Abstract:
A power transmission system for a wheeled personal transportation device such as a bicycle comprises a sequence of at least three operably interconnected sets of gearwheels, a first set in the sequence for receiving rotational force and a last set in the sequence for transmitting rotational force for a driven wheel of the device. The first set and the last set each comprise user-selectable gearwheels. At least one intermediate set in the sequence comprises an input gearwheel subset and an output gearwheel subset, at least one of the input gearwheel subset and the output gearwheel subset comprising a plurality of user-selectable gearwheels. A frame for a personal transportation device comprises a base and a steering shaft on the base for supporting a steering column. Crank connection means are provided on the base for operably receiving a crank/pedal combination and an associated first set of user-selectable gearwheels. An upper-rearward extension extends from a rear of the base for operably receiving a second set of gearwheels comprising an input gearwheel subset and an output gearwheel subset. At least one of the input gearwheel subset and the output gearwheel subset comprise a plurality of user-selectable gearwheels. The frame further comprises a subextension associated with the upper-rearward extension for supporting a gearwheel-change mechanism associated with a respective one of the output gearwheel subset and the input gearwheel subset; and a lower-rearward extension extending from the rear of the base for supporting the driven wheel and a rotatable third set of gearwheels.

Description:
FIELD OF THE INVENTION  
       [0001]     The system disclosed herein relates generally to personal transportation devices and more specifically, to a power transmission system for a wheeled personal transportation device.  
       BACKGROUND OF THE INVENTION  
       [0002]     It is well known that a relatively large crank shaft sprocket wheel on wheeled transportation device such as a bicycle or geared tricycle when interconnected via chain with a small sprocket on a driven wheel will give a higher rotation speed than would be the case with a small crank shaft sprocket.  
         [0003]     U.S. Pat. No. 1,360,032 (Schiffner) discloses a bicycle gearing system for increasing the speed for a given rotation of the pedal shaft without enlarging the crank shaft sprocket wheel. A single front sprocket on the crank shaft is connected by chain to a small sprocket on a second shaft. The small sprocket on the second shaft turns in unison with a larger sprocket on the second shaft, which is in turn connected by chain to a single small sprocket co-axial with the rear wheel. Numerous variants of the system proposed in the above-mentioned Schiffner patent have been proposed, for example in U.S. Pat. No. 1,535,714 (Burke), U.S. Pat. No. 5,102,155 (Chou) and U.S. Pat. No. 6,394,478 (Balajadia).  
         [0004]     The prior art designs for increasing rotation speed of a driven wheel of a bicycle suffer drawbacks, such as limited or no available gear selection, configurations that in practice prove physically difficult or inconvenient for a user to employ, and great complexity.  
         [0005]     It is an object of an aspect of this invention to provide a power transmission system for a personal transportation device such as a bicycle that overcomes some or all of these drawbacks in the prior art systems.  
       SUMMARY OF THE INVENTION  
       [0006]     According to one aspect, there is provided a power transmission system for a wheeled personal transportation device, comprising:  
         [0007]     a sequence of at least three operably interconnected sets of gearwheels, a first set in the sequence for receiving rotational force and a last set in the sequence for transmitting rotational force for a driven wheel of the device, the first set and the last set each comprising user-selectable gearwheels;  
         [0008]     at least one intermediate set in the sequence comprising an input gearwheel subset and an output gearwheel subset, at least one of the input gearwheel subset and the output gearwheel subset comprising a plurality of user-selectable gearwheels.  
         [0009]     According to another aspect, there is provided a power transmission system for a wheeled personal transportation device, comprising:  
         [0010]     a first set of user-selectable gearwheels for receiving rotational force;  
         [0011]     a second set of gearwheels comprising an input gearwheel subset operably interconnected with the first set, and an output gearwheel subset, at least one of the input gearwheel subset and the output gearwheel subset comprising a plurality of user-selectable gearwheels; and  
         [0012]     a third set of user-selectable gearwheels operably interconnected with the output gearwheel subset for transmitting rotational force for a driven wheel of the device.  
         [0013]     According to yet another aspect, there is provided a frame for a personal transportation device, comprising:  
         [0014]     a base;  
         [0015]     a steering shaft on the base for supporting a steering column;  
         [0016]     crank connection means on the base for operably receiving a crank/pedal combination and an associated first set of user-selectable gearwheels;  
         [0017]     an upper-rearward extension extending from a rear of the base for operably receiving a second set of gearwheels comprising an input gearwheel subset and an output gearwheel subset, at least one of the input gearwheel subset and the output gearwheel subset comprising a plurality of user-selectable gearwheels;  
         [0018]     a subextension associated with the upper-rearward extension for supporting a gearwheel-change mechanism associated with a respective one of the output gearwheel subset and the input gearwheel subset;  
         [0019]     a lower-rearward extension extending from the rear of the base for supporting the driven wheel and a rotatable third set of gearwheels.  
         [0020]     The system described herein provides numerous advantages. In particular, increased maximum theoretical speed is possible with the additional advantage of providing a small average mechanical ratio step size between gear changes. This feature provides the user with the option of reduced effort when traversing available speeds, and therefore improved efficiency. Furthermore, the disclosed frame configuration supports an intermediate user-selectable set of gearwheels to be kept separate from the user&#39;s legs during use of the personal transportation device. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0021]     Embodiments will now be described more fully with reference to the accompanying drawings, in which:  
         [0022]      FIG. 1  is a side view of a bicycle incorporating a power transmission system and frame according to an embodiment of the invention;  
         [0023]      FIG. 2  is a perspective view of an isolated power transmission system according to one embodiment of the invention;  
         [0024]      FIG. 3  is a rear elevational view of an intermediate sprocket set having an input subset and an output subset of gearwheels, the output subset associated with a single derailleur;  
         [0025]      FIG. 4  is a rear elevational view of an alternative intermediate sprocket set having an input subset and an output subset of sprockets, each associated with a respective derailleur;  
         [0026]      FIG. 5  is a rear perspective view of an embodiment of a bicycle frame for supporting a power transmission system;  
         [0027]      FIG. 6  is a top partial view of a bicycle with the transmission system distributed on both sides of the frame, according to one embodiment;  
         [0028]      FIG. 7  is a graph illustrating theoretical speed v. sprocket combination for a fifty-four-speed bicycle with three sets of user-selectable sprockets;  
         [0029]      FIG. 8  is a graph illustrating theoretical speed v. sprocket combination for a bicycle similar to that charted in  FIG. 6  having three sets of sprockets, two of which are user-selectable;  
         [0030]      FIG. 9  is a graph illustrating theoretical speed v. sprocket combination for an illustrative prior art eighteen-speed bicycle with two sets of user-selectable sprockets;  
         [0031]      FIG. 10  is a graph illustrating theoretical speed v. sprocket combination for a thirty-six-speed bicycle with three sets of user-selectable sprockets;  
         [0032]      FIG. 11  is a graph illustrating theoretical speed v. sprocket combination for a bicycle similar to that charted in  FIG. 9  having three sets of sprockets, two of which are user-selectable;  
         [0033]      FIG. 12  is a graph illustrating theoretical speed v. sprocket combination for an alternative thirty-six-speed bicycle with three sets of user-selectable sprockets;  
         [0034]      FIG. 13  is a graph illustrating theoretical speed v. sprocket combination for a bicycle similar to that charted in  FIG. 11  having three sets of sprockets, two of which are user-selectable;  
         [0035]      FIG. 14  is a graph illustrating theoretical speed v. sprocket combination for a second alternative thirty-six-speed bicycle with three sets of user-selectable sprockets;  
         [0036]      FIG. 15  is a graph illustrating theoretical speed v. sprocket combination for a bicycle similar to that charted in  FIG. 13  having three sets of sprockets, two of which are user-selectable;  
         [0037]      FIG. 16  is a graph illustrating theoretical speed v. sprocket combination for a fifty-four-speed bicycle with three sets of user-selectable sprockets;  
         [0038]      FIG. 17  is a graph illustrating theoretical speed v. sprocket combination for a bicycle similar to that charted in  FIG. 16  having three sets of sprockets, two of which are user-selectable;  
         [0039]      FIG. 18  is a graph illustrating theoretical speed v. sprocket combination for a fifty-four-speed bicycle with three sets of user-selectable sprockets;  
         [0040]      FIG. 19  is a graph illustrating theoretical speed v. sprocket combination for a bicycle similar to that charted in  FIG. 18  having three sets of sprockets, two of which are user-selectable;  
         [0041]      FIG. 20  is a graph illustrating theoretical speed v. sprocket combination for a fifty-four-speed bicycle with three sets of user-selectable sprockets;  
         [0042]      FIG. 21  is a graph illustrating theoretical speed v. sprocket combination for a bicycle similar to that charted in  FIG. 20  having three sets of sprockets, two of which are user-selectable;  
         [0043]      FIG. 22  is a graph illustrating theoretical speed v. sprocket combination for a fifty-four-speed bicycle with three sets of user-selectable sprockets; and  
         [0044]      FIG. 23  is a graph illustrating theoretical speed v. sprocket combination for a bicycle similar to that charted in  FIG. 22  having three sets of sprockets, two of which are user-selectable. 
     
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS  
       [0045]      FIG. 1  is a side view of a bicycle  10  incorporating a power transmission system  30  mounted to a frame  60  of bicycle  10 . Front wheel  12  is rotatably mounted to front wheel forks  16  of a steering column, which may rotated about a rotation axis relative to steering shaft  64  of frame  30  to which it is mounted, using handle bars  14 . A seat  22  mounted to seat shaft  68  extends upwards from a base  62  of frame  60 . Pedals  18  and a crank  20  form a combination for providing rotational power to the power transmission system  30 . Power transmission system  30 , in turn, transmits rotational power to the rear wheel  24  to which it is connected.  
         [0046]      FIG. 2  is a perspective view of the power transmission system  30 , shown without rear wheel  24  and frame  60  of bicycle  10  to which it would be mounted for operation. A first sprocket set  32  comprises multiple sprockets that rotate as a unit when force is applied to pedals  18  to turn crank  20 . A first set derailleur  36  provides a user with the option of selecting which sprocket in first sprocket set  32  is coupled with a first chain  38 . As is typical of multiple-speed bicycles, each of the sprockets in the first sprocket set respectively have a different diameter, and accordingly a different number of sprocket teeth.  
         [0047]     First chain  38  is also coupled to a sprocket in a second sprocket set  40 , providing an interconnection between first sprocket set  32  and second sprocket set  40 . More specifically, first chain  38  is coupled to the single sprocket in an input subset  41  of second sprocket set  40 . A tension is maintained in first chain  38  by spring tensioner  56  which comprises a bar with rotating sprockets that are in rolling contact with first chain  38 . The bar of spring tensioner  56  is spring biased to put a small pressure on first chain  38  via the rotating sprockets of spring tensioner  56  when smaller sprockets are employed in first sprocket set  32 . Where a larger sprocket is to be employed in first sprocket set  32 , the bar of spring tensioner  56  is able to twist against its spring bias by the increased tension of first chain  38  around the larger sprocket, so as to accommodate for the inherent additional tension from contact of first chain  38  with the larger sprocket.  
         [0048]     When input subset  41  receives force from first sprocket set  32  with which it is interconnected through first chain  38 , output subset  44  is caused to rotate by virtue of second axle  43 . An output subset derailleur  45  provides a user with the option of selecting which sprocket in output subset  42  of second sprocket set  40  is coupled with a second chain  46 . Output subset derailleur  44  is arranged with respect to the input subset  41  and output subset  42  to prevent first chain  38  from interfering with second chain  46  during operation.  
         [0049]     The sprockets in the output subset  42  of second sprocket set  40  respectively have a different diameter, and accordingly a different number of sprocket teeth. Depending on a designer&#39;s choice, the single sprocket in input subset  41  may have the same or a different diameter and number of sprocket teeth as one of the sprockets in output subset  42 .  
         [0050]     Second chain  46  is also coupled to a sprocket in a third sprocket set  48 , providing an interconnection between second sprocket set  40  and third sprocket set  48 . When third sprocket set  48  receives force from output subset  42  with which it is interconnected by second chain  46 , third sprocket set  48  rotates about the axis of third axle  50 , which in turn causes rear wheel  24  to rotate.  
         [0051]     A third set derailleur/tensioner  54  provides a user with the option of selecting which sprocket in third sprocket set  48  is coupled with second chain  46 . The adjustable derailleur/tensioner  54  also ensures that second chain  46  remains taut but still moveable between sprocket combinations.  
         [0052]      FIG. 3  is a rear elevational view of the second sprocket set  40  with input subset  41  and output subset  42 . Three sprockets in output subset  42  are selectable by a user with the output subset derailleur  45 . First chain  38  remains on the single sprocket in input subset  41 .  
         [0053]      FIG. 4  is a rear elevational view of an alternative second sprocket set  40  with input subset of sprockets  41  and output subset of sprockets  42 , where input subset of sprockets  41  has two user-selectable sprockets. An input subset derailleur  44  provides a user with the option of selecting which sprocket in input subset  41  is coupled with first chain  38 . The provision of an additional sprocket selection provides the power transmission system  30  with twice the number of user-selectable sprocket combinations. The input subset  41  and output subset  42  may be spaced apart for the purpose of partly straddling the rear wheel. Such a design choice would be based on the type and/or model of bicycle and the associated rear wheel diameter, tire width, and other such dimensions.  
         [0054]      FIG. 5  is a rear perspective view of the bicycle frame  60  of  FIG. 1 , shown connected with the steering column including front forks  16  but without front wheel  12 , rear wheel  24  and power transmission system  30  which would be normally connected for operation. Base  62  of frame  60  connects steering shaft  64  to first sprocket set shaft  66  and seat shaft  68 . First sprocket set shaft receives an axle of crank  20  for rotatably mounting pedals  18 , crank  20  and first sprocket set  32  of power transmission system  30 .  
         [0055]     An upper rearward extension  70  extends from base  62  just behind seat shaft  68 , and includes a second sprocket set shaft  72  for receiving second axle  43  of second sprocket set  40 . A subextension  74  extends still further rearward from second sprocket shaft  72 , in order to provide a mount for input derailleur  44  and/or output derailleur  45 . Advantageously, the location of upper rearward extension  70  behind seat shaft  68  ensures that second sprocket set  40 , input and/or output derailleurs  44 , 45  are out of the way of a user&#39;s legs during operation.  
         [0056]     Rear wheel forks  80  are spaced to straddle rear wheel  24 , and extend downwardly from upper rearward extension  70  to meet with a lower rearward extension  76 . Lower rearward extension includes a mount  78  for mounting an axle of rear wheel  24  and third sprocket set  48  using appropriate hardware (not shown).  
         [0057]      FIG. 6  is a top partial view of a bicycle with the transmission system distributed on both sides of the frame, according to one embodiment. According to this embodiment, which is compatible with the frame  60  shown in  FIG. 5 , first sprocket set  32 , first chain  38  and input subset  41  of second sprocket set  40  are positioned substantially on the right side of frame  60 . Second axle  43  spans the width of frame  60  so as to cause output subset  42  of second sprocket set  32  to be positioned substantially on the left side of frame  60  from input subset  41 . Second chain  46  and third sprocket set  48  are also substantially disposed on the left side of frame  60 . With this configuration, better weight balance of bicycle  10  is achieved. It will be understood that a mirror-image configuration, wherein the first sprocket set  32  is on the left side and the third sprocket set  48  is on the right side, is possible. It will also be understood that the largest sprocket in a sprocket set may be the farthest away from the associated wheel or frame, or the closest to the associated wheel or frame. For example, in  FIG. 6  the largest sprocket in the third set  48  is closest to the rear wheel  24  but a designer may arrange the sprockets such that the largest sprocket in the third set  48  is farthest from rear wheel  24  and the sprockets progressively get smaller towards rear wheel  24 .  
         [0058]     Table 1 summarizes a configuration of the embodiment of the power transmission system  30  shown in  FIG. 2 , in which first sprocket set  32  has three user-selectable sprockets, input subset  41  of second sprocket set  40  has a single sprocket, output subset  42  of second sprocket set  40  has three user-selectable sprockets, and third sprocket set  48  has six user-selectable sprockets. The number of selectable sprocket combinations is 54.  
                                                                         TABLE 1                                   First Set       Second Set       Third Set                                        #1   48 teeth   Input   14   #1   28 teeth           #2   38 teeth   Output #1   48   #2   24 teeth           #3   28 teeth   Output #2   38   #3   21 teeth                   Output #3   28   #4   18 teeth                           #5   16 teeth                           #6   14 teeth                      
 
         [0059]     Table 2 summarizes the speed ratios and theoretical speeds possible with the 54-speed configuration of Table 1, given a rear wheel outer diameter of 26″, and a maximum efficiency cadence of 80 rpm at the pedals.  
                                           TABLE 2                           #       #   Third   #       Speed       First set   Teeth   Second Set   Teeth   Set   Teeth   Ratio   (mph)                                                                           #1   28   1:5.88   36.37                       #2   24   1:6.86   42.43                       #3   21   1:7.84   48.49                       #4   18   1:9.14   56.58                       #5   16    1:10.29   63.65                                                                                           Output #2   38   #1   28   1:4.65   28.79                       #2   24   1:5.43   33.59                       #3   21   1:6.20   38.39                       #4   18   1:7.24   44.79                       #5   16   1:8.14   50.39                       #6   14   1:9.31   57.59               Output #3   28   #1   28   1:3.43   21.22                       #2   24   1:4.00   24.75                       #3   21   1:4.57   28.29                       #4   18   1:5.33   33.00                       #5   16   1:6.00   37.13                       #6   14   1:6.86   42.43       #2   38   Output #1   48   #1   28   1:4.65   28.79                       #2   24   1:5.43   33.59                       #3   21   1:6.20   38.39                       #4   18   1:7.24   44.79                       #5   16   1:8.14   50.39                       #6   14   1:9.31   57.59               Output #2   38   #1   28   1:3.68   22.79                       #2   24   1:4.30   26.59                       #3   21   1:4.91   30.39                       #4   18   1:5.73   35.46                       #5   16   1:6.45   39.89                       #6   14   1:7.37   45.59               Output #3   28   #1   28   1:2.71   16.80                       #2   24   1:3.17   19.60                       #3   21   1:3.62   22.39                       #4   18   1:4.22   26.13                       #5   16   1:4.75   29.39                       #6   14   1:5.43   33.59       #3   28   Output #1   48   #1   28   1:3.43   21.22                       #2   24   1:4.00   24.75                       #3   21   1:4.57   28.29                       #4   18   1:5.33   33.00                       #5   16   1:6.00   37.13                       #6   14   1:6.86   42.43               Output #2   38   #1   28   1:2.71   16.80                       #2   24   1:3.17   19.60                       #3   21   1:3.62   22.39                       #4   18   1:4.22   26.13                       #5   16   1:4.75   29.39                       #6   14   1:5.43   33.59               Output #3   28   #1   28   1:2.00   12.38                       #2   24   1:2.33   14.44                       #3   21   1:2.67   16.50                       #4   18   1:3.11   19.25                       #5   16   1:3.50   21.66                       #6   14   1:4.00   24.75                  
 
         [0060]     As can be seen, with the configuration of Table 1, a maximum theoretical speed of 72.74 miles per hour is possible, with 54 selectable combinations of sprockets, yielding 33 unique ratios from 2.00 to 11.76. Thus, the average ratio step size is (11.76−2.00)/33=0.295. It will be understood that the maximum theoretical speed calculation has been provided for illustration without factoring mechanical and surface friction, air drag and the like.  
         [0061]      FIG. 7  is a graph illustrating theoretical speed v. sprocket combination for the 54-speed bicycle configuration of Table 1. It is advantageous to maintain a low average mechanical ratio step size so that a user can experience a comfortable transition from low to high speeds. It has been found that prior art power transmission systems for achieving higher speeds with three or more sets of gearwheels are particularly disadvantageous in this regard. This is because all ratios are effectively amplified with the addition of the third unselectable sprocket, accordingly amplifying the ratio step size and making the power transmission system increasing difficult to use across the range of speeds. As a result, with these prior art systems, a user must tolerate providing greater effort for traversing the available speeds, and diminished efficiency while attempting to achieve maximum speed.  
         [0062]      FIG. 8  shows a graph illustrating theoretical speed v. sprocket combination for a power transmission system having the first and second sets of user-selectable gearwheels identical to the configuration of Table 1, and the third set fixed on sprocket #6. In this case, the theoretical maximum achievable speed is the same. However, it can be seen in the graph of  FIG. 8  that the smaller incremental ratios are not available to the user. Thus, the average ratio step size is high at (11.76−4.00)/9=0.862.  
         [0063]     In order to illustrate the operation of the invention relative to the prior art, Table 3 shows a typical prior art 18-speed power transmission system configuration, having three user-selectable sprockets in a first set associated with the pedal and driving sprockets, and six user-selectable sprockets in a second set associated with the driven wheel.  
                                                           TABLE 3                           Prior Art.                First Set       Second Set   # Teeth                            #1   48 teeth   #1   28 teeth           #2   38 teeth   #2   24 teeth           #3   28 teeth   #3   21 teeth                   #4   18 teeth                   #5   16 teeth                   #6   14 teeth                      
 
         [0064]     Table 4 summarizes rotation ratios and theoretical achievable speeds with the 18-speed power transmission system configuration shown in Table 3, in which driven wheel outer diameter is 26″, and a maximum efficiency cadence at the first set is 80 rpm.  
                                                                   TABLE 4                           Prior Art.                                Speed       First Set   #Teeth   Second Set   #Teeth   Ratio   (mph)                                                #1   28   1:1.71   10.61               #2   24   1:2.00   12.38               #3   21   1:2.29   14.14               #4   18   1:2.67   16.50               #5   16   1:3.00   18.56                                                                           #2   38   #1   28   1:1.36   8.40               #2   24   1:1.58   9.80               #3   21   1:1.81   11.20               #4   18   1:2.11   13.06               #5   16   1:2.38   14.70               #6   14   1:2.71   16.80       #3   28   #1   28   1:1.00   6.19               #2   24   1:1.17   7.22               #3   21   1:1.33   8.25               #4   18   1:1.56   9.63               #5   16   1:1.75   10.83               #6   14   1:2.00   12.38                  
 
         [0065]     The maximum theoretical speed achievable with the 18-speed configuration shown in Table 3 is 21.22 miles per hour, achievable using the #1 gearwheel in the first set, and the #6 gearwheel in the second set to provide the maximum available ratio. In total, there are 18 selectable combinations of sprockets, yielding 17 unique input/output rotation ratios from 1.00 to 3.43. The average ratio step size is therefore: (3.43−1.00)/17=0.142.  
         [0066]      FIG. 9  is a graph illustrating theoretical maximum speed v. sprocket combination for the 18-speed bicycle configuration of Table 3. It can be seen that there is a low average mechanical gear ratio with this configuration.  
         [0067]     Table 5 shows a 36-speed transmission configuration according to an alternative embodiment of the invention, in which first sprocket set  32  has three user-selectable sprockets, input subset  41  of second sprocket set  40  has two user-selectable sprockets, output subset  42  of second sprocket set  40  a single sprocket with 28 teeth, and third sprocket set  48  has six user-selectable sprockets. The number of selectable sprocket combinations is 36.  
                                                                         TABLE 5                                   First Set       Second Set       Third Set                                        #1   48 teeth   Input #1   14   #1   28 teeth           #2   38 teeth   Input #2   16   #2   24 teeth           #3   28 teeth   Output   28   #3   21 teeth                           #4   18 teeth                           #5   16 teeth                           #6   14 teeth                      
 
         [0068]     Table 6 summarizes the rotation ratios and theoretical achievable speeds with the 36-speed transmission configuration shown in Table 5, in which driven wheel outer diameter is 26″, and a maximum efficiency cadence at the first set is 80 rpm.  
                                           TABLE 6                           #       #   Thrid   #       Speed       First set   Teeth   Second Set   Teeth   Set   Teeth   Ratio   (mph)                                                                           #1   28   1:3.43   21.22                       #2   24   1:4.00   24.75                       #3   21   1:4.57   28.29                       #4   18   1:5.33   33.00                       #5   16   1:6.00   37.13                                                                                           Input #2   16   #1   28   1:3.00   18.56                       #2   24   1:3.50   21.66                       #3   21   1:4.00   24.75                       #4   18   1:4.67   28.88                       #5   16   1:5.25   32.49                       #6   14   1:6.00   37.13       #2   38   Input #1   14   #1   28   1:2.71   16.80                       #2   24   1:3.17   19.60                       #3   21   1:3.62   22.39                       #4   18   1:4.22   26.13                       #5   16   1:4.75   29.39                       #6   14   1:5.43   33.59               Input #2   16   #1   28   1:2.38   14.70                       #2   24   1:2.77   17.15                       #3   21   1:3.17   19.60                       #4   18   1:3.69   22.86                       #5   16   1:4.16   25.72                       #6   14   1:4.75   29.39       #3   28   Input #1   14   #1   28   1:2.00   12.38                       #2   24   1:2.33   14.44                       #3   21   1:2.67   16.50                       #4   18   1:3.11   19.25                       #5   16   1:3.50   21.66                       #6   14   1:4.00   24.75               Input #2   16   #1   28   1:1.75   10.83                       #2   24   1:2.04   12.63                       #3   21   1:2.33   14.44                       #4   18   1:2.72   16.85                       #5   16   1:3.06   18.95                       #6   14   1:3.50   21.66                  
 
         [0069]     As can be seen, with the configuration of Table 5, a maximum theoretical speed of 42.43 miles per hour is possible, with 36 selectable combinations of sprockets, yielding 28 unique ratios from 1.75 to 6.86. Thus, the average step size is (6.86−1.75)/28=0.182. While this is a greater step size than that available with the 18-speed bicycle example above, the theoretical maximum achievable speed is significantly increased over the prior art 18-speed bicycle.  
         [0070]      FIG. 10  is a graph illustrating theoretical speed v. sprocket combination for the 36-speed bicycle configuration of Table 5.  
         [0071]      FIG. 11  shows a graph illustrating theoretical speed v. sprocket combination for a power transmission system having the first and second sets of user-selectable sprockets identical to the configuration of Table 5, and the third set fixed on sprocket #6. In this case, the theoretical maximum achievable speed is the same. However, it can be seen in the graph of  FIG. 11  the smaller incremental ratios are not available to the user, as there are only six selectable sprocket combinations. Thus, the average ratio step size is high at (6.86−3.50)/6=0.56.  
         [0072]     Table 7 shows a 36-speed transmission configuration according to an alternative embodiment of the invention, in which first sprocket set  32  has three user-selectable sprockets, input subset  41  of second sprocket set  40  has two user-selectable sprockets, output subset  42  of second sprocket set  40  has a single sprocket, and third sprocket set  48  has six user-selectable sprockets. The number of selectable sprocket combinations is 36. The configuration is identical to that shown in Table 5, except that the output gearwheel in the second set has 38 teeth, instead of 28 teeth.  
                                                                         TABLE 7                                   First Set       Second Set       Thired Set                                        #1   48 teeth   Input #1   14   #1   28 teeth           #2   38 teeth   Input #2   16   #2   24 teeth           #3   28 teeth   Output   38   #3   21 teeth                           #4   18 teeth                           #5   16 teeth                           #6   14 teeth                      
 
         [0073]     Table 8 summarizes the speed ratios and theoretical speeds possible with the 36-speed configuration of Table 7, given a rear wheel outer diameter of 26″, and a maximum efficiency cadence of 80 rpm at the pedals.  
                                           TABLE 8                           #       #   Third           Speed       First Set   Teeth   Second Set   Teeth   Set   # Teeth   Ratio   (mph)                                                                           #1   28   1:4.65   28.79                       #2   24   1:5.43   33.59                       #3   21   1:6.20   38.39                       #4   18   1:7.24   44.79                       #5   16   1:8.14   50.39                                                                                           Input #2   16   #1   28   1:4.07   25.19                       #2   24   1:4.75   29.39                       #3   21   1:5.43   33.59                       #4   18   1:6.33   39.19                       #5   16   1:7.13   32.49                       #6   14   1:8.14   50.39       #2   38   Input #1   14   #1   28   1:3.68   22.79                       #2   24   1:4.30   26.59                       #3   21   1:4.91   30.39                       #4   18   1:5.73   35.46                       #5   16   1:6.45   39.89                       #6   14   1:7.37   45.59               Input #2   16   #1   28   1:3.22   19.95                       #2   24   1:3.76   23.27                       #3   21   1:4.30   26.59                       #4   18   1:5.01   31.03                       #5   16   1:5.64   34.90                       #6   14   1:6.45   39.89       #3   28   Input #1   14   #1   28   1:2.71   16.80                       #2   24   1:3.17   19.60                       #3   21   1:3.62   22.39                       #4   18   1:4.22   26.13                       #5   16   1:4.75   29.39                       #6   14   1:5.43   33.59               Input #2   16   #1   28   1:2.38   14.70                       #2   24   1:2.77   17.15                       #3   21   1:3.17   19.60                       #4   18   1:3.69   22.86                       #5   16   1:4.16   25.72                       #6   14   1:4.75   29.39                  
 
         [0074]     As can be seen, with the configuration of Table 7, a maximum theoretical speed of 57.59 miles per hour is possible, with thirty-six selectable combinations of sprockets, yielding 28 unique ratios from 2.38 to 9.31. Thus, the average step size is (9.31−2.38)/28=0.248.  
         [0075]      FIG. 12  is a graph illustrating theoretical speed v. sprocket combination for the 36-speed bicycle configuration of Table 7.  
         [0076]      FIG. 13  shows a graph illustrating theoretical speed v. sprocket combination for a power transmission system having the first and second sets of user-selectable gearwheels identical to the configuration of Table 7, with the third set fixed on sprocket #6. In this case, the theoretical maximum achievable speed is the same. However, it can be seen in the graph of  FIG. 13  that the smaller incremental ratios are not available to the user. Thus, the average ratio step size is (9.31−4.75)/6=0.76.  
         [0077]     Table 9 shows a 36-speed transmission configuration according to an alternative embodiment of the invention, in which first sprocket set  32  has three user-selectable sprockets, input subset  41  of second sprocket set  40  has two user-selectable sprockets, output subset  42  of second sprocket set  40  has a single sprocket, and third sprocket set  48  has six user-selectable sprockets. The number of selectable sprocket combinations is 36. The configuration is identical to that shown in Table 5, except that the output gearwheel in the second set has 48 teeth, instead of 28 teeth.  
                                                                         TABLE 9                                   First Set       Second Set       Third Set                                        #1   48 teeth   Input #1   14   #1   28 teeth           #2   38 teeth   Input #2   16   #2   24 teeth           #3   28 teeth   Output   48   #3   21 teeth                           #4   18 teeth                           #5   16 teeth                           #6   14 teeth                      
 
         [0078]     Table 10 summarizes the speed ratios and theoretical speeds possible with the 36-speed configuration of Table 9, given a rear wheel outer diameter of 26″, and a maximum efficiency cadence of 80 rpm at the pedals.  
                                           TABLE 10                           #       #   Third   #       Speed       First Set   Teeth   Second Set   Teeth   Set   Teeth   Ratio   (mph)                                                                           #1   28   1:5.88   36.37                       #2   24   1:6.86   42.43                       #3   21   1:7.84   48.49                       #4   18   1:9.14   56.58                       #5   16    1:10.29   63.65                                                                                           Input #2   16   #1   28   1:5.14   31.82                       #2   24   1:6.00   37.13                       #3   21   1:6.86   42.43                       #4   18   1:8.00   49.50                       #5   16   1:9.00   55.69                       #6   14    1:10.29   63.65       #2   38   Input #1   14   #1   28   1:4.65   28.79                       #2   24   1:5.43   33.59                       #3   21   1:6.20   38.39                       #4   18   1:7.24   44.79                       #5   16   1:8.14   50.39                       #6   14   1:9.31   57.59               Input #2   16   #1   28   1:4.07   25.19                       #2   24   1:4.75   29.39                       #3   21   1:5.43   33.59                       #4   18   1:6.33   39.19                       #5   16   1:7.13   44.09                       #6   14   1:8.14   50.39       #3   28   Input #1   14   #1   28   1:3.43   21.22                       #2   24   1:4.00   24.75                       #3   21   1:4.57   28.29                       #4   18   1:5.33   33.00                       #5   16   1:6.00   37.13                       #6   14   1:6.86   42.43               Input #2   16   #1   28   1:3.00   18.56                       #2   24   1:3.50   21.66                       #3   21   1:4.00   24.75                       #4   18   1:4.67   28.88                       #5   16   1:5.25   32.49                       #6   14   1:6.00   37.13                  
 
         [0079]     As can be seen, as with the configuration of Table 9, a maximum theoretical speed of 72.74 miles per hour is possible, with thirty-six selectable combinations of sprockets, yielding 28 unique ratios from 3.00 to 11.76. Thus, the average ratio step size is (11.76−3.00)/28=0.312.  
         [0080]      FIG. 14  is a graph illustrating theoretical speed v. sprocket combination for the 36-speed bicycle configuration of Table 9.  
         [0081]      FIG. 15  shows a graph illustrating theoretical speed v. sprocket combination for a power transmission system having the first and second sets of user-selectable gearwheels identical to the configuration of Table 9, with the third set fixed on sprocket #6. In this case, the theoretical maximum achievable speed is the same. However, it can be seen in the graph of  FIG. 15  that the smaller incremental ratios are not available to the user. Thus, the average ratio step size is (11.76−6.00)/6=0.96.  
         [0082]     Table 11 summarizes a configuration of the embodiment of the power transmission system  30  shown in  FIG. 2 , in which first sprocket set  32  has three user-selectable sprockets, input subset  41  of second sprocket set  40  has a single sprocket, output subset  42  of second sprocket set  40  has three user-selectable sprockets, and third sprocket set  48  has six user-selectable sprockets. The number of selectable sprocket combinations is 54.  
                                                 TABLE 11                       First Set   Second Set   Third Set                                #1   48 teeth   Input   14 teeth   #1   28 teeth       #2   38 teeth   Output #1   48 teeth   #2   24 teeth       #3   28 teeth   Output #2   38 teeth   #3   21 teeth               OutPut #3   28 teeth   #4   18 teeth                       #5   16 teeth                       #6   14 teeth                  
 
         [0083]     Table 12 summarizes the speed ratios and theoretical speeds possible with the 54-speed configuration of Table 11, given a rear wheel outer diameter of 26″, and 120 rpm at the pedals.  
                                           TABLE 12                           #       #   Third   #       Speed       First Set   Teeth   Second Set   Teeth   Set   Teeth   Ratio   (mph)                                                                           #1   28   1:5.88   54.56                       #2   24   1:6.86   63.65                       #3   21   1:7.84   72.74                       #4   18   1:9.14   84.86                       #5   16    1:10.29   95.47                                                                                           Output #2   38   #1   28   1:4.65   43.19                       #2   24   1:5.43   50.39                       #3   21   1:6.20   57.59                       #4   18   1:7.24   67.18                       #5   16   1:8.14   75.58                       #6   14   1:9.31   86.38               Output #3   28   #1   28   1:3.43   31.82                       #2   24   1:4.00   37.13                       #3   21   1:4.57   42.43                       #4   18   1:5.33   49.50                       #5   16   1:6.00   55.69                       #6   14   1:6.86   63.65       #2   38   Output #1   48   #1   28   1:4.65   43.19                       #2   24   1:5.43   50.39                       #3   21   1:6.20   57.59                       #4   18   1:7.24   67.18                       #5   16   1:8.14   75.58                       #6   14   1:9.31   86.38               Output #2   38   #1   28   1:3.68   34.19                       #2   24   1:4.30   39.89                       #3   21   1:4.91   45.59                       #4   18   1:5.73   53.19                       #5   16   1:6.45   59.84                       #6   14   1:7.37   68.38               Output #3   28   #1   28   1:2.71   25.19                       #2   24   1:3.17   29.39                       #3   21   1:3.62   33.59                       #4   18   1:4.22   39.19                       #5   16   1:4.75   44.09                       #6   14   1:5.43   50.39       #3   28   Output #1   48   #1   28   1:3.43   31.82                       #2   24   1:4.00   37.13                       #3   21   1:4.57   42.43                       #4   18   1:5.33   49.50                       #5   16   1:6.00   55.69                       #6   14   1:6.86   63.65               Output #2   38   #1   28   1:2.71   25.19                       #2   24   1:3.17   29.39                       #3   21   1:3.62   33.59                       #4   18   1:4.22   39.19                       #5   16   1:4.75   44.09                       #6   14   1:5.43   50.39               Output #3   28   #1   28   1:2.00   18.56                       #2   24   1:2.33   21.66                       #3   21   1:2.67   24.75                       #4   18   1:3.11   28.88                       #5   16   1:3.50   32.49                       #6   14   1:4.00   37.13                  
 
         [0084]     As can be seen, with the configuration of Table 11, where an increased rpm of 120 is achieved by the user, a maximum theoretical speed of 109.11 miles per hour is possible, with 54 selectable combinations of sprockets, yielding 33 unique ratios from 2.00 to 11.76. Thus, the average ratio step size is (11.76−2.00)/33=0.295.  
         [0085]      FIG. 16  is a graph illustrating theoretical speed v. sprocket combination for the 54-speed bicycle configuration of Table 11.  
         [0086]      FIG. 17  shows a graph illustrating theoretical speed v. sprocket combination for a power transmission system having the first and second sets of user-selectable gearwheels identical to the configuration of Table 11, and the third set fixed on sprocket #6. In this case, the theoretical maximum achievable speed is the same. However, it can be seen in the graph of  FIG. 17  that the smaller incremental ratios are not available to the user. Thus, the average ratio step size is high at (11.76−3.11)/9 =0.961.  
         [0087]     Table 13 summarizes a configuration of the embodiment of the power transmission system  30  shown in  FIG. 2 , in which first sprocket set  32  has three user-selectable sprockets, input subset  41  of second sprocket set  40  has a single sprocket, output subset  42  of second sprocket set  40  has three user-selectable sprockets, and third sprocket set  48  has six user-selectable sprockets. The number of selectable sprocket combinations is 54. The number of teeth on the sprockets is different from the embodiments shown above.  
                                                 TABLE 13                       First Set   Second Set   Third Set                                #1   48 teeth   Input   28 teeth   #1   28 teeth       #2   36 teeth   Output #1   48 teeth   #2   24 teeth       #3   24 teeth   Output #2   36 teeth   #3   21 teeth               Output #3   24 teeth   #4   18 teeth                       #5   16 teeth                       #6   14 teeth                  
 
         [0088]     Table 14 summarizes the speed ratios and theoretical speeds possible with the 54-speed configuration of Table 13, given a rear wheel outer diameter of 26″, and 80 rpm at the pedals.  
                                                                             TABLE 14                           #   Second   #       #       Speed       First Set   Teeth   Set   Teeth   Third Set   Teeth   Ratio   (mph)                                                                                        #1   28   1:2.94   18.19                       #2   24   1:3.43   21.22                       #3   21   1:3.92   24.25                       #4   18   1:4.57   28.29                       #5   16   1:5.14   31.82                                                                                           Output #2   36   #1   28   1:2.20   13.64                       #2   24   1:2.57   15.91                       #3   21   1:2.94   18.19                       #4   18   1:3.43   21.22                       #5   16   1.3.86   23.87                       #6   14   1:4.41   27.28               Output #3   24   #1   28   1:1.47   9.09                       #2   24   1:1.71   10.61                       #3   21   1:1.96   12.12                       #4   18   1:2.29   14.14                       #5   16   1:2.57   15.91                       #6   14   1:2.94   18.19       #2   36   Output #1   48   #1   28   1:2.20   13.64                       #2   24   1:2.57   15.91                       #3   21   1:2.94   18.19                       #4   18   1:3.43   21.22                       #5   16   1:3.86   23.87                       #6   14   1:4.41   27.28               Output #2   36   #1   28   1:1.65   10.23                       #2   24   1:1.93   11.93                       #3   21   1:2.20   13.64                       #4   18   1:2.57   15.91                       #5   16   1:2.89   17.90                       #6   14   1:3.31   20.46               Output #3   24   #1   28   1:1.10   6.82                       #2   24   1:1.29   7.96                       #3   21   1:1.47   9.09                       #4   18   1:1.71   10.61                       #5   16   1:1.93   11.93                       #6   14   1:2.20   13.64       #3   24   Output #1   48   #1   28   1:1.47   9.09                       #2   24   1:1.71   10.61                       #3   21   1:1.96   12.12                       #4   18   1:2.29   14.14                       #5   16   1:2.57   15.91                       #6   14   1:2.94   18.19               Output #2   36   #1   28   1:1.10   6.82                       #2   24   1:1.29   7.96                       #3   21   1:1.47   9.09                       #4   18   1:1.71   10.61                       #5   16   1:1.93   11.93                       #6   14   1:2.20   13.64               Output #3   24   #1   28   1:0.73   4.55                       #2   24   1:0.86   5.30                       #3   21   1:0.98   6.06                       #4   18   1:1.14   7.07                       #5   16   1:1.29   7.96                       #6   14   1:1.47   9.09                  
 
         [0089]     As can be seen, with the configuration of Table 13, where a rpm of 80 is achieved by the user, a maximum theoretical speed of 36.37 miles per hour is possible, with 54 selectable combinations of sprockets, yielding 24 unique ratios from 0.73 to 5.88. Thus, the average ratio step size is (5.88−0.73)/24=0.215.  
         [0090]      FIG. 18  is a graph illustrating theoretical speed v. sprocket combination for the 54-speed bicycle configuration of Table 13.  
         [0091]      FIG. 19  shows a graph illustrating theoretical speed v. sprocket combination for a power transmission system having the first and second sets of user-selectable gearwheels identical to the configuration of Table 13, and the third set fixed on sprocket #6. In this case, the theoretical maximum achievable speed is the same. However, it can be seen in the graph of  FIG. 19  that the smaller incremental ratios are not available to the user. Thus, the average ratio step size is high at (5.88−1.14)/9 =0.527.  
         [0092]     Table 15 summarizes a configuration of the embodiment of the power transmission system  30  shown in  FIG. 2 , in which first sprocket set  32  has three user-selectable sprockets, input subset  41  of second sprocket set  40  has a single sprocket, output subset  42  of second sprocket set  40  has three user-selectable sprockets, and third sprocket set  48  has six user-selectable sprockets. The number of selectable sprocket combinations is 54. This configuration is similar to that shown in Table 13, except that the input sprocket on the second set has 14, instead of 28 teeth.  
                                                 TABLE 15                       First Set   Second Set   Third Set                                #1   48 teeth   Input   14 teeth   #1   28 teeth       #2   36 teeth   Output #1   48 teeth   #3   24 teeth       #3   24 teeth   Output #2   36 teeth   #4   21 teeth               Output #3   24 teeth   #4   18 teeth                       #5   16 teeth                       #6   14 teeth                  
 
         [0093]     Table 16 summarizes the speed ratios and theoretical speeds possible with the 54-speed configuration of Table 15, given a rear wheel outer diameter of 26″, and 80 rpm at the pedals.  
                                                                             TABLE 16                           #   Second   #       #       Speed       First Set   Teeth   Set   Teeth   Third Set   Teeth   Ratio   (mph)                                                                                        #1   28   1:5.88   36.37                       #2   24   1:6.86   42.43                       #3   21   1:7.84   48.49                       #4   18   1:9.14   56.58                       #5   16   1:10.29   63.65                                                                                           Output #2   36   #1   28   1:4.41   27.28                       #2   24   1:5.14   31.82                       #3   21   1:5.88   36.37                       #4   18   1:6.86   42.43                       #5   16   1:7.71   47.74                       #6   14   1:8.82   54.56               Output #3   24   #1   28   1:2.94   18.19                       #2   24   1:3.43   21.22                       #3   21   1:3.92   24.25                       #4   18   1:4.57   28.29                       #5   16   1:5.14   31.82                       #6   14   1:5.88   36.37       #2   36   Output #1   48   #1   28   1:4.41   27.28                       #2   24   1:5.14   31.82                       #3   21   1:5.88   36.37                       #4   18   1:6.86   42.43                       #5   16   1:7.71   47.74                       #6   14   1:8.82   54.56               Output #2   36   #1   28   1:3.31   20.46                       #2   24   1:3.86   23.87                       #3   21   1:4.41   27.28                       #4   18   1:5.14   31.82                       #5   16   1:5.79   35.80                       #6   14   1:6.61   40.92               Output #3   24   #1   28   1:2.20   13.64                       #2   24   1:2.57   15.91                       #3   21   1:2.94   18.19                       #4   18   1:3.43   21.22                       #5   16   1:3.86   23.87                       #6   14   1:4.41   27.28       #3   24   Output #1   48   #1   28   1:2.94   18.19                       #2   24   1:3.43   21.22                       #3   21   1:3.92   24.25                       #4   18   1:4.57   28.29                       #5   16   1:5.14   31.82                       #6   14   1:5.88   36.37               Output #2   36   #1   28   1:2.20   13.64                       #2   24   1:2.57   15.91                       #3   21   1:2.94   18.19                       #4   18   1:3.43   21.22                       #5   16   1:3.86   23.87                       #6   14   1:4.41   27.28               Output #3   24   #1   28   1:1.47   9.09                       #2   24   1:1.71   10.61                       #3   21   1:1.96   12.12                       #4   18   1:2.29   14.14                       #5   16   1:2.57   15.91                       #6   14   1:2.94   18.19                  
 
         [0094]     As can be seen, with the configuration of Table 15, where a rpm of 80 is achieved by the user, a maximum theoretical speed of 72.74 miles per hour is possible, with 54 selectable combinations of sprockets, yielding 24 unique ratios from 1.47 to 11.76. Thus, the average ratio step size is (11.76−1.47)/24=0.429.  
         [0095]      FIG. 20  is a graph illustrating theoretical speed v. sprocket combination for the 54-speed bicycle configuration of Table 15.  
         [0096]      FIG. 21  shows a graph illustrating theoretical speed v. sprocket combination for a power transmission system having the first and second sets of user-selectable gearwheels identical to the configuration of Table 15, and the third set fixed on sprocket #6. In this case, the theoretical maximum achievable speed is the same. However, it can be seen in the graph of  FIG. 21  that the smaller incremental ratios are not available to the user. Thus, the average ratio step size is high at (11.76−2.29)/9=1.05.  
         [0097]     Table 17 summarizes a configuration of the embodiment of the power transmission system  30  shown in  FIG. 2 , in which first sprocket set  32  has three user-selectable sprockets, input subset  41  of second sprocket set  40  has a single sprocket, output subset  42  of second sprocket set  40  has three user-selectable sprockets, and third sprocket set  48  has six user-selectable sprockets. The number of selectable sprocket combinations is 54.  
                                                 TABLE 17                       First Set   Second Set   Third Set                                #1   48 teeth   Input   14 teeth   #1   28 teeth       #2   38 teeth   Output #1   48 teeth   #2   24 teeth       #3   28 teeth   Output #2   38 teeth   #3   21 teeth               Output #3   28 teeth   #4   18 teeth                       #5   16 teeth                       #6   14 teeth                  
 
         [0098]     Table 18 summarizes the speed ratios and theoretical speeds possible with the 54-speed configuration of Table 17, given a rear wheel outer diameter of 26″, and 100 rpm at the pedals.  
                                           TABLE 18                           #   Second   #       #       Speed       First Set   Teeth   Set   Teeth   Third Set   Teeth   Ratio   (mph)                                                                           #1   28   1:5.88   45.46                       #2   24   1:6.86   53.04                       #3   21   1:7.84   60.62                       #4   18   1:9.14   70.72                       #5   16   1:10.29   79.56                                                                                           Output #2   38   #1   28   1:4.65   35.99                       #2   24   1:5.43   41.99                       #3   21   1:6.20   47.99                       #4   18   1:7.24   55.99                       #5   16   1:8.14   62.98                       #6   14   1:9.31   71.98               Output #3   28   #1   28   1:3.43   26.52                       #2   24   1:4.00   30.94                       #3   21   1:4.57   35.36                       #4   18   1:5.33   41.25                       #5   16   1:6.00   46.41                       #6   14   1:6.86   53.04       #2   38   Output #1   48   #1   28   1:4.65   35.99                       #2   24   1:5.43   41.99                       #3   21   1:6.20   47.99                       #4   18   1:7.24   55.99                       #5   16   1:8.14   62.98                       #6   14   1:9.31   71.98               Output #2   38   #1   28   1:3.68   28.49                       #2   24   1:4.30   33.24                       #3   21   1:4.91   37.99                       #4   18   1:5.73   44.32                       #5   16   1:6.45   49.86                       #6   14   1:7.37   56.99               Output #3   28   #1   28   1:2.71   20.99                       #2   24   1:3.17   24.49                       #3   21   1:3.62   27.99                       #4   18   1:4.22   32.66                       #5   16   1:4.75   36.74                       #6   14   1:5.43   41.99       #3   28   Output #1   48   #1   28   1:3.43   26.52                       #2   24   1:4.00   30.94                       #3   21   1:4.57   35.36                       #4   18   1:5.33   41.25                       #5   16   1:6.00   46.41                       #6   14   1:6.86   53.04               Output #2   38   #1   28   1:2.71   20.99                       #2   24   1:3.17   24.49                       #3   21   1:3.62   27.99                       #4   18   1:4.22   32.66                       #5   16   1:4.75   36.74                       #6   14   1:5.43   41.99               Output #3   28   #1   28   1:2.00   15.47                       #2   24   1:2.33   18.05                       #3   21   1:2.67   20.63                       #4   18   1:3.11   24.06                       #5   16   1:3.50   27.07                       #6   14   1:4.00   30.94                  
 
         [0099]     As can be seen, with the configuration of Table 17, where a rpm of 100 is achieved by the user, a maximum theoretical speed of 90.93 miles per hour is possible, with 54 selectable combinations of sprockets, yielding 32 unique ratios from 2.00 to 11.76. Thus, the average ratio step size is (11.76−2.00)/32=0.305.  
         [0100]      FIG. 22  is a graph illustrating theoretical speed v. sprocket combination for the 54-speed bicycle configuration of Table 17.  
         [0101]      FIG. 23  shows a graph illustrating theoretical speed v. sprocket combination for a power transmission system having the first and second sets of user-selectable gearwheels identical to the configuration of Table 17, and the third set fixed on sprocket #6. In this case, the theoretical maximum achievable speed is the same. However, it can be seen in the graph of  FIG. 23  that the smaller incremental ratios are not available to the user. Thus, the average ratio step size is high at (11.76−3.11)/9 =0.961  
         [0102]     The particular sprocket selector switches used to move the derailleurs as required may be any sort compatible with the particular derailleurs employed. Cable and cable sheath connections between the sprocket selector switches and respective derailleurs would be routed along or within frame  60  as would be known. For example, the cable and cable sheath connecting a gear selector switch with second sprocket set  40  could be routed along the frame from handle bars  14 , along upper rearward extension  70  to subextension  74  in order to connect with input derailleur  44  or output derailleur  45 .  
         [0103]     The mechanisms that allow the rear wheel to turn freely during downhill coasting, those that provide braking action/control and other such considerations are considered within the scope of understanding of a person skilled in bicycle construction, design, and maintenance.  
         [0104]     While particular embodiments of the invention have been described, it will be understood that other embodiments may be conceived that are within the scope and purpose of the invention.  
         [0105]     For example, while the first set of user-selectable sprockets has been shown to be directly connected to the pedal/crank combination, it will be understood that the first set of user-selectable sprockets may receive rotational power directly from another means or, for example, from an additional crank-powered sprocket set via an additional chain. Alternatively, or even in combination, the third set of user-selectable sprockets may not be co-axial with the driven wheel, but rather connected by chain to an additional sprocket co-axial with the driven wheel. It will be understood that receipt of power from an additional, unselectable sprocket may serve to amplify the power output without accordingly providing for a desirably low average mechanical ratio step size. The invention, however, would advantageously serve to reduce the average ratio step size.  
         [0106]     Furthermore, additional intermediate sprocket sets in the sequence may be provided, having respective input and output subsets of sprockets, one or both of which may comprise multiple user-selectable sprockets.  
         [0107]     Sprockets, chains and chain derailleurs are common parts which may be combined with minimum modification to achieve the objects of the invention. However, it may be contemplated to use alternative gearwheels such as pulleys, alternative gearwheel selection means, and alternative interconnection means such as different types of chains without departing from the spirit and scope of the invention described herein.  
         [0108]     Particular combinations of sprockets have been disclosed, but it will occur to the designer of a bicycle or other personal transportation device having a power transmission system to select combinations of sprockets yielding different teeth number combinations that achieve the desired theoretical maximum speed and provide a sufficiently low mechanical ratio step size through the speed range.  
         [0109]     A particular frame configuration has been shown in which the upper rearward extension, lower rearward extension, and base are formed as a single piece. However, it may be contemplated to form each or some as a single piece in order to facilitate manufacture, or otherwise to cater to a particular aftermarket where applicable.  
         [0110]     The power transmission system has been described for application in a bicycle. However, it will be contemplated that the invention could be employed in other, similar personal transportation devices such as multiple-speed tricycles. In the case of the tricycle, the third sprocket set could have an elongated common axle with two rear wheels.  
         [0111]     Other alternatives may be contemplated by those of ordinary skill in the art and it will be appreciated that variations and modifications may be made without departing from the spirit and scope thereof as defined by the appended claims.