Abstract:
A family of transmission gearing arrangements produces up to nine forward and one reverse speed ratios by selective engagement of three shift elements in various combinations. Each disclosed transmission includes four planetary gear sets and six elements. Two of the arrangements feature planetary gear sets that are separated radially and are particularly suited to applications that require reduced axial length.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a division of U.S. application Ser. No. 13/760,203 filed Feb. 6, 2013, the disclosure of which is hereby incorporated in its entirety by reference herein. 
     
    
     TECHNICAL FIELD 
       [0002]    This disclosure relates to the field of automatic transmissions for motor vehicles. More particularly, the disclosure pertains to an arrangement of gears, clutches, and the interconnections among them in a power transmission. 
       BACKGROUND 
       [0003]    Many vehicles are used over a wide range of vehicle speeds, including both forward and reverse movement. Some types of engines, however, are capable of operating efficiently only within a narrow range of speeds. Consequently, transmissions capable of efficiently transmitting power at a variety of speed ratios are frequently employed. When the vehicle is at low speed, the transmission is usually operated at a high speed ratio such that it multiplies the engine torque for improved acceleration. At high vehicle speed, operating the transmission at a low speed ratio permits an engine speed associated with quiet, fuel efficient cruising. Typically, a transmission has a housing mounted to the vehicle structure, an input shaft driven by an engine crankshaft, and an output shaft driving the vehicle wheels, often via a differential assembly which permits the left and right wheel to rotate at slightly different speeds as the vehicle turns. 
       SUMMARY OF THE DISCLOSURE 
       [0004]    In a first embodiment, a transmission includes first, second, and third gearing arrangements, a first clutch, and first and second brakes, configured to selectively establish nine forward and one reverse speed ratio between an input shaft and an output shaft. The first gearing arrangement selectively constrains the speed of a second shaft to fall between the speeds of the input shaft and a fourth shaft. The second gearing arrangement fixedly constrains the speed of a third shaft to fall between the speeds of the second shaft and the fourth shaft. The third gearing arrangement selectively constrains the speed of the output shaft to fall between zero and the speed of the third shaft and selectively constrains the speed of the input shaft to fall between the speeds of the third shaft and the output shaft. The first clutch selectively couples the input shaft to the second shaft. The first and second brakes selectively hold the second and fourth shafts, respectively, against rotation. 
         [0005]    In a second embodiment, a transmission includes first, second, and third gearing arrangements, a first clutch, and a first brake, configured to selectively establish nine forward and one reverse speed ratio between an input shaft and an output shaft. The first gearing arrangement selectively constrains the speed of a third shaft to fall between zero and the speed of a second shaft and selectively constrains the speed of the second shaft to fall between the speeds of the input shaft and the third shaft. The second gearing arrangement selectively constrains the speed of the output shaft to fall between zero and the speed of the third shaft. The third gearing arrangement selectively constrains the speed of the input shaft to fall between the speeds of the third shaft and the output shaft. The first clutch selectively couples the input shaft to the second shaft. The first brake selectively holds the second shaft against rotation. 
         [0006]    In a third embodiment, a transmission includes first, second, and third gearing arrangements, first and second clutches, and a first brake, configured to selectively establish nine forward and one reverse speed ratio between an input shaft and an output shaft. The first gearing arrangement fixedly constrains the speed of a second shaft to fall between the speeds of a first shaft and a third shaft. The second gearing arrangement selectively constrains the speed of the third shaft to fall between zero and the speed of the first shaft. The third gearing arrangement selectively constrains the speed of the output shaft to fall between zero and the speed of the third shaft and selectively constrains the speed of the input shaft to fall between the speeds of the third shaft and the output shaft. The first and second clutches selectively couple the input shaft to the second and first shafts, respectively. The first brake selectively holds the second shaft against rotation. 
         [0007]    In a fourth embodiment, a transmission includes first, second, and third gearing arrangements, a first clutch, and first and second brakes, configured to selectively establish nine forward and one reverse speed ratio between an input shaft and an output shaft. The first gearing arrangement selectively constrains the speed of a third shaft to fall between the speeds of the input shaft and a fourth shaft. The second gearing arrangement fixedly constrains the speed of the third shaft to fall between the speeds of a second shaft and the fourth shaft. The third gearing arrangement selectively constrains the speed of the output shaft to fall between zero and the speed of the third shaft and selectively constrains the speed of the input shaft to fall between the speeds of the third shaft and the output shaft. The first clutch selectively couples the input shaft to the second shaft. The first and second brakes selectively hold the second and fourth shafts, respectively, against rotation. 
         [0008]    In a fifth embodiment, a transmission includes first, second, and third gearing arrangements, first and second clutches, and a first brake, configured to selectively establish nine forward and one reverse speed ratio between an input shaft and an output shaft. The first gearing arrangement selectively constrains the speed of a second shaft to fall between zero and the speed of a first shaft. The second gearing arrangement fixedly constrains the speed of the second shaft to fall between the speeds of the first shaft and a third shaft. The third gearing arrangement selectively constrains the speed of the output shaft to fall between zero and the speed of the third shaft and selectively constrains the speed of the input shaft to fall between the speeds of the third shaft and the output shaft. The first and second clutches selectively couple the input shaft to the second and first shafts, respectively. The first brake selectively holds the second shaft against rotation. 
         [0009]    In a sixth embodiment, a transmission includes first, second, and third gearing arrangements, first and third clutches, and a first brake, configured to selectively establish nine forward and one reverse speed ratio between an input shaft and an output shaft. The first gearing arrangement selectively constrains the speed of a third shaft to fall between zero and the speed of a second shaft and selectively constrains the speed of the second shaft to fall between the speeds of the input shaft and the third shaft. The second gearing arrangement selectively constrains the speed of a fifth shaft to fall between zero and the speed of a third shaft. The third gearing arrangement fixedly constrains the speed of the fifth shaft to fall between the speeds of the third shaft and the output shaft. The first and third clutches selectively couple the input shaft to the second and fifth shafts, respectively. The first brake selectively holds the second shaft against rotation. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  is a schematic diagram of a first transmission gearing arrangement. 
           [0011]      FIG. 2  is a lever diagram corresponding to the first transmission gearing arrangement. 
           [0012]      FIG. 3  is a schematic diagram of a second transmission gearing arrangement also corresponding to the lever diagram of  FIG. 2 . 
           [0013]      FIG. 4  is a schematic diagram of a third transmission gearing arrangement also corresponding to the lever diagram of  FIG. 2 . 
           [0014]      FIG. 5  is a schematic diagram of a fourth transmission gearing arrangement also corresponding to the lever diagram of  FIG. 2 . 
       
    
    
     DETAILED DESCRIPTION 
       [0015]    Embodiments of the present disclosure are described herein. It is to be understood, however, that the disclosed embodiments are merely examples and other embodiments can take various and alternative forms. The figures are not necessarily to scale; some features could be exaggerated or minimized to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the present invention. As those of ordinary skill in the art will understand, various features illustrated and described with reference to any one of the figures can be combined with features illustrated in one or more other figures to produce embodiments that are not explicitly illustrated or described. The combinations of features illustrated provide representative embodiments for typical applications. Various combinations and modifications of the features consistent with the teachings of this disclosure, however, could be desired for particular applications or implementations. 
         [0016]    A gearing arrangement is a collection of rotating elements and shift elements configured to impose specified speed relationships among the rotating elements. Some speed relationships, called fixed speed relationships, are imposed regardless of the state of any shift elements. Other speed relationships, called selective speed relationships, are imposed only when particular shift elements are fully engaged. A discrete ratio transmission has a gearing arrangement that selectively imposes a variety of speed ratios between an input shaft and an output shaft. 
         [0017]    A group of rotating elements are fixedly coupled to one another if they are constrained to rotate as a unit in all operating conditions. Rotating elements can be fixedly coupled by spline connections, welding, press fitting, machining from a common solid, or other means. Slight variations in rotational displacement between fixedly coupled elements can occur such as displacement due to lash or shaft compliance. One or more rotating elements that are all fixedly coupled to one another may be called a shaft. In contrast, two rotating elements are selectively coupled by a shift element when the shift element constrains them to rotate as a unit whenever it is fully engaged and they are free to rotate at distinct speeds in at least some other operating condition. A shift element that holds a rotating element against rotation by selectively connecting it to the housing is called a brake. A shift element that selectively couples two or more rotating elements to one another is called a clutch. Shift elements may be actively controlled devices such as hydraulically or electrically actuated clutches or brakes or may be passive devices such as one way clutches or brakes. 
         [0018]    An example transmission is schematically illustrated in  FIG. 1 . The transmission utilizes four simple planetary gear sets  30 ,  40 ,  50 , and  60 . A planet carrier  32  rotates about a central axis and supports a set of planet gears  34  such that the planet gears rotate with respect to the planet carrier. External gear teeth on the planet gears mesh with external gear teeth on a sun gear  36  and with internal gear teeth on a ring gear  38 . The sun gear and ring gear are supported to rotate about the same axis as the carrier. A simple planetary gear set is a type of gearing arrangement that imposes a fixed speed relationship. The speed of the carrier is constrained to be between the speed of the sun gear and the speed of the ring gear. (This relationship is defined to include the condition in which all three rotate at the same speed.) More specifically, the speed of the carrier is a weighted average of the speed of the sun gear and the speed of the ring gear with weighting factors determined by the number of teeth on each gear. Similar fixed speed relationships are imposed by other known types of gearing arrangements. For example, a double pinion planetary gear set fixedly constrains the speed of the ring gear to be a weighted average between the speed of the sun gear and the speed of the carrier. Gear sets  40 ,  50 , and  60  are similarly structured. 
         [0019]    A suggested ratio of gear teeth for each planetary gear set is listed in Table 1. 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 Ring 38/Sun 36 
                 1.80 
               
               
                   
                 Ring 48/Sun 46 
                 1.80 
               
               
                   
                 Ring 58/Sun 56 
                 1.50 
               
               
                   
                 Ring 68/Sun 66 
                 2.00 
               
               
                   
                   
               
             
          
         
       
     
         [0020]    In the transmission of  FIG. 1 , sun gear  36  is fixedly coupled to sun gear  46 , carrier  32  is fixedly coupled to ring gear  48 , carrier  42  is fixedly coupled to sun gear  56  and sun gear  66 , and output shaft  12  is fixedly coupled to carrier  52  and ring gear  68 . Carrier  32  is selectively held against rotation by brake  18  and selectively coupled to input shaft  10  by clutch  24 . Sun gears  36  and  46  are selectively held against rotation by brake  16 . Input shaft  10  is selectively coupled to ring gear  38  by clutch  22  and selectively coupled to carrier  62  by clutch  20 . Sun gears  56  and  56  are selectively held against rotation by brake  26 . The combination of gear set  30  and clutch  22  selectively impose a speed relationship between carrier  32 , sun gear  36 , and input shaft  10 . Specifically, carrier  32  is constrained to rotate at a speed between the speeds of input shaft  10  and sun gear  36  whenever clutch  22  is engaged. Similarly, the combination of gear set  60  and clutch  20  selectively impose a speed relationship that input shaft  10  is constrained to rotate at a speed between the speeds of output shaft  12  and sun gear  66  whenever clutch  20  is engaged. Also, the combination of gear set  50  and brake  26  selectively impose a speed relationship that output shaft  12  is constrained to rotate at a speed between zero and the speed of sun gear  56  whenever brake  26  is engaged. 
         [0021]    As shown in Table 2, engaging the shift elements in combinations of three establishes nine forward speed ratios and one reverse speed ratio between input shaft  10  and output shaft  12 . An X indicates that the shift element is required to establish the speed ratio. An (X) indicates the clutch can be applied but is not required. In 4th gear, clutch  20  and brake  26  establish the power flow path between input shaft  10  and output shaft  12 . Any one of the remaining shift elements can also be applied. Applying clutch  24  ensures that all single and two step shifts from 4th gear can be accomplished by engaging only one shift element and releasing only one shift element. When the gear sets have tooth numbers as indicated in Table 1, the speed ratios have the values indicated in Table 2. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 16 
                 18 
                 20 
                 22 
                 24 
                 26 
                 Ratio 
                 Step 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Rev 
                   
                 X 
                   
                 X 
                   
                 X 
                 −3.89 
                 64% 
               
               
                 1 st   
                 X 
                   
                   
                 X 
                   
                 X 
                 6.05 
               
               
                 2 nd   
                 X 
                   
                   
                   
                 X 
                 X 
                 3.89 
                 1.56 
               
               
                 3 rd   
                   
                   
                   
                 X 
                 X 
                 X 
                 2.50 
                 1.56 
               
               
                 4 th   
                   
                   
                 X 
                   
                 (X) 
                 X 
                 1.50 
                 1.67 
               
               
                 5 th   
                   
                   
                 X 
                 X 
                 X 
                   
                 1.00 
                 1.50 
               
               
                 6 th   
                 X 
                   
                 X 
                   
                 X 
                   
                 0.85 
                 1.18 
               
               
                 7 th   
                 X 
                   
                 X 
                 X 
                   
                   
                 0.77 
                 1.10 
               
               
                 8 th   
                 X 
                 X 
                 X 
                   
                   
                   
                 0.67 
                 1.16 
               
               
                 9 th   
                   
                 X 
                 X 
                 X 
                   
                   
                 0.55 
                 1.21 
               
               
                   
               
             
          
         
       
     
         [0022]      FIG. 2  shows a lever diagram corresponding to the gearing arrangement of  FIG. 1 . Levers  72  and  74  represent gearing arrangements that fixedly constrain the rotational speeds of four shafts to be linearly related. Ring gear  38  forms the first shaft, the combination of carrier  32  and ring gear  48  forms the second shaft, the combination of carrier  42  and sun gears  56  and  66  forms the third shaft, the combination of sun gears  36  and  46  forms the fourth shaft, carrier  62  forms the fifth shaft, and ring gear  58  forms the sixth shaft. There are many gearing arrangements that can be represented by a four node lever such as levers  72  or  74 . Any pair of planetary gear sets wherein two rotating elements of the first gear set are respectively fixedly coupled to two rotating elements of the second gear set will impose the linear speed relationship represented by a four node lever. 
         [0023]    Any gearing arrangement that corresponds to the lever diagram of  FIG. 2  will impose several selective speed relationships. The combination of lever  72 , brake  16 , and clutch  22  selectively imposes two speed relationships. The second shaft is constrained to rotate at a speed between the speeds of input shaft  10  and the third shaft whenever clutch  22  is engaged. The third shaft is constrained to rotate at a speed between zero and the speed of the second shaft whenever brake  16  is engaged. The combination of lever  74 , brake  26 , and clutch  20  selectively imposes two similar speed relationships. The input shaft  10  is constrained to rotate at a speed between the speeds of third shaft and the output shaft whenever clutch  20  is engaged. The output shaft is constrained to rotate at a speed between zero and the speed of the third shaft whenever brake  16  is engaged. 
         [0024]    Another example transmission corresponding to the lever diagram of  FIG. 2  is illustrated in  FIG. 3 . The transmission utilizes four simple planetary gear sets  80 ,  90 ,  100 , and  110 . Suggested numbers of gear teeth for each planetary gear set is listed in Table 3. 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 3 
               
               
                   
                   
               
             
             
               
                   
                 Ring 88/Sun 86 
                 2.00 
               
               
                   
                 Ring 98/Sun 96 
                 1.90 
               
               
                   
                 Ring 108/Sun 106 
                 2.00 
               
               
                   
                 Ring 118/Sun 116 
                 1.50 
               
               
                   
                   
               
             
          
         
       
     
         [0025]    Sun gear  86  is fixedly coupled to sun gear  96 , ring gear  88  and carrier  92  are fixedly coupled to sun gear  116 , ring gear  108  is fixedly coupled to carrier  112 , and output shaft  12  is fixedly coupled to carrier  102  and ring gear  118 . Carrier  82  is selectively held against rotation by brake  18  and selectively coupled to input shaft  10  by clutch  24 . Ring gear  98  is selectively held against rotation by brake  16 . Input shaft  10  is selectively coupled to sun gears  86  and  96  by clutch  22  and selectively coupled to ring gear  108  and carrier  112  by clutch  20 . Sun gear  106  is selectively held against rotation by brake  26 . The combination of gear set  90  and brake  16  selectively constrains carrier  92  to rotate at a speed between zero and the speed of sun gear  96  whenever brake  16  is engaged. Similarly, the combination of gear set  100  and brake  26  selectively constrains output shaft  12  to rotate at a speed between zero and the speed of ring gear  108  whenever brake  26  is engaged. 
         [0026]    Gear sets  80  and  90  of  FIG. 3  correspond to lever  72  of  FIG. 2 . The combination of sun gears  86  and  96  forms the first shaft, carrier  82  forms the second shaft, the combination of ring gear  88 , carrier  92 , and sun gears  116  forms the third shaft, and ring gear  98  forms the fourth shaft. Gear sets  100  and  110  of  FIG. 3  correspond to lever  74  of  FIG. 2 . The combination of ring gear  108  and carrier  112  forms the fifth shaft, and sun gear  106  forms the sixth shaft. 
         [0027]    As shown in Table 4, engaging the clutches and brakes in combinations of three establishes nine forward speed ratios and one reverse speed ratio between input shaft  10  and output shaft  12 . When the gear sets have tooth numbers as indicated in Table 3, the speed ratios have the values indicated in Table 4. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 16 
                 18 
                 20 
                 22 
                 24 
                 26 
                 Ratio 
                 Step 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Rev 
                   
                 X 
                   
                 X 
                   
                 X 
                 −4.50 
                 69% 
               
               
                 1 st   
                 X 
                   
                   
                 X 
                   
                 X 
                 6.53 
               
               
                 2 nd   
                 X 
                   
                   
                   
                 X 
                 X 
                 3.68 
                 1.78 
               
               
                 3 rd   
                   
                   
                   
                 X 
                 X 
                 X 
                 2.25 
                 1.63 
               
               
                 4 th   
                   
                   
                 X 
                   
                 (X) 
                 X 
                 1.50 
                 1.50 
               
               
                 5 th   
                   
                   
                 X 
                 X 
                 X 
                   
                 1.00 
                 1.50 
               
               
                 6 th   
                 X 
                   
                 X 
                   
                 X 
                   
                 0.80 
                 1.26 
               
               
                 7 th   
                 X 
                   
                 X 
                 X 
                   
                   
                 0.70 
                 1.14 
               
               
                 8 th   
                 X 
                 X 
                 X 
                   
                   
                   
                 0.60 
                 1.16 
               
               
                 9 th   
                   
                 X 
                 X 
                 X 
                   
                   
                 0.50 
                 1.20 
               
               
                   
               
             
          
         
       
     
         [0028]    A third example transmission corresponding to the lever diagram of  FIG. 2  is illustrated in  FIG. 4 . The transmission utilizes four simple planetary gear sets  120 , 130 ,  140 , and  150 . To reduce the axial length of the transmission, gear set  130  is located radially outside gear set  120  and gear set  150  is located radially outside gear set  140 . An output member, which may be either a gear or a sprocket, is fixedly attached to output shaft  12 . The output member is engaged with a member on another axis, not shown, to transfer power to vehicle wheels via a differential assembly. Suggested numbers of gear teeth for each planetary gear set is listed in Table 5. 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 5 
               
               
                   
                   
               
             
             
               
                   
                 Ring 128/Sun 126 
                 1.50 
               
               
                   
                 Ring 138/Sun 136 
                 1.80 
               
               
                   
                 Ring 148/Sun 146 
                 1.80 
               
               
                   
                 Ring 158/Sun 156 
                 1.80 
               
               
                   
                   
               
             
          
         
       
     
         [0029]    Ring gear  128  is fixedly coupled to sun gear  136 , carrier  122  and carrier  132  are fixedly coupled to ring gear  148  and sun gear  156 , carrier  142  is fixedly coupled to carrier  152 , and output shaft  12  is fixedly coupled to ring gear  158 . Ring gear  138  is selectively held against rotation by brake  18  and selectively coupled to input shaft  10  by clutch  24 . Ring gear  128  and sun gear  136  are selectively held against rotation by brake  16 . Input shaft  10  is selectively coupled to sun gear  126  by clutch  22  and selectively coupled to carriers  142  and  152  by clutch  20 . Sun gear  146  is selectively held against rotation by brake  26 . The combination of gear set  120  and clutch  22  selectively constrains carrier  122  to rotate at a speed between the speeds of ring gear  128  and input shaft  10  whenever clutch  22  is engaged. Similarly, the combination of gear set  140  and brake  26  selectively constrains carrier  142  to rotate at a speed between zero and the speed of ring gear  148  whenever brake  26  is engaged. 
         [0030]    Gear sets  120  and  130  of  FIG. 4  correspond to lever  72  of  FIG. 2 . Sun gear  126  forms the first shaft, ring gear  138  forms the second shaft, the combination of carriers  122 , carrier  132 , ring gear  148 , and sun gear  156  forms the third shaft, and the combination of ring gear  128  and sun gear  136  forms the fourth shaft. Gear sets  140  and  150  of  FIG. 5  correspond to lever  74  of  FIG. 2 . The combination of carrier  142  and carrier  152  forms the fifth shaft, and sun gear  146  forms the sixth shaft. 
         [0031]    As shown in Table 6, engaging the clutches and brakes in combinations of three establishes nine forward speed ratios and one reverse speed ratio between input shaft  10  and output shaft  12 . When the gear sets have tooth numbers as indicated in Table 5, the speed ratios have the values indicated in Table 6. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                 16 
                 18 
                 20 
                 22 
                 24 
                 26 
                 Ratio 
                 Step 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Rev 
                   
                 X 
                   
                 X 
                   
                 X 
                 −3.83 
                 61% 
               
               
                 1 st   
                 X 
                   
                   
                 X 
                   
                 X 
                 6.30 
               
               
                 2 nd   
                 X 
                   
                   
                   
                 X 
                 X 
                 3.75 
                 1.68 
               
               
                 3 rd   
                   
                   
                   
                 X 
                 X 
                 X 
                 2.25 
                 1.68 
               
               
                 4 th   
                   
                   
                 X 
                   
                 (X) 
                 X 
                 1.45 
                 1.56 
               
               
                 5 th   
                   
                   
                 X 
                 X 
                 X 
                   
                 1.00 
                 1.45 
               
               
                 6 th   
                 X 
                   
                 X 
                   
                 X 
                   
                 0.82 
                 1.22 
               
               
                 7 th   
                 X 
                   
                 X 
                 X 
                   
                   
                 0.74 
                 1.11 
               
               
                 8 th   
                 X 
                 X 
                 X 
                   
                   
                   
                 0.64 
                 1.15 
               
               
                 9 th   
                   
                 X 
                 X 
                 X 
                   
                   
                 0.53 
                 1.21 
               
               
                   
               
             
          
         
       
     
         [0032]    A fourth example transmission corresponding to the lever diagram of  FIG. 2  is illustrated in  FIG. 5 . The transmission utilizes four simple planetary gear sets  160 , 170 ,  140 , and  150 . To reduce the axial length of the transmission, gear set  170  is located radially outside gear set  160  and gear set  150  is located radially outside gear set  140 . An output member, which may be either a gear or a sprocket, is fixedly attached to output shaft  12 . The output member is engaged with a member on another axis, not shown, to transfer power to vehicle wheels via a differential assembly. Suggested numbers of gear teeth for each planetary gear set is listed in Table 7. 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 7 
               
               
                   
                   
               
             
             
               
                   
                 Ring 128/Sun 126 
                 1.50 
               
               
                   
                 Ring 138/Sun 136 
                 1.80 
               
               
                   
                 Ring 148/Sun 146 
                 1.80 
               
               
                   
                 Ring 158/Sun 156 
                 1.80 
               
               
                   
                   
               
             
          
         
       
     
         [0033]    Ring gear  168  is fixedly coupled to sun gear  176 , carrier  162  is fixedly coupled to carrier  172 , ring gear  178  is fixedly coupled to ring gear  148  and sun gear  156 , carrier  142  is fixedly coupled to carrier  152 , and output shaft  12  is fixedly coupled to ring gear  158 . Carrier  162  and  172  are selectively held against rotation by brake  18  and selectively coupled to input shaft  10  by clutch  24 . Sun gear  166  is selectively held against rotation by brake  16 . Input shaft  10  is selectively coupled to ring gear  168  and sun gear  176  by clutch  22  and selectively coupled to carriers  142  and  152  by clutch  20 . Sun gear  146  is selectively held against rotation by brake  26 . The combination of gear set  160  and brake  16  selectively constrains carrier  162  to rotate at a speed between zero and the speed of ring gear  168  whenever brake  16  is engaged. Similarly, the combination of gear set  140  and brake  26  selectively constrains carrier  142  to rotate at a speed between zero and the speed of ring gear  148  whenever brake  26  is engaged. 
         [0034]    Gear sets  160  and  170  of  FIG. 5  correspond to lever  72  of  FIG. 2 . The combination of ring gear  168  and sun gear  176  forms the first shaft, the combination of carrier  162  and carrier  172  forms the second shaft, the combination of ring gear  178 , ring gear  148 , and sun gear  156  forms the third shaft, and sun gear  166  forms the fourth shaft. Gear sets  140  and  150  of  FIG. 5  correspond to lever  74  of  FIG. 2 . The combination of carrier  142  and carrier  152  forms the fifth shaft, and sun gear  146  forms the sixth shaft. 
         [0035]    As shown in Table 8, engaging the clutches and brakes in combinations of three establishes nine forward speed ratios and one reverse speed ratio between input shaft  10  and output shaft  12 . When the gear sets have tooth numbers as indicated in Table 7, the speed ratios have the values indicated in Table 8. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 8 
               
               
                   
                   
               
               
                   
                 16 
                 18 
                 20 
                 22 
                 24 
                 26 
                 Ratio 
                 Step 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Rev 
                   
                 X 
                   
                 X 
                   
                 X 
                 −3.38 
                 61% 
               
               
                 1 st   
                 X 
                   
                   
                 X 
                   
                 X 
                 5.56 
               
               
                 2 nd   
                 X 
                   
                   
                   
                 X 
                 X 
                 3.57 
                 1.56 
               
               
                 3 rd   
                   
                   
                   
                 X 
                 X 
                 X 
                 2.25 
                 1.59 
               
               
                 4 th   
                   
                   
                 X 
                   
                 (X) 
                 X 
                 1.45 
                 1.56 
               
               
                 5 th   
                   
                   
                 X 
                 X 
                 X 
                   
                 1.00 
                 1.45 
               
               
                 6 th   
                 X 
                   
                 X 
                   
                 X 
                   
                 0.83 
                 1.21 
               
               
                 7 th   
                 X 
                   
                 X 
                 X 
                   
                   
                 0.75 
                 1.10 
               
               
                 8 th   
                 X 
                 X 
                 X 
                   
                   
                   
                 0.64 
                 1.17 
               
               
                 9 th   
                   
                 X 
                 X 
                 X 
                   
                   
                 0.52 
                 1.24 
               
               
                   
               
             
          
         
       
     
         [0036]    While exemplary embodiments are described above, it is not intended that these embodiments describe all possible forms encompassed by the claims. The words used in the specification are words of description rather than limitation, and it is understood that various changes can be made without departing from the spirit and scope of the disclosure. As previously described, the features of various embodiments can be combined to form further embodiments of the invention that may not be explicitly described or illustrated. While various embodiments could have been described as providing advantages or being preferred over other embodiments or prior art implementations with respect to one or more desired characteristics, those of ordinary skill in the art recognize that one or more features or characteristics can be compromised to achieve desired overall system attributes, which depend on the specific application and implementation. These attributes can include, but are not limited to cost, strength, durability, life cycle cost, marketability, appearance, packaging, size, serviceability, weight, manufacturability, ease of assembly, etc. As such, embodiments described as less desirable than other embodiments or prior art implementations with respect to one or more characteristics are not outside the scope of the disclosure and can be desirable for particular applications.