Abstract:
A multi-positionable mounting device that provides a substantially stable, load-bearing but relatively adjustable ball and socket mounting device. An interior surface of the socket is formed of first and second opposing part hemispherical socket portions that are relatively orientable with one another for forming therebetween a part spherical cavity. The interior surface of one socket portion is formed with multiple facets at a predetermined radial distance from a spherical center point of the cavity. The first and second opposing part hemispherical socket portions are securable in a relationship which forms the part spherical cavity therebetween. A part-spherical coupler substantially fills the spherical cavity. The mechanical securing means applies clamping force that acts between the first and second opposing socket portions and secures the coupler therebetween in fixed orientation with one of the faceted socket portion.

Description:
The present application is related to application Ser. No. 09/855,162 entitled “Positively-Positionable Mounting Apparatus” filed on the same day herewith in the name of the same named inventor and is incorporated in its entirety herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to flexible mounting apparatus and particularly, to molded plastic interconnecting ball and socket elements in combination with opposing universally mountable base and universal coupler interconnected thereto. 
     Various couplers and especially those of ball and socket variety are generally known in this art. However, except for the inventor&#39;s own ball-and-socket universally positionable mounting device disclosed in U.S. Pat. No. 5,845,885, the complete disclosure of which is incorporated herein by reference, the known couplers typically hold by friction and are prone to various degrees of slippage under load. 
     SUMMARY OF THE INVENTION 
     The present invention is a multi-positionable mounting device that provides a substantially stable, load-bearing but relatively adjustable ball and socket mounting device. The present invention provides a highly positionable mounting device formed of a base adapted for permanent mounting on a substantially flat surface and an equipment mounting element either directly interconnected or optionally interconnected by one or more rotatably interconnecting ball and socket elements. 
     According to one aspect of the invention, the interior surface of the socket is formed of first and second opposing part hemispherical socket portions that are relatively orientable with one another for forming therebetween a part spherical cavity which defines a spherical center point therein. The interior surface of the first socket portion is formed with multiple facets that are formed at a predetermined radial distance from a spherical center point of the part spherical cavity. A mechanical means secures the first and second opposing part hemispherical socket portions together in a relationship wherein the part spherical cavity is formed therebetween. A part-spherical coupler is provided that is sized to substantially fill the spherical cavity formed between the first and second opposing part hemispherical socket portions. The mechanical securing means applies clamping force that acts between the first and second opposing socket portions and secures the coupler therebetween in fixed orientation with one of the first and second socket portions. 
     According to one aspect of the invention, the facets on the interior surface of the first socket portion are each configured as substantially planar triangular facets arranged perpendicularly to the spherical center point of the part spherical cavity. 
     According to another aspect of the invention, the part-spherical coupler is formed as a substantially smooth, spherical shape of a pressure deformable, resilient elastomeric material, which renders it relatively radially compressible. 
     According to still another aspect of the invention, the part-spherical coupler is formed instead as a relatively incompressible material having a plurality of substantially planar triangular facets formed perpendicularly to and at a predetermined radial distance from a spherical center point of the coupler. The facets formed on the surface of the coupler are matched in size and shape to the facets on the interior surface of the first socket portion. 
    
    
     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 isometric view illustrating one embodiment of the multi-positionable mounting device of the present invention; 
     FIG. 2 is a detailed isometric view of one embodiment of the geodesic sphere of the present invention, including an external adaptation formed as a rod projecting from one face thereof; 
     FIG. 3 illustrates one alternative embodiment of geodesic sphere of the present invention formed with an internal adaptation for accepting a mounting instrument; 
     FIG. 4 is a detailed isometric view of one embodiment of a base portion of a socket assembly of the present invention; 
     FIG. 5A illustrates one alternative embodiment of a clamp portion of a socket assembly of the present invention for use with the base portion; 
     FIG. 5B illustrates another alternative embodiment of a clamp portion of a socket assembly of the present invention for use with the base portion clamp, wherein the clamp portion is formed with an internal, substantially smooth, curved surface; 
     FIG. 6 illustrates another alternative embodiment of the present invention wherein a second geodesic sphere is formed on an end of a rod distal from the first geodesic sphere; 
     FIG. 7 illustrates another alternative embodiment of the multi-positionable mounting device of the invention, in which the geodesic sphere and mounting base reverse roles; 
     FIGS. 8A and 8B together illustrate an embodiment of the invention including a coupler having a substantially spherically-shaped head formed at an end of a rod distal from a mounting base, wherein the head is preferably formed of a pressure deformable, resilient elastomeric material, which renders it relatively radially compressible; and 
     FIG. 9 illustrates another alternative embodiment of the invention, wherein geodesic sphere of FIG. 2 is formed of as substantially spherically-shaped head using a pressure deformable, resilient elastomeric material, which renders the spherical head relatively radially compressible. 
    
    
     DETAILED DESCRIPTION 
     In the FIGURES, like numerals indicate like elements. 
     FIG. 1 illustrates one embodiment of the geodesic sphere and mounting base of the multi-positionable mounting device of the invention. Other embodiments are disclosed and shown in subsequent FIGURES. The embodiment of a multi-positionable mounting device  10  of the invention illustrated in FIG. 1 includes part-spherical coupler  12  formed as a partial geodesic sphere, i.e., a part spherical body having a surface that is formed with a plurality of discrete substantially planar, triangularly-shaped areas  14  intersecting at angular joints  16 . Each triangular area  14  is formed as a substantially planar surface oriented perpendicularly to a radius from a spherical center point of part-spherical coupler  12 . Each triangular area  14  is one segment of 3-dimensional geodesic sphere  12 . Geodesic sphere  12  is embodied in any number of 3-dimensional, multifaceted forms. The embodiments of the invention shown in the FIGURES and described herein are examples only and are not intended to limit the scope of the invention in any way. According to one exemplary embodiment of the invention, geodesic sphere  12  is any one of a 3-dimensional icosahedron having twenty triangular facets  14 , a 3-dimensional icositetrahedron having twenty-four triangular facets  14 , or another roughly spherical, 3-dimensional body having a plurality of triangular facets  14 , and other equivalents thereof. Such equivalent configurations of geodesic sphere  12  are considered equivalent and within the scope of the claimed invention. Furthermore, facets  14  of part-spherical coupler  12  are alternatively 3-dimensional rather than planar, thereby forming such alternative surfaces as diamond or pyramid shaped surfaces and other equivalent multi-surface shapes. Alternatively shaped facets  14  are arranged either convexly or concavely relative to part-spherical coupler  12 . That is, alternatively shaped facets  14  are formed either as projections from the surface of part-spherical coupler  12  or as indentations or depressions therein. 
     Geodesic sphere  12  is adapted in part with a means for connection to a user-selected external device (not shown), such as an electronic or computer device. One adaptation  18  providing the means for connection to an external device is, for example, a rod  20  projecting from one face of geodesic sphere  12 . Rod  20  is optionally formed with a skull  138 , which is shown in FIG.  8 B and described in detail below, and geodesic sphere  12  is attached to skull  138  or molded thereabout using, for example, an injection moldable plastic material. Rod  20  is optionally formed as any of a smooth rod (shown) for slidingly engaging the external device, an internally or externally threaded rod threadedly engaging the external device, or another suitable engaging configuration. In other examples, rod  20  is formed with a flat or keyway along one longitudinal surface for accepting a cooperatively keyed external device, optionally including a set screw. Optionally, an end of rod  20  distal from the connection to geodesic sphere  12  is formed with an enlarged diameter, substantially smooth, disc-shaped member (shown in FIG. 7) that is, for example, pierced with one or more apertures for mounting screws. In another example, the disc-shaped member is fitted with a resilient adhesive pad (not shown), commonly known as a Pressure Sensitive Adhesive or PSA. Other suitable adaptations of rod  20  for removably or permanently engaging an external device are considered equivalent and are also within the scope of the claimed invention. 
     According to the embodiment of the invention shown in FIG. 1, multi-positionable mounting device  10  of the invention includes a socket assembly  21  adapted for temporary or permanent mounting to an external surface, such as a desktop, vehicle dashboard or control panel, a wall, bulkhead, railing, or another suitable surface for mounting the user&#39;s external device. For example, socket assembly  21  includes a base  22  that is formed with one or more clearance holes  24  for securing base  22  with screws, nails, or other suitable fasteners (not shown) to the user&#39;s mounting surface. Alternatively, the underside mounting surface  26  of base  22  is formed substantially smoothly to accommodate an adhesive or epoxy bonding material, or a resilient adhesive pad or PSA (not shown), which is equipped with an adhesive on its external surface for bonding to a substantially smooth and substantially flat surface, and is further provided with sufficient resilient thickness to effectively bond to a slightly irregular and/or curved surface. Additionally, other suitable mounting adaptations are considered equivalent and are similarly contemplated by the claimed invention. 
     Base  22  is configured with a socket, which is formed as a concavely-shaped depression or cavity, shown more clearly in subsequent FIGURES and described more completely below. The socket in base  22  is formed with an internal surface configured to mate with the facets  14  formed on the surface of part-spherical coupler  12 . The internal socket surface of base  22  is for example, formed with a plurality of substantially planar, triangular areas that are substantially matched to triangular areas  14  on the surface of geodesic sphere  12 . Alternatively, the internal socket surface of base  22  is for example, formed with alternative 3-dimensional facets, such as diamond or pyramid shaped surfaces and other equivalent shapes, matched to facets  14  of part-spherical coupler  12 . The 3-dimensional facets on the interior socket surface of base  22  are formed, for example, as indentations or depressions therein to match facets  14  formed as projections from the surface of part-spherical coupler  12 . Alternatively, the 3-dimensional facets on the interior socket surface of base  22  are formed, for example, as projections therefrom to match facets  14  formed as indentations or depressions in the surface of part-spherical coupler  12 . 
     In the embodiment illustrated, base  22  is formed with a frame  28  extending above mounting base  22  and containing the matching concavely-shaped cavity or socket therein. Socket assembly  21  further includes a part hemispherical retaining cap portion  30  that is similarly formed with a concavely-shaped socket cavity having an internal surface formed with substantially planar, triangular areas that are substantially matched to triangular areas  14  on the surface of geodesic sphere  12 . Retaining cap  30  is also shown more clearly in subsequent FIGURES and described more completely below. The internal surfaces of respective concavely-shaped cavities in frame  28  and retaining cap  30  together form a socket that is substantially matched in size and form to the outer surface of geodesic sphere  12  when retaining cap  30  is joined to frame  28 . The planes of triangular surfaces  14  on geodesic sphere  12  are securely clamped relative to base  22  by matching surfaces of frame  28  and retaining cap  30  fitting together to form a socket having substantially the same size and the same geodesically spherical shape as geodesic sphere  12 . 
     Retaining cap  30  and frame  28  are generally formed with means for mechanically securing one to the other. For example, each of frame  28  and retaining cap  30  include respective pairs of bosses  32  and  34 , which are each formed with clearance apertures  36  (shown only in bosses  34 ) for accepting therethrough a screw, bolt or other suitable fastener. Such other suitable fasteners are considered equivalent forms and are similarly contemplated by the claimed invention. For example, a well-known mechanical cam arrangement (not shown) shifts frame  28  and retaining cap  30  between first and released and second tightened positions. Tightening of the fasteners, cam or other suitable tightening mechanism generates compressive clamping forces F, as indicated by arrows, in bosses  32  and  34  that are transmitted via respective frame  28  and retaining cap  30  to the socket formed therebetween. The matching flat triangular areas in frame  28  and retaining cap  30  contiguously contact and compress corresponding flat triangular areas  14  on the surface of geodesic sphere  12 , while intersecting angular joints  16  between adjacent triangular areas  14  nest with corresponding angular joints between adjacent triangular areas in each of frame  28  and retaining cap  30 . Geodesic sphere  12  is thus securely locked in relative orientation with base  22  and, therethrough, with any surface to which base  22  is secured. 
     Geodesic sphere  12 , and thus, rod  20  and any external user device attached thereto, is furthermore multiply positionable relative to base  22  and any surface to which base  22  is secured. The fasteners (not shown) through respective bosses  34  and  32  securing retaining cap  30  to frame  28  are loosened and the compressive force F therebetween released. With release of the compressive force F, geodesic sphere  12  is rotatable relative to base  22  within the socket formed between frame  28  and retaining cap  30 . In such a released state, a transverse force, represented by arrows T 1  and T 2 , a clockwise or counter-clockwise rotational force, represented by arrow R, or a combination of two or more of the transverse and rotational forces, applied to rod  20  or to a user device mounted on rod  20  causes geodesic sphere  12  to rotate relatively to frame  28  into a second different orientation thereto. After a user-determined relative orientation is achieved, the fasteners are again secured, which secures retaining cap  30  to frame  28  with compressive forces F. The orientation of geodesic sphere  12  is secured relative to base  22  when matching flat triangular areas in frame  28  and retaining cap  30  contiguously contact and compress corresponding flat triangular areas  14  on the surface of geodesic sphere  12 , and intersecting angular joints  16  between adjacent flat triangular areas  14  nest with corresponding angular joints between adjacent flat triangular areas in frame  28  and retaining cap  30 . 
     According to one or more embodiments of the present invention, retaining cap  30  is further formed with an extended motion slot  38  sized to at least permit entry of rod  20 . Optionally, extended motion slot  38  is sized largely enough to allow rod  20  to move laterally within slot  38 . Extended motion slot  38  thereby provides an additional degree of relative orientation between rod  20  and base  22 . For example, extended motion slot  38  optionally provides as much as 90-degrees to 120-degrees or more of rotation of rod  20  relative to base  22  in a plane perpendicular to mounting surface  26  of base  22  and passing through extended motion slot  38 . 
     FIG. 2 is a detailed isometric view of partial geodesic sphere  12 , including external adaptation  18  formed as rod  20  projecting from one face thereof. As described above, the surface of geodesic sphere  12  is formed with a plurality of triangularly-shaped areas  14  intersecting at angular joints  16 , and each triangular area  14  is one segment of 3-dimensional icosahedron geodesic sphere  12 . Furthermore, each triangularly-shaped area  14  is substantially the same size and shape as every other area  14 . That is, each area  14  is formed as an equilateral triangle, having substantially identical length sides each rotated at substantially 60-degrees from the adjacent sides. The planar face of each area  14  is further formed substantially perpendicularly to a radius R 1  extending from the spherical center Cg (see FIG. 3) of geodesic sphere  12  and is located at a substantially identical radial distance R 1  from spherical center Cg. Given the substantially identical size, shape, and position of each triangular area  14 , each triangular area  14  abuts on three sides adjacent triangular areas  14  forming a substantially identical intersecting angular joint  16 . Therefore, each triangular area  14  and each angular joint  16  is exactly interchangeable with every other triangular area  14  and angular joint  16 , respectively, on the surface of geodesic sphere  12 . Other 3-dimensional facets  14 , such as diamond or pyramid shaped surfaces and other equivalent multi-surface shapes, alternatively formed on the surface of geodesic sphere  12  also abut with adjacent facets  14  forming substantially identical intersecting angular joint  16  therebetween and are similarly interchangeable. 
     The degree of angle of angular joints  16  is a measure of the rotation of each triangular area  14  relative to each adjacent triangular area  14 . The degree of rotation between adjacent triangular areas  14  is a function of the number of triangular areas  14  forming the surface of geodesic sphere  12 : a greater number of triangular areas  14  results in larger angles  16  therebetween, while a smaller number of triangular areas  14  results in smaller angles  16 . The result is that geodesic sphere  12  is multiply orientable with respect to the matching triangular areas and intersecting angular joints formed on the interior concavely-shaped surface of frame  28 . Each of the multiply oriented positions into which geodesic sphere  12  is orientable relative to frame  28  is a discrete position angularly rotated from multiple adjacent discrete positions. In each of the multiple discrete positions into which geodesic sphere  12  is orientable relative to socket assembly  21 , triangular areas  14  mate in contiguous contact with matching triangular areas forming the interior socket surface of frame  28 , and angular joints  16  nest in mating angular joints between the matching triangular areas. Each of the multiple discrete positions into which geodesic sphere  12  is orientable relative to frame  28  is angularly rotated relative to each of the other multiple discrete positions. Adjacent positions are relatively rotated to the same degree as each of triangular areas  14  forming the surface of geodesic sphere  12  is rotated relative to each of the other triangular areas  14 . The degree of angular rotation between adjacent discrete positions is therefore a function of the number of triangular areas  14  forming the surface of geodesic sphere  12 , and the rotational angle of joints  16 . Greater numbers of triangular areas  14  result in greater numbers of adjacent discrete positions with smaller angles of rotation therebetween. Smaller numbers of triangular areas  14  result in smaller numbers of adjacent discrete positions with larger angles of rotation therebetween. 
     FIG. 3 illustrates one alternative embodiment of partial geodesic sphere  12  wherein the means for connection to a user-selected external device is formed as an internal adaptation or bore  40 . Internal adaptation  40  is optionally formed with internal threads (shown) or another adaptation  40 . For example, internal adaptation  40  is alternatively a smooth-bore cylindrical hole formed in geodesic sphere  12  and having an optional hole  42  extending from one of outer triangular surfaces  14  inwardly to intersect bore hole adaptation  40  and formed with internal threads to engage a set-screw  44 . In operation, set-screw  44  is threaded into threaded hole  42  and extends below the surface of triangular area  14 . Set-screw  44  engages a surface of rod  20  (shown in FIG. 2) projecting from a user device into bore hole adaptation  40  to clamp the rod portion in place. Partial geodesic sphere  12  is thereby interlocked with rod  20 . 
     FIG. 4 is a detailed isometric view of one embodiment of base  22 . In FIG. 4, frame  28  is shown extending above the mounting base  22  and formed with a part hemispherical socket portion  46  sized to partially encompass coupler  12 . Part hemispherical socket portion  46  is formed with an internal concavely-shaped surface having a plurality of triangular areas  48  that are substantially matched to triangular areas  14  on the surface of geodesic sphere  12 . Triangularly-shaped areas  48  are formed at a radial distance from the spherical center Cf of concavely-shaped socket surface  46  that is substantially equal to the radial distance R 1  that each triangular area  14  is from the spherical center Cg of geodesic sphere  12 . Each area  48  is further formed substantially perpendicularly to radius R 2  extending from the spherical center Cf of concavely-shaped socket surface  46 . Furthermore, triangularly-shaped areas  48  are substantially the same size and shape as triangularly-shaped areas  14 . That is, each area  48  is also formed as an equilateral triangle, having identical length sides  49  each rotated at 60-degrees from the adjacent sides, the sides being substantially the same length as the sides of triangular areas  14 . 
     Socket cavity  46  is formed sufficiently openly to permit geodesic sphere  12  to pass thereinto along an axis perpendicular to the clamping surface  50  of frame  28 . According to the embodiment illustrated, frame  28  containing therein concavely-shaped socket cavity  46  is cut by a longitudinal plane passing through the approximate spherical center Cf of concavely-shaped surface  46 , thereby firming clamping surface  50 . Therefore, socket cavity  46  approximately forms a quarterspherical shape (¼ sphere). Cavity  46  is thus sufficiently open to permit geodesic sphere  12  to pass thereinto along an axis perpendicular to longitudinal cutting plane  50 . Furthermore, quarterspherically-shaped concave socket surface  46  extends above its spherical center Cf at least a minimum distance D, such that socket  46  is larger than a quartersphere. Therefore, when installed in socket  46 , a portion of geodesic sphere  12  above its equator is captured by extension D, wherein the “equator” is defined by a plane passing through the spherical center Cg of geodesic sphere  12  (see FIG.  3 ). Extension D thus operates as a retaining lip portion formed as an additional quarterspherical zone extending along one axis of the quarterspherical geodesic shape beyond a spherical center of socket cavity  46 . Extension D of socket cavity  46  serves to securely capture geodesic sphere  12  within frame  28  when retaining cap  30  is secured to base  22 . 
     FIGS. 5A and 5B are isometric views illustrating two alternative embodiments of part hemispherical retaining cap  30 . FIG. 5A illustrates one alternative embodiment of the clamping surface  52  of retaining cap  30 A, which preferably either actually or nearly contacts clamping surface  50  of frame  28  (shown in FIG. 4) when secured thereto with geodesic sphere  12  therebetween, as shown in FIG.  1 . Retaining cap  30 A is, for example, secured to frame  28  by threaded fasteners at each of apertures  36 . In FIG. 5A, retaining cap  30 A is formed with an internal, concavely-shaped socket surface  54  shaped substantially identically to concavely-shaped socket surface  46  formed in frame  28 . That is, concavely-shaped socket surface  54  is formed having a plurality of facets  56  that are substantially the same size and shape and have substantially the same arrangement as facets  14  forming the surface of geodesic sphere  12 . For example, facets  56  are formed at a radial distance R 3  from the spherical center Cc of concavely-shaped socket surface  54 . Radial distance R 3  is substantially equal to the radial distance R 1  that triangular areas  14  are from the spherical center Cg of geodesic sphere  12 . Preferably, each facet  56  is a substantially planar triangularly-shaped surface substantially identical in size and shape to triangular areas  14 . That is, each area  56  is also formed as an equilateral triangle, having three sides of identical length each rotated at 60-degrees from the adjacent sides, the sides being substantially the same length as the sides of triangular areas  14 . Each triangular area  56  is further formed substantially perpendicularly to a radius R 3  extending from the spherical center Cc of concavely-shaped surface  54 . 
     Socket cavity  54  is formed with a part hemispherical shape, which is sufficiently open to pass over geodesic sphere  12  along an axis perpendicular to clamping surface  52  of retaining cap  30 A. According to the embodiment illustrated, retaining cap  30  is cut by a longitudinal plane passing through the approximate spherical center Cc of concavely-shaped socket surface  54 , thereby forming clamping surface  52 . Therefore, similarly to socket cavity  46  of frame  28 , socket cavity  54  approximately forms a quarterspherical shape (¼ sphere). Quarterspherically-shaped concave surface  54  also extends above its spherical center Cc at least a minimum distance D forming an additional quarterspherical zone extending along one axis of socket  54 , such that a portion of geodesic sphere  12  above its equator is captured by the extension D (see FIG.  3 ). The extension D of part hemispherical socket cavity  54  serves to make the area covered thereby larger than a quartersphere. The increased coverage in turn increases the security with which geodesic sphere  12  is captured within frame  28  when retaining cap  30  is secured thereto. 
     FIG. 5B illustrates one alternative embodiment retaining cap  30 B, which is formed with an internal, substantially smooth, curve-shaped surface  58  formed at a radial distance R 4  from the spherical center Cc of curve-shaped surface  58 . Radial distance R 4  is substantially equal to the radial distance R 1  that triangular areas  14  are from the spherical center Cg of geodesic sphere  12 . Cavity  58  is formed sufficiently openly to pass over geodesic sphere  12  along an axis perpendicular to clamping surface  52  of retaining cap  30 B. According to the embodiment illustrated, retaining cap  30 B is cut by a longitudinal plane passing through the approximate spherical center Cc of concavely-shaped surface  58 , thereby forming clamping surface  52 . Therefore, similarly to socket cavity  46  of frame  28 , socket cavity  58  approximately forms a quarterspherical shape (¼ sphere). Socket cavity  58  is thus sufficiently open to pass over geodesic sphere  12  along an axis perpendicular to longitudinal cutting plane  52 . Quarterspherically-shaped concave socket surface  58  also extends above its spherical center Cc at least a minimum distance D forming an additional quarterspherical zone extending along one axis of socket  58 , such that a portion of geodesic sphere  12  above its equator is captured by extended portion D (see FIG.  3 ). The extension D of cavity  58  serves to increase the security with which geodesic sphere  12  is captured within frame  28  when retaining cap  30 B is secured thereto. 
     Additional Embodiments 
     FIG. 6 illustrates another alternative embodiment of the present invention in which adaptation  18  is again formed as rod  20  extending from geodesic sphere  12 . In FIG. 6, however, a second part-spherical coupler  12  formed as a second partial geodesic sphere  12 A is formed on the end of rod  20  distal from first partial geodesic sphere  12 . For example, second geodesic sphere  12 A is formed substantially identically to first geodesic sphere  12 . A second socket formed between a second assembly of a base  22  and a retaining cap  30  is mounted on a user-selected external device (not shown), such as an electronic or computer device, for example, using one of above described mounting techniques for temporarily or permanently mounting to an external surface. The second socket is clamped about second geodesic sphere  12 A, as described above in connection with base  22  and retaining cap  30 . Second geodesic sphere  12 A thus vastly increases, in combination with second base  22  and retaining cap  30 , the degrees of freedom available for orienting the external device with respect to the mounting surface of the first base  22 . 
     FIG. 7 illustrates another alternative embodiment of the multi-positionable mounting device  10  of the invention, in which the geodesic sphere and mounting base reverse roles. In FIG. 7, partial geodesic sphere  12  is formed as a coupler  59 . In FIG. 7, geodesic sphere  12  again includes rod  20  projecting from a surface thereof for coupling an attachment thereto. However, rod  20  is formed with a mounting base  60  distal from geodesic sphere  12 . Mounting base  60  is preferably disc-shaped and is adapted for temporary or permanent mounting to an external surface, such as a desktop, vehicle dashboard or control panel, a wall, bulkhead, railing, or another suitable surface (not shown) for mounting the user&#39;s external device. For example, base  60  is formed with one or more clearance holes  62  for securing base  60  with screws, nails, or other suitable fasteners (not shown) to the user&#39;s mounting surface. Alternatively, an underside mounting surface  64  of base  60  opposite from geodesic sphere  12  is formed substantially smoothly to accommodate an adhesive or epoxy bonding material, or a PSA pad for bonding to a slightly irregular and/or curved surface. Additionally, other suitable mounting adaptations are considered equivalent and are also within the scope of the claimed invention. 
     A clamping device such as provided by above described base  22  and retaining cap  30  is optionally mounted on a user-selected external device, for example, using one of above described mounting structures for temporarily or permanently mounting to an external surface. The socket formed of base  22  and retaining cap  30  is clamped about geodesic sphere  12  of coupler  59 , as described above in connection with base  22  and retaining cap  30 . The embodiment thus provides the same degrees of freedom available for orienting the external device with respect to the mounting surface of the first base  22  as provided by the embodiment of FIG.  1 . 
     Alternatively, a split arm assembly  100  is clamped about geodesic sphere  12  of coupler  59 . Split arm assembly  100  includes respective elongated arm sections  102  and  104 , and a clamp mechanism  106  for fastening together arm sections  102  and  104 . Respective arm sections  102  and  104  each include at least one concavely-shaped socket surface  110  and  112 . At least one or the other of concavely-shaped socket surface  110  and  112  is formed having a plurality of triangular areas  114  that are substantially matched to triangular areas  14  on the surface of geodesic sphere  12 . Optionally, the other of respective arm sections  102  and  104  includes at least one concavely-shaped surface  110  and  112 , respectively, having a an internal, substantially smooth, curve-shaped surface formed with a radius that is substantially equal to the radial distance R 1  that triangular areas  14  are from the spherical center Cg of geodesic sphere  12 . According to one embodiment of the invention, respective arm sections  102  and  104  each include at least one concavely-shaped surface  110  and  112 , respectively, having a plurality of triangular areas  114  that are substantially matched to triangular areas  14  on the surface of geodesic sphere  12 . Cavity  110  and/or  112  having triangular areas  114  is formed similarly to above described cavities  46  and  54  formed in frame  28  and retaining cap  30 , respectively. 
     As described in above incorporated U.S. Pat. No. 5,845,885, clamp mechanism  106  includes, for example, an elongated threaded bolt  106 A and an internally threaded knob  106 B with internal threading sized to securely engage threaded bolt  106 A, and diametrically opposing wings formed thereon for ease of turning. Preferably, a washer  106 C is sleeved about the shank of bolt  106 A ahead of knob  106 B. As described in above incorporated U.S. Pat. No. 5,845,885, a coiled spring portion  106 D separates arm sections  102  and  104 , while clamp  106  holds them together against the yieldable bias of spring  106 D. 
     In operation, arm sections  102  and  104  are arranged with respective concavely-shaped surfaces  110  and  112  operatively juxtaposed relative to one another along a line of juncture  116  extending therebetween. The respective rims  118  of concavely-shaped surfaces  110  and  112  include indentations  120  and  122  formed therein along the longitudinal axis of elongated arm sections  102  and  104  and facing toward the other of concavely-shaped surfaces  110  and  112 . Concavely-shaped surfaces  110  and  112  are formed with additional indentations  124  at the extreme ends of arm sections  102  and  104 . Indentations  122  and  124  are provided to permit rod  20  a degree of rotational freedom with respect to line of juncture  116 . Arm sections  102  and  104  are clamped together across line of juncture  116  extending therebetween by tightening of clamp mechanism  106 . According to the embodiment of the invention illustrated in FIG. 7, arm sections  102  and  104  are fastened together by passing the shank of bolt  106 A through an opening  126  in one of arm sections  102  and  104 , through spring  106 D, through an opening  126  in the other of arm sections  102  and  104 , optionally placing sleeving washer  106 C about the projecting threaded end portion of the shank of bolt  106 A, and threadedly engaging knob  106 B with bolt  106 A. Clamp mechanism  106  is thereby capable of subjecting arm sections  102  and  104  to cooperating compressive forces F, as indicated by the arrows. Initially, opposing arm sections  102  and  104  are relatively loosely connected by clamp mechanism  106 , i.e., clamp mechanism  106  is not tightened and spring  106 D is operative to bias arm sections  102  and  104  apart from one another. During this phase of operation, split arm assembly  100  is relatively rotatable with respect to geodesic sphere  12  for changing the orientation therebetween. After a desired orientation is achieved, knob  106 B is increasingly threadedly engaged with bolt  106 A, which compressively engages triangular surfaces  114  of both cavities  110  and  112  with matching triangular surfaces  14  on opposing surfaces geodesic sphere  12 , intersecting angular joints  16  between adjacent triangular areas  14  nesting into corresponding angular joints between adjacent triangular areas  114 . The cooperating compressive forces F provided by clamp mechanism  106  act through arm sections  102  and  104  to securely lock split arm assembly  100  in relative orientation with geodesic sphere  12  and, accordingly, with any surface to which base  60  is secured. 
     According to yet another alternative embodiment of the invention, a second coupler  59 A is provided. Second coupler  59 A includes a second partial geodesic sphere  12 A having a configuration similar to that of first partial geodesic sphere  12 , as described immediately above. In other words, second coupler  59 A includes a rod  20 A (not visible) having a second geodesic sphere  12 A formed at one end thereof and a mounting base  60 A formed at the other end, distal from geodesic sphere  12 A. Mounting base  60 A is also preferably disc-shaped and includes mounting holes  62 A and a substantially planar bottom surface  64 A. Mounting base  60 A is preferably adapted for temporarily or permanently mounting to an external surface, such as a user&#39;s external device, as described above. 
     Each of respective elongated arm sections  102  and/or  104  of split arm assembly  100  further includes a second concavely-shaped socket surface  128  and  130 , respectively, at an end thereof opposite respective first concavely-shaped surfaces  110  and  112 . At least one or the other of second concavely-shaped surfaces  128  and  130  is formed with a plurality of triangular areas  114  that are substantially matched to triangular areas  14  on the surface of geodesic sphere  12 . Socket cavities  128  and  130  having triangular areas  114  are formed similarly to above described cavities  110  and  112  formed in elongated arm sections  102  and  104 , respectively. Second geodesic sphere  12 A is similarly rotatable relative to second concavely-shaped surfaces  128  and  130  while opposing arm sections  102  and  104  are initially relatively loosely connected by clamp mechanism  106  for selecting a desired orientation therebetween. 
     The respective spherical centers Cg of geodesic spheres  12  and  12 A thus form loci  132  and  134  spaced apart by a distance L, which is the predetermined length of opposing arm sections  102  and  104  between the respective spherical centers Ca of first and second concavely-shaped surfaces  110  and  128  of first arm section  102  and between first and second concavely-shaped surfaces  112  and  130  of second arm section  104 . During the clamping phase of operation, while clamp  106  is not yet exerting compressive forces on geodesic spheres  12  and  12 A, relative rotations are accommodated. Each of geodesic spheres  12  and  12 A are angularly and rotationally orientable relative to respective sockets formed by spaced apart cavities  110  and  112  and by cavities  128  and  130  at opposite ends of first and second arm sections  102  and  104 . Stated differently, loosened arm sections  102  and  104  are relatively angularly and rotationally rotatable relative to one or both of geodesic spheres  12  and  12 A. The length L by which loci  132  and  134  are spaced apart determines the distance by which geodesic spheres  12  and  12 A are spaced apart, and consequently, the distance by which the user-selected device mounted on base  60  of geodesic sphere  12 A is spaced away from the surface on which base  60 A of geodesic sphere  12  is mounted. 
     After a desired orientation is achieved between second geodesic sphere  12 A and second concavely-shaped surfaces  128  and  130 , threaded engagement between knob  106 B and bolt  106 A is further increased, which compressively engages triangular surfaces  114  of both cavities  128  and  130  with matching triangular surfaces  14  on opposing surfaces geodesic sphere  12 A. Triangular surfaces  114  of cavities  128  and  130  intersect angular joints  16  between adjacent triangular areas  14 , thereby nesting into corresponding angular joints between adjacent triangular areas  114 . The further cooperating compressive forces F provided by clamp mechanism  106  act through arm sections  102  and  104  to securely lock split arm assembly  100  in relative orientation with geodesic sphere  12 A and, accordingly, with any user&#39;s external device to which base  60 A is secured. 
     FIGS. 8A and 8B together illustrate an embodiment of the invention including a coupler  136 . In FIG. 8A, coupler  136  is optionally formed of a disc shaped base  60 B with a cylindrical rod  20 B projecting therefrom, and a partly spherically-shaped head  12 B formed at an end of rod  20 B distal from base  60 B. Other equivalent structures are also contemplated by the invention and are similarly considered within the scope of the claims. Spherical head  12 B is preferably formed of a pressure deformable, resilient elastomeric material, which renders part spherical head  12 B relatively radially compressible. Part spherical head  12 B is, for example, similar to the radially compressible coupling member described in above incorporated U.S. Pat. No. 5,845,885. The resilient nature of the material forming spherical head  12 B causes it to resume its original part spherically-shaped configuration at the surfaces thereof when a compressive force is removed. Part spherical head  12 B is sized with a diameter appropriate for compression either within cavities  46  of frame  28  and  54  of retaining cap  30  of the multi-positionable mounting device  10  of the invention illustrated in FIG. 1, or within cavities  110  and  112  of respective opposing arm sections  102  and  104  of the invention illustrated in FIG.  7 . Preferably, the diameter of part spherical head  12 B is approximately the same as the maximum diameter of geodesic sphere  12  as measured across opposing points formed at intersecting triangular areas  14  on the surface thereof Thus, part spherical head  12 B is approximately the diameter of the inner peripheral surfaces formed at the intersections of adjacent triangular areas  48  of frame  28 , as measured from the spherical center Cf thereof (see FIG.  4 ). Preferably, base  60 B and columnar rod  20 B projecting therefrom are formed of a relatively rigid material, such as a metal or hard plastic. The end of rod  20 B distal from base  60 B is preferably formed with a skull  138  that is configured for gripping a portion of elastomeric material of partly spherically-shaped head  12 B formed thereon. The configuration of skull  138  is not critical and will likely vary considerably when the invention is practiced by different manufactures. 
     FIG. 8B illustrates one exemplary embodiment of the invention, wherein skull  138  is optionally formed having a generally spherical shape. Optionally, a network of horizontal and vertical gripping elements  140  is formed in relief on the surface of skull  138 . According to another example, skull  138  is optionally formed as a cube. Other equivalent forms of skull  138  include, for example, discs, blocks, cuboids, parallelepipeds, pyramids, cylinders, and spheres, all preferably knurled or formed with grooves, ridges, pockets, fingers, or other artifacts suitable of retaining elastomeric sphere  12 B in position thereon. Such configurations and other configurations suitable for retaining skull  138  securely on rod  20 B are considered to be equivalent configurations contemplated by the invention and falling within the scope of the invention. 
     In operation, head  12 B of coupler  136  is loosely captured within a concavely-shaped socket cavity sized to fit securely thereabout when a clamping force is applied thereto. For example, head  12 B is initially loosely captured within the socket formed between frame  28  and retaining cap  30 . Alternatively, head  12 B is loosely captured between the opposing jaws of a split arm assembly, such as split arm assembly  100 , shown in FIG.  7 . While so loosely engaged, head  12 B is rotationally and angularly orientable relative to the concavely-shaped socket cavity. A clamping force F is applied to the socket cavity after a desired angular and rotational orientation is achieved. The pressure deformable material in the body of head  12 B enables it to be squeezed between the surfaces of the concavely-shaped socket cavity. In response to the applied clamping force F, the pressure deformable elastomeric material of head  12 B is relatively radially compressed between respective concavely-shaped surfaces  46  and  54  of respective frame  28  and retaining cap  30 . Alternatively, head  12 B relatively radially compresses between respective concavely-shaped socket surfaces  110  and  112  of respective elongated arm sections  102  and  104  via clamp mechanism  106 . According to either described embodiment or another equivalent embodiment, head  12 B is compressed into the shape defined by the internal facets formed by respective triangular areas  48  and  114  and flows into the angular interfaces at the intersections between the facets. Head  12 B is thus deformed relative to mating concavely-shaped surfaces  46  and  54  when compressed within the socket formed between frame  28  and retaining cap  30 , assuming the shape of the mating surfaces and nesting within the angular intersections. Alternatively, head  12 B is compressed within the socket formed between  110  and  112  of respective arm sections  102  and  104 , again assuming the shape of the mating surfaces. Thus deformed, head  12 B is substantially immovably secured relative to one of respective socket assembly  21  and split arm assembly  100 . 
     Upon release of the compressive forces F, head  12 B resumes its original partially spherically-shaped configuration. In such uncompressed and part spherical condition, head  12 B is again angularly and rotationally rotatable relative to mating concavely-shaped socket surfaces formed by respective socket assembly  21  and split arm assembly  100 . Head  12 B is angularly and/or rotationally rotated to a different second orientation relative to a socket formed by either socket assembly  21  or split arm assembly  100 , or another equivalent clamp assembly. The opposing members of the clamp assembly are again secured together to form a socket having an interior surface formed, at least partially, of multiple relatively angularly rotated planar or 3-dimensional surfaces. The compressive forces F that the socket assembly exerts on head  12 B again relatively radially compresses the pressure deformable elastomeric material into a mating shape. Head  12 B and rod  20  projecting therefrom are thereby again locked in a fixed angular and rotational orientation with the socket assembly. 
     FIG. 9 illustrates another alternative embodiment of the invention, wherein partial geodesic sphere  12  of FIG. 2 is formed of as partial substantially spherically-shaped head  12 B formed of a pressure deformable, resilient elastomeric material, which renders spherical head  12 B relatively radially compressible. FIG. 9 illustrates a detailed isometric view of geodesic sphere  12 B, including external adaptation  18  formed as rod  20 C projecting from one face thereof According to the embodiment of FIG. 9, rod  20 C is preferably formed of a metal or a sturdy, hard plastic material. Furthermore, rod  20 C is optionally formed with a frame or “skull” portion  138  configured for gripping a portion of elastomeric material formed thereon, similar to above described skull  138  (shown in FIG.  8 B). Thus, pressure deformable head  12 B is angularly and rotationally orientable relative to socket assembly  21  (shown in FIG. 1) when retaining cap  30  is loosened relative to frame  28 . After deformable head  12 B is oriented relative to socket assembly  21 , retaining cap  30  is secured to frame  28 , thereby exerting clamping force F on pressure deformable head  12 B. Head  12 B is squeezed between the surfaces of the concavely-shaped socket cavity formed between respective concavely-shaped surfaces  46  and  54  of frame  28  and retaining cap  30 . Head  12 B is compressed and flows into the shape defined by the internal facets formed by respective facets  48  and angular interfaces at the intersections between the facets, assuming the shape of the mating surfaces and flowing into the angular intersections. Rod  20 C is thus interlocked with socket assembly  21  in a position projecting from socket assembly  21  at a desired rotational and angular orientation. The relative orientation is solidly fixed by radial compression of the pressure deformable elastomeric material into a mating shape with respective concavely-shaped socket surfaces  46  and  54  of frame  28  and retaining cap  30 . 
     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.