Abstract:
A bicycle transmission has among other things a rear hub with a freewheel with an outer freewheel body supporting a plurality of sprockets. A chain is shifted between adjacent pairs of the sprockets by a rear derailleur. Each sprocket includes inner attachment portion and a chain engaging portion having annular root portion and a plurality of teeth. The largest (low gear) sprocket has one or more recesses in the lateral surface that faces towards the center of the bicycle so that the largest (low gear) sprocket overlaps the abutments of the outer freewheel body.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Field of the Invention  
         [0002]     This invention generally relates to a sprocket for a bicycle transmission. More specifically, the present invention relates to a rear sprocket for a bicycle transmission having a large number of rear gears or sprockets.  
         [0003]     2. Background Information  
         [0004]     Bicycling is becoming an increasingly more popular form of recreation as well as a means of transportation. Moreover, bicycling has become a very popular competitive sport for both amateurs and professionals. Whether the bicycle is used for recreation, transportation or competition, the bicycle industry is constantly improving the various components of the bicycle. One component that has been extensively redesigned is the bicycle transmission.  
         [0005]     Over the past several years, bicycle riders have desired an increased number of speeds or gear ratios available in bicycle transmissions. Thus, over the past several years, the bicycle industry has increased the number of sprockets installed on the rear-wheel sprocket assembly of bicycles in order to provide additional different gear ratios. Specifically, road bicycles have seen the number of rear sprockets increase from five (5) to nine (9) to provide additional different gear ratios for the bicycle transmission. Mountain bicycles have also seen the number of rear sprockets increase -similarly. Even more recently, in more recent years, the number of rear sprockets has increased from nine (9) to ten (10) rear sprockets on some bicycles (i.e. road bicycles in particular).  
         [0006]     While these ten (10) speed rear sprocket assemblies work well, they suffer from some deficiencies. In particular, ten (10) speed rear sprocket assemblies are typically wider in the axial direction than the previous nine (9) speed rear sprocket assemblies. Accordingly, it can be difficult or even impossible to mount the ten (10) speed rear sprocket assemblies on some rear freewheel assemblies that were originally designed for nine (9) rear sprockets. Additionally, even if the ten (10) speed rear sprocket assemblies can be mounted on rear freewheel assemblies that were originally designed for nine (9) rear sprockets, shifting performance can be adversely affected.  
         [0007]     More specifically, in the current the ten (10) speed rear sprocket assemblies, the sprockets and the spacers have typically been constructed to be slightly narrower than the previous nine (9) rear sprockets and spacers, and a narrower chain has been utilized in order to achieve the desired shifting performance with the increased number of rear sprockets. However, even when such modifications are made, the ten (10) speed rear sprocket assembly (cassette) is still typically about 1.0 millimeter wider than a nine (9) speed rear sprocket assembly (cassette). Accordingly, if a ten (10) speed rear sprocket assembly (cassette) is mounted in the current manner, the top sprocket (smallest, outermost sprocket) is located laterally outwardly by about 1.0 millimeter more than the top sprocket of a nine (9) speed sprocket assembly (cassette) mounted on the typical freewheel. In some cases, this arrangement may result in the chain touching the bicycle frame when the chain is located on the rear top sprocket (e.g. if the chain is also located on the front top sprocket or largest outermost front chain ring and/or in certain riding conditions).  
         [0008]     In view of the above, it will be apparent to those skilled in the art from this disclosure that there exists a need for an improved rear sprocket for a rear sprocket assembly. This invention addresses this need in the art as well as other needs, which will become apparent to those skilled in the art from this disclosure.  
       SUMMARY OF THE INVENTION  
       [0009]     One object of the present invention is to provide a rear sprocket for a rear bicycle sprocket assembly that includes ten (10) sprockets, which can be mounted on an outer freewheel body in a space normally provided for a nine (9) sprocket assembly.  
         [0010]     Another object of the present invention is to provide a rear sprocket for a rear bicycle sprocket assembly that includes ten (10) sprockets, which optimizes shifting performance without adversely affecting strength.  
         [0011]     Another object of the present invention is to provide a rear sprocket for a rear bicycle sprocket assembly that includes ten (10) sprockets, which projects axially outwardly only about 0.25 millimeter further than a nine (9) sprocket assembly mounted on the same outer freewheel body.  
         [0012]     Another object of the present invention is to provide a rear sprocket for a rear bicycle sprocket assembly, which is relatively simple and inexpensive to manufacture and assemble on the outer freewheel body.  
         [0013]     Yet another object of the present invention is to provide an outer freewheel body that facilitates the mounting of a rear bicycle sprocket assembly that includes ten (10) sprockets as described in the previous objects of the present invention.  
         [0014]     The foregoing objects can basically be attained by providing a rear sprocket for bicycle transmission that comprises an inner attachment portion, an annular root portion and a plurality of teeth. The inner attachment portion has a first lateral surface facing in a first axial direction, a second lateral surface facing in a second axial direction and an inner peripheral edge extending between the first and second lateral surfaces. The annular root portion is located radially outward of the inner attachment portion with the annular root portion having a first side surface facing in the first axial direction and a second side surface facing the second axial direction such that the second side surface and the second lateral surface lie in a common plane. The teeth extend radially outward from an outer periphery of the root portion. The inner attachment portion has at least one recess formed on the first lateral surface and extending radially outward from the inner peripheral edge.  
         [0015]     The foregoing objects can also be basically be attained by providing an outer freewheel body for bicycle transmission that comprises a tubular portion and an abutment surface. The tubular portion has an outer surface with a plurality of sprocket engaging splines extending in an axial direction to define a plurality of sprocket engaging grooves disposed between the splines. The abutment surface is disposed at one end of at least one of the splines and faces in a first direction to limit axial movement of a sprocket. The grooves have bottom surfaces that extend beyond the abutment surface in an opposite axial direction relative to the first direction.  
         [0016]     These and other objects, features, aspects and advantages of the present invention will become apparent to those skilled in the art from the following detailed description, which, taken in conjunction with the annexed drawings, discloses a preferred embodiment of the present invention.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0017]     Referring now to the attached drawings which form a part of this original disclosure:  
         [0018]      FIG. 1  is a side elevational view of a bicycle having a rear wheel with a bicycle sprocket assembly in accordance with a first embodiment of the present invention;  
         [0019]      FIG. 2  is an enlarged, top plan view of the rear hub with the multiple sprocket assembly of the bicycle illustrated in  FIG. 1 , in accordance with the first embodiment of the present invention;  
         [0020]      FIG. 3  is a partially exploded, top plan view of the rear hub and sprocket assembly illustrated in  FIG. 2 ;  
         [0021]      FIG. 4  is an exploded perspective view of the rear hub and sprocket assembly illustrated in  FIGS. 2 and 3 ;  
         [0022]      FIG. 5  is an enlarged, partial cross-sectional view of the rear hub illustrated in  FIGS. 2-4  with only the bottom (largest) sprocket of the sprocket assembly coupled thereto, as seen along section line  5 - 5  of  FIG. 2 ;  
         [0023]      FIG. 6  is an enlarged, partial cross-sectional view of the freewheel side of the rear hub illustrated in  FIGS. 2-4 , as seen along section line  5 - 5  of  FIG. 2 ;  
         [0024]      FIG. 7  is an enlarged, partial cross-sectional view of the outer freewheel body of the freewheel of the rear hub illustrated in  FIGS. 2-6 ;  
         [0025]      FIG. 8  is an enlarged, outside elevational view of the sprocket assembly illustrated in  FIGS. 2-4 ;  
         [0026]      FIG. 9  is an outside elevational view of the bottom sprocket (i.e. the largest, innermost rear sprocket) of the sprocket assembly illustrated in  FIG. 8 ;  
         [0027]      FIG. 10  is an enlarged, cross-sectional view of the sprocket illustrated in  FIG. 9 , as seen along section line  10 - 10  of  FIG. 9 ; and  
         [0028]      FIG. 11  is an outside elevational view of a bottom sprocket (i.e. a largest, innermost rear sprocket) in accordance with a second embodiment of the present invention.  
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0029]     Selected embodiments of the present invention will now be explained with reference to the drawings. It will be apparent to those skilled in the art from this disclosure that the following descriptions of the embodiments of the present invention are provided for illustration only and not for the purpose of limiting the invention as defined by the appended claims and their equivalents.  
         [0030]     Referring initially to  FIGS. 1-4 , a bicycle  10  is illustrated having a rear bicycle hub  11  with a multi-stage rear sprocket assembly (cassette)  12  mounted on a freewheel  13  in accordance with a first embodiment of the present invention. The rear sprocket assembly  12  includes ten (10) rear sprockets S 1 -S 10  that are mounted on the freewheel  13  with a plurality of spacers U 1 -U 9  arranged between the sprockets S 1 -S 10 . The sprocket S 1  is the largest (i.e. has the most teeth), innermost sprocket of the rear sprocket assembly  12 . The sprocket S 10  is the smallest (i.e. has the fewest teeth), outermost sprocket. In the illustrated embodiment, the sprockets S 1 -S 10  have 23T, 21T, 19T, 17T, 16T, 15T, 14T, 13T, 12T, 11T tooth configurations, respectively. However, it will be apparent to those skilled in the bicycle art from this disclosure that the sprockets S 1 -S 10  can have different tooth configurations as needed and/or desired.  
         [0031]     The sprocket assembly  12  and the freewheel  13  are configured and arranged such that the smallest sprocket S 10  is located axially only about 0.25 millimeter or less outwardly of the location normally occupied by the smallest sprocket of a conventional nine (9) speed rear sprocket assembly (cassette), when mounted on the freewheel  13 . In particular, the rear sprocket assembly  12  of the present invention is about 1.0 millimeter wider than a conventional nine (9) speed rear sprocket assembly as measured axially. However, the largest rear sprocket S 1  and the freewheel  13  are configured and arranged such that the rear sprocket assembly  12  is located about 0.75 millimeter or more closer to a center plane P of the bicycle  10  than a conventional nine (9) speed rear sprocket assembly when mounted on the freewheel  13 , as explained below in more detail.  
         [0032]     Referring to  FIG. 1 , the bicycle  10  basically has a frame  14  with front and rear wheels  15  and  16  rotatably coupled thereto. A front fork  17  is pivotally coupled to the front of the frame  14  with the front wheel  15  rotatably coupled thereto in a conventional manner. A handlebar  18  is rigidly attached to the front fork  17  in order to turn the front wheel  15  to steer the bicycle  10 . The rear wheel  16  is rotatably coupled to a rear portion or rear triangle of the frame  14  via the rear hub  11  in a conventional manner. A seat  19  is adjustably coupled to the frame  14  via a seat post in a conventional manner, and a drive train  20  is provided on the bicycle  10  for propelling the bicycle  10 . The bicycle  10  is conventional except for selected parts of the drive train  20 , as discussed below.  
         [0033]     The drive train  20  basically includes the rear multi-stage sprocket assembly  12  of the present invention, a pair of pedals  21 , a front multi-stage sprocket assembly  22  mounted to rotate with the pedals  21 , and a chain  23  extending between the rear multi-stage sprocket assembly  12  and the front multi-stage sprocket assembly  22 . As mentioned above, the rear sprocket assembly  12  is preferably coupled to the rear hub  11  via the freewheel  13 . The pedals  21  are coupled to the front multi-stage sprocket assembly  22  by a conventional crank set to transfer force from the rider to the chain  23 . The force from the chain  23  is selectively transferred to the rear wheel  16  via the rear hub  11  (e.g. via the rear sprocket assembly  12  and the freewheel  13  depending on the direction of rotation) in a conventional manner. The chain  23  used in the drive train  20  is designed to be compatible with the rear ten-stage sprocket assembly  12 . In particular, the chain  23  is preferably slightly narrower than a chain used with a conventional rear nine-stage sprocket assembly due to the width and spacing of the sprockets S 1 -S 10 . Narrower chains such as chain  23  are well known in the bicycle art. Accordingly, the chain  23  will not be explained and/or illustrated in detail herein. Similarly, the front sprocket assembly  22  is configured to be compatible with the relatively narrower chain  23 . Such front sprocket assemblies  22  are well known in the bicycle art. Accordingly, the front sprocket assembly  22  will not be explained and/or illustrated in detail herein.  
         [0034]     The drive train  20  is basically controlled by conventional front and rear shifting units (not shown) that control the lateral positions of front and rear derailleurs  27  and  28  in a conventional manner. Thus, when the rider is pedaling, the front and rear sprocket assemblies  22  and  12  are rotating to circulate or cycle the chain  23  due to the movement of the pedals  21 . The shifting units (not shown) can be actuated by the rider to control the lateral positions of the front and/or rear derailleurs  27  and/or  28 . When the chain  23  is circulated or cycled in the forward (clockwise direction as seen in  FIG. 1 ), the shifting units can be actuated to control the gear ratio of the drive train  20  by controlling the lateral position of the chain  23  via the derailleurs  27  and  28  in a conventional manner. The derailleurs  27  and  28  selectively apply a lateral force inwardly/outwardly to the chain  23  to cause up/down shifts in a conventional manner. The drive train  20  is basically conventional, except for the rear multi-stage sprocket assembly  12  and the freewheel  13 . Thus, the drive train  20  will not be discussed and/or illustrated in further detail herein, except as related to the rear multi-stage sprocket assembly  12  and the freewheel  13 .  
         [0035]     Since the various parts of the bicycle  10  and most of the parts of the drive train  20  are well known in the bicycle art, these parts of the bicycle  10  and the drive train  20  will not be discussed and/or illustrated in detail herein, except as related to the present invention. However, it will be apparent to those skilled in the bicycle art from this disclosure that various conventional bicycle parts such as brakes, different hub structures, etc., which are not illustrated and/or discussed in detail herein, can be used in conjunction with the present invention as needed and/or desired.  
         [0036]     Referring now to  FIGS. 2-10 , the rear sprocket assembly (cassette)  12  in accordance with the present invention will now be explained in more detail. As mentioned above, the rear sprocket assembly  12  includes ten (10) rear sprockets S 1 -S 10  that are mounted on the freewheel  13  with the plurality of spacers U 1 -U 9  arranged between the sprockets S 1 -S 10  such that the sprockets S 1 -S 10  are spaced from each other at predetermined intervals. The sprockets S 1 -S 10  and the spacers U 1 -U 9  are fixedly mounted on the freewheel  13  of the rear hub  11  such that the sprockets S 1 -S 10  rotate together about a center hub rotation axis X. The sprockets S 1 -S 10  typically rotate together in a forward rotational direction R (e.g., in a clockwise direction as viewed in  FIG. 1 ) when the rider is pedaling in a forward (clockwise) direction to propel the bicycle  10  in a forward direction as seen in  FIG. 1 .  
         [0037]     In the illustrated embodiment, each of the spacers U 1 -U 9  preferably has an axial thickness of about 2.35 millimeters in order to provide the desired spacing for the sprockets S 1 -S 10 . Each of the sprockets S 1 -S 10  preferably has a substantially uniform maximum axial thickness T of about 1.60 millimeters. Accordingly, the assembled rear sprocket assembly  12  (i.e. the assembled sprockets S 1 -S 10  and spacers U 1 -U 9 ) preferably has an axial width of about 37.5 millimeters as compared to an axial width of about 36.5 millimeters for a conventional nine (9) speed rear sprocket assembly (not shown) having slightly thicker sprockets and spacers. However, in the illustrated embodiment, the sprocket S 1  is configured and arranged to be located about 0.75 millimeter or more closer to the center plane P of the bicycle  10  than a conventional nine (9) speed rear sprocket assembly, as explained below.  
         [0038]     Referring mainly to  FIGS. 8-10 , the sprocket S 1  basically includes an annular main body portion  30 , an inner annular attachment portion  32  and an annular chain engagement or root portion  34 . Preferably, the main body portion  30 , the inner attachment portion  32  and the annular chain engagement portion  34  are integrally formed together as a one-piece, unitary member from a lightweight, rigid material such as a metallic material (e.g. titanium alloy) with a surface treatment applied thereto in a conventional manner. The inner attachment portion  32  extends radially inwardly from the main body portion  30 , while the chain engagement portion  34  extends radially outwardly from the main body portion  30 .  
         [0039]     The inner attachment portion  32  includes a first annular lateral surface  36 , a second lateral surface  38 , an inner peripheral edge (surface)  40 , a plurality of primary recesses  42  and a position recess  44 . The first lateral surface  36  faces in a first axial direction (i.e. toward the center plane P). The second annular lateral surface  38  faces in a second axial direction (i.e. away from the center plane P). The inner peripheral edge  40  extends between the first and second lateral surfaces  36  and  38 . The recesses  42  and  44  are arranged and configured such that the sprocket S 1  will be located axially closer to the center plane P of the bicycle  10  than a conventional nine (9) speed rear sprocket assembly, as explained below. The first and second lateral surfaces  36  and  38  are preferably parallel to each other, and preferably perpendicular to the inner peripheral edge  40 .  
         [0040]     The inner peripheral edge  40  is preferably a notched surface with a plurality of primary hub engaging projections  41   a  and a positioning hub engaging projection  41   b.  The hub engaging projections  41   a  and  41   b  define a plurality of primary hub engaging slots  43   a  and a positioning hub engaging slot  43   b  disposed between the hub engaging projections  41   a  and  41   b,  as seen in  FIG. 9 . The hub engaging projections  41   a  and  41   b  extend radially inwardly. The inner peripheral edge  40  is configured and arranged to non-rotatably mate with a corresponding exterior surface of the freewheel  13 , explained below. In particular, the positioning hub engaging projection  41   b  and the positioning hub engaging slot  43   b  are arranged in a particular orientation relative to the chain engagement portion  34 . The sprockets S 2 -S 10  have similar structures to orient the teeth of the various sprockets relative to each other to optimize shifting in a conventional manner.  
         [0041]     The recesses  42  and  44  are preferably formed in the first lateral surface  36 . In the illustrated embodiment with the sprocket S 1  having a thickness T of about 1.60 millimeter, the recesses  42  and  44  preferably have an axial depth D of 0.75 millimeter (preferably between 0.75 and 0.80 millimeter). Thus, in the illustrated embodiment the depth D is preferably about one-half or slightly less than one-half of the thickness T of the sprocket S 1 . In any case, in the illustrated embodiment with the sprocket S 1  having a thickness T of about 1.60, the depth D is preferably at least 0.75 millimeter and less than or equal to 1.0 millimeter. Accordingly, with this configuration, the sprocket S 10  will be located between 0.00 and 0.25 millimeter axially outwardly of the normal position of a top (small) sprocket of a conventional nine (9) speed rear sprocket assembly (preferably 0.25 millimeter).  
         [0042]     The primary recesses  42  are disposed radially outwardly of the primary hub engaging slots  43   a,  while the positioning recess  44  is disposed radially outwardly of the positioning hub engaging slot  43   b.  The recesses  42  and  44  permit the sprocket S 1  to be mounted on the freewheel  13  to be axially about 0.75 millimeter closer to the center plane P than a conventional nine (9) speed rear sprocket assembly, as explained in more detail below.  
         [0043]     Each of the recesses  42  and  44  has a mating configuration to engage the freewheel  13 , described below. In particular, each of the recesses  42  and  44  has a substantially rectangular configuration as viewed axially ( FIG. 9 ) with curved inner and outer radially spaced ends. Each of the primary recesses  42  includes a contact surface  45   a  and a curved outer radial end surface  45   b  with axially extending ends  45   c  and  45   d  extending radially inwardly therefrom. The contact surfaces  45   a  are preferably parallel to the first lateral surface  36 , while the surfaces  45   b,    45   c  and  45   d  are preferably perpendicular to the contact surfaces  45   a.  The depth D is measured axially between the contact surfaces  45   a  and the first lateral surface  36 . The positioning recess  44  has a configuration identical to the primary recesses  42 , but is slightly smaller.  
         [0044]     The main body portion  30  of the sprocket S 1  includes a first annular side surface  46  facing in the first axial direction and a second annular side surface  48  facing in the second axial direction with a plurality of cutouts  50  extending between the first and second side surfaces  46  and  48  for the purpose of weight reduction. The first side surface  46  extends radially outwardly from the first lateral surface  36  of the inner attachment portion  32 , while the second side surface  48  extends radially outwardly from the second lateral surface  38  of the inner attachment portion  32 . The first and second side surfaces  46  and  48  are preferably flat, parallel surfaces with the cutouts  50  extending therebetween.  
         [0045]     The annular chain engagement or root portion  34  of the sprocket S 1  includes a plurality of chain engagement teeth  52  with a plurality of roots  54  arranged therebetween in a circumferentially spaced, alternating arrangement, as best seen in  FIG. 9 . A plurality of holes  56  can optionally be formed in the chain engagement portion  34  for weight saving. As mentioned above, in the illustrated embodiment, the sprocket S 1  includes twenty-three chain engagement teeth  52 .  
         [0046]     The sprockets S 2 -S 10  and the spacers U 1 -U 9  are conventional bicycle parts that are well known in the bicycle art. Accordingly, the sprockets S 2 -S 10  and the spacers U 1 -U 9  will not be explained and/or illustrated in detail herein, except as related to the present invention. In other words, the sprockets S 2 -S 10  are substantially identical to the sprocket S 1 , except that they are smaller (have fewer teeth), do not include the recesses  42  and  44 , and may have other conventional modifications due to their decreased size.  
         [0047]     The sprockets S 1 -S 10  and the spacers U 1 -U 9  are non-rotatably, fixedly attached on an external surface of the freewheel  13 . In particular, the sprockets S 1 -S 10  and the spacers U 1 -U 9  are slid onto an external mating surface of the freewheel  13  in an alternating arrangement, as shown in  FIG. 4 . After the sprockets S 1 -S 10  and the spacers U 1 -U 9  are slid onto the freewheel  13 , a locking ring LR ( FIGS. 2 and 3 ) is attached to the freewheel  13  in a conventional manner to retain all of the sprockets S 1  -S 10  and the spacers U 1 -U 9  on the freewheel  13 . The locking ring LR is a conventional member having an externally threaded tubular portion that threads into an end of the freewheel  13  and an annular ring-shaped flange extending from one end of the externally threaded tubular portion. With the above arrangement, sprockets with different numbers of teeth can be substituted relatively easily for the sprockets S 1 -S 10 , as long as the inner most sprocket has an inner attachment portion like that disclosed herein. Of course, it will be apparent to those skilled in the bicycle art from this disclosure that some or all of the sprockets S 1 -S 10  and/or spacers U 1 -U 9  can be fixedly attached to each other via a plurality of fasteners (not shown) such as rivets in a conventional manner prior to mounting on the freewheel  13  as needed and/or desired.  
         [0048]     In the illustrated embodiment, the spacers U 1 -U 9  are identical, i.e. the spacers U 1 -U 9  have the same axial thickness and diameter. However, it will be apparent to those skilled in the bicycle art from this disclosure that the spacers U 1 -U 9  can have different configurations as needed and/or desired. Moreover, it will be apparent to those skilled in the bicycle art from this disclosure that various alternative structures can be provided for mounting and spacing the sprockets without departing from the scope of the present invention, as needed and/or desired.  
         [0049]     Referring now to  FIGS. 2-7 , the rear hub  11  and the freewheel  13  will now be explained in more detail. The freewheel  13  basically includes an outer tubular freewheel body  60 , an inner tubular freewheel body  62  and a one-way clutch  64 . The rear hub basically includes a hub axle  66  and an outer hub body or shell  68  rotatably mounted on the hub axle  66  via bearings or the like in a conventional manner. The hub shell  68  is coupled to the rear bicycle rim via a plurality of spokes in a conventional manner. The inner tubular freewheel body  62  is freely rotatably mounted on the hub axle  66 , and non-rotatably connected to the hub shell  68 . The outer freewheel body  60  is rotatably mounted relative to the inner freewheel body  62  with the one-way clutch  64  disposed therebetween in a conventional manner. Thus, forward rotation R of the rear sprocket assembly  12  rotates the hub shell  68  to propel the bicycle, while rearward rotation (in a direction opposite of R) of the rear sprocket assembly  12  is freely permitted relative to the inner freewheel body  62  and the hub shell  68 .  
         [0050]     The freewheel  13  is conventional, except for the outer tubular freewheel body  60 . Moreover, the outer freewheel body  60  is conventional except for the external configuration thereof, explained below. Accordingly, the freewheel  13  will not be explained and/or illustrated in detail herein, except as related to the present invention. Rather, it will be apparent to those skilled in the bicycle art from this disclosure that the freewheel  13  includes various conventional parts such as bearing assemblies, seals, attachment rings and the like, as best seen in  FIG. 6 . Moreover, it will be apparent to those skilled in the bicycle art from this disclosure that the freewheel  13  operates in a conventional manner once the rear sprocket assembly  12  is mounted thereon and that the locking ring LR is threaded into the free end of the hub body  60 .  
         [0051]     Referring mainly to  FIG. 7 , the outer tubular freewheel body  60  basically includes an outer tubular portion  70  having an outer surface  72  with a plurality of sprocket engaging splines  74  extending in the axial direction to define a plurality of axially extending sprocket engaging grooves  76  between the splines  74  in an alternating manner. The splines  74  are configured to mate with the slots  43   a  and  43   b  of the sprocket S 1 , while the grooves  76  are configured to mate with the projections  41   a  and  41   b  of the sprocket S 1 . In other words, one of the splines  74  is smaller (not shown) than the remaining splines  74  in order to be received in the positioning slot  43   b,  while one of the grooves  76  is larger (not shown) than the remaining grooves  76  in order to receive the positioning projection  41   b  in a conventional manner. Thus, the desired orientation of the sprockets S 1 -S 10  relative to each other can be obtained.  
         [0052]     Each of the splines  74  includes a stop section  78  disposed at one end thereof (i.e. arranged at the inner axial end thereof). The stop sections  78  extend radially outwardly. Each of the stop sections  78  includes an axially facing abutment surface  80  that is configured and arranged to contact the sprocket S 1 . In particular, the stop sections  78  and the abutment surfaces  80  are sized and configured such that the stop sections  78  are at least partially received in the recesses  42  and  44 . Similar to the splines  74  and the grooves  76 , one of the stop sections  78  is smaller (not shown) than the remaining stop sections  78  in order to be received in the positioning recess  44 . In other words, the stop sections  78  are shaped to mate with the recesses  42  and  44  of the sprocket S 1 , with the abutment surfaces  80  contacting the contact surfaces of the recesses  42  and  44  to limit axial movement of the sprocket S 1  . The abutment surfaces  80  face in an axial direction away from the center plane P (i.e. a first axial direction).  
         [0053]     The grooves  76  extend axially toward the center plane P beyond the abutment surfaces  80  in order to accommodate the axially closer position of the sprocket S 1  to the center plane P. In a particular, each of the grooves  76  has a bottom surface  82  that extends axially toward the center plane P (i.e. in a second axial direction opposite the first axial direction) beyond the abutment surfaces  80  by a distance E that is at least 0.75 millimeter. In the illustrated embodiment, the distance E is about 1.0 millimeter, and then the bottom surfaces  82  of the grooves  76  begin to taper outwardly. In any case, the distance E should be at least as large as the depth D of the recesses  42  and  44 .  
       Second Embodiment  
       [0054]     Referring now to  FIG. 11 , a modified bottom sprocket S 1 ′ in accordance with a second embodiment will now be explained. The bottom sprocket S 1 ′ replaces the bottom sprocket S 1  in the rear sprocket assembly  12  of the first embodiment on the freewheel  13  of the rear hub  11 . Thus, a modified rear sprocket assembly is formed when the modified bottom sprocket S 1 ′ is substituted for the bottom sprocket S 1  in the rear sprocket assembly  12  of the first embodiment.  
         [0055]     The sprocket S 1 ′ is identical to the sprocket S 1  of the first embodiment, except the sprocket S 1 ′ includes a single annular recess  42 ′ extending around the inner periphery rather than the multiple recesses  42  and  44  of the first embodiment. The recess  42 ′ functions the same as the multiple recesses  42  and  44  of the first embodiment. In other words, the single annular recess  42 ′ extending around the inner periphery has the same depth as the multiple recesses  42  and  44  of the first embodiment, but simply has a different shape as viewed axially ( FIG. 11 ). The annular shape permits alternate techniques for manufacturing and reduces weight for the sprocket S 1 ′ further. The depth or axial dimension of the single annular recess  42 ′ is the same as the multiple recesses  42  and  44  of the first embodiment. Thus, when the modified rear sprocket assembly is mounted on the rear hub  11 , the single annular recess  42 ′ of the sprocket S 1 ′ will have the same configuration and relationship as shown in  FIG. 5 .  
         [0056]     In view of the similarity between the first and second embodiments, the parts of the second embodiment that are identical to the parts of the first embodiment will be given the same reference numerals as the parts of the first embodiment. Moreover, the descriptions of the parts of the second embodiment that are identical to the parts of the first embodiment may be omitted for the sake of brevity. However, it will be apparent to those skilled in the bicycle art from this disclosure that the descriptions and illustrations of the first embodiment also apply to this second embodiment, except as explained and illustrated herein.  
         [0057]     As used herein, the terms “forward, rearward, above, below, lateral and transverse” as well as any other similar directional terms refer to those directions of a bicycle in its normal riding position, to which the rear sprocket assembly  12  and freewheel  13  are attached. Accordingly, these terms, as utilized to describe the rear sprocket assembly  12  and the freewheel  13  in the claims, should be interpreted relative to the bicycle  10  in its normal riding position. However, the terms “down shift” and “up shift” as used herein in reference to the rear sprocket assembly  12  should be interpreted to mean a shift from smaller to larger sprocket and from larger to smaller sprocket, respectively, as shown in  FIG. 2 .  
         [0058]     In understanding the scope of the present invention, the term “comprising” and its derivatives, as used herein, are intended to be open ended terms that specify the presence of the stated features, elements, components, groups, integers, and/or steps, but do not exclude the presence of other unstated features, elements, components, groups, integers and/or steps. The foregoing also applies to words having similar meanings such as the terms, “including”, “having” and their derivatives. Also, the terms “member” or “element” when used in the singular can have the dual meaning of a single part or a plurality of parts. Finally, terms of degree such as “substantially”, “about” and “approximately” as used herein mean a reasonable amount of deviation of the modified term such that the end result is not significantly changed. These terms of degree should be construed as including a deviation of at least ±5% of the modified term if this deviation would not negate the meaning of the word it modifies.  
         [0059]     While only selected embodiments have been chosen to illustrate the present invention, it will be apparent to those skilled in the art from this disclosure that various changes and modifications can be made herein without departing from the scope of the invention as defined in the appended claims. Furthermore, the foregoing descriptions of the embodiments according to the present invention are provided for illustration only, and not for the purpose of limiting the invention as defined by the appended claims and their equivalents.