Speed change gear system
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to speed change gear systems and more particularly to a speed change gear system which is adapted for application with fluid couplings utilized within motor vehicles, especially automobiles. 
     2. Description of the Prior Art 
     It is preferable to utilize at least four gear sets within the speed change gear systems of large automotive vehicles, such as for example, trucks and buses, and in order to attain a speed change mechanism having more than four speed shifts, three, four or even more sets of simple, single-pinion or double-pinion type planetary gear sets have heretofore been combined. While the combination of these gears may be widely varied, it is preferable however that the following conditions be attained: 
     1. The output shaft should be coupled to the same elements within each speed range. 
     2. In order to reduce the circumferential speed of the bearings of each element of the planetary gear set, the number of its revolutions should be small. 
     3. The tooth load, that is, the tangential force of each element should be small so as to maintain the strength of the gear teeth. 
     4. The gear set should always attain meshing conditions for the number of teeth required. For example, the sun gear, whose diameter is to be minimized, as well as each planetary pinion gear, should have the necessary number of teeth. 
     5. Within the planetary gear set, the coupling relationship among the elements should be simple and the distance from each other should be small. 
     6. During speed shifts, wherein frictional coupling means are utilized during forward drive, such speed shifts should be available through one coupling means alone. 
     SUMMARY OF THE INVENTION 
     Accordingly, it is an object of the present invention to provide a speed change gear system which provides at least four speed ranges for forward drive and one speed range for reverse drive by the use of two planetary gear sets of the single-pinion type and one simple planetary gear set of the double-pinion type, two clutches, and three brakes, whereby the movable members of each of the planetary gear sets are suitably coupled as a result of the coupling or uncoupling of the clutches and brakes so as to attain the various speed ranges. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Various other objects, features and attendant advantages of the present invention will be more fully appreciated as the same becomes better understood from the following detailed description when considered in conjunction with the accompanying drawings, in which like reference characters designate like or corresponding parts throughout the several views, and wherein: 
     FIG. 1A is a schematic view of one embodiment of a speed change gear system constructed in accordance with the present invention and disclosing its cooperative parts; 
     FIG. 2A is a schematic view similar to that of FIG. 1 showing however another embodiment of the present invention; 
     FIG. 3A is a schematic view similar to that of FIG. 1 showing however yet another embodiment of the present invention; 
     FIG. 4A is a schematic view similar to that of FIG. 1 showing however still another embodiment of the present invention; 
     FIG. 5A is a schematic view similar to that of FIG. 1 showing yet still another embodiment of the present invention; 
     FIG. 6A is a schematic view similar to that of FIG. 1 showing however a further embodiment of the present invention; 
     FIG. 7A is a schematic view similar to that of FIG. 1 showing however a yet further embodiment of the present invention; 
     FIG. 8A is a schematic view similar to that of FIG. 1 showing however a still further embodiment of the present invention; and 
     FIG. 9A is a schematic view similar to that of FIG. 1 showing however a yet still further embodiment of the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to the drawings and more particularly to FIG. 1A thereof, the disclosed speed change gear system includes a first planetary gear set generally indicated by the reference character X 1  of the double-pinion type, a second planetary gear set generally indicated by the reference character X 2  of the single-pinion type, and a third planetary gear set generally indicated by the reference character X 3  of the single-pinion type, all of which are interposed between an input shaft and an output shaft. The first planetary gear set X 1  is seen to comprise a first sun gear S 1 , first planetary gear P 1  engaged with the first sun gear S 1 , a second planetary gear P 2  engaged with the first planetary gear P 1 , a first ring gear RG 1  enmeshed with the second planetary gear P 2 , and a first carrier C 1  rotatably supporting the first and second planetary gears P 1 , P 2 , while the second planetary gear set X 2  similarly includes a second sun gear S 2 , a third planetary gear P 3   engaged with the second sun gear S 2 , a second ring gear RG 2  enmeshed with the third planetary gear P 3  and a second carrier C 2  rotatably supporting the third planetary gear P 3  and connected to the output shaft. 
     The third planetary gear set X 3  includes a third sun gear S 3 , a fourth planetary gear P 4  engaged with the third sun gear S 3 , a third ring gear RG 3  enmeshed with the fourth planetary gear P 4 , and a third carrier C 3  rotatably supporting the fourth planetary gear P 4 . The second ring gear RG 2 , the third carrier C 3  and the first carrier C 1  are serially connected with each other and a first clutch CL 1  serves to couple or uncouple the second ring gear RG 2 , the third carrier C 3  and the first carrier C 1  with the input shaft. The first ring gear RG 1  and the third ring gear RG 3  are similarly drivingly engaged with each other and a second clutch CL 2  serves to couple or uncouple the first ring gear RG 1  and the third ring gear RG 3  with the input shaft. Still further, a third clutch CL 3  serves to couple or uncouple the input shaft and the first sun gear S 1 . 
     A first brake B 1  is interposed between the first sun gear S 1  and the gear casing so as to be capable of locking the first sun gear S 1  to the casing when the first brake is actuated and similarly, a second brake B 2  is interposed between the casing and the element set comprising the second ring gear RG 2 , the third carrier C 3  and the first carrier C 1  so as to be capable of locking them to the casing when the second brake is actuated. The second sun gear S 2  and the third sun gear S 3  are drivingly engaged, and a third brake B 3  is disposed between the casing and the second and third sun gears S 2  and S 3  so as to be capable of locking the second and third sun gears S 2  and S 3  to the casing when the brake is actuated. 
     The following equations are given as characteristic of the planetary gear sets X 1 , X 2  and X 3  : 
     
         n.sub.rg.sbsb.1 -(1 - i.sub.1)n.sub.c.sbsb.1 - i.sub.1 n.sub.s.sbsb.1 = 0 
    
     
         n.sub.rg.sbsb.2 -(1 + i.sub.2)n.sub.c.sbsb.2 + i.sub.2 n.sub.s.sbsb.2 = 0 
    
     
         n.sub.rg.sbsb.3 -(1 + i.sub.3)n.sub.c.sbsb.3 + i.sub.3 n.sub.s.sbsb.3 = 0 
    
     wherein: 
     N RG .sbsb.1, N RG .sbsb.2, N RG .sbsb.3 =the number of revolutions of the first, second and third ring gears; 
     N C .sbsb.1, N C .sbsb.2, N C .sbsb.3 =the number of revolutions of the first, second and third carriers; 
     N S .sbsb.1, N S .sbsb.2, N S .sbsb.3 =the number of revolutions of the first, second and third sun gears; and 
     I 1 , I 2 , I 3  = the radial ratios of each ring gear to each sun gear. 
     Within this embodiment, the radial ratios within each speed range are I 1  = 0.419, I 2  = 0.548, I 3  = 0.548. Table 1B shows the relationship between the operation of clutches CL 1 , CL 2  and CL 3  and brakes B 1 , B 2  and B 3  relative to the gear ratio within each speed range, wherein F n  (n =1, 2, 3, . . . ) designates a forward speed range, such as for example, F 1  designates the first forward speed range, F 2  designates the second forward speed range, etc. and R n  (n =1, 2, . . . ) designates a reverse speed range, such as for example, R 1  designates the first reverse speed range, and it may be seen that a reduction gear ratio of 1 : 1.00 can be obtained by desirably and selectively employing two of the clutches CL 1 , CL 2  and CL 3 . Table 1C shows the relationship regarding the number of revolutions and the tangential forces of each of the elements of the planetary gear sets within each speed range. The ratio of the number of revolutions is based upon the assumption that the number of revolutions of the input shaft is 1, while the designated tangential forces are based upon the assumption that the input shaft torque exerted upon the ring gear is 1, the tangential forces of the planetary gears being equal to those of the sun gears and the ring gears. 
     Within Table 1C, like reference characters designate identical or corresponding parts shown within Table 1B, and in addition, A designates a particular speed range, B designates an element of the planetary gear set, N designates the number of revolutions, and W designates the tangential force. Because the reduction gear ratio of the fourth forward speed range F 4  is 1 : 1.00, the number of revolutions N of each sun gear, ring gear, and carrier is 1.00, the number of revolutions N of an individual sun gear, ring gear and carrier is 1.00, and the number of revolutions N of each planetary gear is 0.00. The tangential forces W are therefore considerably less than those produced within the other speed ranges. Within the other speed ranges, the torque of the input shaft is transmitted to all of the elements through only one engaged clutch, while to the contrary, the torque of the input shaft of the fourth speed range F 4  is distributed to all elements as a result of engaging at least two clutches, and accordingly, it is clear that the resulting tangential forces of the elements of such speed range are smaller than those produced as a result of the transmission of torque from the input shaft as a result of coupling only one clutch. Hereinafter, a discussion of the number of revolutions N and the tangential forces W within the speed range having the reduction gear ratio of 1 : 1.00 will be omitted. 
     
                       TABLE 1B                                                    
______________________________________                                    
                                          Reduction                       
CL1     CL2    CL3    B1   B2   B3   B4   gear ratio                      
______________________________________                                    
F1                 O              O         1 : 3.57                      
F2          O                     O         1 : 2.40                      
F3   O                            O         1 : 1.55                      
F4   O      O                               1 : 1.00                      
F5   O                  O                   1 : 0.79                      
F6          O           O                   1 : 0.46                      
R1                 O         O              1 : -3.70                     
R2          O                O              1 : -1.55                     
______________________________________                                    
 
    
     
                                           TABLE 1C                                
__________________________________________________________________________
B    X1                    X2                 X3                          
A    S1  C1  RG1 P1   P2   S2   C2   RG2 P3   S3   C3  RG3 P4             
__________________________________________________________________________
F1 N 1.00                                                                 
         0.43                                                             
             0.67                                                         
                 -0.86                                                    
                      0.86 0.0  0.28 0.43                                 
                                         0.68 0.0  0.43                   
                                                       0.67               
                                                           1.05           
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31                                 
                                         2.31 2.39 4.77                   
                                                       2.39               
                                                           2.39           
F2 N 1.49                                                                 
         0.65                                                             
             1.00                                                         
                 -1.29                                                    
                      1.29 0.00 0.42 0.65                                 
                                         1.01 0.0  0.65                   
                                                       1.00               
                                                           1.57           
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.55 3.10 1.55                                 
                                         1.55 1.00 2.00                   
                                                       1.00               
                                                           1.00           
F3 N 2.31                                                                 
         1.00                                                             
             1.55                                                         
                 -1.99                                                    
                      1.99 0.0  0.65 1.00                                 
                                         1.57 0.0  1.00                   
                                                       1.55               
                                                           2.42           
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00                                 
                                         1.00 0.00 0.00                   
                                                       0.00               
                                                           0.00           
F4 N 0.0 1.00                                                             
             0.58                                                         
                 1.52 -1.52                                               
                           1.76 1.27 1.00                                 
                                         -1.20                            
                                              1.76 1.00                   
                                                       0.58               
                                                           1.85           
   W 0.51                                                                 
         1.02                                                             
             0.51                                                         
                 0.51 0.51 0.51 1.02 0.51                                 
                                         0.51 0.51 1.02                   
                                                       0.51               
                                                           0.51           
F5 N 0.0 1.72                                                             
             1.00                                                         
                 2.62 -2.62                                               
                           3.04 2.19 1.72                                 
                                         -2.06                            
                                              3.04 1.72                   
                                                       1.00               
                                                           3.19           
   W 1.30                                                                 
         2.59                                                             
             1.30                                                         
                 1.30 1.30 0.30 0.59 0.30                                 
                                         0.30 0.30 0.59                   
                                                       0.30               
                                                           0.30           
R1 N 1.00                                                                 
         0.0 0.42                                                         
                 -1.52                                                    
                      1.52 -0.76                                          
                                -0.27                                     
                                     0.0 1.20 -0.76                       
                                                   0.0 0.42               
                                                           1.85           
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39                                 
                                         2.39 2.39 4.77                   
                                                       2.39               
                                                           2.39           
R2 N 2.39                                                                 
         0.0 1.00                                                         
                 -3.64                                                    
                      3.64 -1.82                                          
                                -0.65                                     
                                     0.0 2.86 -1.82                       
                                                   0.0 1.00               
                                                           4.42           
   W 0.0 0.0 0.00                                                         
                 0.00 0.00 1.00 2.00 1.00                                 
                                         1.00 1.00 2.00                   
                                                       1.00               
                                                           1.00           
__________________________________________________________________________
 
    
     Referring now to FIG. 2A there is shown another embodiment of the present invention wherein a fourth planetary gear set generally indicated by the reference character X 4  of the single-pinion type is interposed between the third planetary gear set X 3  and the output shaft, such fourth planetary gear set X 4  including a fourth sun gear S 4  connected to the output shaft as well as to the second carrier C 2 , a fifth planetary gear P 5  engaged with the fourth sun gear S 4 , a fourth ring gear RG 4  enmeshed with the fifth planetary gear P 5 , and a fourth carrier C 4  rotatably supporting the fifth planetary gear P 5 . The fourth ring gear RG 4  is also drivingly engaged with the second and third sun gears S 2  and S 3  and is additionally locked, in conjunction with the second and third sun gears S 2  and S 3 , to the gear casing when the third brake B3 is actuated. A fourth brake B 4  is also interposed between the fourth carrier C 4  and the casing so as to be capable of locking the former to the latter when the brake is actuated. 
     The following formula is given as characteristic of the fourth planetary gear set X 4  : 
     
         n.sub.rg.sbsb.4 - (1 + i.sub.4)n.sub.c.sbsb.4 + i.sub.4 n.sub.s.sbsb.4 = 0 
    
     wherein: 
     N RG .sbsb.4 =the number of revolutions of the fourth ring gear; 
     N C .sbsb.4 = the number of revolutions of the fourth carrier; 
     N S .sbsb.4 = the number of revolutions of the fourth sun gear; and 
     I 4  = the radial ratio of the fourth ring gear to the fourth sun gear. 
     Within this embodiment, the radial ratio within each speed range is I 4  = 0.562. Table 2B shows the relationship between the operation of all clutches CL 1 , CL 2 , and CL 3  and brakes B 1 , B 2 , B 3  and B 4  with respect to the reduction gear ratio within each speed range and Table 2C shows the relationship regarding the number of revolutions and the tangential forces of the elements of the planetary gear sets within each speed range. 
     
                       TABLE 2B                                                    
______________________________________                                    
                                          Reduction                       
CL1     CL2    CL3    B1   B2   B3   B4   gear ratio                      
______________________________________                                    
F1                 O                   O    1 : 5.02                      
F2                 O              O         1 : 3.57                      
F3          O                          O    1 : 3.18                      
F4          O                     O         1 : 2.40                      
F5   O                                 O    1 : 1.86                      
F6   O                            O         1 : 1.55                      
F7   O      O                               1 : 1.00                      
F8   O                  O                   1 : 0.79                      
F9          O           O                   1 : 0.46                      
R1                 O         O              1 : -3.70                     
R2          O                O              1 : -1.55                     
______________________________________                                    
 
    
     
                                           TABLE 2C                                
__________________________________________________________________________
B    X1                    X2                                             
A    S1  C1  RG1 P1   P2   S2   C2   RG2  P3                              
__________________________________________________________________________
F1 N 1.00                                                                 
         0.37                                                             
             0.63                                                         
                 -0.96                                                    
                      0.96 -0.11                                          
                                0.20 0.37 0.75                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F2 N 1.00                                                                 
         0.43                                                             
             0.67                                                         
                 -0.86                                                    
                      0.86 0.0  0.28 0.43 0.68                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F3 N 1.58                                                                 
         0.58                                                             
             1.00                                                         
                 -1.51                                                    
                      1.51 -0.18                                          
                                0.31 0.58 1.19                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F4 N 1.49                                                                 
         0.65                                                             
             1.00                                                         
                 -1.29                                                    
                      1.29 0.0  0.42 0.65 1.01                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F5 N 2.70                                                                 
         1.00                                                             
             1.71                                                         
                 -2.60                                                    
                      2.60 -0.30                                          
                                0.54 1.00 2.00                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F6 N 2.31                                                                 
         1.00                                                             
             1.55                                                         
                 -1.99                                                    
                      1.99 0.0  0.65 1.00 1.57                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F8 N 0.0 1.00                                                             
             0.58                                                         
                 1.52 -1.52                                               
                           1.76 1.27 1.00 - 1.20                          
   W 0.51                                                                 
         1.02                                                             
             0.51                                                         
                 0.51 0.51 0.51 1.02 0.51 0.51                            
F9 N 0.0 1.72                                                             
             1.00                                                         
                 2.62 -2.62                                               
                           3.04 2.19 1.72 -2.06                           
   W 1.30                                                                 
         2.59                                                             
             1.30                                                         
                 1.30 1.30 0.30 0.59 0.30 0.30                            
R1 N 1.00                                                                 
         0.0 0.42                                                         
                 -1.52                                                    
                      1.52 -0.76                                          
                                -0.27                                     
                                     0.0  1.20                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39 2.39                            
R2 N 2.39                                                                 
         0.0 1.00                                                         
                 -3.64                                                    
                      3.64 -1.82                                          
                                -0.65                                     
                                     0.0  2.86                            
   W 0.0 0.0 0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
__________________________________________________________________________
 B   X3                    X4                                             
A    S3    C3   RG3  P4    S4   C4   RG4  P5                              
__________________________________________________________________________
F1 N -0.11 0.37 0.63 1.17  0.20 0.00 -0.11                                
                                          -0.51                           
   W 2.39  4.77 2.39 2.39  2.57 5.15 2.57 2.57                            
F2 N 0.0   0.43 0.67 1.05  0.28 0.10 0.0  -0.46                           
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
F3 N -0.18 0.58 1.00 1.84  0.31 0.00 -0.18                                
                                          -0.81                           
   W 1.00  2.00 1.00 1.00  1.40 2.79 1.40 1.40                            
F4 N 0.0   0.65 1.00 1.57  0.42 0.15 0.0  -0.69                           
   W 1.00  2.00 1.00 1.00  0.0  0.0  0.0  0.0                             
F5 N -0.30 1.00 1.71 3.16  0.54 0.00 -0.30                                
                                          -1.38                           
   W 0.00  0.00 0.00 0.00  0.55 1.10 0.55 0.55                            
F6 N 0.0   1.00 1.55 2.42  0.65 0.23 0.0  -1.06                           
   W 0.00  0.00 0.00 0.00  0.0  0.0  0.0  0.0                             
F8 N 1.76  1.00 0.58 -1.85 1.27 1.59 1.76 0.81                            
   W 0.51  1.02 0.51 0.51  0.0  0.0  0.0  0.0                             
F9 N 3.04  1.72 1.00 -3.19 2.19 2.73 3.04 1.40                            
   W 0.30  0.59 0.30 0.30  0.0  0.0  0.0  0.0                             
R1 N -0.76 0.00 0.42 1.85  -0.27                                          
                                -0.59                                     
                                     -0.76                                
                                          -0.81                           
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
R2 N -1.82 0.00 1.00 4.42  -0.65                                          
                                -1.40                                     
                                     -1.82                                
                                          -1.94                           
   W 1.00  2.00 1.00 1.00  0.0  0.0  0.0  0.0                             
__________________________________________________________________________
 
    
     Referring now to FIG. 3A, yet another embodiment of the present invention is disclosed wherein the fourth planetary gear set X 4  of the single-pinion type includes a fourth sun gear S 4  drivingly engaged with the second and third sun gears S 2  and S 3  and being capable of being locked, together with the second and third sun gears S 2  and S 3 , to the gear casing when the third brake B 3  is actuated. The fourth brake B 4  is interposed between the fourth carrier C 4  and the casing so as to be capable of locking the fourth carrier C 4  thereto when B 4  is actuated, and the ring gear RG 4  is connected to the output shaft. Within this embodiment, the radial ratio within each speed range is I 4  = 0.562 and Table 3B shows the relationship between the operation of the clutches and brakes with respect to the reduction gear ratios within each speed range while Table 3C shows the relationship regarding the number of revolutions and the tangential forces of the elements of the planetary gear sets within each speed range. 
     
                       TABLE 3B                                                    
______________________________________                                    
                                          Reduction                       
CL1     CL2    CL3    B1   B2   B3   B4   gear ratio                      
______________________________________                                    
F1                 O                   O    1 : 8.15                      
F2          O                          O    1 : 4.88                      
F3                 O              O         1 : 3.57                      
F4   O                                 O    1 : 2.52                      
F5          O                     O         1 : 2.40                      
F6   O                            O         1 : 1.55                      
F7   O      O                               1 : 1.00                      
F8   O                  O                   1 : 0.79                      
F9          O           O                   1 : 0.46                      
R1                 O         O              1 : -3.70                     
R2          O                O              1 : -1.55                     
______________________________________                                    
 
    
     
                                           TABLE 3C                                
__________________________________________________________________________
B    X1                    X2                                             
A    S1  C1  RG1 P1   P2   S2   C2   RG2  P3                              
__________________________________________________________________________
F1 N 1.00                                                                 
         0.31                                                             
             0.60                                                         
                 -1.05                                                    
                      1.05 -0.22                                          
                                0.12 0.31 0.83                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F2 N 1.67                                                                 
         0.52                                                             
             1.00                                                         
                 -1.76                                                    
                      1.76 -0.36                                          
                                0.20 0.52 1.38                            
   W 0.0 0.00                                                             
             0.0 0.0  0.0  1.55 3.10 1.55 1.55                            
F3 N 1.00                                                                 
         0.43                                                             
             0.67                                                         
                 -0.86                                                    
                      0.86 0.00 0.28 0.43 0.68                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F4 N 3.23                                                                 
         1.00                                                             
             1.93                                                         
                 -3.40                                                    
                      3.40 -0.71                                          
                                0.40 1.00 2.67                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F5 N 1.49                                                                 
         0.65                                                             
             1.00                                                         
                 -1.29                                                    
                      1.29 0.0  0.42 0.65 1.01                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F6 N 2.31                                                                 
         1.00                                                             
             1.55                                                         
                 -1.99                                                    
                      1.99 0.0  0.65 1.00 1.57                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F8 N 0.0 1.00                                                             
             0.58                                                         
                 1.52 -1.52                                               
                           1.76 1.27 1.00 - 1.20                          
   W 0.51                                                                 
         1.02                                                             
             0.51                                                         
                 0.51 0.51 0.51 1.02 0.51 0.51                            
F9 N 0.0 1.72                                                             
             1.00                                                         
                 2.62 -2.62                                               
                           3.04 2.19 1.72 -2.06                           
   W 1.30                                                                 
         2.59                                                             
             1.30                                                         
                 1.30 1.30 0.30 0.59 0.30 0.30                            
R1 N 1.00                                                                 
         0.0 0.42                                                         
                 -1.52                                                    
                      1.52 -0.76                                          
                                -0.27                                     
                                     0.0  1.20                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39 2.39                            
R2 N 2.39                                                                 
         0.0 1.00                                                         
                 -3.64                                                    
                      3.64 -1.82                                          
                                -0.65                                     
                                     0.0  2.86                            
   W 0.0 0.0 0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
__________________________________________________________________________
B    X3                    X4                                             
A    S3    C3   RG3  P4    S4   C4   RG4  P5                              
__________________________________________________________________________
F1 N -0.22 0.31 0.60 1.28  -0.22                                          
                                -0.00                                     
                                     0.12 0.56                            
   W 2.39  4.77 2.39 2.39  4.58 9.16 4.58 4.58                            
F2 N -0.36 0.52 1.00 2.14  -0.36                                          
                                -0.00                                     
                                     0.20 0.94                            
   W 1.00  2.00 1.00 1.00  2.48 4.97 2.48 2.48                            
F3 N 0.0   0.43 0.67 1.05  0.0  0.18 0.23 0.46                            
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
F4 N -0.71 1.00 1.93 4.13  -0.71                                          
                                0.0  0.40 1.81                            
   W 0.00  0.00 0.00 0.00  0.98 1.95 0.98 0.98                            
F5 N 0.0   0.65 1.00 1.57  0.0  0.27 0.42 0.69                            
   W 1.00  2.00 1.00 1.00  0.0  0.0  0.0  0.0                             
F6 N 0.0   1.00 1.55 2.42  0.0  0.41 0.65 1.06                            
   W 0.00  0.00 0.00 0.00  0.0  0.0  0.0  0.0                             
F8 N 1.76  1.00 0.58 -1.85 1.76 1.45 1.27 -0.81                           
   W 0.51  1.02 0.51 0.51  0.00 0.0  0.0  0.0                             
F9 N 3.04  1.72 1.00 -3.19 3.04 2.49 2.19 -1.40                           
   W 0.30  0.59 0.30 0.30  0.00 0.0  0.0  0.0                             
R1 N -0.76 0.00 0.42 1.85  -0.76                                          
                                -0.45                                     
                                     -0.27                                
                                          0.81                            
   W 2.39  4.77 2.39 2.39  0.00 0.0  0.0  0.0                             
R2 N -1.82 0.00 1.00 4.42  -1.82                                          
                                -1.07                                     
                                     -0.65                                
                                          1.94                            
   W 1.00  2.00 1.00 1.00  0.00 0.0  0.0  0.0                             
__________________________________________________________________________
 
    
     A fourth embodiment of a speed change gear system constructed in accordance with the present invention is illustrated within FIG. 4A and includes a fourth planetary gear set X 4  of the single-pinion type interposed between the third planetary gear set X 3  and the output shaft, the fourth carrier C 4  being drivingly engaged with the second and third sun gears S 2  and S 3  so as to be capable of being locked to the gear casing when the third brake B 3  is actuated. The fourth brake B 4  is disposed between the fourth sun gears S 4  and the casing so as to be capable of locking the fourth sun gear S 4  thereto when the brake B 4  is actuated, and the fourth ring gear RG 4  is drivingly engaged with the second carrier C 2  through means of the output shaft. Within this embodiment, the radial ratio within each speed range is I 4  = 0.562, and Table 4B shows the relationship between the operation of the clutches and brakes with respect to the reduction gear ratio within each speed range while Table 4C shows the relationship regarding the number of revolutions and the tangential forces of all of the embodiments of the planetary gear sets within each speed range. 
     
                       TABLE 4B                                                    
______________________________________                                    
                                          Reduction                       
CL1     CL2    CL3    B1   B2   B3   B4   gear ratio                      
______________________________________                                    
F1                 O                   O    1 : 3.57                      
F2          O                     O         1 : 2.40                      
F3                 O                   O    1 : 1.93                      
F4   O                            O         1 : 1.55                      
F5          O                          O    1 : 1.52                      
F6   O                                 O    1 : 1.20                      
F7   O      O                               1 : 1.00                      
F8   O                  O                   1 : 0.79                      
R1                 O         O              1 : -3.70                     
R2          O                O              1 : -1.55                     
______________________________________                                    
 
    
     
                                           TABLE 4C                                
__________________________________________________________________________
B    XI                    X2                                             
A    S1  C1  RG1 P1   P2   S2   C2   RG2  P3                              
__________________________________________________________________________
F1 N 1.00                                                                 
         0.43                                                             
             0.67                                                         
                 -0.86                                                    
                      0.86 0.0  0.28 0.43 0.68                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F2 N 1.49                                                                 
         0.65                                                             
             1.00                                                         
                 -1.29                                                    
                      1.29 0.0  0.42 0.65 1.01                            
   W 0.0 0.0 0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F3 N 1.00                                                                 
         0.62                                                             
             0.78                                                         
                 -0.58                                                    
                      0.58 0.33 0.52 0.62 0.45                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F4 N 2.31                                                                 
         1.00                                                             
             1.55                                                         
                 -1.99                                                    
                      1.99 0.0  0.65 1.00 1.57                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F5 N 1.28                                                                 
         0.80                                                             
             1.00                                                         
                 -0.74                                                    
                      0.74 0.43 0.67 0.80 0.58                            
   W 0.0 0.0 0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F6 N 1.61                                                                 
         1.00                                                             
             1.25                                                         
                 -0.93                                                    
                      0.93 0.53 0.84 1.00 0.73                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F8 N 0.0 1.00                                                             
             0.58                                                         
                 1.52 -1.52                                               
                           1.76 1.27 1.00 -1.20                           
   W 0.51                                                                 
         1.02                                                             
             0.51                                                         
                 0.51 0.51 0.51 1.02 0.51 0.51                            
R1 N 1.00                                                                 
         0.0 0.42                                                         
                 -1.52                                                    
                      1.52 -0.76                                          
                                -0.27                                     
                                     0.0  1.20                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39 2.39                            
R2 N 2.39                                                                 
         0.0 1.00                                                         
                 -3.64                                                    
                      3.64 -1.82                                          
                                -0.65                                     
                                     0.0  2.86                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
__________________________________________________________________________
B    X3                    X4                                             
A    S3    C3   RG3  P4    S4   C4   RG4  P5                              
__________________________________________________________________________
F1 N 0.0   0.43 0.67 1.05  -0.50                                          
                                0.0  0.28 1.28                            
   W 2.39  4.77 2.39 2.39  0.0  0.00 0.00 0.00                            
F2 N 0.0   0.65 1.00 1.57  -0.74                                          
                                0.0  0.42 1.91                            
   W 1.00  2.00 1.00 1.00  0.0  0.00 0.00 0.00                            
F3 N 0.33  0.62 0.78 0.70  0.0  0.33 0.52 0.85                            
   W 2.39  4.77 2.39 2.39  1.65 3.29 1.65 1.65                            
F4 N 0.0   1.00 1.55 2.42  -1.15                                          
                                0.0  0.65 2.95                            
   W 0.00  0.00 0.00 0.00  0.0  0.00 0.00 0.00                            
F5 N 0.43  0.80 1.00 0.90  0.0  0.43 0.67 1.09                            
   W 1.00  2.00 1.00 1.00  0.89 1.79 0.89 0.89                            
F6 N 0.53  1.00 1.25 1.13  0.0  0.53 0.84 1.37                            
   W 0.00  0.00 0.00 0.00  0.35 0.70 0.35 0.35                            
F8 N 1.76  1.00 0.58 -1.85 2.64 1.76 1.27 -2.26                           
   W 0.51  1.02 0.51 0.51  0.0  0.00 0.00 0.00                            
R1 N -0.76 0.00 0.42 1.85  -1.64                                          
                                -0.76                                     
                                     -0.27                                
                                          2.26                            
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
R2 N -1.82 0.00 1.00 4.42  -3.92                                          
                                -1.82                                     
                                     -0.65                                
                                          5.38                            
   W 1.00  2.00 1.00 1.00  0.0  0.00 0.0  0.0                             
__________________________________________________________________________
 
    
     Referring now to FIG. 5A, a further embodiment of the invention is disclosed wherein the fourth planetary gear set X 4  of the single-pinion type is disposed between the third planetary gear set X 3  and the output shaft and wherein further the fourth carrier C 4  is drivingly engaged with the second and third sun gears S 2  and S 3  so as to capable of being locked in conjunction with the second and third sun gears S 2  and S 3  to the gear casing when the third brake B 3  is actuated. A fourth brake B 4  is disposed between the fourth ring gear RG 4  and the casing so as to be capable of locking the fourth ring gear RG 4  thereto when the brake B 4  is actuated and the fourth sun gear S 4  is drivingly engaged with the second carrier C 2  through means of the output shaft. Within this embodiment, the radial ratio within each speed range is I 4  = 0.562 and Table 5B shows the relationship between the operation of the clutches and brakes with respect to the reduction gear ratio within each speed range while Table 5C shows the relationship regarding the number of revolutions and the tangential forces of the elements within the planetary gear sets within each speed range. 
     
                       TABLE 5B                                                    
______________________________________                                    
                                          Reduction                       
CL1     CL2    CL3    B1   B2   B3   B4   gear ratio                      
______________________________________                                    
F1                 O              O         1 : 3.57                      
F2                 O                   O    1 : 2.65                      
F3          O                     O         1 : 2.40                      
F4          O                          O    1 : 1.89                      
F5   O                            O         1 : 1.55                      
F6   O                                 O    1 : 1.35                      
F7   O      O                               1 : 1.00                      
F8   O                  O                   1 : 0.79                      
F9          O      O    O                   1 : 0.46                      
R1                 O         O              1 : -3.70                     
R2          O                O              1 : -1.55                     
______________________________________                                    
 
    
     
                                           TABLE 5C                                
__________________________________________________________________________
B    X1                    X2                                             
A    S1  C1  RG1 P1   P2   S2   C2   RG2  P3                              
__________________________________________________________________________
F1 N 1.00                                                                 
         0.43                                                             
             0.67                                                         
                 -0.86                                                    
                      0.86 0.0  0.28 0.43 0.68                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F2 N 1.00                                                                 
         0.51                                                             
             0.72                                                         
                 -0.75                                                    
                      0.75 0.14 0.38 0.51 0.59                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F3 N 1.49                                                                 
         0.65                                                             
             1.00                                                         
                 -1.29                                                    
                      1.29 0.00 0.42 0.65 1.01                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F4 N 1.40                                                                 
         0.71                                                             
             1.00                                                         
                 -1.04                                                    
                      1.04 0.19 0.53 0.71 0.82                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F5 N 2.31                                                                 
         1.00                                                             
             1.55                                                         
                 -1.99                                                    
                      1.99 0.00 0.65 1.00 1.57                            
   W 0.00                                                                 
         0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F6 N 1.96                                                                 
         1.00                                                             
             1.40                                                         
                 -1.46                                                    
                      1.46 0.27 0.74 1.00 1.15                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F8 N 0.0 1.00                                                             
             0.58                                                         
                 1.52 -1.52                                               
                           1.76 1.27 1.00 -1.20                           
   W 0.51                                                                 
         1.02                                                             
             0.51                                                         
                 0.51 0.51 0.51 1.02 0.51 0.51                            
F9 N 0.0 1.72                                                             
             1.00                                                         
                 2.62 2.62 3.04 2.19 1.72 -2.06                           
   W 1.30                                                                 
         2.59                                                             
             1.30                                                         
                 1.30 1.30 0.30 0.59 0.30 0.30                            
R1 N 1.00                                                                 
         0.0 0.42                                                         
                 -1.52                                                    
                      1.52 -0.76                                          
                                -0.27                                     
                                     0.0  1.20                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39 2.39                            
R2 N 2.39                                                                 
         0.0 1.00                                                         
                 -3.64                                                    
                      3.64 -1.82                                          
                                -0.65                                     
                                     0.0  2.86                            
   W 0.0 0.00                                                             
             0.0 0.0  0.0  1.00 2.00 1.00 1.00                            
__________________________________________________________________________
B    X3                    X4                                             
A    S3    C3   RG3  P4    S4   C4   RG4  P5                              
__________________________________________________________________________
F1 N 0.0   0.43 0.67 1.05  0.28 0.00 -0.16                                
                                          -0.72                           
   W 2.39  4.77 2.39 2.39  0.00 0.00 0.00 0.00                            
F2 N 0.14  0.51 0.72 0.91  0.38 0.14 0.0  -0.62                           
   W 2.39  4.77 2.39 2.39  1.65 3.29 1.65 1.65                            
F3 N 0.00  0.65 1.00 1.57  0.42 0.00 -0.23                                
                                          -1.07                           
   W 1.00  2.00 1.00 1.00  0.00 0.00 0.00 0.00                            
F4 N 0.19  0.71 1.00 1.27  0.53 0.19 0.0  -0.87                           
   W 1.00  2.00 1.00 1.00  0.89 1.79 0.89 0.89                            
F5 N 0.00  1.00 1.55 2.42  0.65 0.00 -0.36                                
                                          -1.66                           
   W 0.00  0.00 0.00 0.00  0.00 0.00 0.00 0.00                            
F6 N 0.27  1.00 1.40 1.78  0.74 0.27 0.0  -1.22                           
   W 0.00  0.00 0.00 0.00  0.35 0.70 0.35 0.35                            
F8 N 1.76  1.00 0.58 -1.85 1.27 1.76 2.04 1.27                            
   W 0.51  1.02 0.51 0.51  0.00 0.00 0.00 0.00                            
F9 N 3.04  1.72 1.00 -3.19 2.19 3.04 3.51 2.18                            
   W 0.30  0.59 0.30 0.30  0.00 0.00 0.00 0.00                            
R1 N -0.76 0.00 0.42 1.85  -0.27                                          
                                -0.76                                     
                                     -1.04                                
                                          -1.27                           
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
R2 N -1.82 0.00 1.00 4.42  -0.65                                          
                                -1.82                                     
                                     -2.49                                
                                          -3.03                           
   W 1.00  2.00 1.00 1.00  0.0  0.0  0.0  0.0                             
__________________________________________________________________________
 
    
     Turning now to the embodiment illustrated within FIG. 6A, the fourth planetary gear set X 4  of the single-pinion type is disposed between the third planetary gear set X 3  and the output shaft and includes the fourth sun gear S 4  drivingly engaged with the second and third sun gears S 2  and S 3  so as to be capable of being locked therewith to the gear casing when the third brake B 3  is actuated. The fourth brake B 4  is disposed between the fourth ring gear RG 4  and the casing so as to be capable of locking the fourth ring gear RG 4  when the brake B 4  is actuated and the fourth carrier C 4  is drivingly engaged with the second carrier C 2  through means of the output shaft. Within this embodiment, the radial ratio within each speed range is I 4  = 0.437 and Table 6B shows the relationship between the operation of the clutches and brakes with respect to the reduction gear ratio within each speed range while Table 6C shows the relationship regarding the number of revolutions and the tangential forces of the elements of the planetary gear sets within each speed range. 
     
                       TABLE 6B                                                    
______________________________________                                    
                                          Reduction                       
CL1     CL2    CL3    B1   B2   B3   B4   gear ratio                      
______________________________________                                    
F1                 O              O         1 : 3.57                      
F2          O                     O         1 : 2.40                      
F3   O                            O         1 : 1.55                      
F4   O      O                               1 : 1.00                      
F5   O                  O                   1 : 0.79                      
F6          O           O                   1 : 0.46                      
R1                 O                   O    1 : -4.89                     
R2                 O         O              1 : -3.70                     
R3          O                          O    1 : -2.20                     
R4          O                O              1 : -1.55                     
______________________________________                                    
 
    
     
                                           TABLE 6C                                
__________________________________________________________________________
B    X1                    X2                                             
A    S1  C1  RG1 P1   P2   S2   C2   RG2  P3                              
__________________________________________________________________________
F1 N 1.00                                                                 
         0.43                                                             
             0.67                                                         
                 -0.86                                                    
                      0.86 0.0  0.28 0.43 0.68                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F2 N 1.49                                                                 
         0.65                                                             
             1.00                                                         
                 -1.29                                                    
                      1.29 0.0  0.42 0.65 1.01                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F3 N 2.31                                                                 
         1.00                                                             
             1.55                                                         
                 -1.99                                                    
                      1.99 0.0  0.65 1.00 1.57                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F5 N 0.0 1.00                                                             
             0.58                                                         
                 1.52 -1.52                                               
                           1.76 1.27 1.00 -1.20                           
   W 0.51                                                                 
         1.02                                                             
             0.51                                                         
                 0.51 0.51 0.51 1.02 0.51 0.51                            
F6 N 0.0 1.72                                                             
             1.00                                                         
                 2.62 -2.62                                               
                           3.04 2.19 1.72 -2.06                           
   W 1.30                                                                 
         2.59                                                             
             1.30                                                         
                 1.30 1.30 0.30 0.59 0.30 0.30                            
R1 N 1.00                                                                 
         0.05                                                             
             0.45                                                         
                 -1.44                                                    
                      1.44 -0.67                                          
                                0.20 0.05 1.14                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
R2 N 1.00                                                                 
         0.0 0.42                                                         
                 -1.52                                                    
                      1.52 -0.76                                          
                                -0.27                                     
                                     0.0  1.20                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39 2.39                            
R3 N 2.23                                                                 
         0.12                                                             
             1.00                                                         
                 -3.22                                                    
                      3.22 -1.50                                          
                                -0.46                                     
                                     0.12 2.53                            
   W 0.0 0.0 0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
R4 N 2.39                                                                 
         0.0 1.00                                                         
                 -3.64                                                    
                      3.64 -1.82                                          
                                -0.65                                     
                                     0.0  2.86                            
   W 0.0 0.0 0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
__________________________________________________________________________
B    X3                    X4                                             
A    S3    C3   RG3  P4    S4   C4   RG4  P5                              
__________________________________________________________________________
F1 N 0.0   0.43 0.67 1.05  0.0  0.28 0.40 0.43                            
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
F2 N 0.0   0.65 1.00 1.57  0.0  0.42 0.60 0.65                            
   W 1.00  2.00 1.00 1.00  0.0  0.0  0.0  0.0                             
F3 N 0.0   1.00 1.55 2.42  0.0  0.65 0.93 1.00                            
   W 0.00  0.00 0.00 0.00  0.0  0.0  0.0  0.0                             
F5 N 1.76  1.00 0.58 -1.85 1.76 1.27 1.05 -0.77                           
   W 0.51  1.02 0.51 0.51  0.00 0.0  0.0  0.0                             
F6 N 3.04  1.72 1.00 -3.19 3.04 2.19 1.82 -1.32                           
   W 0.30  0.59 0.30 0.30  0.00 0.0  0.0  0.0                             
R1 N -0.67 0.05 0.45 1.76  -0.67                                          
                                -0.20                                     
                                     0.00 0.73                            
   W 2.39  4.77 2.39 2.39  5.89 11.77                                     
                                     5.89 5.89                            
R2 N -0.76 -0.00                                                          
                0.42 1.85  -0.76                                          
                                -0.27                                     
                                     -0.05                                
                                          0.77                            
   W 2.39  4.77 2.39 2.39  0.00 0.0  0.0  0.0                             
R3 N -1.50 0.12 1.00 3.91  -1.50                                          
                                -0.46                                     
                                     0.00 1.62                            
   W 1.00  2.00 1.00 1.00  3.20 6.39 3.20 3.20                            
R4 N -1.82 -0.00                                                          
                1.00 4.42  -1.82                                          
                                -0.65                                     
                                     -0.13                                
                                          1.83                            
   W 1.00  2.00 1.00 1.00  0.00 0.0  0.0  0.0                             
__________________________________________________________________________
 
    
     Referring now to the embodiment of the invention illustrated within FIG. 7A, the fourth planetary gear set X 4  of the single-pinion type is disposed between the third planetary gear set X 3  and the output shaft and includes the fourth ring gear RG 4  drivingly engaged with the second and third sun gears S 2  and S 3  so as to be capable of being locked therewith when the third brake B 3  is actuated. The fourth brake B 4  is disposed between the fourth sun gear S 4  and the casing so as to be capable of locking the fourth sun gear S 4  when the brake B 4  is actuated, and the fourth carrier C 4  is drivingly engaged with the second carrier C 2  through means of the output shaft. Within this embodiment, the radial ratio within each speed range is I 4  = 0.562 and Table 7B shows the relationship between the operation of the clutches and brakes with respect to the reduction gear ratio within each speed range while Table 7C shows the relationship regarding the number of revolutions and the tangential forces of all of the elements of the planetary gear sets within each speed range. 
     
                       TABLE 7B                                                    
______________________________________                                    
                                          Reduction                       
CL1     CL2    CL3    B1   B2   B3   B4   gear ratio                      
______________________________________                                    
F1                 O              O         1 : 3.57                      
F2          O                     O         1 : 2.40                      
F3   O                            O         1 : 1.55                      
F4   O      O                               1 : 1.00                      
F5   O                  O                   1 : 0.79                      
F6   O                                 O    1 : 0.69                      
F7          O           O                   1 : 0.46                      
R1                 O         O              1 : -3.70                     
R2          O                O              1 : -1.55                     
R3                 O                   O    1 : -0.45                     
______________________________________                                    
 
    
     
                                           TABLE 7C                                
__________________________________________________________________________
B    X1                    X2                                             
A    S1  C1  RG1 P1   P2   S2   C2   RG2  P3                              
__________________________________________________________________________
F1 N 1.00                                                                 
         0.43                                                             
             0.67                                                         
                 -0.86                                                    
                      0.86 0.0  0.28 0.43 0.68                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F2 N 1.49                                                                 
         0.65                                                             
             1.00                                                         
                 -1.29                                                    
                      1.29 0.0  0.42 0.65 1.01                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F3 N 2.31                                                                 
         1.00                                                             
             1.55                                                         
                 -1.99                                                    
                      1.99 0.0  0.65 1.00 1.57                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F5 N 0.0 1.00                                                             
             0.58                                                         
                 1.52 -1.52                                               
                           1.76 1.27 1.00 -1.20                           
   W 0.51                                                                 
         1.02                                                             
             0.51                                                         
                 0.51 0.51 0.51 1.02 0.51 0.51                            
F6 N -0.64                                                                
         1.00                                                             
             0.31                                                         
                 2.51 -2.51                                               
                           2.26 1.45 1.00 -1.97                           
   W 0.0 0.0 0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F7 N 0.0 1.72                                                             
             1.00                                                         
                 2.62 -2.62                                               
                           3.04 2.19 1.72 -2.06                           
   W 1.30                                                                 
         2.59                                                             
             1.30                                                         
                 1.30 1.30 0.30 0.59 0.30 0.30                            
R1 N 1.00                                                                 
         0.0 0.42                                                         
                 -1.52                                                    
                      1.52 -0.76                                          
                                - 0.27                                    
                                     0.0  1.20                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39 2.39                            
R2 N 2.39                                                                 
         0.0 1.00                                                         
                 -3.64                                                    
                      3.64 -1.82                                          
                                -0.65                                     
                                     0.0  2.86                            
   W 0.0 0.0 0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
R3 N 1.00                                                                 
         -1.55                                                            
             -0.48                                                        
                 -3.89                                                    
                      3.89 -3.50                                          
                                -2.24                                     
                                     -1.55                                
                                          3.06                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
__________________________________________________________________________
B    X3                    X4                                             
A    S3    C3   RG3  P4    S4   C4   RG4  P5                              
__________________________________________________________________________
F1 N 0.0   0.43 0.67 1.05  0.78 0.28 0.0  -1.28                           
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
F2 N 0.0   0.65 1.00 1.57  1.16 0.42 0.0  -1.91                           
   W 1.00  2.00 1.00 1.00  0.0  0.0  0.0  0.0                             
F3 N 0.0   1.00 1.55 2.42  1.80 0.65 0.0  -2.95                           
   W 0.00  0.00 0.00 0.00  0.0  0.0  0.0  0.0                             
F5 N 1.76  1.00 0.58 -1.85 0.39 1.27 1.76 2.26                            
   W 0.51  1.02 0.51 0.51  0.0  0.0  0.0  0.0                             
F6 N 2.26  1.00 0.31 -3.05 0.0  1.45 2.26 3.71                            
   W 0.00  0.00 0.00 0.00  0.55 1.10 0.55 0.55                            
F7 N 3.04  1.72 1.00 -3.19 0.67 2.19 3.04 3.88                            
   W 0.30  0.59 0.30 0.30  0.0  0.0  0.0  0.0                             
R1 N -0.76 0.00 0.42 1.85  -0.61                                          
                                -0.27                                     
                                     -0.76                                
                                          -2.26                           
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
R2 N -1.82 0.00 1.00 4.42  1.45 -0.65                                     
                                     -1.82                                
                                          -5.38                           
   W 1.00  2.00 1.00 1.00  0.0  0.0  0.0  0.0                             
R3 N -3.50 -1.55                                                          
                -0.48                                                     
                     4.73  0.0  -2.24                                     
                                     -3.50                                
                                          -5.76                           
   W 2.39  4.77 2.39 2.39  2.57 5.15 2.57 2.57                            
__________________________________________________________________________
 
    
     Referring now to FIG. 8A, still another embodiment of the present invention is disclosed wherein the fourth planetary gear set X 4  of the single-pinion type is disposed between the third planetary gear set X 3  and the output shaft and is seen to include the fourth ring gear RG 4  being drivingly engaged with the second ring gear RG 2 , the third carrier C 3 , and the first carrier C 1  through means of the intermediate shaft whereby such components may be locked to the gear casing when the second brake B 2  is actuated. Similarly, the fourth brake B 4  is disposed between the fourth sun gear S 4  and the casing so as to be capable of locking the fourth sun gear S 4  and the casing when the brake B 4  is actuated and the fourth carrier C 4  is drivingly engaged with the second carrier C 2  as well as with the output shaft. Within this embodiment, the radial ratio within each speed range is I 4  = 0.280 and Table 8B shows the relationship between the operation of the clutches and brakes and the reduction gear ratio within each speed range while Table 8C shows the relationship regarding the number of revolutions and the tangential forces of all of the elements of the planetary gear sets within each speed range. 
     
                       TABLE 8B                                                    
______________________________________                                    
                                          Reduction                       
CL1     CL2    CL3    B1   B2   B3   B4   gear ratio                      
______________________________________                                    
F1                 O              O         1 : 3.57                      
F2          O                     O         1 : 2.40                      
F3                 O                   O    1 : 2.31                      
F4          O                          O    1 : 1.71                      
F5   O                            O         1 : 1.55                      
F6   O                                 O    1 : 1.28                      
F7   O      O                               1 : 1.00                      
F8   O                  O                   1 : 0.79                      
F9          O           O                   1 : 0.46                      
R1                 O         O              1 : -3.70                     
R2          O                O              1 : -1.55                     
______________________________________                                    
 
    
     
                                           TABLE 8C                                
__________________________________________________________________________
B    X1                    X2                                             
A    S1  C1  RG1 P1   P2   S2   C2   RG2  P3                              
__________________________________________________________________________
F1 N 1.00                                                                 
         0.43                                                             
             0.67                                                         
                 -0.86                                                    
                      0.86 0.0  0.28 0.43 0.68                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F2 N 1.49                                                                 
         0.65                                                             
             1.00                                                         
                 -1.29                                                    
                      1.29 0.0  0.42 0.65 1.01                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F3 N 1.00                                                                 
         0.55                                                             
             0.74                                                         
                 -0.68                                                    
                      0.68 0.21 0.43 0.55 0.54                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39 2.39                            
F4 N 1.35                                                                 
         0.75                                                             
             1.00                                                         
                 -0.92                                                    
                      0.92 0.29 0.58 0.75 0.72                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F5 N 2.31                                                                 
         1.00                                                             
             1.55                                                         
                 -1.99                                                    
                      1.99 0.0  0.65 1.00 1.57                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F6 N 1.81                                                                 
         1.00                                                             
             1.34                                                         
                 -1.23                                                    
                      1.23 0.38 0.78 1.00 0.97                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 0.00 0.00 0.00 0.00                            
F8 N 0.0 1.00                                                             
             0.58                                                         
                 1.52 -1.52                                               
                           1.76 1.27 1.00 -1.20                           
   W 0.51                                                                 
         1.02                                                             
             0.51                                                         
                 0.51 0.51 0.51 1.02 0.51 0.51                            
F9 N 0.0 1.72                                                             
             1.00                                                         
                 2.62 -2.62                                               
                           3.04 2.19 1.72 -2.06                           
   W 1.30                                                                 
         2.59                                                             
             1.30                                                         
                 1.30 1.30 0.30 0.59 0.30 0.30                            
R1 N 1.00                                                                 
         0.0 0.42                                                         
                 -1.52                                                    
                      1.52 -0.76                                          
                                -0.27                                     
                                     0.0  1.20                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39 2.39                            
R2 N 2.39                                                                 
         0.0 1.00                                                         
                 -3.64                                                    
                      3.64 -1.82                                          
                                -0.65                                     
                                     0.0  2.86                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
__________________________________________________________________________
B    X3                    X4                                             
A    S3    C3   RG3  P4    S4   C4   RG4  P5                              
__________________________________________________________________________
F1 N 0.0   0.43 0.67 1.05  -0.27                                          
                                0.28 0.43 0.43                            
   W 2.39  4.77 2.39 2.39  0.0  0.00 0.00 0.00                            
F2 N 0.0   0.65 1.00 1.57  -0.40                                          
                                0.42 0.65 0.64                            
   W 1.00  2.00 1.00 1.00  0.0  0.00 0.00 0.00                            
F3 N 0.21  0.55 0.74 0.83  0.0  0.43 0.55 0.34                            
   W 2.39  4.77 2.39 2.39  4.69 9.39 4.69 4.69                            
F4 N 0.29  0.75 1.00 1.12  0.0  0.58 0.75 0.45                            
   W 1.00  2.00 1.00 1.00  2.55 5.10 2.55 2.55                            
F5 N 0.0   1.00 1.55 2.42  -0.62                                          
                                0.65 1.00 0.98                            
   W 0.00  0.00 0.00 0.00  0.0  0.00 0.00 0.00                            
F6 N 0.38  1.00 1.34 1.50  0.0  0.78 1.00 0.61                            
   W 0.00  0.00 0.00 0.00  1.00 2.00 1.00 1.00                            
F8 N 1.76  1.00 0.58 -1.85 2.24 1.27 1.00 -0.75                           
   W 0.51  1.02 0.51 0.51  0.0  0.00 0.00 0.00                            
F9 N 3.04  1.72 1.00 -3.19 3.85 2.19 1.72 -1.29                           
   W 0.30  0.59 0.30 0.30  0.0  0.00 0.00 0.00                            
R1 N -0.76 0.0  0.42 1.85  -1.24                                          
                                -0.27                                     
                                     0.0  0.75                            
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
R2 N -1.82 0.0  1.00 4.42  -2.95                                          
                                -0.65                                     
                                     0.0  1.79                            
   W 1.00  2.00 1.00 1.00  0.0  0.0  0.0  0.0                             
__________________________________________________________________________
 
    
     Turning now to FIG. 9A a still further embodiment of the present invention is illustrated wherein the fourth planetary gear set X 4  of the single-pinion type is disposed between the third planetary gear set X 3  and the output shaft and the fourth sun gear S 4  is drivingly engaged with the second ring gear RG 2 , the third carrier C 3 , and the first carrier C 1 , through means of the intermediate shaft, such elements being locked to the gear casing when the second brake B 2  is actuated. The fourth brake B 4  is disposed between the fourth ring gear RG 4  and the casing so as to be capable of locking the fourth ring gear RG 4  thereto when the brake B 4  is actuated and the fourth carrier C 4  is drivingly engaged with the second carrier C 2  as well as with the output shaft. Within this embodiment, the radial ratio within each speed range is I 4  = 0.280 and Table 9B shows the relationship between the operation of the clutches and brakes and the reduction gear ratio within each speed range while Table 9C shows the relationship regarding the number of revolutions and the tangential forces of all of the elements of the planetary gear sets witin each speed range. 
     
                       TABLE 9B                                                    
______________________________________                                    
                                          Reduction                       
CL1     CL2    CL3    B1   B2   B3   B4   gear ratio                      
______________________________________                                    
F1                 O                   O    1 : 17.77                     
F2          O                          O    1 : 10.10                     
F3   O                                 O    1 : 4.57                      
F4                 O              O         1 : 3.57                      
F5          O                     O         1 : 2.40                      
F6   O                            O         1 : 1.55                      
F7   O      O                               1 : 1.00                      
F8   O                  O                   1 : 0.79                      
F9          O           O                   1 : 0.46                      
R1                 O         O              1 : -3.70                     
R2          O                O              1 : -1.55                     
______________________________________                                    
 
    
     
                                           TABLE 9C                                
__________________________________________________________________________
B    X1                    X2                                             
A    S1  C1  RG1 P1   P2   S2   C2   RG2  P3                              
__________________________________________________________________________
F1 N 1.00                                                                 
         0.26                                                             
             0.57                                                         
                 -1.13                                                    
                      1.13 -0.31                                          
                                0.06 0.26 0.89                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39 2.39                            
F2 N 1.76                                                                 
         0.45                                                             
             1.00                                                         
                 -1.99                                                    
                      1.99 -0.55                                          
                                0.10 0.45 1.56                            
   W 0.0 0.00                                                             
             0.0 0.0  0.0  1.00 2.00 1.00 1.00                            
F3 N 3.89                                                                 
         1.00                                                             
             2.21                                                         
                 -4.40                                                    
                      4.40 -1.21                                          
                                0.22 1.00 3.46                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 0.00 0.00 0.00 0.00                            
F4 N 1.00                                                                 
         0.43                                                             
             0.67                                                         
                 -0.86                                                    
                      0.86 0.0  0.28 0.43 0.68                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.31 4.62 2.31 2.31                            
F5 N 1.49                                                                 
         0.65                                                             
             1.00                                                         
                 -1.29                                                    
                      1.29 0.0  0.42 0.65 1.01                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.55 3.10 1.55 1.55                            
F6 N 2.31                                                                 
         1.00                                                             
             1.55                                                         
                 -1.99                                                    
                      1.99 0.0  0.65 1.00 1.57                            
   W 0.0 0.00                                                             
             0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
F8 N 0.0 1.00                                                             
             0.58                                                         
                 1.52 -1.52                                               
                           1.76 1.27 1.00 - 1.20                          
   W 0.51                                                                 
         1.02                                                             
             0.51                                                         
                 0.51 0.51 0.51 1.02 0.51 0.51                            
F9 N 0.0 1.72                                                             
             1.00                                                         
                 2.62 -2.62                                               
                           3.04 2.19 1.72 -2.06                           
   W 1.30                                                                 
         2.59                                                             
             1.30                                                         
                 1.30 1.30 0.30 0.59 0.30 0.30                            
R1 N 1.00                                                                 
         0.0 0.42                                                         
                 -1.52                                                    
                      1.52 -0.76                                          
                                -0.27                                     
                                     0.0  1.20                            
   W 2.39                                                                 
         4.77                                                             
             2.39                                                         
                 2.39 2.39 2.39 4.77 2.39 2.39                            
R2 N 2.39                                                                 
         0.0 1.00                                                         
                 -3.64                                                    
                      3.64 -1.82                                          
                                -0.65                                     
                                     0.0  2.86                            
   W 0.0 0.0 0.00                                                         
                 0.00 0.00 1.00 2.00 1.00 1.00                            
__________________________________________________________________________
B    X3                    X4                                             
A    S3    C3   RG3  P4    S4   C4   RG4  P5                              
__________________________________________________________________________
F1 N -0.31 0.26 0.57 1.38  0.26 0.06 0.0  -0.16                           
   W 2.39  4.77 2.39 2.39  16.77                                          
                                33.53                                     
                                     16.77                                
                                          16.77                           
F2 N -0.55 0.45 1.00 2.42  0.45 0.10 0.0  -0.28                           
   W 1.00  2.00 1.00 1.00  9.10 18.20                                     
                                     9.10 9.10                            
F3 N -1.21 1.00 2.21 5.35  1.00 0.22 0.0  -0.61                           
   W 0.00  0.00 0.00 0.00  3.57 7.14 3.57 3.57                            
F4 N 0.0   0.43 0.67 1.05  0.43 0.28 0.24 -0.12                           
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
F5 N 0.0   0.65 1.00 1.57  0.65 0.42 0.35 -0.18                           
   W 1.00  2.00 1.00 1.00  0.0  0.0  0.0  0.0                             
F6 N 0.0   1.00 1.55 2.42  1.00 0.65 0.55 -0.28                           
   W 0.00  0.00 0.00 0.00  0.0  0.0  0.0  0.0                             
F8 N 1.76  1.00 0.58 -1.85 1.00 1.27 1.35 0.21                            
   W 0.51  1.02 0.51 0.51  0.0  0.0  0.0  0.0                             
F9 N 3.04  1.72 1.00 -3.19 1.72 2.19 2.32 0.36                            
   W 0.30  0.59 0.30 0.30  0.0  0.0  0.0  0.0                             
R1 N -0.76 0.0  0.42 1.85  0.0  -0.27                                     
                                     -0.35                                
                                          -0.21                           
   W 2.39  4.77 2.39 2.39  0.0  0.0  0.0  0.0                             
R2 N -1.82 0.0  1.00 4.42  0.0  -0.65                                     
                                     -0.83                                
                                          -0.50                           
   W 1.00  2.00 1.00 1.00  0.0  0.0  0.0  0.0                             
__________________________________________________________________________
 
    
     Thus, it may be seen from the illustrated embodiments that the speed change gear systems of the present invention have important advantages over the prior art systems in that speed change shifts through at least four speed ranges for forward drive can be attained by utilizing three basic planetary gear sets. 
     Obviously, many modifications and variations of the present invention are possible in light of the above teachings. It is to be understood therefore that within the scope of the appended claims the present invention may be practiced otherwise than as specifically described herein.