enough to accept the columnar rod or neck  73  connecting the ball mount  17  to the mounting base  69 , as illustrated in  FIG. 7 . According to one embodiment of the invention, the hemicircular opening  39  in the end face opposite from the end face  119  of the arm sections  111 ,  113  is large enough relative to the columnar neck  73  to permit the ball mount  17  to rotate into different angular positions relative to the arm sections  111 ,  113  when assembled into the split-arm assembly  114 .  
      According to one embodiment of the invention, the part hemispherical socket-shaped cavity  123  optionally includes one or more relief or indentation  37 . The one or more reliefs  37  are shown in  FIG. 7  at the opposite extents of the part hemispherical socket-shaped cavity  123 . Thus structured, the reliefs  37  in one arm section  111  cooperate with corresponding reliefs  37  in the other arm section  113  to provide side openings in the socket large enough to permit entry of the neck  73 . Thus, the cooperating reliefs  37  in the two arm sections  111 ,  113  expand the original conical range of motion of the split-arm assembly  114  relative to the ball mount  17  into a fan-shaped section, as disclosed in U.S. Pat. No. 6,561,476, which is incorporated herein by reference. According to one embodiment of the invention, the cooperating reliefs  37  permit the split-arm assembly  114  to rotate within the fan-shaped section as much as +/−90 degrees or more relative to the ball mount  17 .  
      According to one embodiment of the invention, each of the arm sections  111 ,  113  is also formed with the aperture  47  that is sized to pass a shoulder bolt or another equivalent threaded fastener, as described in  FIG. 7 . The aperture  47  is optionally surrounded by the shoulder or boss  49  that helps support the clamping force applied by the threaded clamp assembly  5  when the arm sections  111 ,  113  are secured together.  
       FIG. 7  illustrates one embodiment of the ball mount  17  by which objects are securely and fixedly mounted relative to a fixed surface by the multiply configurable support and multiply positionable mounting platform apparatus  10  of the prior art as disclosed by Carnevali in U.S. Pat. No. 6,561,476. As disclosed by Carnevali in U.S. Pat. No. 5,845,885, which is incorporated herein by reference, the ball mount or ball-shaped head  17  is formed on the neck  73  projecting from the mounting base  69 . The ball mount or head  17 , neck  73  and mounting base  69  together form the ball mount assembly or “coupler”  13  wherein the mounting base  69  is formed with the substantially planar platform surface P opposite from the ball head  17  and neck  73  for permanently attaching the object to be supported (object) using either mechanical fasteners through the clearance holes  85  or an adhesive bond such as a resilient adhesive pad, commonly known as a Pressure Sensitive Adhesive (PSA)  125 , applied between the platform surface P and the object. The ball mount  17  is a substantially smooth, part spherical-shaped member formed of a pressure deformable, resilient elastomeric material, which renders part spherical the ball mount  17  relatively radially compressible. The ball mount  17  is structured for attachment of an external device. The pressure deformable material of which the ball mount  17  is composed permits its part-spherical shape to be deformed to conform to the internal contours of the arm sections  111 ,  113  when sufficient compressive pressure is applied. The pressure is applied by the threaded clamp assembly  5 . The resilient nature of the material causes it to resume its original part spherically-shaped configuration when the clamp assembly  5  is released, whereby the compressive pressure is removed.  
       FIG. 7  illustrates assembly and operation of the multiply positionable mounting apparatus  101 . Accordingly, the split-arm assembly  114  is simultaneously assembled with the ball mount or ball-shaped head  17  at one end and the positively-positionable wheel-and-axle mounting platform coupler  102  at the opposite end. The pair of rigid arm sections  111 ,  113  of the split-arm assembly  114  are secured together by the threaded clamp assembly  5  embodied, for example, the threaded shoulder bolt  55  and the wing nut-type knob  65 . Alternatively, the clamp assembly  5  is formed with either a cam or another over-center clamp (not shown) that may include means, such as threaded means, for adjusting the clamping pressure exerted upon the rigid arm sections  111 ,  113 .  
      During assembly, the pair of rigid arm sections  111 ,  113  are operatively juxtaposed to simultaneously form one socket section structured to fit securely around the ball-shaped head  17  and another socket section provided by the pair of convex polygon-shaped apertures  117  structured to fit securely around the positively-positionable wheel-and-axle mounting platform coupler  102 . The bolt  55  and nut  65  clamp the arm sections  111 ,  113  securely around both the ball-shaped head  17  and the positively-positionable wheel-and-axle mounting platform coupler  102  in any of a variety of relative rotational orientations. The ball mount or ball-shaped head  17  can be oriented anywhere within a conical zone or a fan-shaped zone, and can be rotated throughout a full 360 degrees about the longitudinal axis L of the of the ball mount or ball-shaped head  17  and the cylindrical female collar  94 . Simultaneously, the coupler portion C may be oriented in a fixed orientation with the positively-positionable wheel-and-axle mounting platform coupler  102  in one of several rotationally consecutive positively locking positions.  
      The convex polygon-shaped apertures  117  of the pair of operatively juxtaposed rigid arm sections  111 ,  113  cooperate to form a convex polygon-shaped collar around the positively-positionable wheel-and-axle mounting platform coupler  102  at one end of the split-arm assembly  114 . The planar surfaces  109   a  through  109   n  of the axle portion  103  coordinate with the planar wall surfaces  121   a  through  121   n  of the shaped apertures  117  to orient the split-arm assembly  114  in any of the several rotationally relative positively locking positions. While the axle portion  103  is nested within the shaped apertures  117 , the disc-shaped wheel portion  105  is fitted within the hollowed out socket portion  122  of the arm sections  111 ,  113  and captured behind the end face  119 .  
      The socket-shaped cavities  123  of the pair of operatively juxtaposed rigid arm sections  111 ,  113  also coordinate to form a collar around the ball mount or ball-shaped head  17  at the other end of the split-arm assembly  114 . The columnar neck  73  between the ball mount or head  17  and the mounting base  69  cooperates with the generally circular openings  39  in the pair of arm sections  111 ,  113  to orient the split-arm assembly  114  in any of the several relative locking positions within conical or fan-shaped zones.  
      The operatively juxtaposed rigid arm sections  111 ,  113  are clamped together by the bolt  55  passing through the respective apertures  47  and threading the nut  65  onto the bolt  55 . The apertures  47  are formed with the hexagonal counter-bores  51 . The hexagonal head  59  at one end of the shank  57  is seated in the hexagonal counter-bore  51  of one arm section  111 , which retains the bolt  110  against rotation during tightening and loosening of the nut  65 .  
      Clamping pressure is applied by tightening the head of bolt  55  and face of the nut  65  against outer surfaces of the respective arm sections  111 ,  113 . The clamping pressure is thus be applied in stages. Applying the clamping pressure in stages causes the operative portions of the positively-positionable wheel-and-socket coupler  102  of the multiply positionable mounting apparatus  101  to become substantially fixed or locked in one relative rotational position, while the operative portions of the ball-and-socket structure remain loose and, therefore, relatively adjustable. The partially applied clamping pressure causes the multiple flat or planar surfaces  109   a  through  109   n  of the axle portion  103  of the positively-positionable wheel-and-socket apparatus  101  to nest with the corresponding planar wall surfaces  121   a  through  121   n  of the shaped apertures  117 . The partially applied clamping pressure thus securely orients the split-arm assembly  114  relative to the support base  107 .  
      Continued tightening of the nut  65  onto the bolt  55  increases the applied clamping pressure. The increased clamping pressure brings the inner peripheral surfaces of the socket-shaped cavities  123  into snug contact with the pressure deformable ball mount or ball-shaped head  17 , such that motion of the split-arm assembly  114  relative to the mounting base  69  of the ball mount assembly or coupler  13  becomes more difficult. When forced together across the pressure deformable ball or head  17  by tightening the nut  65  onto the bolt  55 , the inner peripheral surfaces of the part hemispherical socket-shaped cavities  123  are forced closer together than the unconstrained diameter of the deformable ball or head  17 . Firmly tightening the nut  65  onto the bolt  55  applies sufficient clamping pressure between the cooperating socket-shaped cavities  123  and the pressure deformable ball or head  17  to deform the normally spherical shape of the ball or head  17 . The split-arm assembly  114  thus interlocks the ball or head  17  in a relative angular orientation with the arm sections  111 ,  113  by conforming the pressure deformable ball or head  17  to the inner peripheral surfaces of the socket-shaped cavities  123 . The firmly applied clamping pressure thus securely orients the split-arm assembly  114  relative to the mounting base  69  of the ball mount assembly  13 . Thus deformed, the ball or head  17  is substantially immovably secured relative to the socket-shaped cavities  123  and the split-arm assembly  114 .  
      Upon partial release of the clamping force, the ball or head  17  resiliently resumes its original part spherical-shaped configuration. In such uncompressed and part spherical condition, the ball or head  17  is again angularly and rotationally rotatable relative to the mating concavely-shaped socket surfaces  123  of the arm sections  111 ,  113 . The ball or head  17  is optionally angularly and/or rotationally rotated to a different orientation relative to the split-arm assembly  114 . The pressure is again applied by the clamp assembly  5  to the ball or head  17 . The pressure again relatively radially compresses the pressure deformable elastomeric material into a shape that mates with the inner peripheral surfaces of the socket-shaped cavities  123 . The ball or head  17  and the attached mounting base  69  are thereby again locked in a fixed angular and rotational orientation with the split-arm assembly  114 .  
       FIG. 8  is another embodiment of the positively-positionable positionable wheel-and-axle mounting apparatus  101  of the prior art as disclosed by Carnevali in U.S. Pat. No. 6,561,476 having the pressure deformable ball mount or part-spherical head  17  embodied as a partial geodesic sphere  127  of the type disclosed by Carnevali in U.S. Pat. No. 6,561,476 and in U.S. Pat. No. 6,581,892, entitled “G EODESIC M   OUNTING  A PPARATUS ,” issued Jun. 24, 2003, which is incorporated herein by reference. The partial geodesic sphere  127  is a part spherical body formed of a substantially rigid material and having a surface that is formed with a plurality of discrete substantially planar, triangularly-shaped facets  129  intersecting at angular joints. Each triangular facet  129  is formed as a substantially planar surface oriented perpendicularly to a radius from a spherical center point of part-spherical geodesic sphere  127 . Each triangular facet  129  is one segment of the 3-dimensional geodesic sphere  127 . Geodesic sphere  127  is embodied in any number of multifaceted 3-dimensional forms. The partial geodesic sphere  127  is formed on the stem or neck  73  projected from the mounting base  69  formed with the substantially planar platform surface P. Matching facets  131  are formed on the inner surface  133  of the socket-shaped cavities  123  of the pair of operatively juxtaposed rigid arm sections  111 ,  113 .  
      However, these well-known universally positionable ball-and-socket mounting apparatus are limited by the bifurcated clamping devices by which they support the otherwise relatively movable object.  
     SUMMARY OF THE INVENTION  
      The present invention is a mounting device that overcomes limitations of the prior art by providing first and second couplers that are spaced apart along a line of juncture extending therebetween and a split arm assembly that is formed by first and second arm sections having sockets formed at opposite ends thereof, the sockets being structured to cooperate with the couplers. A clamping mechanism is structured to squeeze together the first and second arm sections with the pair of couplers captured between the cooperating sockets thereof A third coupler is secured to an external surface of one of the first and second arm sections between the opposite ends thereof.  
      According to another aspect of the invention, the clamping mechanism is formed of a threaded rod operating through apertures formed in the arm sections. The third coupler is formed with internal threads that mate with one end of the threaded rod, and a hexagonal or other non-round shape that is matched by a similarly non-round shape formed in an external surface of one of the arm sections surrounding the aperture formed therein for constraining the threaded rod from rotating relative to the arm section while the nut is being moved along its length. A nut with threads that mate with an end of the threaded rod, such as a wing nut or a knob having internal threads, is engaged to move along the length of the threaded rod external of the split arm assembly at the end opposite from the third coupler. Moving the nut along the threaded rod serves to squeeze the arm sections together with the sockets clamping the couplers in substantially fixed mutual rotational angular and spatial orientation. A second split arm assembly is optionally coupled in like manner to the third coupler, whereby a fourth coupler that is spaced apart form the third coupler along another line of juncture extending therebetween is clamped in substantially fixed mutual rotational, angular and spatial orientation with the third coupler when the second split arm assembly is squeezed together with the sockets formed therein clamping the third and fourth couplers therebetween.  
      According to another aspect of the invention, the threaded rod of the clamping mechanism is a bolt having the threaded rod formed on one face of a non-round head, and having a stem formed on the opposite face with the third coupler formed on the stem spaced away from the head. The non-round head of the bolt cooperates with the non-round shape formed in an external surface of one of the arm sections surrounding the aperture formed therein for constraining the threaded rod from rotating relative to the arm section while the nut is being moved along its length. Moving the nut along the threaded rod of the bolt serves to squeeze the arm sections together with the sockets clamping the couplers in substantially fixed mutual rotational, angular and spatial orientation.  
      Other aspects of the invention are detailed herein. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The foregoing aspects and many of the attendant advantages of this invention will become more readily appreciated as the same becomes better understood by reference to the following detailed description, when taken in conjunction with the accompanying drawings, wherein:  
       FIG. 1  is an exploded view of the ball-and-socket mounting device of the prior art as disclosed by Carnevali in U.S. Pat. No. 5,845,885;  
       FIG. 2  is a detail view of one portion of the mounting device of the prior art illustrated in  FIG. 1 ;  
       FIG. 3  is a detail view of one portion of the mounting device of the prior art illustrated in  FIG. 2 ;  
       FIG. 4  is a detailed side view illustration of a coupler portion of a positively-positionable positionable wheel-and-axle mounting apparatus of the prior art as disclosed by Carnevali in U.S. Pat. No. 6,561,476;  
       FIG. 5  is a cross-section view taken through the coupler portion of the positively-positionable positionable wheel-and-axle mounting apparatus of the prior art illustrated in  FIG. 4 ;  
       FIG. 6  illustrates one embodiment of one of two relatively rigid arm sections of a split-arm assembly of the positively-positionable positionable wheel-and-axle mounting apparatus of the prior art structured for operation with the coupler portion illustrated in  FIG. 4 ;  
       FIG. 7  illustrates one embodiment of the apparatus of the prior art as disclosed by Carnevali in U.S. Pat. No. 6,561,476 by which objects are securely and fixedly mounted relative to a fixed support surface;  
       FIG. 8  is another embodiment of the positively-positionable positionable wheel-and-axle mounting apparatus of the prior art as disclosed by Carnevali in U.S. Pat. No. 6,561,476;  
       FIG. 9  is an exploded view of a ball-and-socket mounting device of the present invention having the split arm assembly clamped by the clamping mechanism of the present invention;  
       FIG. 10  illustrates an alternative embodiment of the ball-and-socket mounting device of the present invention having the split arm assembly clamped by an alternative clamping mechanism of the present invention;  
       FIG. 11  is a side view illustration of one embodiment of the ball-and-socket mounting device of the present invention; and  
       FIG. 12  is a side view illustration of one alternative embodiment of the ball-and-socket mounting device of the present invention. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENT  
      In the Figures, like reference numerals indicate like elements.  
       FIG. 9  is an exploded view of a ball-and-socket mounting device  200  based upon and having at its core the ball-and-socket mounting device  1  of the prior art as disclosed by Carnevali in U.S. Pat. No. 5,845,885, the complete disclosure of which is incorporated herein by reference, so that in the Figures, like reference numerals indicate like elements. The mounting device  200  is formed of the split arm assembly  3  formed of the pair of elongated relatively rigid arm sections  7  and  9 , the compression coil spring  11  for biasing apart the pair of arm sections  7 ,  9 , and the pair of resiliently deformable ball-end mounts or “couplers”  13  and  15  with the part-spherical heads  17  and  19  formed on the reduced diameter stems or “necks”  73  relatively upstanding on base  69  and  71 . The split arm assembly  3  is clamped to the part-spherical heads  17  and  19  of the ball-end mounts  13 ,  15 , respectively, by a clamping mechanism  202  of the present invention when the device  200  is put to use in mounting a relatively movable supported object on the support platform P in relation to the relatively stationary object or support surface S. The respective arm sections  7 ,  9  are substantially identical, and are in operatively juxtaposed arrangement to one another along a line of juncture  21  extending between the first locus  79  at the center of the head  17  and the second locus  81  at the center of the head  19 . The respective arm sections  7 ,  9  have the inner faces  23  (shown in  FIG. 1 ) thereon which are operatively opposed to one another across the plane  25  (shown in  FIG. 2 ) coincident with the line of juncture  21 . The respective arm sections  7 ,  9  also include the pairs of corresponding first and second head or “end” portions  27  and  29  thereof that are operatively opposed to one another across the plane  25 , as described herein, having the pairs of recesses in the faces of which are formed the pairs of operatively opposing first and second sockets  31  and  33 , respectively. The respective pairs of sockets  31 ,  33  include the rims  35  that are cut away by the indentations  37  and  39  formed therein. The respective pairs of sockets  31 ,  33  optionally include the cruciate grooves  41  formed therein at the inner peripheries thereof, as discussed herein.  
      The faces  23  of the respective arm sections  7 ,  9  are hollowed-out by the elongated lengthwise recesses  43  formed therein between the first and second sockets  31 ,  33  of the first and second heads or end portions  27 ,  29 . Rounded bosses  45  are formed in the hollowed-out recesses  43  for retaining the compression coil spring  11  between the arm sections  7 ,  9 .  
      The apertures  47  are formed through the respective arm sections  7 ,  9  at the center of the bosses or lands  49  that are positioned midway between the first and second sockets  31 ,  33 . The hexagonal counter-bores  51  are formed at the mouths of the apertures  47  on the outer surfaces of the arm sections  7 ,  9 . When the pair of arm sections  7 ,  9  is operatively juxtaposed to one another to form the split arm assembly  3 , the apertures  47  are arranged in a substantially coaxial relationship with one another and the compression spring  11  is interposed between the pair of rounded bosses  45  in the hollowed-out recesses  43  of the arm sections  7 ,  9  so as to be caged lengthwise between the pair of arm sections  7 ,  9  when the pair of arm sections is squeezed together by the clamping mechanism  202  of the present invention. The compression spring  11  yieldably biases the arm sections  7 ,  9  to relatively separate from one another when the clamping mechanism  202  is relaxed, and compresses between the pair of arm sections  7 ,  9  when the arm sections are squeezed together by the clamping mechanism  202 .  
      The clamping mechanism  202  operates between the pair of arm sections  7 ,  9  along the axis  53  of the apertures  47 .  
      The clamping mechanism  202  of the present invention is formed of a threaded connector  204  embodied, by example and without limitation, as an elongated threaded rod  206  that is structured to threadedly engage and mate with the internally threaded knob  65  and sized to be inserted through the apertures  47  of arm sections  7 ,  9  as well as the one or more washers  63 . A discrete resiliently deformable ball-end mount  208  is provided with a one of the part-spherical heads  17 ,  19  of the type disclosed by Carnevali in U.S. Pat. No. 5,845,885, which is formed of a resiliently deformable elastomeric material with a substantially smooth part spherical outer surface  75 , as described by Carnevali in U.S. Pat. No. 5,845,885. The ball-end mount  208  has at its center the first locus  209  of, by example and without limitation, another of the ball-and-socket mounting devices  1  of the prior art as disclosed in U.S. Pat. No. 5,845,885, and is operable with such a device  1  so as to form therewith one of the ball-and-socket type joints  77 .  
      The part-spherical ball-end mount  208  is provided, by example and without limitation, on a short substantially rigid and internally-threaded stem  210  that is structured on an extended stem portion  210   a  (shown in dashed) with means for fixedly retaining the elastomeric material of the ball-end mount  208  when molded over the extended stem portion  210   a , such retaining means being, by example and without limitation, knurling, undercutting, shaping, serrating, and other retaining means as are well-known in the art.  
      The stem  210  is provided with an internally threaded longitudinal bore  212  that is structured to engage the threaded rod  206 . An outer end of the stem adjacent to the threaded bore  212  is formed with a hex-shaped lip  214  sized to be received into and mate with the hexagonal counter-bore  51  at the at the center of the boss or land  49  surrounding the aperture  47  formed through either one of the respective arm sections  7 ,  9 . The stem  210  is thus provided with means for fixing the ball-end mount  208  against rotation relative to the respective arm sections  7 ,  9  during threading and unthreading of the threaded knob  65  in operation.  
      The threaded knob  65  and the elongated threaded rod  206  function as the clamping mechanism  202  to squeeze the pair of arm sections  7 ,  9  together along the longitudinal axis  53  of the threaded rod  206  against the bias of the compression spring  11  by threading the knob  65  relatively inwardly along the length of the threaded rod  206  in the direction of the hex-shaped lip  214  and ball-end mount  208 . The pair of arm sections  7 ,  9  are allowed to separate from one another by unthreading the knob  65  along the length of the threaded rod  206  in the opposite direction, to allow the bias of the compression spring  11  to separate the pair of arm sections  7 ,  9  from one another. In both cases, because of the eccentricity of the compression spring  11  with respect to the axis  53  of the threaded rod  206 , there is a differential in the reaction of the respective pairs of first and second head or end portions  27 ,  29  of the arm sections  7 ,  9  to the clamping forces generated by the clamping mechanism  202 .  
      The mounting device  200  has the same two principal stages of operation described U.S. Pat. No. 5,845,885 for the mounting device  1 : a first stage in which the split arm assembly  3  and the clamping mechanism  202  make a loose connection between the object and the support surface S; and a second stage in which that connection is rigidified so as to support one the object on the support surface S. Between the two stages, there is also the same intermediate stage in which the angular orientation of the line of juncture  21  between the pair of arm sections  7 ,  9  is variable with respect to either or both of the object and the support surface S, so as to vary the angular orientation of object with respect to the support surface S. The connection may be made to have sufficient rigidity at one end thereof,  3 ,  13 ,  3 , moreover, that the adjustment can be made at the other end thereof,  4 ,  15 ,  4  while the rigidity of the one end  3 ,  13 ,  3  is relied on to maintain the angular orientation of the line of juncture  21  with respect to the object at the one end of the connection.  
       FIG. 10  illustrates an alternative embodiment of the ball-and-socket mounting device  200  of the invention having an alternative embodiment of the clamping mechanism  220  for clamping together the part-spherical heads  17  and  19  of the respective ball-end mounts  13 ,  15  by the split arm assembly  3 . As discussed herein, the split arm assembly  3  formed of the pair of elongated relatively rigid arm sections  7  and  9 , the compression coil spring  11  for biasing apart the pair of arm sections  7 ,  9 , and the pair of resiliently deformable ball-end mounts or “couplers”  13  and  15  with the part-spherical heads  17  and  19 . The split arm assembly  3  is clamped to the part-spherical heads  17  and  19  of the ball-end mounts  13 ,  15 , respectively, by the alternative clamping mechanism  220  of the present invention when the device  200  is put to use in mounting a relatively movable supported object on the support platform P in relation to the relatively stationary object or support surface S.  
      The clamping mechanism  220  operates between the pair of arm sections  7 ,  9  along the axis  53  of the apertures  47 .  
      The clamping mechanism  220  of the present invention is formed of the threaded connector  204  which is embodied, by example and without limitation, as an elongated threaded bolt  222  that is structured to threadedly engage and mate with the internally threaded knob  65  and sized to be inserted through the apertures  47  of arm sections  7 ,  9  as well as the one or more washers  63 . The discrete resiliently deformable ball-end mount  208  is provided with a one of the part-spherical heads  17 ,  19  of the type disclosed by Carnevali in U.S. Pat. No. 5,845,885, which is formed of a resiliently deformable elastomeric material with a substantially smooth part spherical outer surface  75 , as described by Carnevali in U.S. Pat. No. 5,845,885. As discussed herein, the ball-end mount  208  has at its center the first locus  209  of, by example and without limitation, another of the ball-and-socket mounting devices  1  of the prior art as disclosed in U.S. Pat. No. 5,845,885, and is operable with such a device  1  so as to form a ball-and-socket joint  77  therewith.  
      The part-spherical ball-end mount  208  is provided, by example and without limitation, on an extended stem portion  224   a  (shown in dashed) of a short substantially rigid stem portion  224  of the bolt  222 , the extended stem portion  224   a  being formed with one of the well-known means for fixedly retaining the elastomeric material of the ball-end mount  208  when molded over the extended stem portion  224   a , as discussed herein.  
      The bolt  222  is provided with a threaded longitudinal shaft or shank  226  that is structured to engage the internally threaded knob  65 . A head portion  228  of the bolt  222  adjacent to the threaded shank  226  includes the stem portion  224  that is formed adjacent to the shank  226  with the hex-shaped lip  214  that is sized to be received into and mate with the hexagonal counter-bore  51  at the at the center of the boss or land  49  surrounding the aperture  47  that is formed through either one of the respective arm sections  7 ,  9 . The threaded connector  204  is thus provided with means for fixing the ball-end mount  208  against rotation relative to the respective arm sections  7 ,  9  during threading and unthreading of the threaded knob  65  in operation.  
      The threaded knob  65  and the elongated threaded bolt  222  function as the clamping mechanism  220  to squeeze the pair of arm sections  7 ,  9  together along the longitudinal axis  53  of the threaded shank  226  against the bias of the compression spring  11  by threading the knob  65  relatively inwardly along the length of the threaded shank  226  in the direction of the hex-shaped head  228  and ball-end mount  208 . The pair of arm sections  7 ,  9  are allowed to separate from one another by unthreading the knob  65  along the length of the threaded shank  226  in the opposite direction, to allow the bias of the compression spring  11  to separate the pair of arm sections  7 ,  9  from one another. In both cases, because of the eccentricity of the spring  11  with respect to the axis  53  of the threaded shank  226 , there is a differential in the reaction of the respective pairs of first and second head or end portions  27 ,  29  of the arm sections  7 ,  9  to the clamping forces generated by the clamping mechanism  220 .  
       FIG. 11  is a side view illustration of the ball-and-socket mounting device  200  of the present invention based upon and having at its core the ball-and-socket mounting device  1  of the prior art as disclosed by Carnevali in U.S. Pat. No. 5,845,885. Accordingly, the ball-and-socket mounting device  200  of the present invention is illustrated having the pair of elongated arm sections  7  and  9  of the split arm assembly  3  squeezed together by the clamping mechanism  202  of the present invention operating between along the axis  53  of the threaded connector  204  and the apertures  47 . The clamping mechanism  202  being formed by the threaded connector  204  having the discrete resiliently deformable ball-end mount  208  threadedly engaged therewith at one end and with one or more washers  63  and the internally threaded knob  65  engaged at the opposite end.  
       FIG. 12  illustrates the ball-and-socket mounting device  200  of the present invention based upon and having at its core the positively-positionable positionable wheel-and-axle mounting apparatus  101  of the prior art as disclosed by Carnevali in U.S. Pat. No. 6,561,476 having the pair of arm sections  111 ,  113  of the split-arm assembly  114  clamped around the multisided stem or axle portion  103  of the positively-positionable wheel-and-axle mounting coupler  102  projecting from the base  107  that is fixed to the support surface S and the resiliently deformable part-spherical head  17  on the base  69  having the support platform P for mounting the relatively movable supported object (object). According to one embodiment of the present invention, the part-spherical head  17  is alternatively embodied as the substantially rigid partial geodesic sphere  127  the plurality of discrete substantially planar, triangularly-shaped facets  129  formed on its surface, and the inner surface of the socket-shaped cavities  123  of the arm sections  111  and  113  of the split-arm assembly  114  are formed with the matching facets  131 .  
      The arm sections  111 ,  113  of the split-arm assembly  114  are squeezed together by the clamping mechanism  202  of the present invention operating between along the axis  53  of the threaded connector  204  and the apertures  47 . The clamping mechanism  202  being formed by the threaded connector  204  having the discrete resiliently deformable ball-end mount  208  threadedly engaged therewith at one end and with one or more washers  63  and the internally threaded knob  65  engaged at the opposite end.  
      While the preferred embodiment of the invention has been illustrated and described, it will be appreciated that various changes can be made therein without departing from the spirit and scope of the invention. For example, the hexagonal counter-bore  51  at the at the center of the boss or land  49  surrounding the aperture  47  and the mating lip  214  or head  228  portions of the threaded connector  204  are alternatively formed with cooperating octagonal, square, star or other mating shapes as are known in the art. Alternatively, a lock washer or other means for locking the threaded connector  204  are provided between the ball mount  17  and the shoulder or boss  49 , whereby the counter-bore  51  surrounding the aperture  47  and the mating lip  214  or head  228  portions of the threaded connector  204  are eliminated. Additionally, the stem portion  210  of the part-spherical ball-end mount  208  is integrated with the shoulder or boss  49  on the outer surface of one of the appropriate arm sections  7 ,  111 , whereby the ball mount  17  is prohibited from rotating relative to the arm section  7 ,  111 . For example, the stem portion  210  of the ball-end mount  208  is welded, soldered, brazed, or otherwise fused to the shoulder or boss  49 . Alternatively, the stem portion  210  is integrally formed with the shoulder or boss  49  on the outer surface of one of the appropriate arm sections  7 ,  111  during a casting, molding, matching or other integral manufacturing process; and the elongated threaded connector  204  is engaged with the internally threaded longitudinal bore  212  that is structured to engage the threaded rod  206 . Alternatively, the threaded rod  206  is formed integrally with an inside surface of the arm section  7 ,  111  along the axis  53  of the aperture  47  in the opposing arm section  9 ,  113 . Furthermore, the knob  65  is alternatively formed with a rounded “wheel” or cut “gear” shape or another shape convenient for finger or hand operation, as is known in the art. According different embodiments of the present invention, each of the embodiments is optionally practiced using the different couplers  17 ,  19  and  102  and  127  with an appropriate one of the different pairs of arm sections  7 ,  9  and  111 ,  113 , as discussed herein. Thus, according to one embodiment of the present invention, one or both of the two ball mounts  17 ,  19  is formed as the partial geodesic sphere  127  of the type disclosed by Carnevali in U.S. Pat. No. 6,561,476 and in U.S. Pat. No. 6,581,892, and the inner faces  23  of the pairs of operatively opposing first and second sockets  31  and  33  of the respective arm sections  7 ,  9  are formed with the matching facets  131 . Therefore, the inventor makes the following claims.