Abstract:
A bicycle is disclosed with a triangulated crank structure that replaces the single span crank arm which connects the spindle to the foot pedal on bicycles today. Said triangulated crank structure is typically comprised of several sections including two linear spans of structural material arranged so that one end of each linear span connects with the other to form the vertex of an acute angle, proximate to a pedal attachment area. From said vertex, said linear spans diverge and each connects at its opposite end to separate locations on a structural element attached to an end of the bicycle&#39;s crankshaft or spindle.

Description:
This is a continuation-in-part of application Ser. No. 09/489,602 filed Jan. 20, 2000. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates primarily to bicycles, but also to any other human powered vehicles, watercraft, or exercise devices which utilize a foot pedal or handgrip for the operator to convert rotational motion and/or linear motion of his feet or hands, into work, in order to activate the device. 
     2. Description of Prior Art 
     Bicycle crank arms in general, provide a means for physically connecting the foot pedals of the bicycle to the crankshaft of the bicycle. In some cases, one of the crank arms is also attached to a chain sprocket, or a set of axially concentric sprockets, which drives a chain for the purpose of transmitting power to the drive wheel of the bicycle. Whether the sprocket is attached directly to the crankshaft or spindle, or indirectly to the spindle through one of the crank arm assemblies, the crank arms enable force exerted on the foot pedals to be transferred into power to propel the bicycle as the foot pedals sweep through each stroke. 
     Bicycles have evolved from their earliest designs with a pair of bilaterally symmetric and inversely synchronized foot pedals, each connected to the crankshaft or spindle of the vehicle by a generally straight crank arm. As bicycle consumers have come to put more emphasis on light weight and performance, bicycle manufacturers have endeavored to manufacture lighter and better performing bicycles. This quest has led many manufacturers to utilize computer aided design techniques and exotic materials in the creation of their products. Today, the weights of many components on bicycles are usually communicated in gram units, because the emphasis on weight reduction is so great that the units of pounds and ounces are insufficiently explicit for many consumers. 
     One of the largest concentrations of structural material in a typical bicycle is in the crank arm. That often corresponds to one of the largest concentrations of weight on a bicycle, despite some manufacturers&#39; use of exotic lightweight materials at this location. Reducing weight by using such materials usually leads to a significant cost penalties or other tradeoffs. 
     SUMMARY OF THE INVENTION 
     This invention replaces the double ended crank arm design currently used on bicycles, with a triangulated crank structure. Triangulation is accomplished by replacing a straight bar type structure that connects the spindle to the pedal shaft end of a crank arm, with a split structure that has two separate tube segments, spaced away from a line between the spindle end and the corresponding pedal shaft attachment location, that line being the neutral axis of the structure. During the rider&#39;s power stroke, one such tube segment would be mostly under tension while the other would be mostly under compression. This largely eliminates high bending stresses associated with the straight crank design. It does so by moving structural material much further away from the neutral axis of the crank than is possible with a straight crank design. 
     Mechanical triangulation when applied to bicycle cranks permits a maximum structural efficiency defined as the minimum amount of structural material possible to support a given load. The inherent structural efficiency problem in a triangulated design is the requirement for multiple structural segments. Furthermore, the shortest distance between the spindle end and the pedal shaft attachment means, and therefore the shortest total length of structural material required to connect them, is the straight segment of the prior art. 
     This invention preferably uses hollow tubes to save weight in the multiple segments. The hollow tubes are structurally optimized to resist both torsion loads due to the offset pedal, and the lateral bending loads perpendicular to the applied force that the tubes experience during cyclical power transmission peaks. The hollow tubes also approach an ideal design for resisting crank deflection when the rider&#39;s weight is pushing on the pedal while at or near the top or bottom of the stroke. Also, this invention preferably uses only two structural segments or struts to connect the hollow tubes to the spindle and/or sprocket assembly. Lastly, the crank structure on the same side of the vehicle as the drive sprocket uses two structural segments or struts to connect the structure efficiently to four sprocket bolts on a five bolt sprocket, or to two sprocket bolts on a four bolt sprocket. 
     The primary object of the invention is to improve structural efficiency of bicycle cranks, thereby decreasing weight without any reduction in strength or stiffness. The invention can provide bicycle cranks with both strength enhancement and weight reduction benefits. 
    
    
     BRIEF DESCRIPTIONS OF THE DRAWINGS 
     FIG. 1 is a side perspective view of one preferred embodiment of the triangulated bicycle crank structure disclosed in this invention. 
     FIG. 2 is a cross sectional perspective view of an elliptical main tube assembly according to one preferred embodiment of this invention. 
     FIG. 3 is a side view of a triangulated bicycle crank structure where the orientation of the two tubes is adjusted to attach to a second pair of tubes that extend further from the spindle attachment location according to another preferred embodiment of this invention. 
     FIG. 4 is a side view of a triangulated crank structure according to another preferred embodiment of this invention wherein two of the adjoining tube segments shown in FIG. 3 are approximately collinear and comprise a single tube. 
     FIG. 5 shows a side view of the triangulated crank structure shown in FIG. 1 which also includes four flanges for attaching a sprocket (assembly) directly to the triangulated crank structure. 
     FIG. 6 shows a side view of the triangulated crank structure shown in FIG. 1 which also includes tapped holes for attaching a sprocket (assembly) to the triangulated crank structure. 
     FIG. 7 shows a side view of a triangulated crank structure that incorporates non-parallel adjacent structural segments for connecting the hub area of the crank structure to the attachment location of the main tubes of the structure. 
     FIG. 8 shows a side perspective view of a triangulated crank structure according to one preferred embodiment of this invention. 
     FIG. 9 shows a cross-sectional view of a crank arm according to one preferred embodiment of this invention. 
     FIG. 10 shows a diagrammatic cross-sectional view of a hypothetical crank arm. 
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     FIG. 1 discloses a structure  1  for rotatively connecting the pedal of a bicycle to the spindle of a bicycle. Structure  1  comprises a hub  6  which includes an opening  5  to receive the end of a spindle, which rotates on an axis  2 . Hub  6  further includes internal threading  8  recessed from its outer face for the purpose of securing a threaded cap which can cover the outer opening of the hub. According to one preferred embodiment of this invention structure  1  comprises two struts, preferably a first connection strut  10  and a second connection strut  16 , attached to hub  6 , which extend radially away from the center of hub  6 , preferably at an attachment angle  84  of less than 200° and optimally less than 180°. While these struts  10 ,  16  are generally round and hollow in the preferred embodiment, they may be of any cross sectional profile, including rectangular, round, elliptical, “C” or “D” or “I beam” shaped, etc. First connection strut  10  and second connection strut  16  may or may not taper, and may or may not be partially or completely hollow. Outside exterior reinforcing webs  11  and inside exterior reinforcing web  12  are included in one preferred embodiment of this invention to reduce material stresses where first connection strut  10  and second connection strut  16  attach to hub  6  at spindle shaft end  50 . While these reinforcing webs  11  and  12  are shown in FIG. 1 in a plane that approximately bisects the first and second connection struts  10  and  16 , the quantity, size, configuration, and location of the reinforcing webs are not necessarily constrained as shown by FIG.  1 . It is actually intended for the reinforcing webs  11  and  12  to have different characteristics depending on whether they are on the crank structure associated with the right side or the left side of the bicycle. On the right side of the bicycle, typically the sprocket side, webs  11  and  12  would be positioned relatively flush with the inside face of hub  6  to facilitate sprocket attachment. 
     FIG. 1 also shows two knuckles  15  for attaching crank arms, namely, first arm  20  and second arm  21  to the outer end of first and second connection struts  10  and  16 . Depending on the cross sectional profile of connection struts  10  and  16 , it may be practical to manufacture knuckles  15  as extensions of first and second connection struts  10  and  16 , rather than as separate pieces to be attached during assembly. Unless first arm  20  and second arm  21  have a round cross sectional outer profile at their respective ends, they cannot be threaded and screwed into knuckles  15 . Since the cross sectional shape of first arm  20  and second arm  21  in the preferred embodiment is elliptical, a preferable means of attaching first arm  20  and second arm  21  to the corresponding knuckle  15  at a first crank end  52  and a second crank end  54 , respectively, is a powerful adhesive applied to the outside walls of the ends of first arm  20  and second arm  21  prior to insertion into an appropriately shaped hole in knuckle  15 . Knuckles  15  can be similarly attached to struts  10  and  16  in the event that first and second connection struts  10  and  16 , and knuckles  15  do not comprise a single piece. 
     FIG. 1 further discloses a junction  30  at a pedal attachment area  59 . Junction  30  is the physical means for connecting first arm  20  and second arm  21  at their first distal end  56  and second distal end  58 , respectively. Junction  30  thereby creates a connection angle  82  between first arm  20  and second arm  21 . Junction  30  preferably includes internal threads  31  or a similar pedal attachment area  59  for receiving the shaft of a pedal assembly, with said shaft preferably aligned with axis  3 . According to one preferred embodiment of this invention, the junction  30  attaches to first arm  20  and second arm  21  in a similar manner as first arm  20  and second arm  21  connect to knuckles  15 . Because first arm  20  and second arm  21  are non-parallel when assembled into structure  1 , two of them cannot be inserted into knuckles  15  and junction  30  without severely bending at least one of them. Although this assembly problem can be solved by splitting one knuckle  15  or junction  30  into two pieces; using oversize holes with shims; or by putting a backside hole in one of them, such solutions are not shown in FIG.  1 . Nor are notches, screws, dowels, or other means for positively and redundantly connecting first arm  20  and second arm  21  to knuckles  15 , or to junction  30  shown in FIG.  1 . It should be noted that the components of FIG. 1 could be manufactured as a single piece, if a material with flexible fabrication properties such as carbon fiber is used. 
     According to a preferred embodiment of this invention, structure  1  is interchangeably applicable to either a sprocket side or a non-sprocket side of a bicycle. Therefore, structure  1  does not depend upon a sprocket of a bicycle for attachment and use. 
     FIG. 2 shows a perspective end view of second arm  21 . The preferred embodiment comprises a hollow or tubular second arm  21 , and first arm  20  preferably identical to second arm  21 , having generally elliptical cross sections. This cross sectional shape is optimized for resisting a combination of torsional loads and bending loads in the plane of the major axis of the ellipse. The resistance to bending loads in the plane of the major axis of the ellipse is further enhanced by increases in the wall thickness where the major transverse axis of the ellipse comprising the cross section of second arm  21  intersects the second arm  21 . The second arm  21  of FIG. 2 does not show any deviation from an elliptical cross section, although replacing the smooth elliptical outer and/or inner profile of one or both narrow sides of the ellipse with a more rectangular design, thus adding structural material, would further improve resistance to bending forces in the plane of the major transverse axis. Any tube cross sectional shape that overlapped the approximate shape of an ellipse will benefit from the structural characteristics of the ellipse in this application. Similarly, first arm  20  and/or second arm  21  could be used in combination with other shapes such as “I” beams to adjust properties in different bending modes. Alternative tube designs, including those with more circular cross sections could be substituted for the elliptical design, which may additionally include an internal and/or external bead or web along a diameter to better resist bending in the plane of that diameter. The preferred embodiment comprises a first arm  20  and a second arm  21  that are straight along their length. Depending on requirements for clearance with other components of the vehicle, first arm  20  and/or second arm  21  could curve, bend or vary in cross sectional profile at various locations along their lengths. Another preferred embodiment replaces first arm  20  and/or second arm  21  with adjacent round tubes, thus allowing threaded connections with knuckles  15  and/or junction  30 . Another preferred embodiment replaces the hollow tubes of first arm  20  and/or second arm  21  with “C” sections, and additionally preferably includes a facia covering the opening between first arm  20  and second arm  21 . 
     Because it is difficult to use high strength alloys such as aluminum alloys to manufacture a seamless tube, such as the preferred embodiment of second arm  21 , with the aspect ratio and elliptical cross sectional shape and the different wall thickness necessary to structurally optimize its design, a multi-piece assembly is utilized in one preferred embodiment of this invention to manufacture an elliptical tube. Two halves of an elliptical tube including a lower piece  23  and an upper piece  24  are mated together to produce a tube with an elliptical cross section. In order to properly align pieces  23  and  24  relative to one another, and to mate them more securely to each other, one or more rectangular keys  22  may be included on each side of the assembly. The keys  22  fit into corresponding slots on pieces  23  and  24 . The preferred method for attaching pieces  23 ,  24  and keys  22  is with a powerful adhesive, although more traditional attachment means such as welding, screws, collars, etc., are possible. When an adhesive is used, keys  22  afford shear planes, typically perpendicular to the primary mating plane of pieces  23  and  24 , that improves the performance of the adhesive. While it is possible to machine one or more keys or shear planes into the mating surface of lower piece  23  and/or upper piece  24 , one or more separate keys  22  on each side of first arm  20  and/or second arm  21  are normally simpler from a manufacturing standpoint. 
     Because of the triangulated orientation of first arm  20  and second arm  21  in the crank structure  1 , the design of first arm  20  and/or second arm  21  is optimized for resisting deflection regardless of whether the crank structure  1  is in the vertical or horizontal position while being subjected to a vertical load. 
     FIG. 3 shows a side elevational view of a crank structure  1  with a spindle attachment hole  5 , and a pedal shaft receiving hole  31 , or similar pedal attachment area  59  at its other end. In this figure, first and second connection struts  10  and  16  are longer than a preferred embodiment shown in FIG. 1, and incorporate a smaller attachment angle  84  between them. First and second connection struts  10  and  16  have approximately the same proportions as first arm  20  and second arm  21 , which are correspondingly shorter than the design of FIG. 1. A bridge  26  serves both as a means to attach the middle ends of first and second connection struts  10  and  16 , and first arm  20  and second arm  21  together, and to complete the triangle otherwise formed by first and second connection struts  10  and  16 , and first arm  20  and second arm  21  on either of its sides, thereby maximizing the rigidity of the structure. Additional bridges  26 , not shown, can be included at other locations than the junction of first and second connection struts  10  and  16 , and first and second arms  20  and  21 , in order to further stiffen the structure. Bridge  26  is shown in this figure as a flat plate viewed from the side, although it could be a truss section, thereby effectively shortening first connection strut  10  and/or second connection strut  16 , and first arm  20  and/or second arm  21 , at the expense of cost and complexity. It is presumed that there would be weight saving techniques, such as the inclusion of holes in bridge  26 , utilized during the manufacture of crank structure  1 . In this design, first and second connection struts  10  and  16 , and first arm  20  and second arm  21  may be identical. This structure offers the same advantage as the design of FIG. 1 in terms of reduced material weight by virtue of the structural material being located away from the neutral axis of the crank structure  1 . The neutral axis for the entire crank structure  1  is the axis through the structure which intersects the axis of rotation of the spindle and the axis of rotation of the pedal. Although this design has the same high material stress levels as a traditional single span crank where first connection strut  10  intersects hub  6 , it is structurally superior, and therefore potentially lighter and stronger, to a traditional single span crank along most of its length. 
     FIG. 4 shows a side elevational view of a triangulated crank structure  1  wherein second connection strut  16  of the previous designs extends directly from the vicinity of hub  6  to the vicinity of junction  30  thereby eliminating the need for a separate second arm  21 . A bridge  26  is included in this design to provide the necessary triangulation and interconnection means to first connection strut  10  and first arm  20 . It is possible to modify current single span cranks to become triangulated designs by attaching a first connection strut  10 , a first arm  20 , and a bridge  26  to current non-triangulated crank designs to increase their stiffness and/or reduce their weight. While the design of FIG. 4 shows the triangulating first connection strut  10 , first arm  20 , and bridge  26  above the second connection strut  16 , there is no reason that the design could not be inverted with respect to a horizontal axis. 
     FIG. 5 shows a side elevational view of a crank structure  1  which includes a plurality of locations to fasten the structure  1  to a sprocket or sprocket assembly. FIG. 5 further shows a radially symmetric arrangement of five dashed lines  41  intersecting at the center of hub  6 , and a circular dashed line  42  concentric with hub  6 . The locations of the intersections of lines  41  and a circle  42 , of which only one is shown, represent the bolt hole  37  locations of a typical five bolt pattern for attaching a sprocket assembly to the crank structure  1 . Flanges  35  allow the sprocket to be attached directly to first and second connection struts  10  and  16 , thus avoiding a sprocket attachment means emanating from hub  6 , such as flange  36 . This eliminates opportunities for creaking or breaking at the junction between the hub  6  and any radially concentric sprocket mounting hole array attached thereto. Furthermore, attaching flanges  35  directly to first and second connection struts  10  and  16  improves structural efficiency over other designs since first and second connection struts  10  and  16  are already in the immediate vicinity of the sprocket attachment points, represented by the location of bolt holes  37 , and therefore less material is necessary than would otherwise be required to connect flanges  35  to hub  6 . Braces  38  may be included to provide additional reinforcement to flange  36 . The arrangement of flanges  35  in FIG. 5 represent just one of numerous possible configurations that take advantage of the proximity of first and second connection struts  10  and  16  to industry standard sprocket mounting holes locations  37 . It should be noted that while flanges  35  are attached to first and second connection struts  10  and  16  in the preferred embodiment, they could be attached to other components of the crank structure  1  on other crank structure designs that are modifications of the preferred embodiment, wherein said other components may be in close proximity to standard or non-standard sprocket mounting locations. 
     FIG. 6 also shows a side elevational view of a crank structure  1  which includes a plurality of locations to fasten the structure  1  to a sprocket or sprocket assembly. FIG. 6 further shows a radially symmetric pattern of four dashed lines  41  intersecting at the center of hub  6 , and a circular dashed line  42  which is concentric with hub  6 . Only one such circular dashed line  42  is shown, although additional ones concentric with hub  6  are representative of bolt pattern diameters typical of multi-speed bicycles today. The locations of the intersections of lines  41  and circle  42  represent the bolt hole  37  locations of a typical four bolt pattern for attaching a sprocket assembly to the crank structure  1 . Connection strut holes  39  allow the sprocket to be attached directly to first and second connection struts  10  and  16 , thus avoiding a sprocket attachment means emanating from hub  6 , such as flange  36 . The arrangement of strut holes  39  in FIG. 6 represent just one of numerous possible configurations that take advantage of the proximity of first and second connection struts  10  and  16  to industry standard sprocket mounting holes locations  37 . 
     FIG. 7 shows a side elevational view of a crank structure  1  with a hub  6 , a first arm  20  and second arm  21 , and a junction  30  which are all interconnected. The interconnection means between hub  6  and knuckles  15  of the previous structure is comprised of first and second connection struts  10  and  16  each comprised of a single element. In this figure, single element design of first and second connection struts  10  and  16  is replaced with a multi-element connection strut design consisting of first connection strut segments  10   a  and  10   b,  and second connection strut segments  16   a  and  16   b.  While it is certainly possible to have more than two such strut segments coming off one side of hub  6 , the benefit of additional struts is marginal at best compared to a single strut or double strut design. In this embodiment, first connection strut segments  10   a  and  10   b,  and second connection strut segments  16   a  and  16   b,  are non-parallel, thus providing a degree of triangulation in the attachment of knuckles  15 . Each knuckle  15  of this embodiment has a third hole to accommodate the additional strut segment of the design. In another preferred embodiment, knuckles  15  are integral with first connection strut segments  10   a  and  10   b,  and second connection strut segments  16   a  and  16   b.  In this preferred embodiment, hub  6  also has holes or solid connection means to rigidly secure one of each of the ends of first and second pairs of connection strut segments  10   a  and  10   b,  and  16   a  and  16   b.  This design offers the manufacturing advantage of economically fabricating hub  6  and/or knuckles  15  as castings, then utilizing round tubes or tubes comprising a cross section such as that of first arm  20 , or alternative non-tubular interconnection means, to interconnect hub  6  and knuckles  15  with minimal weight. When non-tubular connection strut segments  10   a  and  10   b,  and  16   a  and  16   b  are utilized in the design, the manufacturing option to fabricate hub  6 , knuckles  15 , and interconnecting strut segments  10   a,    10   b,    16   a,  and  16   b  from a single piece of structural material such as metal becomes more practical. Knuckles  15  or first and second arms  20  and  21 , can be fabricated to include flanges with bolt holes or other means for attachment directly to a sprocket or sprocket assembly, since that can be more practical than attaching a sprocket or sprocket assembly directly to first connection strut segments  10   a  and  10   b,  second connection strut segments  16   a  and  16   b,  or to a rigid fixture attached thereto, depending on the proximity of said components relative to the sprocket attachment points. 
     A structure  1  is disclosed comprising first connection strut  10  and a second connection strut  16  radially emanating asymmetrically from hub  6 . First and second connection struts  10  and  16  include a reinforcing web  11  on their respective sides facing away from the pedal attachment area  59 . In the preferred embodiment shown in FIG. 8, outside reinforcing webs  11  are located on the inboard halves of first and second connection struts  10  and  16 , relative to the plane of the bicycle. 
     FIG. 8 also shows a reinforcing web  12  that mates with first connection strut  10  and second connection strut  16  on their respective sides facing toward pedal attachment area  59 . In this preferred embodiment, reinforcing webs  12  are located on the outboard halves of first and second connection struts  10  and  16 , relative to the plane of the bicycle. 
     By positioning reinforcing webs  11  and  12  on the inboard and outboard corners of first and second connection struts  10  and  16  respectively, regardless of the presence of a chain drive sprocket, they line up much better with the point where the load of the rider&#39;s weight is applied to a pedal attached to the structure. That alignment makes the structure stiffer and stronger than it would be if reinforcing webs  11  and  12  were aligned more along the centerlines of first and second connection struts  10  and  16 . It should be noted that reinforcing webs  11  and  12  are essentially nothing more than concentrations of structural material positioned somewhat diagonally in the cross-section of first and second connection struts  10  and  16 . It is not imperative that such concentrations represented by reinforcing webs  11  and  12  be positioned along the exterior faces of first and second connection struts  10  and  16 , as long as they are in that general vicinity. The fore and/or aft faces of first and second connection struts  10  and  16  may be thickened and/or widened so that their exterior surfaces become flush with reinforcing webs  11  and  12 , while still maintaining the functional benefit of reinforcing webs  11  and  12 . 
     In the present invention, first connection strut  10  and second connection strut  16  include or are attached to knuckles  15 . In FIG. 8, one of the knuckles  15  has a backside hole  71  for receiving arm  21 . Because of the triangulated nature of the structure, and the fact that its preferred embodiment is assembled by inserting rigid arms  20  and  21  into knuckles  15 , a novel assembly technique for triangulated crank structures is disclosed. The assembly technique of sliding end fittings with blind holes over a single linear segment will not work in a triangulated crank structure. In order to avoid the need to fabricate at least one of knuckles  15  (or junction  59 ) from multiple pieces for a multi-piece structure requiring assembly, a backside hole  71  in knuckle  15  is preferred. Backside hole  71  allows the structure to be assembled by inserting arm  21  into and through knuckle  15  a sufficient distance to allow the other arm  20  to be capped by both pedal attachment area  59  and knuckle  15  to the extent necessary for that portion of the structure to be properly assembled. Once the first arm  20  is assembled, the remaining arm  21  which has been inserted through hole  71  can be slid back out of the hole until its second distal end  58  is properly located in pedal attachment area  59 , leaving enough of second crank end  54  still inside knuckle  15  to facilitate a properly secure attachment thereto. An optional cover for backside hole  71  could be included in the final assembly steps. The portion of arm  21  which is inserted through knuckle  15  during the assembly process should be generally uniform in outer cross-section profile to avoid the need for shims when utilizing this technique. 
     Depending on the assembly apparatus used, it may be more practical to assemble both arms utilizing a backside hole  71  in each of knuckles  15  in order to duplicate one insertion process rather than have two separate arm insertion procedures. The backside hole simplifies fabrication of knuckles  15  (or pedal attachment area  59 ) by allowing them to be manufactured without a separable subcomponent to secure first arm  20  or second arm  21  once it is in place. 
     FIG. 8 also shows arm webs  70  which brace the connection between first arm  20  and second arm  21 . These arm webs  70  are structurally more efficient than a bridge structure spanning first arm  20  and second arm  21  that is perpendicular to the plane of their axes. Arm webs  70  are the most efficient means of controlling stresses and deflections within the pedal attachment area  59 . They also help the pedal attachment area  59  resist the lateral bending of first arm  20  and second arm  21 , which reduces the lateral deflections in those arms, allowing them to be made lighter than would possible for a given load capacity without arm webs  70 . It should be noted that arm webs  70  exist by virtue of the elimination of structural material at the convergence area of first arm  20  and second arm  21 . While the term “web” is appropriate to describe the elements shown in FIG. 8, “web” is intended as functionally equivalent to any other arrangement which laterally biases the distribution of structural material at the interior side of the convergence area of first arm  20  and second arm  21 . 
     Finally, the first arm  20  of FIG. 8 is non-uniform in cross-sectional area along its length. The actual cross-sectional profile is not a factor in this regard as long as the mass of the half of the arm which includes first distal end  56 , adjusted for changes in material density, is less than the mass of the half of the arm indicated by first crank end  52 . This variation in cross sectional area allows either or both of first and second arms  20  or  21  to be optimized based on the varying stresses across their lengths. The lateral bending stresses of first arm  20  and second arm  21  are much greater at their first and second distal ends  56  and  58  respectively, when a load is applied to a pedal attached to pedal attachment area  59 . 
     FIG. 9 is a cross-sectional view of a straight or curved first arm  20  (which may be interchangeable with second arm  21 ). It shows arm  20  comprising an interior ellipse. When arm  20  is fabricated from a structural fiber composite material, the elliptical core  25  is composed of interlaced structural fibers with a non-axial orientation. Even when it is very thin, this elliptical core  25  serves as an attachment surface for a surrounding layer of outer axial fibers  26  aligned generally axially with respect to longitudinal axis of the arm  20 . The elliptical nature of the core  25  gives arm  20  enhanced crush resistance, since unlike ovals or box sections, an ellipse has no flat surfaces on its cross-section. Flat surfaces lack curvature by definition, and convex surfaces can support greater loads than can comparable flat surfaces. A circle would typically provide better crush resistance for arm  20  than an ellipse for forces applied in line with the minor axis of the ellipse, 
     While it is possible to construct an arm  20  with inner fibers aligned generally axially, surrounded by interlaced outer fibers with a non-axial component, to do so would either constrain the exterior shape to that of an ellipse, or compromise the above described crush resistant benefits. Constructing arm  20  with an outer elliptical shell of interwoven non-axial fibers would limit the ability of the designer to optimize the lateral stiffness of the arm  20  for a given weight and exterior size. Because the axial fibers  26  of FIG. 9 are located outside the elliptical core  25 , it is easier to layer those axial fibers  26  thicker in some sections, than in others, without losing the benefits of the elliptical core  25 . In doing so, it is possible to create flanges or other features such as lobes  28 , which can be included at any part of the arm to increase bending stiffness or provide other benefits. While it is possible to include such features on the interior surface of arm  20 , that generally presents a greater manufacturing challenge. 
     A benefit of the inner elliptical core  25  is that the outer axial fibers  26  can be formed to include lobes  28  or other features that can improve lateral bending stiffness or other properties of arm  20 . Lobes  28 , such as shown in FIG. 9, preferably include increased material placed along peripheral outer surfaces of arm  20 . When the pedal associated with structure  1  is subjected to the load of the rider&#39;s weight, arm  20  is subjected to lateral bending stresses almost exclusively. 
     The “I-beam” is generally acknowledged as being at the pinnacle of structural efficiency for bending resistant applications. The cross-sectional shape of FIG. 9 may be considered similar to a modified I-beam, wherein the modification equates to splitting the web of an I-beam into two symmetric slightly arched webs which form an ellipse when combined with appropriately contoured flange sections. This allows the minimum cross-sectional dimension of arm  20  to be increased dramatically compared to the thin web of an I-beam with a similar area moment of inertia, while minimizing the amount of material that equates to the web of the I-beam. If an I-beam were used as the cross-section for arm  20 , its web would have to have a thickness compatible with the minimum width gap that could be deeply milled into receiving structures. Such a thick web would add unnecessary weight with very little increase in lateral bending stiffness. Another drawback of the I-beam cross section is its tendency to accumulate mud when used in muddy locations. 
     FIG. 10 shows a diagram of a cross-section of arm  20  according to a desirable configuration of the present invention. Arm  20  preferably includes a cross-section wherein the product of the average area of structural material  115  on each lateral side of a neutral lateral bending plane  105  times the square of the perpendicular distance from the neutral lateral bending plane  105  to the centroid of that structural material  115  on each lateral side of the neutral lateral bending plane  105  plus the moment of inertia of that area about an axis parallel to the neutral lateral bending plane  105  and through its centroid, is greater than the product of the average area of structural material  115  on the lateral sides of the neutral antilateral bending plane  110  times the square of the perpendicular distance from the neutral antilateral bending plane  110  to the two centroids of structural material  115  lateral to the neutral antilateral bending plane  110  plus the moment of inertia of that area about an axis parallel to the neutral antilateral bending plane  110  and through its centroid. 
     While in the foregoing specification this invention has been described in relation to certain preferred embodiments thereof, and many details have been set forth for purpose of illustration, it will be apparent to those skilled in the art that the apparatus according to this invention is susceptible to additional embodiments and that certain of the details described herein can be varied considerably without departing from the basic principles of the invention.