Change-speed transmission with selective bypass of hydrokinetic unit
This is a division of application Ser. No. 274,292, filed June 16, 1981, now U.S. Pat. No. 4,369,672, which is a continuation application of Ser. No. 899,991, filed Apr. 25, 1978, now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates to a change-speed transmission and more particularly to an automatic transmission comprising a hydrokinetic unit, such as a torque converter or a hydraulic coupling, a divider in the form of a planetary gear set, and a planetary gear train. 
     The conventional automatic transmissions using a hydrokinetic unit will provide smooth and effortless start-up of the automobile and shockless shifting as compared to the conventional manual transmissions. However, as there is a slip in a hydrokinetic unit, the automobile equipped with an automatic transmission using a hydrokinetic unit is worse in fuel economy than the automobile equipped with a manual transmission. 
     In order to improve fuel economy of an automobile equipped with an automatic transmission having a hydrokinetic unit, it has been proposed to provide a torque flow path bypassing the hydrokinetic unit which is selectively established by means of a clutch so that when the first forward speed is to be selected, the clutch is disengaged or uncoupled to make full use of the slip characteristics of the hydrokinetic unit for ease of start-up of the automobile. When another forward speed is to be selected, the clutch is engaged or coupled to establish the torque flow path so as to allow a portion of the input torque to flow through this direct path, although the balance portion of the engine torque is transmitted by the hydrokinetic unit. This torque split arrangement results in substantial reductions in the fuel consumption of the automobile. 
     There is known a two-speed automatic transmission, embodying the proposal described above, in which all of the input torque on an input member is transmitted through a hydrokinetic unit to provide the first forward speed and in which, to provide the second forward speed, the transmission of a portion of the input torque is effected through a first or torque split clutch bypassing the hydrokinetic unit with the balance portion of the input torque being transmitted by the hydrokinetic unit. This known transmission comprises: an input member; an output member; a hydrokinetic unit having a pump connected to the input member and a turbine; a divider in the form of a planetary gear set which has a ring gear connected to the turbine, a sun gear, and a carrier, which is in turn connected to the output member. The sun gear is connectable through a first or forward clutch to the input member. The first clutch is engaged upon selection of the second forward speed to permit a portion of the input torque to be transmitted directly to the output member bypassing the hydrokinetic unit. This automatic transmission has limited application, and particularly is not well suited for an automobile, such as a passenger car of the type in use today, because it has only two forward speeds so that it can not meet the varied demands for every day operating conditions. 
     SUMMARY OF THE INVENTION 
     Thus, an object of the invention is to provide a change-speed automatic transmission for an automobile, particularly a passenger car, which substantially increases the fuel economy of the automobile. 
     Another object of the invention is to provide a change-speed automatic transmission, including a divider in the form of a planetary gear set and a torque split clutch, providing more than two forward speeds and at least a portion of the upper or higher speeds of the transmission bypassing the hydrokinetic unit. 
     Still another object of the invention is to provide a change-speed automatic transmission having a wide range of gear ratios constructed of a minimum number of key subcombination component parts, namely, (1) a torque split clutch to bypass the hydrokinetic unit, (2) a divider, and (3) planetary gear train of one or more planetary gear sets. 
     A change-speed transmission of the invention comprises: an input member; a hydrokinetic unit having a pump connected to the input member and a turbine; a divider in the form of a planetary gear set which has a first, a second and a third rotary element; a planetary gear train having a first, a second and a third rotary element; and an output member. The divider and planetary gear train is so interconnected as to reduce the component parts needed for an effective full-range automotive transmission, thus reducing the initial cost as well as the operating expenses. More particularly, the first rotary element of the divider is connected to the first rotary element of the planetary gear train, while, the second rotary element of the divider is connectable through a clutch (a second clutch) to the second rotary element of the gear train. 
     The output member in two series of embodiments of the present invention is connected to the third rotary element of the planetary gear train. In this case, the turbine is connected to one of the second or third rotary elements of the divider, while, the input member is connectable through another clutch (a first clutch) to the other one of these rotary elements of the divider. In at least one embodiment, a fourth rotary element of said gear train is connected to the second rotary element of the divider. 
     Another series of alternative embodiments are provided. For example, if desired, the output member may be connected to the third rotary element of the divider. In this case, the turbine is connected to the third rotary element of the gear train, while, the input member is connectable through a clutch to the second rotary element of the divider. 
     Accordingly, various embodiments of a change-speed transmission of the invention are illustrated in the accompanying drawings, as follows. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     In the accompaning drawings: 
     FIGS. 1 to 8 are schematic diagrams of a first series of eight embodiments of a change-speed transmission of the invention which has the common features: (1) an output member is connected to a third rotary element of a planetary gear train; (2) a turbine of a hydrokinetic unit is connected to a third rotary element of a divider in the form of a planetary gear set; and (3) an input member connected to a pump of the hydrokinetic unit being also connectable through a first clutch (C 1 ) to a second rotary element of the divider. 
     FIGS. 9 to 17 are schematic diagrams of a second series of nine additional embodiments of a change-speed transmission of the invention which has the common feature: (1) an output member is connected to a third rotary element of a planetary gear train; (2) a turbine of a hydrokinetic unit is connected to a second rotary element of a divider in the form of a planetary gear set; and (3) an input member connected to a pump of the hydrokinetic unit is connectable through a first clutch (C 1 ) to a third rotary element of the divider. 
     FIGS. 18 and 19 are schematic diagrams of still another or third series of two additional embodiments of a change-speed transmission of the invention which has the common feature: (1) an output member is connected to a third rotary element of a divider in the form of a planetary gear set; (2) a turbine of a hydrokinetic unit is connected to a third rotary element of a planetary gear train, and (3) an input member connected to a pump of the hydrokinetic unit is connectable through a first clutch (C 1 ) to a second rotary element of the divider. 
    
    
     GENERAL DESCRIPTION OF THE EMBODIMENTS 
     To facilitate understanding of and comparison between the embodiments illustrated in FIGS. 1 to 19, a divider in the form of a planetary gear set is enclosed by a broken (dash) line box, while, a planetary gear train enclosed by an imaginary (dash-dot) line box; a first or a torque split clutch is denoted by C 1  and a second clutch by C 2 . 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 shows a first embodiment of a change-speed transmission according to the invention in which the reference numeral 1 indicates an input shaft, the reference numeral 2 an output shaft and three planetary gear sets X, Y and Z are arranged with their axes aligned with the input and output shafts 1 and 2. 
     First planetary gear set X is a basic or simple planetary gear set and is used in this combination as a divider. The gear set comprises a first sun gear S 1 , a first ring gear R 1  and a carrier A 1  rotatably supporting a plurality of first pinions P 1 , each meshing both with the sun gear S 1  and ring gear R 1 . 
     Second planetary gear set Y is a simple planetary gear set, similar to the first planetary gear set, which comprises a second sun gear S 2 , a second ring gear R 2  and a second carrier A 2  rotatably carrying a plurality of second pinions P 2 , each meshing both with the sun gear S 2  and ring gear R 2 . 
     Third planetary gear set Z is a dual-intermeshed planet pinion planetary gear set which comprises two third sun gears S 3  and S 3  &#39;, a third ring gear R 3  and a third carrier A 3  rotatably supporting a plurality of pairs of intermeshing pinions P 3  and P 3  &#39;. Each pinion P 3   meshes with both of the third sun gears S 3  and S 3  &#39;, while, each pinion P 3  &#39; meshes with the ring gear R 3 . The third gear set Z in combination with the second gear set Y forms the planetary gear train of this first series of embodiments. 
     In the first planetary gear set X, the following equation holds. 
     
         N.sub.R1 +α.sub.1 N.sub.S1 =(1+α.sub.1)N.sub.A1 (1) 
    
     In second planetary gear set Y, the following equation holds. 
     
         N.sub.R2 +α.sub.2 N.sub.S2 =(1+α.sub.2)N.sub.A2 (2) 
    
     In third planetary gear set Z, the following equation holds. 
     
         N.sub.R3 -α.sub.3 N.sub.S3 =(1-α.sub.3)N.sub.A3 (3) 
    
     where, N R1 , N R2  and N R3  denote number of rotations of the ring gears of three planetary gear sets X, Y and Z, respectively. 
     N S1 , N S2  and N S3  denote number of rotations of the sun gears of three planetary gear sets X, Y and Z, respectively. 
     N A1 , N A2  and N A3  denote number of rotations of the carriers of the three planetary gear sets X, Y and Z; 
     α 1 , α 2  and α 3  denote the ratio of number of teeth of a sun gear to that of a ring gear in the three planetary gear sets X, Y and Z, respectively. 
     The transmission comprises an input shaft 1 for supplying the input torque and a hydrokinetic unit or hydraulic torque converter 3 having a pump 3a connected to said input shaft 1 for simultaneous rotation therewith. A turbine 3b is connected to ring gear R 1  for simultaneous rotation therewith. Sun gear S 1  is connectable to input shaft 1 through a first clutch C 1  and connectable also to sun gear S 3  through a second clutch C 2 . Carrier A 1  is connected to ring gear R 2  for simultaneous rotation therewith and both can be braked by means of a first brake B 1 . Sun gear S 2  is connected to ring gear R 3  for simultaneous rotation therewith and can be braked by means of a second brake B 2 . Carrier A 2  is connected to carrier A 3  for simultaneous rotation therewith and the carrier A 3  is connected to output shaft 2 to provide the output torque of the transmission. Sun gear S 3  &#39; can be braked by means of a third brake B.sub. 3. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of the transmission is tabulated in Table 1, in which legend O denotes engagement condition of a clutch or application condition of a brake. Gear ratio and direct transmission rate, i.e., the rate of a portion of a torque transmitted through clutch C 1  bypassing torque converter 3 to all of the input torque, are calculated on the assumption that α 1  =α 2  =α 3  =0.45. 
     
                                           TABLE 1                                 
__________________________________________________________________________
                                        Direct                            
                                        Trans-                            
                                    Gear                                  
                                        mission                           
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3               Ratio                                 
                                        Rate (%)                          
__________________________________________________________________________
1st speed                                                                 
        O   O                                                             
                 ##STR1##           2.652                                 
                                        O                                 
  2nd speed                                                               
      O     O   1 + α.sub.2   1.450                                 
                                        31                                
3rd speed                                                                 
      O       O 1 + α.sub.2 α.sub.3                           
                                    1.202                                 
                                        31                                
4th speed                                                                 
      O O       1.0                 1.000                                 
                                        42.6                              
  Rev.  O O                                                               
                 ##STR2##           -2.672                                
                                        O                                 
__________________________________________________________________________
 
    
     Referring to FIGS. 2 through 19, the other embodiments will be described hereinafter In these embodiments, like reference numerals and characters to those used in FIG. 1 are used to denote like component parts. Since the same or similar function is being carried out in each instance by the parts with like references, no additional or distinguishing identification is necessary or desirable 
     In the second embodiment shown in FIG. 2, a first planetary gear set X is a dual-intermeshed planet pinion planetary gear set which comprises a first sun gear S 1 , a first ring gear R 1  and a first carrier A 1  rotatably carrying a plurality of pairs of intermeshing pinions P 1  and P 1  &#39;. Each pinion P 1  meshes with the sun gear S 1 , while each pinion P 1  &#39; meshes with the ring gear R 1 . 
     Second planetary gear set Y of this embodiment is a basic planetary gear set which comprises two second sun gears S 2  and S 2  &#39;, a second ring gear R 2  and a carrier A 2  rotatably carrying a plurality of second pinions P 2  each meshing with both of the sun gears S 2  and S 2  &#39; and ring gear R 2 . 
     Third planetary gear set Z of this embodiment is a dual-intermeshed planet pinion planetary gear set which comprises a third sun gear S 3 , a third ring gear R 3  and a third carrier A 3  rotatably supporting a plurality pairs of intermeshed pinions P 3  and P 3  &#39;. Each pinion P 3  meshes with the sun gear S 3 , while each pinion P 3  &#39; meshes with ring gear R 3 . 
     In the first planetary gear set X of this embodiment, the following equation holds. 
     
         N.sub.R1 -α.sub.1 N.sub.S1 =(1-α.sub.1)N.sub.A1 (4) 
    
     In the second and third planetary gear sets Y and Z of this embodiment, the above equations (2) and (3) hold, respectively. 
     The transmission comprises an input shaft 1 supplying driving torque and a hydrokinetic unit in the form of a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith. A turbine 3b is connected to carrier A 1  for simultaneous rotation therewith. Sun gear S 1  is connectable to input shaft 1 through a first clutch C 1  and connectable also to sun gear S 2  through a second clutch C 2 . Ring gear R 1   and ring gear R 2  are connected to each other for simultaneous rotation and are brakeable by means of a first brake B 1 . Sun gear S 2  &#39; is connected to ring gear R 3  for simultaneous rotation therewith and the combination may be braked by means of a second brake B 2 . Carriers A 2  and A 3  are connected to output shaft 2 for simultaneous rotation therewith and sun gear S 3  is brakeable by means of a third brake B 3 . 
     The operating sequence of the two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  is tabulated in Table 2 on the assumption that α 1  =α 2  =α 3  =0.45. 
     
                       TABLE 2                                                     
______________________________________                                    
                                             Direct                       
                                             Trans-                       
                                             mission                      
                                       Gear  Rate                         
C.sub.1  C.sub.2                                                          
               B.sub.1                                                    
                     B.sub.2                                              
                         B.sub.3       Ratio (%)                          
______________________________________                                    
1st speed    O         O                                                  
                                ##STR3## 2.636 O                          
  2nd  O               O       1 + α.sub.2                          
                                         1.430 45                         
speed                                                                     
3rd speed                                                                 
       O                   O   1 + α.sub.2 α.sub.3            
                                         1.202 45                         
4th speed                                                                 
       O     O                 1.0       1.000 62                         
  Rev.       O     O                                                      
                                ##STR4## -2.636                           
                                               O                          
______________________________________                                    
 
    
     In the third embodiment shown in FIG. 3, a first planetary gear set X and a third planetary gear set Z are a basic planetary gear set and a dual-intermeshed planet pinion planetary gear set similar to those of the first embodiment, respectively. A second planetary gear set Y is a dual-intermeshed planet pinion planetary gear set which comprises a second sun gear S 2 , a second ring gear R 2  and a second carrier A 2  rotatably supporting a plurality pairs of intermeshing pinions P 2  and P 2  &#39;. Each pinion P 2  meshes with the sun gear S 2 , each pinion P 2  &#39; meshes with the ring gear R 2 . 
     Equations (1) and (3) hold for the first and third planetary gear sets X and Z of this embodiment. In the second planetary gear set Y of this embodiment, the following equation holds. 
     
         N.sub.R2 -α.sub.2 N.sub.S2 =(1-α.sub.2)N.sub.A2 (5) 
    
     Explaining different structural portions of this embodiment from the FIG. 1 embodiment, the carrier A 1  and carrier A 2  are connected to each other for simultaneous rotation and they are brakeable by means of a first brake B 1 , and ring gear R 2  and carrier A 3  are connected to each other for simultaneous rotation. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this embodiment is tabulated in Table 3 on the assumption that α 1  =α 2  =α 3  =0.45. 
     
                                           TABLE 3                                 
__________________________________________________________________________
                                  Direct                                  
                                  Trans-                                  
                              Gear                                        
                                  mission                                 
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3         Ratio                                       
                                  Rate (%)                                
__________________________________________________________________________
1st speed                                                                 
        O   O                                                             
                 ##STR5##     3.186                                       
                                  O                                       
  2nd speed                                                               
      O     O                                                             
                 ##STR6##     1.818                                       
                                  31                                      
  3rd speed                                                               
      O       O                                                           
                 ##STR7##     1.368                                       
                                  31                                      
  4th speed                                                               
      O O       1.0           1.000                                       
                                  49.6                                    
  Rev.  O O                                                               
                 ##STR8##     -1.672                                      
                                  O                                       
__________________________________________________________________________
 
    
     In the fourth embodiment shown in FIG. 4, a first planetary gear set X is a dual-intermeshed planet pinion planetary gear set which has two first sun gears S 1  and S 1  &#39;. A second planetary gear set Y is a basic planetary gear set having two second ring gears R 2  and R 2  &#39;; and a third planetary gear set Z is a basic planetary gear set which has a ring gear R 3 , a sun gear S 3  and a carrier A 3  rotatably supporting a plurality of pinions P 3  each meshing with both the ring gear R 3  and sun gear S 3 . 
     Equations (4) and (2) hold for the first and second planetary gearings X and Y, while the following equation holds for the third planetary gearing Z. 
     
         N.sub.R3 +α.sub.3 N.sub.S3 =(1+α.sub.3)N.sub.A3 (6) 
    
     This transmission also comprises an input shaft 1, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to the carrier A 1  for simultaneous rotation therewith. Sun gear S 1  &#39; is connectable to input shaft 1 through a first clutch C 1 , while another sun gear S 1  is connectable to ring gear R 3  through a second clutch C 2 . Ring gear R 3  is brakeable by means of a first brake B 1 . Ring gear R 1 , sun gear S 3  and ring gear R 2  &#39; are connected to each other for simultaneous rotation. Carrier A 3  and sun gear S 2  are connected to each other for simultaneous rotation and are brakeable by means of a second brake B 2 . Ring gear R 2  is brakeable by means of third brake B 3 . Carrier A 2  is connected to output shaft 2 for providing the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this transmission is tabulated in Table 4 on the assumption that α 1  =α 2  =α 3  =0.45. 
     
                                           TABLE 4                                 
__________________________________________________________________________
                                  Direct                                  
                                  Trans-                                  
                              Gear                                        
                                  mission                                 
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3         Ratio                                       
                                  Rate (%)                                
__________________________________________________________________________
1st speed                                                                 
        O   O                                                             
                 ##STR9##     3.170                                       
                                  O                                       
  2nd speed                                                               
      O     O   1 + α.sub.2                                         
                              1.450                                       
                                  55                                      
  3rd speed                                                               
      O   O                                                               
                 ##STR10##    1.272                                       
                                  55                                      
  4th speed                                                               
      O O       1.0           1.000                                       
                                  57                                      
  Rev.  O     O                                                           
                 ##STR11##    -3.823                                      
                                  O                                       
__________________________________________________________________________
 
    
     In the fifth embodiment shown in FIG. 5, a first planetary gear set X is a basic planetary gear set, while, second and third planetary gear sets Y and Z are dual-intermeshed planet pinion planetary gear sets. 
     Equations (1), (5) and (3) hold for the first, second and third planetary gear sets X, Y and Z, respectively. 
     This embodiment of the transmission has an input shaft 1, a torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to carrier A 2  for simultaneous rotation therewith. The pump 3a is connectable to sun gear S 2  through a first clutch C 1 . The sun gear S 1  is connectable to sun gear S 2  through a second clutch C 2 . Sun gear S 1  is brakeable by means of a first brake B 1 . Carrier A 1  and ring gears R 2  and R 3  are connected to one another for simultaneous rotation and they are brakeable by means of a second brake B 2 . Ring gear R 1  and sun gear S 3  are connected to each other for simultaneous rotation and they are brakeable by brake B 3 . Carrier A 3  is coupled to output shaft 2 for providing the output torque. 
     In this embodiment, the planetary gear train (dash-dot lines) is made up of gear sets X and Z and the divider (dashed lines) is formed by gear set Y (See also embodiments of FIGS. 8 and 14). 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  is tabulated in Table 5 on the assumption that α 1  =0.55,α 2  =0.45 and α 3  =0.35 
     
                                           TABLE 5                                 
__________________________________________________________________________
                                  Direct                                  
                                  Trans-                                  
                              Gear                                        
                                  mission                                 
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3         Ratio                                       
                                  Rate (%)                                
__________________________________________________________________________
1st speed                                                                 
        O O                                                               
                 ##STR12##    2.583                                       
                                  O                                       
  2nd speed                                                               
      O   O                                                               
                 ##STR13##    1.421                                       
                                  45                                      
  3rd speed                                                               
      O O       1.0           1.000                                       
                                  55                                      
4th speed                                                                 
      O       O 1 - α.sub.3                                         
                              0.650                                       
                                  45                                      
  Rev.  O   O                                                             
                 ##STR14##    -2.763                                      
                                  O                                       
__________________________________________________________________________
 
    
     In the sixth embodiment shown in FIG. 6, first and a second planetary gear sets X and Y are dual-intermeshed planet pinions planetary gear sets, while, a third planetary gear set Z is a dual-intermeshed planet pinion planetary gear set with two ring gears R 3  and R 3  &#39;. 
     Equations (4), (5) and (3) hold for first, second, and third planetary gear sets X, Y and Z of this transmission embodiment. 
     This transmission comprises an input shaft providing the input torque, a torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith, and turbine 3b connected to carrier A 1  for simultaneous rotation therewith. The pump 3a is connectable to sun gear S 1  through a first clutch C 1 . The sun gear S 1  is connectable to carrier A 2  through a second clutch C 2 . The carrier A 2  is brakeable by means of a first brake B 1 . Sun gears S 2  and S 3  are connected to each other for simultaneous rotation and are brakeable by means of a second brake B 2 . Ring gear R 2  and carrier A 3  are connected to each other for simultaneous rotation. Ring gear R 1  and ring gear R 3  &#39; are connected to each other for simulaneous rotation. Ring gear R 3  is brakeable by means of a third brake B 3 . Carrier A 3  is connected to an output shaft 2 to provide the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of the transmission is tabulated in Table 6 on the assumption that α 1  =α 2  =α 3  =0.45. 
     
                                           TABLE 6                                 
__________________________________________________________________________
                                 Direct                                   
                                 Trans-                                   
                             Gear                                         
                                 mission                                  
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3        Ratio                                        
                                 Rate (%)                                 
__________________________________________________________________________
1st speed                                                                 
        O O                                                               
                 ##STR15##   2.818                                        
                                 O                                        
  2nd speed                                                               
      O   O                                                               
                 ##STR16##   1.550                                        
                                 45                                       
  3rd speed                                                               
      O O       1.0          1.000                                        
                                 65                                       
4th speed                                                                 
      O     O   1 - α.sub.3                                         
                             0.55                                         
                                 45                                       
  Rev.  O     O                                                           
                 ##STR17##   -2.306                                       
                                 O                                        
__________________________________________________________________________
 
    
     In the seventh embodiment shown in FIG. 7, a first planetary gear set X and a third planetary gear set Z are dual-intermeshed planet pinion planetary gear sets, respectively, while a second planetary gear set Y is a basic planetary gear set. 
     Equations (4), (2) and (3) hold for the first, second and third planetary gear sets X, Y and Z, respectively. 
     This transmission has an input shaft 1 and a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to carrier A 1  (third rotary element of this particular embodiment) for simultaneous rotation therewith. 
     Pump 3a which is connected to input shaft 1 for simultaneous rotation therewith, is connectable to sun gear S 1  (second rotary element of this particular embodiment) through a first clutch C 1 . The sun gear S 1  is connectable to sun gear S 2  through a second clutch C 2 . Ring gear R 1  (first rotary element of this particular embodiment) and carrier A 2  (first rotary element of this particular embodiment) are connected to each other for simultaneous rotation and are brakeable by means of a first brake B 1 . Ring gear R 2  and sun gear S 3   are connected to each other for simultaneous rotation and are brakeable by means of a second brake B 2 . Sun gear S 2  and carrier A 3  (second rotary element of this particular embodiment) are connected to each other for simultaneous rotation and are brakeable by means of a third brake B 3 . Ring gear R 3  (third rotary element of this particular embodiment) is connected to an output shaft 2 for simultaneous rotation to provide the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of the transmission is tabulated in Table 7 on the assumption that α 1  =0.40, α 2  =0.55 and α 3  =0.45. 
     
                                           TABLE 7                                 
__________________________________________________________________________
                                   Direct                                 
                                   Trans-                                 
                               Gear                                       
                                   mission                                
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3          Ratio                                      
                                   Rate (%)                               
__________________________________________________________________________
1st speed                                                                 
        O     O                                                           
                 ##STR18##     2.841                                      
                                   O                                      
  2nd speed                                                               
      O       O                                                           
                 ##STR19##     1.563                                      
                                   45                                     
  3rd speed                                                               
      O O       1.0            1.000                                      
                                   35                                     
  4th speed                                                               
      O     O                                                             
                 ##STR20##     0.625                                      
                                   45                                     
  Rev.  O O                                                               
                 ##STR21##     -2.273                                     
                                   O                                      
__________________________________________________________________________
 
    
     In the eighth embodiment shown in FIG. 8, first planetary gear set X and third planetary gear set Z are dual-intermeshed planet pinion planetary gear sets. Also, second planetary gear set Y is a dual-intermeshed planet pinion planetary gear set. 
     Equations (4), (5) and (3) hold for first, second and third planetary gear sets, respectively. 
     This embodiment of the transmission has an input shaft 1, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to carrier A 2  for simultaneous rotation therewith. The pump 3a is connectable to sun gear S 1  through a first clutch C 1 . Sun gears S 1  and S 2  are connected to each other for simultaneous rotation and are connectable to carrier A 1  through a second clutch C 2 . Carrier A 1  is brakeable by means of a first brake B 1 . Ring gear R 1  and sun gear S 3  are connected to each other for simultaneous rotation and are brakeable by means of a second brake B 2 . Ring gear R 2  and carrier A 3  are connected to each other for simultaneous rotation and are brakeable by means of a third brake B 3 . Ring gear R 3  is connected to output shaft 2 providing the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of the transmission is tabulated in Table 8 on the assumption that α 1  =0.60, α 2  =0.60 and α 3  =0.45. 
     
                       TABLE 8                                                     
______________________________________                                    
                                Direct                                    
                                Trans-                                    
                        Gear    mission                                   
C.sub.1 C.sub.2 B.sub.1 B.sub.2 B.sub.3                                   
                        Ratio   Rate (%)                                  
______________________________________                                    
1st speed                                                                 
      OO                                                                  
                   ##STR22##    4.545 O                                   
  2nd speed                                                               
      OO                                                                  
                   ##STR23##    1.818 60                                  
  3rd speed                                                               
      OO                                                                  
                   ##STR24##    1.220 73                                  
  4th OO          1.0           1.000 78                                  
speed                                                                     
  Rev.                                                                    
      OO                                                                  
                   ##STR25##    -3.333                                    
                                       0                                  
______________________________________                                    
 
    
     In the ninth embodiment shown in FIG. 9, first planetary gear set X and second planetary gear set Y are basic planetary gear sets, respectively, while, a third planetary gear set Z is a dual intermeshed planet pinion planetary gear set which has two ring gears R 3  and R 3  &#39; meshing with each pinion P 3  &#39;. 
     Equations (1), (2) and (3) hold for first, second and third planetary gear sets X, Y and Z, respectively. 
     This transmission comprises an input shaft 1, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to sun gear S 1  for simultaneous rotation therewith. The pump 3a is connectable to ring gear R 1  through a first clutch C 1 . Sun gear S 1  is connectable to carrier A 3  through a second clutch C 2 . Carrier A 3  is brakeable by means of a first brake B 1 . Carrier A 1 , ring gear R 2  and ring gear R 3  are connected to one another for simultaneous rotation. Ring gear R 3  &#39; can be braked by means of a second brake B 2 . Sun gears S 2  and S 3  are connected to each other for simultaneous rotation and are brakeable by means of a third brake B 3 . Carrier A 2  is connected to the output shaft 2 for simultaneous rotation therewith and providing the output torque of the transmission. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this transmission is tabulated in Table 9 on the assumption that α 1  =α 2  =0.45 and α 3  =0.50. 
     
                       TABLE 9                                                     
______________________________________                                    
                                            Direct                        
                                            Trans-                        
                                      Gear  mission                       
C.sub.1 C.sub.2                                                           
              B.sub.1                                                     
                    B.sub.2                                               
                        B.sub.3       Ratio Rate (%)                      
______________________________________                                    
1st speed   O             O                                               
                               ##STR26##                                  
                                        2.900 O                           
  2nd O                   O   1 + α.sub.2                           
                                        1.450 69                          
speed                                                                     
3rd   O     O                 1.0       1.000 90                          
speed                                                                     
  4th speed                                                               
      O           O                                                       
                               ##STR27##                                  
                                        0.763 69                          
  Rev.      O         O                                                   
                               ##STR28##                                  
                                        -2.929                            
                                               0                          
______________________________________                                    
 
    
     In the tenth embodiment shown in FIG. 10, first planetary gear set X and second planetary gear set Y are dual-intermeshed planet pinion planetary gear sets, respectively, while a third planetary gear set Z is a basic planetary gear set. 
     Equations (4), (5) and (6) hold for the first, second and third planetary gear sets X, Y and Z, respectively. 
     This transmission comprises an input shaft 1, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to a carrier A 1  for simultaneous rotation therewith. The pump 3a is connectable to sun gear S 1  of gear set X through a first clutch C 1 . Carrier A 1  is selectively connectable to carrier A 2  through a second clutch C 2 . The carrier A 2  and sun gear S 3  are connected to each other for simultaneous rotation and are brakeable by means of a second brake B 2 . Ring gears R 1  and R 2  are connected to each other for simultaneous rotation and are brakeable by means of a first brake B 1 . Sun gear S 2  and ring gear R 3  are connected to each other for simultaneous rotation and they are brakeable by means of a third brake B 3 . Carrier A 3  is connected to an output shaft 2 for simultaneous rotation therewith and thus to provide the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this transmission is tabulated in Table 10 on the assumption that α 1  =α 2  =α 3  =0.50. 
     
                                           TABLE 10                                
__________________________________________________________________________
                              Direct                                      
                          Gear                                            
                              Transmission                                
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3     Ratio                                           
                              Rate (%)                                    
__________________________________________________________________________
1st speed                                                                 
        O     O                                                           
                 ##STR29##                                                
                          3.000                                           
                              O                                           
  2nd speed                                                               
      O       O                                                           
                 ##STR30##                                                
                          1.500                                           
                              50                                          
  3rd speed                                                               
      O O       1.0       1.000                                           
                              67                                          
4th speed                                                                 
      O     O   α.sub.2 (1 + α.sub.3)                         
                          0.750                                           
                              50                                          
  Rev.  O O                                                               
                 ##STR31##                                                
                          -3.000                                          
                              O                                           
__________________________________________________________________________
 
    
     In the eleventh embodiment shown in FIG. 11, a first planetary gear set X is a basic planetary gear set having two sun gears S 1  and S 1  &#39; meshing with each pinion P 1 , while, a second planetary gear set Y and a third planetary gear set Z are basic planetary gear sets, respectively. 
     Equations (1), (5) and (6) hold for the first, second, and third planetary gear sets X, Y and Z of this transmission, respectively. 
     This transmission comprises an input shaft 1, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to sun gear S 1  &#39; for rotation therewith. The pump 3a is connectable to ring gear R 1  through a first clutch C 1 . Sun gear S 1  is connectable to carrier A 2  through a second clutch C 2 . Carrier A 2  is connected to sun gear S 3  for simultaneous rotation therewith. Carrier A 1  and ring gear R 2  are connected to each other for simultaneous rotation and are brakeable by means of a first brake B 1 . Carrier A 2  is brakeable by means of a second brake B 2 . Sun gear S 2  and ring gear R 3  are connected to each other for simultaneous rotation and are brakeable by means of a third brake B 3 . Carrier A 3  is connected to an output shaft 2 for simultaneous rotation therewith and thus providing the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this transmission is tabulated in Table 11 on the assumption that α 1  =α 2  =α 3  0.50. 
     
                                           TABLE 11                                
__________________________________________________________________________
                               Direct                                     
                           Gear                                           
                               Transmission                               
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3      Ratio                                          
                               Rate (%)                                   
__________________________________________________________________________
1st speed                                                                 
        O     O                                                           
                 ##STR32## 3.000                                          
                               O                                          
  2nd speed                                                               
      O       O                                                           
                 ##STR33## 1.500                                          
                               67                                         
  3rd speed                                                               
      O O       1.0        1.000                                          
                               89                                         
4th speed                                                                 
      O     O   α.sub.2 (1 + α.sub.3)                         
                           0.750                                          
                               67                                         
  Rev.  O O                                                               
                 ##STR34## -3.000                                         
                               O                                          
__________________________________________________________________________
 
    
     In the twelfth embodiment shown in FIG. 12, first planetary gear set X and second planetary gear set Y are dual-intermeshed planet pinion planetary gear sets, respectively, while, a third planetary gear set Z is a basic planetary gear set having two sun gears S 3  and S 3  &#39; meshing with each pinion P 3 . 
     Equations (4), (5) and (6) hold for the first, second and third planetary gear sets of this transmission, respectively. 
     This transmission comprises an input shaft 1 supplying the input torque, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to carrier A 1  for simultaneous rotation therewith. The pump 3a is connectable to sun gear S 1  through a first clutch C 1 . Carrier A 1  is connectable to sun gear S 3  through a second clutch C 2 . Ring gear R 1  and carrier A 2  are connected to each other for simultaneous rotation and are brakeable by means of a first brake B 1 . Sun gear S 2  and ring gear R 3  are connected to each other for simultaneous rotation and they are brakeable by means of a second brake B 2 . Ring gear R 2  and carrier A 3  are connected to each other for simultaneous rotation and are connected to an output shaft 2 for simultaneous rotation therewith and thus providing the output torque. Sun gear S 3  &#39; is brakeable by means of a third brake B 3 . 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this transmission is tabulated in Table 12 on the assumption that α 1  =α 2  =α 3  =0.35. 
     
                                           TABLE 12                                
__________________________________________________________________________
                              Direct                                      
                          Gear                                            
                              Transmission                                
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3     Ratio                                           
                              Rate (%)                                    
__________________________________________________________________________
1st speed                                                                 
        O   O                                                             
                 ##STR35##                                                
                          3.857                                           
                              O                                           
  2nd speed                                                               
      O     O                                                             
                 ##STR36##                                                
                          1.539                                           
                              35                                          
  3rd speed                                                               
      O O       1.0       1.000                                           
                              57                                          
  4th speed                                                               
      O       O                                                           
                 ##STR37##                                                
                          0.812                                           
                              35                                          
  Rev.  O O                                                               
                 ##STR38##                                                
                          - 4.306                                         
                              O                                           
__________________________________________________________________________
 
    
     In the thirteenth embodiment shown in FIG. 13, first planetary gear set X, second planetary gear set Y and third planetary gear set Z are dual-intermeshed planet pinion planetary gear sets, respectively. 
     Equations (4), (5) and (3) hold for the first, second and third planetary gear sets X, Y and Z of this transmission, respectively. 
     This transmission comprises an input shaft 1 supplying the input torque, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for rotation therewith and a turbine 3b connected to sun gear S 1  for simultaneous rotation therewith. The pump 3a is connectable to carrier A 1  through a first clutch C 1 . Sun gear S 1  connected to the turbine 3b for simultaneous rotation therewith, is connectable to carrier A 3 . The carrier A 3  is brakeable by means of a first brake B 1 . Sun gears S 2  and S 3  are connected to each other for simultaneous rotation and are brakeable by means of a second brake B 2 . Ring gear R 1 , carrier A 2  and carrier A 3  are connected to one another for simultaneous rotation and are brakeable by means of a third brake B 3 . Ring gear R 2  is connected to an output shaft 2 for simultaneous rotation therewith and thus providing the output torque. 
     The operating sequence of two clutches and three brakes is tabulated in Table 13 on the assumption that α 1  =α 2  =0.45 and α 3  =0.55. 
     
                                           TABLE 13                                
__________________________________________________________________________
                              Direct                                      
                          Gear                                            
                              Transmission                                
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3     Ratio                                           
                              Rate (%)                                    
__________________________________________________________________________
1st speed                                                                 
        O   O                                                             
                 ##STR39##                                                
                          4.040                                           
                              O                                           
  2nd speed                                                               
      O     O                                                             
                 ##STR40##                                                
                          1.818                                           
                              55                                          
  3rd speed                                                               
      O O       1.0       1.000                                           
                              75                                          
  4th speed                                                               
      O   O                                                               
                 ##STR41##                                                
                          0.788                                           
                              55                                          
  Rev.  O     O                                                           
                 ##STR42##                                                
                          -2.716                                          
                               0                                          
__________________________________________________________________________
 
    
     In the fourteenth embodiment shown in FIG. 14, first planetary gear set X and third planetary gear set Z are basic planetary gear sets, while, a second planetary gear set Y is a dual-intermeshed planet pinion planetary gear set. In this embodiment, the torque divider of the transmission is planetary gear set Y. 
     Equations (1), (5) and (6) hold for the first, second and third planetary gear sets X, Y and Z of this transmission, respectively. 
     This transmission comprises an input shaft 1 supplying the input torque, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to sun gear S 2  for simultaneous rotation therewith. The pump 3a is connectable to carrier A 2  through a first clutch C 1 . Sun gear S 2 , connected to the turbine 3b for simultaneous rotation therewith, is connectable to sun gear S 1  through a second clutch C 2 . The sun gear S 1  is brakeable by means of a first brake B 1 . Carrier A 1 , and ring gears R 2  and R 3  are connected to one another for simultaneous rotation and are brakeable by means of a second brake B 2 . Sun gear S 3  is brakeable by means of a third brake B 3 . Ring gear R 1  and carrier A 3  are connected to each other for simultaneous rotation and are connected to an output shaft 2 for simultaneous rotation therewith and thus providing the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this transmission is tabulated in Table 14 on the assumption that α 1  =α 2  =0.35 and α 3  =0.50. 
     
                                           TABLE 14                                
__________________________________________________________________________
                                  Direct                                  
                                  Trans-                                  
                             Gear mission                                 
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3        Ratio                                        
                                  Rate (%)                                
__________________________________________________________________________
1st speed                                                                 
        O     O                                                           
                 ##STR43##   2.929                                        
                                  O                                       
  2nd speed                                                               
      O       O 1 + α.sub.3                                         
                             1.500                                        
                                  65                                      
3rd speed                                                                 
      O O       1.0          1.000                                        
                                  88                                      
  4th speed                                                               
      O   O                                                               
                 ##STR44##   0.741                                        
                                  65                                      
  Rev.  O   O                                                             
                 ##STR45##   -2.857                                       
                                  O                                       
__________________________________________________________________________
 
    
     In the fifteenth embodiment shown in FIG. 15, a first planetary gear set X is a basic planetary gear set having two sun gears S 1  and S 1  &#39; meshing with each pinion P 1 , a second planetary gear set Y is a dual-intermeshed planet pinion planetary gear set, and a third planetary gear set Z is a basic planetary gear set having two sun gears S 3  and S 3  &#39; meshing with each pinion P 3 . 
     Equations (1), (5) and (6) hold for the first, second and third planetary gear sets X, Y and Z of this transmission, respectively. 
     This transmission comprises an input shaft 1 supplying the input torque, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to sun gear S 1  &#39; for simultaneous rotation therewith. The pump 3a is connectable to ring gear R 1  through a first clutch C 1 . Sun gear S 1  is connectable to sun gear S 3  through a second clutch C 2 . Carrier A 1  and carrier A 2  are connected to each other for simultaneous rotation and are brakeable by means of a first brake B 1 . Sun gear S 2  and ring gear R 3  are connected to each other for simultaneous rotation and are brakeable by means of a second brake B 2 . Sun gear R 3  &#39; is brakeable by means of a third brake B 3 . Ring gear R 2  and carrier A 3  are connected to each other for simultaneous rotation and are connected to an output shaft 2 for simultaneous rotation therewith and providing the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this transmission is tabulated in Table 15 on the assumption that α 1  =0.45, α 2  =0.35 and α 3  =0.45. 
     
                                           TABLE 15                                
__________________________________________________________________________
                              Direct                                      
                          Gear                                            
                              Transmission                                
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3     Ratio                                           
                              Rate (%)                                    
__________________________________________________________________________
1st speed                                                                 
        O   O                                                             
                 ##STR46##                                                
                          3.222                                           
                              O                                           
  2nd speed                                                               
      O     O                                                             
                 ##STR47##                                                
                          1.538                                           
                              69                                          
  3rd speed                                                               
      O O       1.0       1.000                                           
                              90                                          
  4th speed                                                               
      O       O                                                           
                 ##STR48##                                                
                          0.758                                           
                              69                                          
  Rev.  O O                                                               
                 ##STR49##                                                
                          -3.126                                          
                              O                                           
__________________________________________________________________________
 
    
     In the sixteenth embodiment shown in FIG. 16, first planetary gear set X and third planetary gear set Z are dual-intermeshed planet pinion planetary gear sets, respectively, while a second planetary gear set Y is a basic planetary gear set. 
     Equations (4), (2) and (3) hold for the first, second and third planetary gear sets X, Y and Z, respectively. 
     This transmission has an input shaft 1 supplying the input torque, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3 b  connected to sun gear S 1  for simultaneous rotation therewith. The pump 3a is connectable to carrier A 1  through a first clutch C 1 . The sun gear S 1 , connected to turbine 3b for simultaneous rotation therewith, is connectable to sun gear S 2  through a second clutch C 2 . The sun gear S 2  is brakeable by means of a first brake B 1 . Ring gear R 1 , carrier A 2  and carrier A 3  are connected to one another for simultaneous rotation and are brakeable by means of a second brake B 2 . Ring gears R 2  and R 3  are connected to each other for simultaneous rotation and are connected to an output shaft 2 for simultaneous rotation therewith and thus providing the output torque. Sun gear S 3  is brakeable by means of a third brake B 3 . 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this transmission is tabulated in Table 16 on the assumption that α 1  =α 3  =0.40 and α 3  =0.35. 
     
                       TABLE 16                                                    
______________________________________                                    
                                            Direct                        
                                            Trans-                        
                                      Gear  mission                       
C.sub.1  C.sub.2                                                          
               B.sub.1                                                    
                     B.sub.2                                              
                         B.sub.3      Ratio Rate (%)                      
______________________________________                                    
1st speed    O             O                                              
                                ##STR50##                                 
                                        2.885 O                           
  2nd speed                                                               
       O                   O                                              
                                ##STR51##                                 
                                        1.538 60                          
  3rd  O     O                 1.0      1.000 84                          
speed                                                                     
  4th speed                                                               
       O           O                                                      
                                ##STR52##                                 
                                        0.714 60                          
  Rev.       O         O                                                  
                                ##STR53##                                 
                                        -2.500                            
                                              0                           
______________________________________                                    
 
    
     In the seventeenth embodiment shown in FIG. 17, a first planetary gear set X is a basic planetary gear set, while, a second planetary gear set Y and a third planetary gear set Z are dual-intermeshed planet pinion planetary gear sets, respectively. 
     Equations (1), (5) and (3) hold for the first, second and third planetary gear sets X, Y and Z of this transmission. 
     This transmission comprises an input shaft 1 supplying the input torque, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to sun gear S 1  for simultaneous rotation therewith. The input shaft 1 and the pump 3a are connectable to ring gear R 1  through a first clutch C 1 . The sun gear S 1 , connected to turbine 3b for simultaneous rotation therewith, is connectable to carrier A 2  through a second clutch C 2 . The carrier A 2  is brakeable by means of a first brake B 1 . Sun gears S 2  and S 3  are connected to each other for simultaneous rotation and are brakeable by means of a second brake B 2 . Carrier A 1 , ring gear R 2  and carrier A 3  are connected to one another for simultaneous rotation and are brakeable by means of a third brake B 3 . Ring gear R 3  is connected to an output shaft 2 for simultaneous rotation therewith and thus providing the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this transmission is tabulated in Table 17 on the assumption that α 1  α 2  =0.50 and α 3  =0.45. 
     
                                           TABLE 17                                
__________________________________________________________________________
                               Direct                                     
                          Gear Transmission                               
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3     Ratio                                           
                               Rate (%)                                   
__________________________________________________________________________
1st speed                                                                 
        O   O                                                             
                 ##STR54##                                                
                          3.333                                           
                               O                                          
  2nd speed                                                               
      O     O                                                             
                 ##STR55##                                                
                          1.667                                           
                               67                                         
  3rd speed                                                               
      O O       1.0       1.000                                           
                               93                                         
  4th speed                                                               
      O   O                                                               
                 ##STR56##                                                
                          0.714                                           
                               67                                         
  Rev.  O     O                                                           
                 ##STR57##                                                
                          -2.500                                          
                               0                                          
__________________________________________________________________________
 
    
     In the eighteenth embodiment shown in FIG. 18, a first planetary gear set X is a dual-intermeshed planet pinion planetary gear set, a second planetary gear set Y is a basic planetary gear set, and a third planetary gear set Z is a basic planetary gear set Z having two sun gears S 3  and S 3  &#39; meshing with each pinion P 3 . In this embodiment, as well as the embodiment of FIG. 19, the torque divider is the third planetary gear set Z. 
     Equations (4), (2) and (6) hold for the first, second and third planetary gear sets X, Y and Z of this transmission, respectively. 
     This transmission comprises an input shaft 1 supplying the input torque, a hydraulic torque converter 3 having a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to ring gear R 2  for simultaneous rotation therewith. The pump 3a is connectable to sun gear S 3  through a first clutch C 1 . Sun gear S 3  &#39; is connectable to ring gear R 1  through a second clutch C 2 . Sun gear S1, carrier A 2  and ring gear R 3  are connected to one another for simultaneous rotation and are brakeable by means of a first brake B 1 . Carrier A 1  and sun gear S 2  are connected to each other for simultaneous rotation and are brakeable by means of a second brake B 2 . Ring gear R 1  is brakeable by means of a third brake B 3 . Carrier A 3  is connected to an output shaft 2 for simultaneous rotation therewith and thus providing the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of this transmission is tabulated in Table 18 on the assumption that α 1  =0.35 and α 2  =α 3  =0.45. 
     
                                           TABLE 18                                
__________________________________________________________________________
                                      Direct                              
                                      Trans-                              
                                  Gear                                    
                                      mission                             
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3             Ratio                                   
                                      Rate (%)                            
__________________________________________________________________________
1st speed                                                                 
        O     O                                                           
                 ##STR58##        2.453                                   
                                      O                                   
  2nd speed                                                               
      O       O                                                           
                 ##STR59##        1.526                                   
                                      47                                  
  3rd speed                                                               
      O     O                                                             
                 ##STR60##        1.273                                   
                                      39                                  
  4th speed                                                               
      O O       1.0               1.000                                   
                                      63                                  
  Rev.  O O                                                               
                 ##STR61##        -2.230                                  
                                      0                                   
__________________________________________________________________________
 
    
     In the nineteenth embodiment shown in FIG. 19, first planetary gear set X and third planetary gear set Z are basic planetary gear sets, respectively, while, a second planetary gear set Y is a dual-intermeshed planet pinion planetary gear set. 
     Equations (1), (5) and (6) hold for first, second and third planetary gear sets X, Y and Z, respectively. 
     This transmission comprises an input shaft 1 supplying the input torque, a pump 3a connected to the input shaft 1 for simultaneous rotation therewith and a turbine 3b connected to both sun gears S 1  and S 2  for simultaneous rotation therewith. The pump 3a is connectable to sun gear S 3  through a first clutch C 1 . The sun gear S 3  is connectable to carrier A 2  through a second clutch C 2 . The carrier A 2  and carrier A 1  are connected to each other for simultaneous rotation and are breakable by means of a first brake B 1 . Ring gear R 1  is brakeable by means of a second brake B 2 . Ring gears R 2  and R 3  are connected to each other for simultaneous rotation and are brakeable by means of a third brake B 3 . Carrier A 3  is connected to an output shaft 2 for simultaneous rotation therewith and thus providing the output torque. 
     The operating sequence of two clutches C 1  and C 2  and three brakes B 1 , B 2  and B 3  of the transmission is tabulated in Table 19 on the assumption that α 1  =α 2  =α 3  =0.45. 
     
                                           TABLE 19                                
__________________________________________________________________________
                                 Direct                                   
                                 Trans-                                   
                             Gear                                         
                                 mission                                  
C.sub.1 C.sub.2                                                           
          B.sub.1                                                         
            B.sub.2                                                       
              B.sub.3        Ratio                                        
                                 Rate (%)                                 
__________________________________________________________________________
1st speed                                                                 
        O O                                                               
                 ##STR62##   3.222                                        
                                 O                                        
  2nd speed                                                               
      O   O                                                               
                 ##STR63##   1.611                                        
                                 50                                       
  3rd speed                                                               
      O     O                                                             
                 ##STR64##   1.354                                        
                                 42                                       
  4th speed                                                               
      O O       1.0          1.000                                        
                                 31                                       
Rev.    O     O                                                           
                 ##STR65##   -3.938                                       
                                 0                                        
__________________________________________________________________________
 
    
     In the operation of several embodiments of the change-speed transmission, the shift may be made from first through the fourth speeds in an obvious manner illustrated in each of the Tables 1-19. The torque path in each speed of each embodiment is simply traced through the transmission by properly considering the noted operative or inoperative condition of the clutches C 1 , C 2  and brakes B 1 , B 2  and B 3 . As noted above in discussing each individual embodiment, when a clutch C 1 , C 2  is noted as engaged, the two rotary elements are coupled for simultaneous rotation, and when a brake B 1 , B 2 , B 3  is noted as applied the gear and/or carrier involved is anchored against rotation. 
     Advantageously, the shift from one gear ratio to the other is capable of being performed smoothly. Most importantly, because of the partial direct interconnection between the input member 1 and the output member 2 in the upper gear ratios, a substantial increase in fuel economy is realized. 
     This transmission of the present invention also provides a wide range of gear ratios and is highly suitable for automotive use. With the use of the torque split clutch, the divider and planetary gear train, a reduction in initial cost can be obtained in addition to holding the operating expenses to a minimum. 
     The overall change-speed transmission is more compact in design then previous arrangements wherein a full complement of forward gears (four speeds) and a reverse are provided. The transmission is also clearly adaptable to be manufactured in quantity since all of the rotary elements are planetary gear sets; which sets are used for both the divider and the planetary gear train. 
     It will also be appreciated from this description of the various preferred embodiments of the invention, that obvious changes and modifications can be made without departing from the spirt and scope of the invention.