Abstract:
A family of transmissions produces at least eight forward and one reverse speed ratio by selective engagement of various combinations of three clutches or brakes. Each transmission includes two fixed gearing arrangements that establish fixed speed relationships between an input shaft, and output shaft, and four other elements. Specifically, the input shaft is constrained to rotate at a speed between that of the first and second elements while the output shaft is constrained to rotate at a speed between that of the third and fourth elements. Additional gearing, clutches, and brakes establish specified selective speed relationships among these elements.

Description:
TECHNICAL FIELD 
     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 
     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. 
     A gearing arrangement is a collection of rotating elements and clutches configured to impose specified speed relationships among elements. Some speed relationships, called fixed speed relationships, are imposed regardless of the state of any clutches. A gearing arrangement imposing only fixed relationships is called a fixed gearing arrangement. Other speed relationships are imposed only when particular clutches are fully engaged. A gearing arrangement that selectively imposes speed relationships is called a shiftable gearing arrangement. A discrete ratio transmission has a shiftable gearing arrangement that selectively imposes a variety of speed ratios between an input shaft and an output shaft. 
     A group of elements are fixedly coupled to one another if they are constrained to rotate as a unit in all operating conditions. Elements may 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. In contrast, two elements are selectively coupled by a clutch when the clutch constrains them to rotate as a unit whenever the clutch is fully engaged and they are free to rotate at distinct speeds in at least some other operating condition. Clutches include actively controlled devices such as hydraulically or electrically actuated clutches and passive devices such as one way clutches. A clutch that holds an element against rotation by selectively connecting the element to the housing may be called a brake. A group of elements are coupled if they are fixedly coupled or selectively coupled. 
     SUMMARY OF THE DISCLOSURE 
     A family of transmissions is disclosed. Each transmission includes an input shaft, an output shaft, a number of rotating elements, and gearing arrangements and clutches that impose specified fixed and selectable speed relationships. 
     In one embodiment, a transmission includes at least first, second, third, fourth, fifth, and sixth elements in addition to the input shaft and output shaft. A first gearing arrangement fixedly constrains the speed of the input shaft to be between the speeds of the first and second elements. The first gearing arrangement may be, for example, a simple planetary gear set having a sun gear as the second element, a planet carrier fixedly coupled to the input shaft, and a ring gear as the first element. A second gearing arrangement fixedly constrains the speed of the output shaft to be between the speeds of the third and fourth elements. The second gearing arrangement may be, for example, a simple planetary gear set having a sun gear as the third element, a planet carrier fixedly coupled to the output shaft, and a ring gear as the fourth element. A third gearing arrangement fixedly constrains the speed of the fifth element to be between zero and the speed the sixth element. The fifth element is coupled to the fourth element and the sixth element is coupled to the second element. The third gearing arrangement may be, for example, a simple planetary gear set having a sun gear as the sixth element fixedly coupled to the second element, a planet carrier as the fifth element selectively coupled to the fourth element, and a ring gear fixedly held against rotation. Alternatively, the third gearing arrangement may be, as another example, a simple planetary gear set having a sun gear selectively coupled to the second element, a planet carrier fixedly coupled to the fourth element, and a ring gear fixedly held against rotation. A fourth gearing arrangement selectively constrains the speed of the fourth element to be between the speeds of the first element and the third element. The fourth gearing arrangement may be, for example, a double pinion planetary gear set having a sun gear fixedly coupled to the third element, a planet carrier selectively coupled to the first element, and a ring gear fixedly coupled to the fourth element. Eight speed embodiments have clutches and brakes which selectively hold the second element against rotation, selectively couple the third element to the input shaft, and selectively couple the first element to the third element. Ten speed embodiments additionally have a clutch selectively coupling the first element to the fourth element. 
     In another embodiment, a transmission includes at least first, second, third, fourth, fifth, and sixth elements in addition to the input shaft and output shaft. A first gearing arrangement fixedly constrains the speed of the input shaft to be between the speeds of the first and second elements. The first gearing arrangement may be, for example, a simple planetary gear set having a sun gear as the second element, a planet carrier fixedly coupled to the input shaft, and a ring gear as the first element. A second gearing arrangement fixedly constrains the speed of the output shaft to be between the speeds of the third and fourth elements. The second gearing arrangement may be, for example, a simple planetary gear set having a sun gear as the third element, a planet carrier fixedly coupled to the output shaft, and a ring gear as the fourth element. A third gearing arrangement fixedly constrains the speed of the fourth element to be between the speeds of the fifth and sixth elements. The fifth element is coupled to the first element and the sixth element is coupled to the third element. The third gearing arrangement may be, for example, a double pinion planetary gear set having a sun gear as the sixth element fixedly coupled to the third element, a planet carrier as the fifth element selectively coupled to the first element, and a ring gear fixedly coupled to the fourth element. A fourth gearing arrangement selectively constrains the speed of the fourth element to be between zero and the speed the second element. The fourth gearing arrangement may be, for example, a simple planetary gear set having a sun gear selectively coupled to the second element by a clutch, a planet carrier fixedly coupled to the fourth element, and a ring gear fixedly held against rotation. Alternatively, the fourth gearing arrangement may be, as another example, a simple planetary gear set having a sun gear fixedly coupled to the second element, a planet carrier selectively coupled to the fourth element by a clutch, and a ring gear fixedly held against rotation. Eight speed embodiments have clutches and brakes which selectively hold the second element against rotation, selectively couple the third element to the input shaft, and selectively couple the first element to the third element. Ten speed embodiments additionally have a clutch selectively coupling the first element to the fourth element. 
     In another embodiment, a transmission includes at least first, second, third, fourth, fifth, sixth, and seventh elements in addition to the input shaft and output shaft. A first gearing arrangement fixedly constrains the speed of the input shaft to be between the speeds of the first and second elements. The first gearing arrangement may be, for example, a simple planetary gear set having a sun gear as the second element, a planet carrier fixedly coupled to the input shaft, and a ring gear as the first element. A second gearing arrangement fixedly constrains the speed of the output shaft to be between the speeds of the third and fourth elements. The second gearing arrangement may be, for example, a simple planetary gear set having a sun gear as the third element, a planet carrier fixedly coupled to the output shaft, and a ring gear as the fourth element. A third gearing arrangement fixedly constrains the speed of the seventh element to be between the speeds of the fifth and sixth elements. The fifth element is coupled to the first element, the sixth element is coupled to the third element, and the seventh element is coupled to the fourth element. The third gearing arrangement may be, for example, a double pinion planetary gear set having a sun gear as the sixth element fixedly coupled to the third element, a planet carrier as the fifth element selectively coupled to the first element, and a ring gear as the seventh element fixedly coupled to the fourth element. Alternatively, the third gearing arrangement may be, as another example, a double pinion planetary gear set having a sun gear as the sixth element fixedly coupled to the third element, a planet carrier as the fifth element fixedly coupled to the first element, and a ring gear as the seventh element selectively coupled to the fourth element. A fourth gearing arrangement selectively constrains the speed of the fourth element to be between zero and the speed the second element. The fourth gearing arrangement may be, for example, a simple planetary gear set having a sun gear fixedly coupled to the second element, a planet carrier fixedly coupled to the fourth element, and a ring gear selectively held against rotation. Alternatively, the fourth gearing arrangement may be, as another example, a simple planetary gear set having a sun gear fixedly coupled to the second element, a planet carrier selectively coupled to the fourth element by a clutch, and a ring gear fixedly held against rotation. Clutches and brakes selectively hold the second element against rotation, selectively couple the third element to the input shaft, selectively couple the first element to the third element, and selectively coupling the first element to the fourth element. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of a first transmission gearing arrangement; 
         FIG. 2  is a schematic diagram of a second transmission gearing arrangement; 
         FIG. 3  is a schematic diagram of a third transmission gearing arrangement; and 
         FIG. 4  is a schematic diagram of a fourth transmission gearing arrangement. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present disclosure are described herein. It is to be understood, however, that the disclosed embodiments are merely examples and other embodiments may 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 may 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. 
     An example transmission is schematically illustrated in  FIG. 1 . The transmission utilizes four planetary gear sets  20 ,  30 ,  40 , and  50 . Gear sets  20 ,  30 , and  50  are simple planetary gear sets. A simple planetary gear set is a type of fixed gearing arrangement. A planet carrier  22  rotates about a central axis and supports a set of planet gears  24  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  26  and with internal gear teeth on a ring gear  28 . The sun gear and ring gear are supported to rotate about the same axis as the carrier. A simple planetary gear set imposes the fixed speed relationship that the speed of the carrier is 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. 
     Gear set  40  is a double pinion planetary gear set, which is another type of fixed gearing arrangement. A planet carrier  42  rotates about a central axis and supports an inner set of planet gears  44  and an outer set of planet gears  45 . External gear teeth on each of the inner planet gears  44  mesh with external gear teeth on a sun gear  46  and with internal gear teeth on one of the outer planet gears  45 . External gear teeth on each of the outer planet gears  45  mesh with internal gear teeth on a ring gear  48 . The sun gear and ring gear are supported to rotate about the same axis as the carrier. A double pinion planetary gear set imposes the fixed speed relationship that the speed of the ring gear is between the speed of the sun gear and the speed of the carrier. (This relationship is defined to include the condition in which all three rotate at the same speed.) More specifically, the speed of the ring gear is a weighted average of the speed of the sun gear and the speed of the carrier with weighting factors determined by the number of teeth on each gear. Similar speed relationships are imposed by other known types of fixed gearing arrangements. 
     A suggested ratio of gear teeth for each planetary gear set in  FIG. 1  is listed in Table 1. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 Ring 28/Sun 26 
                 2.40 
               
               
                   
                 Ring 38/Sun 36 
                 2.20 
               
               
                   
                 Ring 48/Sun 46 
                 2.10 
               
               
                   
                 Ring 58/Sun 56 
                 3.80 
               
               
                   
                   
               
             
          
         
       
     
     Input shaft  10  is fixedly coupled to carrier  32 . Output shaft  12  is fixedly coupled to carrier  52 . Carrier  22 , ring gear  48 , and ring gear  58  are fixedly coupled to one another. Ring gear  28  is fixedly held against rotation. Sun gear  46  is fixedly coupled to sun gear  56 . Sun gear  36  is selectively held against rotation by brake  60  and selectively coupled to sun gear  26  by clutch  62 . Sun gear  46  and sun gear  56  are selectively coupled to input shaft  10  and carrier  32  by clutch  64 . Ring gear  38  is selectively coupled to carrier  42  by clutch  66  and selectively coupled to sun gear  46  and sun gear  56  by clutch  68 . 
     As shown in Table 2, engaging the clutches and brakes in combinations of three establishes eight forward speed ratios and one reverse speed ratio between input shaft  10  and output shaft  12 . An X indicates that the clutch is engaged to establish the speed ratio. All shifts between adjacent speed ratios and all two step shifts can be accomplished by the coordinated release of one clutch or brake and the engagement of one other clutch or brake. When the gear sets of  FIG. 1  have tooth numbers as indicated in Table 1, the speed ratios have the values indicated in Table 2. 
     
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
                 60  
                 62 
                 64 
                 66 
                 68 
                 Ratio 
                 Step 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Rev 
                 X 
                 X 
                   
                 X 
                   
                 −3.00 
                 63% 
               
               
                   
                 1 st   
                 X 
                 X 
                 X 
                   
                   
                 4.80 
                   
               
               
                   
                 2 nd   
                 X 
                 X 
                   
                   
                 X 
                 3.30 
                 1.45 
               
               
                   
                 3 rd   
                   
                 X 
                 X 
                   
                 X 
                 2.27 
                 1.46 
               
               
                   
                 4 th   
                   
                 X 
                   
                 X 
                 X 
                 1.75 
                 1.30 
               
               
                   
                 5 th   
                   
                 X 
                 X 
                 X 
                   
                 1.33 
                 1.31 
               
               
                   
                 6 th   
                   
                   
                 X 
                 X 
                 X 
                 1.00 
                 1.33 
               
               
                   
                 7 th   
                 X 
                   
                 X 
                 X 
                   
                 0.84 
                 1.19 
               
               
                   
                 8 th   
                 X 
                   
                   
                 X 
                 X 
                 0.69 
                 1.22 
               
               
                   
                   
               
             
          
         
       
     
     Another example transmission is illustrated in  FIG. 2 . The transmission utilizes three simple planetary gear sets  20 ,  30 , and  50  and one double pinion planetary gear set  40 . A suggested ratio of gear teeth for each planetary gear set in  FIG. 2  is listed in Table 3. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 3 
               
               
                   
                   
               
             
             
               
                   
                 Ring 28/Sun 26 
                 2.40 
               
               
                   
                 Ring 38/Sun 36 
                 1.80 
               
               
                   
                 Ring 48/Sun 46 
                 1.90 
               
               
                   
                 Ring 58/Sun 56 
                 3.80 
               
               
                   
                   
               
             
          
         
       
     
     Input shaft  10  is fixedly coupled to carrier  32 . Output shaft  12  is fixedly coupled to carrier  52 . Ring gear  48  is fixedly coupled to ring gear  58 . Ring gear  28  is fixedly held against rotation. Sun gear  26  is fixedly coupled to sun gear  36 . Sun gear  46  is fixedly coupled to sun gear  56 . Sun gear  26  and sun gear  36  are selectively held against rotation by brake  60 . Sun gear  46  and sun gear  56  are selectively coupled to input shaft  10  and carrier  32  by clutch  64 . Ring gear  38  is selectively coupled to carrier  42  by clutch  66 , selectively coupled to sun gear  46  and sun gear  56  by clutch  68 , and selectively coupled to ring gear  48  and ring gear  58  by clutch  70 . Carrier  22  is selectively coupled to ring gear  48  and ring gear  58  by clutch  72 . 
     As shown in Table 4, engaging the clutches and brakes in combinations of three establishes ten forward speed ratios and one reverse speed ratio between input shaft  10  and output shaft  12 . When the gear sets of  FIG. 2  have tooth numbers as indicated in Table 3, the speed ratios have the values indicated in Table 4. 
     
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                   
                 60 
                 64 
                 66 
                 68 
                 70 
                 72 
                 Ratio 
                 Step 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Rev 
                 X 
                   
                 X 
                   
                   
                 X 
                 −3.43 
                 71% 
               
               
                 1 st   
                 X 
                 X 
                   
                   
                   
                 X 
                 4.80 
                   
               
               
                 2 nd   
                 X 
                   
                   
                 X 
                   
                 X 
                 3.09 
                 1.56 
               
               
                 3 rd   
                   
                 X 
                   
                 X 
                   
                 X 
                 2.27 
                 1.36 
               
               
                 4 th   
                   
                   
                   
                 X 
                 X 
                 X 
                 1.86 
                 1.22 
               
               
                 5 th   
                   
                 X 
                   
                   
                 X 
                 X 
                 1.58 
                 1.18 
               
               
                 6 th   
                   
                 X 
                 X 
                   
                   
                 X 
                 1.36 
                 1.16 
               
               
                 7 th   
                   
                 X 
                 X 
                   
                 X 
                   
                 1.00 
                 1.36 
               
               
                 8 th   
                 X 
                 X 
                 X 
                   
                   
                   
                 0.83 
                 1.21 
               
               
                 9 th   
                 X 
                 X 
                   
                   
                 X 
                   
                 0.70 
                 1.20 
               
               
                 10 th   
                 X 
                   
                 X 
                   
                 X 
                   
                 0.64 
                 1.08 
               
               
                   
               
             
          
         
       
     
     All shifts between adjacent speed ratios can be accomplished by the coordinated release of one clutch or brake and the engagement of one other clutch or brake. Similar, all two step shifts except 4 th  to 6 th  and many of the three step shifts can be accomplished by the coordinated release of one friction element and engagement of one other friction element. Additional shift are possible by utilizing alternate combinations of clutches for certain speed ratios. Specifically, 4 th  gear can be established by engaging clutch  72  while engaging any two of clutches  66 ,  68 , and  70 . Similarly, 7 th  gear can be established by engaging clutch  64  while engaging any two of clutches  66 ,  68 , and  70  and 10 th  gear can be established by engaging brake  60  while engaging any two of clutches  66 ,  68 , and  70 . For example, a shift from 4 th  gear to 6 th  gear can be accomplished by engaging clutch  66 , then releasing clutch  68 , and then coordinating the release of clutch  70  with the engagement of clutch  64 . 
     A third example transmission is illustrated in  FIG. 3 . The transmission utilizes three simple planetary gear sets  20 ,  30 , and  50  and one double pinion planetary gear set  40 . Input shaft  10  is fixedly coupled to carrier  32 . Output shaft  12  is fixedly coupled to carrier  52 . Carrier  22  is fixedly coupled to ring gear  58 . Sun gear  26  is fixedly coupled to sun gear  36 . Ring gear  38  is fixedly coupled to carrier  42 . Sun gear  46  is fixedly coupled to sun gear  56 . Brake  60  selectively holds sun gear  26  and sun gear  36  against rotation. Sun gear  46  and sun gear  56  are selectively coupled to input shaft  10  and carrier  32  by clutch  64  and selectively coupled to ring gear  38  and carrier  42  by clutch  68 . Carrier  22  and ring gear  58  are selectively coupled to ring gear  38  and carrier  42  by clutch  70  and selectively coupled to ring gear  48  by clutch  76 . Brake  74  selectively holds ring gear  28  against rotation. 
     As shown in Table 5, engaging the clutches and brakes in combinations of three establishes ten forward speed ratios and one reverse speed ratio between input shaft  10  and output shaft  12 . When the gear sets of  FIG. 3  have tooth numbers as indicated in Table 3, the speed ratios have the values indicated in Table 5. 
     
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                   
                 60 
                 64 
                 68 
                 70 
                 74 
                 76  
                 Ratio 
                 Step 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Rev 
                 X 
                   
                   
                   
                 X 
                 X 
                 −3.43 
                 71% 
               
               
                 1 st   
                 X 
                 X 
                   
                   
                 X 
                   
                 4.80 
                   
               
               
                 2 nd   
                 X 
                   
                 X 
                   
                 X 
                   
                 3.09 
                 1.56 
               
               
                 3 rd   
                   
                 X 
                 X 
                   
                 X 
                   
                 2.27 
                 1.36 
               
               
                 4 th   
                   
                   
                 X 
                 X 
                 X 
                   
                 1.86 
                 1.22 
               
               
                 5 th   
                   
                 X 
                   
                 X 
                 X 
                   
                 1.58 
                 1.18 
               
               
                 6 th   
                   
                 X 
                   
                   
                 X 
                 X 
                 1.36 
                 1.16 
               
               
                 7 th   
                   
                 X 
                   
                 X 
                   
                 X 
                 1.00 
                 1.36 
               
               
                 8 th   
                 X 
                 X 
                   
                   
                   
                 X 
                 0.83 
                 1.21 
               
               
                 9 th   
                 X 
                 X 
                   
                 X 
                   
                   
                 0.70 
                 1.20 
               
               
                 10 th   
                 X 
                   
                   
                 X 
                   
                 X 
                 0.64 
                 1.08 
               
               
                   
               
             
          
         
       
     
     A fourth example transmission is illustrated in  FIG. 4 . The transmission utilizes three simple planetary gear sets  20 ,  30 , and  50  and one double pinion planetary gear set  40 . Input shaft  10  is fixedly coupled to carrier  32 . Output shaft  12  is fixedly coupled to carrier  52 . Carrier  22  is fixedly coupled to ring gear  58 . Sun gear  26  is fixedly coupled to sun gear  36 . Ring gear  38  is fixedly coupled to carrier  42 . Sun gear  46  is fixedly coupled to sun gear  56 . Brake  60  selectively holds sun gear  26  and sun gear  36  against rotation. Sun gear  46  and sun gear  56  are selectively coupled to input shaft  10  and carrier  32  by clutch  64  and selectively coupled to ring gear  48  by clutch  78 . Carrier  22  and ring gear  58  are selectively coupled to ring gear  38  and carrier  42  by clutch  70  and selectively coupled to ring gear  48  by clutch  76 . Brake  74  selectively holds ring gear  28  against rotation. 
     When clutch  78  is engaged, all members of gear set  40  are forced to rotate as a single unit. Consequently, because ring gear  38  is fixedly coupled to carrier  42  and sun gear  56  is fixedly coupled to sun gear  46 , engaging clutch  78  operatively couples ring gear  38  to sun gear  56  even though it does not directly couple these two elements. 
     As shown in Table 6, engaging the clutches and brakes in combinations of three establishes ten forward speed ratios and one reverse speed ratio between input shaft  10  and output shaft  12 . When the gear sets of  FIG. 4  have tooth numbers as indicated in Table 3, the speed ratios have the values indicated in Table 6. 
     
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                   
                 60 
                 64 
                 70 
                 74 
                 76 
                 78 
                 Ratio 
                 Step 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Rev 
                 X 
                   
                   
                 X 
                 X 
                   
                 −3.43 
                 71% 
               
               
                 1 st   
                 X 
                 X 
                   
                 X 
                   
                   
                 4.80 
                   
               
               
                 2 nd   
                 X 
                   
                   
                 X 
                   
                 X 
                 3.09 
                 1.56 
               
               
                 3 rd   
                   
                 X 
                   
                 X 
                   
                 X 
                 2.27 
                 1.36 
               
               
                 4 th   
                   
                   
                 X 
                 X 
                   
                 X 
                 1.86 
                 1.22 
               
               
                 5 th   
                   
                 X 
                 X 
                 X 
                   
                   
                 1.58 
                 1.18 
               
               
                 6 th   
                   
                 X 
                   
                 X 
                 X 
                   
                 1.36 
                 1.16 
               
               
                 7 th   
                   
                 X 
                 X 
                   
                 X 
                   
                 1.00 
                 1.36 
               
               
                 8 th   
                 X 
                 X 
                   
                   
                 X 
                   
                 0.83 
                 1.21 
               
               
                 9 th   
                 X 
                 X 
                 X 
                   
                   
                   
                 0.70 
                 1.20 
               
               
                 10 th   
                 X 
                   
                 X 
                   
                 X 
                   
                 0.64 
                 1.08 
               
               
                   
               
             
          
         
       
     
     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 may be made without departing from the spirit and scope of the disclosure. As previously described, the features of various embodiments may 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 may 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.