Abstract:
This invention relates to a transmission gearbox family to provide five, six, seven, eight and nine speed ratios with a reverse speed ratio and a neutral condition in motor vehicles. The invention arranges a plurality of gearwheels in parallel shaft systems such that minimum number of gearwheels is obtained by either combination of clutches with synchronizers for transmission gearboxes with a torque converter and direct clutch to clutch gearboxes without a torque converter, or synchronizers for automated manual transmission gearboxes. For total number of the gearwheels involving in forward driving, five-speed transmission gearboxes have eight gearwheels, six-speed transmission gearboxes have minimum of nine gearwheels, seven-speed transmission gearboxes have minimum of nine gearwheels, eight-speed transmission gearboxes have minimum of nine gearwheels and nine-speed transmission gearboxes have minimum of nine gearwheels, respectively. Each family member has three parallel shafts with either selectively or continuously interconnected with the gearwheels through the engaged single or multiple torque transmitting mechanisms. The direct clutch-to-clutch gearboxes without a torque converter and automated manual gearboxes have a mechanical damper and a main clutch.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]      
         [0000]    
       
         
               
               
               
             
           
               
                   
               
             
             
               
                 7,305,900 
                 Dec. 10, 2007 
                 Suzuki, et al. 
               
               
                 7,294,091 
                 Nov. 13, 2007 
                 Yasui, et al. 
               
               
                 7,082,850 
                 Aug. 1, 2006 
                 Hughes, et al. 
               
               
                 6,715,597 
                 Apr. 6, 2004 
                 Buchanan, et al. 
               
               
                 6,705,967 
                 Mar. 16, 2004 
                 Raghavan, et al. 
               
               
                 6,656,078 
                 Dec. 2, 2003 
                 Raghavan, et al. 
               
               
                 6,463,821 
                 Oct. 15, 2002 
                 Reed, Jr., et al. 
               
               
                 5,950,781 
                 Sep. 14, 1999 
                 Adamis, et al. 
               
               
                 5,106,352 
                 Apr. 21, 1992 
                 Lepelletier 
               
               
                   
               
             
          
         
       
     
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not Applicable 
       THE NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT 
       [0003]    Not Applicable 
       INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISC 
       [0004]    Not Applicable 
       BACKGROUND OF THE INVENTION 
       [0005]    A powertrain system used in a passenger vehicle is comprised of an engine, multi-speed transmission and a differential or final drive system. The premier function of transmission is to extend the operating range of the vehicle by allowing the engine to perform in the torque range several times higher than the engine torque as the transmission ratio increases and also allows the engine to perform in the output speed range higher than engine speed as transmission ratio reduces, such as in the overdrive speed. 
         [0006]    With advent of five and six speed automatic transmissions (U.S. Pat. Nos. 5,106,352 and 6,656,078), the step size between ratios is reduced and the shift quality of the transmission by making the ratio interchanges is substantially improved comparing with three and four speed transmissions. Multi-speed transmissions, such as five and six speed automatic transmissions, also have advantages over fewer speed transmissions, such as three and four speed automatic transmissions, to achieve desirable fuel economy. 
         [0007]    Such multi-speed transmissions still use the conventional torque converter for comfort shifting, but have quite low mechanical efficiency. Torque converters typically include impeller assemblies that are operatively connected with input shaft from an internal combustion engine, a turbine assembly that is fluidly connected with the impeller assembly and a stator or reactor assembly. These assemblies together form a substantially toroidal flow passage for kinetic fluid in the torque converter. Each assembly includes a plurality of blades or vanes that act to convert mechanical energy to hydrokinetic energy and back to mechanical energy. 
         [0008]    The stator assembly of a conventional torque converter is locked against rotation in one direction but is free to spin about an axis in the direction of rotation of the impeller assembly and turbine assembly. When the stator assembly is locked against rotation by a so-called one-way clutch, the torque is multiplied by the torque converter. During torque multiplication, the output torque is greater than the input torque for the torque converter. On the other hand, when there is no torque multiplication, the torque converter becomes a fluid coupling. Torque converter slip exists when the speed ratio is less than 1.0. The inherent slip reduces the efficiency of the torque converter. Although lock-up device is usually equipped in newly developed transmissions, only a few gears can be locked up to avoid energy loss and the lock-up usually is not complete because partial slippery still exists to prevent the noise and vibration. Therefore, its overall efficiency is still low as long as the torque converter is used and the torque converter is considered as a big technical barrier to efficiency improvement. 
         [0009]    Automated manual transmission (AMT), another type of automatic shifting transmission used in motor vehicles, improves the efficiency by removing the torque converter. Such automated manual transmissions typically include a plurality of power-operated actuators that are controlled by a transmission controller or some type of electronic control unit (ECU) to automatically shift synchronized clutches that control the engagement of meshed gearwheels traditionally found in manual transmissions. It does the function of interchanging the speed ratio by automatically disengaging the clutch disc, choosing the right gear ratio, shifting to the gear and engaging clutch automatically. Although this shifting procedure causes discontinuous torque delivery and harsh shift feel to passengers, it still has been used in some of the motor vehicles, since the efficiency can be as good as manual transmissions. 
         [0010]    The transmission using twin-clutch, known as dual-clutch transmission (U.S. Pat. Nos. 5,950,781 and 6,463,821), also removes the torque converter to improve the mechanical efficiency. The dual clutch structure has two coaxially and cooperatively configured clutches that derive power input from a singular engine crankshaft. It consists of two independent transmission systems that have two concentric driving shafts, one is hollow and the other is solid within the hollow shaft. The first, third and fifth driving gears are on one of the driving shafts and the second, forth and sixth gears are on the other shaft. The third shaft is a driven shaft that has all the driven gears on it. The gear shifting operation is activated by dogs and sliding sleeves on driving and driven shafts. When a gear is shifted to the next gear for ratio interchange, it engages one of the clutches while the other is still in engagement. Due to the two-clutch engagement at the same time, one of them or both of them must create relative slip motion to prevent gearwheel from damages while the output speed takes the transition for a gradual change to the next gear. The shifting operation can provide comfort feel that is similar to the one by using a torque converter. The dual-clutch transmission soon receives increasing popularity in the applications of passenger cars. However, the clutch assembly working within the dual-clutch transmission generates a considerable amount of heat (U.S. Pat. No. 6,715,597). Especially, when the vehicle starts to launch and heavily loaded, the high pressure acts on the clutch discs while slip is required for smooth transition (U.S. Pat. No. 6,463,821). The slip in dual clutch is quite high compared to that in conventional automatic transmissions where the clutch slip is limited between driving and driven clutch discs. These conventional automatic transmissions, either using planetary gear sets or parallel shafts with external gear sets, usually have an uncontrolled way to dissipate the heat that is generated from torque converter, clutches, gears and actuators, etc., by using a transmission fluid cooler. It has been proven to be reliable and economic for long time operations through the reduced pump pressure to circulate the flow. However, in the dual-clutch transmission, since more heat can be generated in a short period of time, this cooling method is insufficient to maintain the required fluid temperature. The requirements to the materials in friction elements are, hence, higher, and the way to cool down the transmission fluid and its control procedures are much more complicated (U.S. Pat. No. 6,715,597). Although dual-clutch transmission provides high mechanical efficiency and shifting quality, it can only be used in limited types of lighter duty vehicles due to these disadvantages. 
         [0011]    The above mentioned transmission systems have to be packaged in the limited space provided by under hood compartment in a motor vehicle. In a planetary gear system, six, seven and eight speed transmissions are invented to use only three planetary gear sets. Dual-clutch transmission systems contain only twelve forward external driving gearwheels. A technique to reduce shaft center distance and number of gearwheels is to repeatedly use gear sets by interlocking the tow input shafts. However, the drawbacks of this technique are the need to install additional damper in the large diameter gearwheel and the introduction of bending moment to engine crankshaft (U.S. Pat. No. 7,305,900). 
       BRIEF SUMMARY OF THE INVENTION 
       [0012]    One of the objectives of the present invention is to introduce a new transmission family by using the gearwheels as minimum numbers as possible to achieve the full range of the gear ratios which overcomes the disadvantages in automatic transmissions, automated manual transmissions (AMT) and dual-clutch transmissions (DCT) which typically require more gearwheels. The virtue of this invention is to obtain each selected gear ratio by interconnecting multiple gearwheels and or multiple gear sets simultaneously instead of using one gear set for only one selected gear ratio. Therefore, the total number of gearwheels is reduced to a minimum level, the size of the gearbox is designed to a compact level and the bending moment is limited in a negligible level in such parallel shaft transmission system. Another objective of the present invention is to reduce the relative clutch slippery speed between driving and driven clutch pads and to increase the durability of the transmission by minimizing the heat in the transmission gearboxes that are equipped with hydraulic clutches. Meanwhile, the cost effective material for the clutch pad can be used without compromising the basic cooling requirement and the longevity of the gearbox. 
         [0013]    In one aspect of the present invention, the transmission gearbox comprises three parallel shafts and multiple external gear sets. Each of the external gear sets consists of external gearwheels which are selectively interconnected to each of the mentioned three parallel shafts for the forward driving speeds. In another aspect of the present invention, the external gear sets contain the continuously interconnected gearwheels which reduce the center distance between the parallel shafts whenever it becomes necessary. 
         [0014]    In yet another aspect of the present invention, each of the external gear sets is selectively controlled by torque transmitting mechanisms to produce at least five forward speed ratios and one reverse ratio. Herein, the torque transmitting mechanisms consist of clutches and synchronizers. 
         [0015]    In still yet another aspect of the present invention, in the five-speed transmission gearboxes, six of eight gearwheels are used for more than one forward speed ratio. In yet a further aspect of the present invention, in the six-speed transmission gearboxes with ten forward driving gearwheels, nine of ten gearwheels are used for more than one forward speed ratio. In yet a further aspect of the present invention, in the six-speed transmission gearboxes with eleven forward driving gearwheels, ten of eleven gearwheels are used for more than one forward speed ratio. In yet a further aspect of the present invention, in the six-speed transmission gearboxes with nine forward driving gearwheels, nine of nine gearwheels are used for more than one forward speed ratio. In yet a further aspect of the present invention, in seven-speed, eight-speed and nine-speed transmission gearboxes, nine of nine gearwheels are used for more than one forward speed ratio. These features give the maximum reduction of the total number of gearwheels. 
         [0016]    The present invention is embodied in a family of transmission gearboxes that utilize the minimum numbers of forward driving gearwheels to obtain the multiple gear speed ratios in the selected five, six, seven, eight and nine speed gear ratios, which provide a significantly low cost for massive production. In further description, five forward speeds are achieved by selectively interconnecting a minimum of the eight forward speed gearwheels of the five-speed transmission gearboxes; herewith, six forward speeds are achieved by selectively interconnecting a minimum of nine forward speed gearwheels of the six-speed transmission gearboxes; herewith, seven forward speeds are achieved by selectively interconnecting a minimum of nine forward speed gearwheels of the seven-speed transmission gearboxes; herewith, eight forward speeds are achieved by selectively interconnecting a minimum of nine forward speed gearwheels of the eight-speed transmission gearboxes and herewith, nine forward speeds are also achieved by selectively interconnecting a minimum of nine forward speed gearwheels of the transmission gearboxes. 
         [0017]    Another embodiment of the present invention is to provide a new type of direct clutch-to-clutch transmission gearboxes, which is operated at a lower clutch slippery speed with more reliable and lower heat generation than a dual-clutch transmission gearbox. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S) 
         [0018]      FIG. 1  is a schematic diagram of a five-speed direct clutch-to-clutch transmission gearbox using eight forward driving gearwheels with clutches and synchronizers 
           [0019]      FIG. 2  is a truth table of shift sequence of the transmission gearbox in  FIG. 1  and ratio steps between adjacent drive ratios 
           [0020]      FIG. 3  is a schematic diagram of a five-speed transmission gearbox using a torque converter and eight forward driving gearwheels with clutches and synchronizers 
           [0021]      FIG. 4  is a truth table of shift sequence of the transmission gearbox in  FIG. 3  and ratio steps between adjacent drive ratios 
           [0022]      FIG. 5  is a schematic diagram of a five-speed automated manual transmission gearbox using eight forward driving gearwheels with synchronizers 
           [0023]      FIG. 6  is a truth table of shift sequence of the transmission gearbox in  FIG. 5  and ratio steps between adjacent drive ratios 
           [0024]      FIG. 7  is a schematic diagram of a six-speed direct clutch-to-clutch transmission gearbox using nine forward driving gearwheels with clutches and synchronizers 
           [0025]      FIG. 8  is a truth table of shift sequence of the transmission gearbox in  FIG. 7  and ratio steps between adjacent drive ratios 
           [0026]      FIG. 9  is a schematic diagram of a six-speed transmission gearbox using a torque converter and nine forward driving gearwheels with clutches and synchronizers 
           [0027]      FIG. 10  is a truth table of shift sequence of the transmission gearbox in  FIG. 9  and ratio steps between adjacent drive ratios 
           [0028]      FIG. 11  is a schematic diagram of a six-speed automated manual transmission gearbox using nine forward driving gearwheels with clutches and synchronizers 
           [0029]      FIG. 12  is a truth table of shift sequence of the transmission gearbox in  FIG. 11  and ratio steps between adjacent drive ratios 
           [0030]      FIG. 13  is a schematic diagram of a six-speed direct clutch-to-clutch transmission gearbox using ten forward driving gearwheels with clutches and synchronizers 
           [0031]      FIG. 14  is a truth table of shift sequence of the transmission gearbox in  FIG. 13  and ratio steps between adjacent drive ratios 
           [0032]      FIG. 15  is a schematic diagram of a six-speed transmission gearbox using a torque converter and ten forward driving gearwheels with clutches and synchronizers 
           [0033]      FIG. 16  is a truth table of shift sequence of the transmission gearbox in  FIG. 15  and ratio steps between adjacent drive ratios 
           [0034]      FIG. 17  is a schematic diagram of a six-speed automated manual transmission gearbox using ten forward driving gearwheels with clutches and synchronizers 
           [0035]      FIG. 18  is a truth table of shift sequence of the transmission gearbox in  FIG. 17  and ratio steps between adjacent drive ratios 
           [0036]      FIG. 19  is a schematic diagram of a six-speed direct clutch-to-clutch transmission gearbox using eleven forward driving gearwheels with clutches and synchronizers 
           [0037]      FIG. 20  is a truth table of shift sequence of the transmission gearbox in  FIG. 19  and ratio steps between adjacent drive ratios 
           [0038]      FIG. 21  is a schematic diagram of a six-speed transmission gearbox using a torque converter and eleven forward driving gearwheels with clutches and synchronizers 
           [0039]      FIG. 22  is a truth table of shift sequence of the transmission gearbox in  FIG. 21  and ratio steps between adjacent drive ratios 
           [0040]      FIG. 23  is a schematic diagram of a six-speed automated manual transmission gearbox using eleven forward driving gearwheels with clutches and synchronizers 
           [0041]      FIG. 24  is a truth table of shift sequence of the transmission gearbox in  FIG. 23  and ratio steps between adjacent drive ratios 
           [0042]      FIG. 25  is a schematic diagram of a seven-speed direct clutch-to-clutch transmission gearbox using ten forward driving gearwheels with clutches and synchronizers 
           [0043]      FIG. 26  is a truth table of shift sequence of the transmission gearbox in  FIG. 25  and ratio steps between adjacent drive ratios 
           [0044]      FIG. 27  is a schematic diagram of a seven-speed transmission gearbox using a torque converter and ten forward driving gearwheels with clutches and synchronizers 
           [0045]      FIG. 28  is a truth table of shift sequence of the transmission gearbox in  FIG. 27  and ratio steps between adjacent drive ratios 
           [0046]      FIG. 29  is a schematic diagram of a seven-speed automated manual transmission gearbox using ten forward driving gearwheels with clutches and synchronizers 
           [0047]      FIG. 30  is a truth table of shift sequence of the transmission gearbox in  FIG. 29  and ratio steps between adjacent drive ratios 
           [0048]      FIG. 31  is a schematic diagram of a transmission gearbox for seven-speed, eight-speed and nine-speed transmissions using nine forward driving gearwheels, clutches and synchronizers 
           [0049]      FIG. 32  is a truth table of shift sequence of the transmission gearbox in  FIG. 31  and ratio steps between adjacent drive ratios for seven speeds 
           [0050]      FIG. 33  is a truth table of shift sequence of the transmission gearbox in  FIG. 31  and ratio steps between adjacent drive ratios for eight speeds 
           [0051]      FIG. 34  is a truth table of shift sequence of the transmission gearbox in  FIG. 31  and ratio steps between adjacent drive ratios for nine speeds 
           [0052]      FIG. 35  is a schematic diagram of a transmission gearbox for seven-speed, eight-speed and nine-speed automated manual transmissions using nine forward driving gearwheels, a clutch and synchronizers 
           [0053]      FIG. 36  is a truth table of shift sequence of the transmission gearbox in  FIG. 35  and ratio steps between adjacent drive ratios for seven speeds 
           [0054]      FIG. 37  is a truth table of shift sequence of the transmission gearbox in  FIG. 35  and ratio steps between adjacent drive ratios for eight speeds 
           [0055]      FIG. 38  is a truth table of shift sequence of the transmission gearbox in  FIG. 35  and ratio steps between adjacent drive ratios for nine speeds 
           [0056]      FIG. 39  is a schematic diagram of transmission gearbox for seven-speed, eight-speed and nine-speed direct clutch-to-clutch transmissions using ten forward driving gearwheels, clutches and synchronizers 
           [0057]      FIG. 40  is a truth table of shift sequence of the transmission gearbox in  FIG. 39  and ratio steps between adjacent drive ratios for seven speeds 
           [0058]      FIG. 41  is a truth table of shift sequence of the transmission gearbox in  FIG. 39  and ratio steps between adjacent drive ratios for eight speeds 
           [0059]      FIG. 42  is a truth table of shift sequence of the transmission gearbox in  FIG. 39  and ratio steps between adjacent drive ratios for nine speeds 
           [0060]      FIG. 43  is a schematic diagram of a transmission gearbox for seven-speed, eight-speed and nine-speed automated manual transmissions using ten forward driving gearwheels, a clutch and synchronizers 
           [0061]      FIG. 44  is a truth table of shift sequence of the transmission gearbox in  FIG. 43  and ratio steps between adjacent drive ratios for seven speeds 
           [0062]      FIG. 45  is a truth table of shift sequence of the transmission gearbox in  FIG. 43  and ratio steps between adjacent drive ratios for eight speeds 
           [0063]      FIG. 46  is a truth table of shift sequence of the transmission gearbox in  FIG. 43  and ratio steps between adjacent drive ratios for nine speeds 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0064]    A powertrain system  501 , shown in  FIG. 1 , has a conventional engine  501 E and a five-speed transmission gearbox  501 G. 
         [0065]    The five-speed transmission gearbox  501 G includes a mechanical damper  501 D, a main clutch  501 C 0 , an input shaft  501 A 1 , an output shaft  501 A 2  which has a fixed output gearwheel  501 GO to transmit torque to a final drive(not shown) and an intermediate shaft  501 A 3 .  501 A 1  is selectively interconnected with  501 C 0 .  501 G also includes a plurality of forward driving gearwheels  501 G 1 , which is fixed on  501 A 1 ,  501 G 2 ,  501 G 4 ,  501 G 5 ,  501 G 6 ,  501 G 7 ,  501 G 8  and  501 G 9  which are free to rotate and selectively interconnected with input shaft  501 A 1 , the output shaft  501 A 2  and the intermediate shaft  501 A 3  by clutches  501 C 1 ,  501 C 2 ,  501 C 3 ,  501 C 4  and  501 C 5 , and a synchronizer  501 S 1 , respectively.  501 G 6  and  501 G 9  are linked with each other on the intermediate shaft  501 A 3 .  501 G also has a reverse driving gearwheel  501 GR 1  which is free to rotate and selectively interconnected with the intermediate shaft  501 A 3 , a reverse driven gearwheel  501 GR 2  which is fixed on output shaft  501 A 2  and  501 GI which serves as an idler to change rotating direction. The clutches allow  501 G 4  and  501 G 7  to be selectively interconnected with the input shaft  501 A 1 , and  501 G 2 ,  501 G 5  and  501 G 8  to be selectively interconnected with the output shaft  501 A 2 , respectively. The engagement and disengagement of torque transmitting mechanisms are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0066]    A static truth table, shown in  FIG. 2 , gives shift sequence of transmission of  FIG. 1  and ratio steps between adjacent drive ratios. 
         [0067]    When a forward speed is accomplished, main clutch  501 C 0  is always engaged. In addition, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  501 C 1  and  501 C 3 . This results in gearwheel  501 G 4  driving gearwheel  501 G 5  to provide first forward speed ratio. The second forward speed ratio is established by engagement of clutches  501 C 2  and  501 C 3 . This results in  501 G 7  driving  501 G 9  through the idler  501 G 8 . Since  501 G 6  and  501 G 9  are linked,  501 G 6  drives  501 G 5  through the clutch  501 C 2 &#39;s engagement to give reduced speed at the output shaft  501 A 2 . The third forward speed ratio is established by engagement of clutches  501 C 1  and  501 C 5 . This results in  501 G 4  driving  501 G 6  through the idler  501 G 5 . Since  501 G 6  and  501 G 9  is linked,  501 G 9  drives  501 G 8  through the  501 C 5 &#39;s engagement to give third reduced speed at the output shaft  501 A 2 . The fourth forward speed ratio is established by engagement of clutches  501 C 4  only. This results in  501 G 1  driving  501 G 2  through the  501 C 4 &#39;s engagement to give fourth speed at the output shaft  501 A 2 . The fifth forward speed ratio is established by engagement of clutches  501 C 2  and  501 C 5 . This results in  501 G 7  driving  501 G 8  to give the fifth speed at the output shaft  501 A 2 . The reverse speed ratio is established by the engagements of clutch  501 C 1  and synchronizer  501 SR. This results in  501 G 4  driving  501 G 6  through the idler  501 G 5 . Since  501 G 6  and  501 GR 1  are linked through engagement of synchronizer  501 SR,  501 GR 1  drives  501 GR 2  through the idler  501 GI to give a reverse speed in reverse direction at the output shaft  501 A 2 . 
         [0068]    A powertrain system  502 , shown in  FIG. 3 , has a conventional engine  502 E, torque converter  502 TC and a five-speed transmission gearbox  502 G. 
         [0069]    The five-speed transmission gearbox  502 G includes an input shaft  502 A 1 , an output shaft  502 A 2  which has a fixed output gearwheel  502 GO to transmit torque to a final drive(not shown) and an intermediate shaft  502 A 3 .  502 A 1  is selectively interconnected with  502 C 0 .  502 G also includes a plurality of forward driving gearwheels  502 G 1 , which is fixed on  502 A 1 ,  502 G 2 ,  502 G 4 ,  502 G 5 ,  502 G 6 ,  502 G 7 ,  502 G 8  and  502 G 9  which are free to rotate and selectively interconnected with input shaft  502 A 1 , the output shaft  502 A 2  and the intermediate shaft  502 A 3  by clutches  502 C 1 ,  502 C 2 ,  502 C 3 ,  502 C 4  and  502 C 5 , and a synchronizer  502 S 1 , respectively.  502 G 6  and  502 G 9  are linked with each other and fixed on the intermediate shaft  502 A 3 .  502 G also has a reverse driving gearwheel  502 GR 1  which is free to rotate and selectively interconnected with the intermediate shaft  502 A 3 , a reverse driven gearwheel  502 GR 2  which is fixed on output shaft  502 A 2  and  502 GI which serves as an idler to change rotating direction. The clutches allow  502 G 4  and  502 G 7  to be selectively interconnected with the input shaft  502 A 1 , and  502 G 2 ,  502 G 5  and  502 G 8  to be selectively interconnected with the output shaft  502 A 2 , respectively. The engagement and disengagement of torque transmitting mechanisms are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0070]    A static truth table, shown in  FIG. 4 , gives shift sequence of transmission of  FIG. 3  and ratio steps between adjacent drive ratios. 
         [0071]    When a forward speed is accomplished, main clutch  502 C 0  is always engaged. In addition, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  502 C 1  and  502 C 3 . This results in gearwheel  502 G 4  driving gearwheel  502 G 5  to provide first forward speed ratio. The second forward speed ratio is established by engagement of clutches  502 C 2  and  502 C 3 . This results in  502 G 7  driving  502 G 9  through the idler  502 G 8 . Since  502 G 6  and  502 G 9  are linked,  502 G 6  drives  502 G 5  through the clutch  502 C 2 &#39;s engagement to give reduced speed at the output shaft  502 A 2 . The third forward speed ratio is established by engagement of clutches  502 C 1  and  502 C 5 . This results in  502 G 4  driving  502 G 6  through the idler  502 G 5 . Since  502 G 6  and  502 G 9  is linked,  502 G 9  drives  502 G 8  through the  502 C 5 &#39;s engagement to give third reduced speed at the output shaft  502 A 2 . The fourth forward speed ratio is established by engagement of clutches  502 C 4  only. This results in  502 G 1  driving  502 G 2  through the  502 C 4 &#39;s engagement to give fourth speed at the output shaft  502 A 2 . The fifth forward speed ratio is established by engagement of clutches  502 C 2  and  502 C 5 . This results in  502 G 7  driving  502 G 8  to give the fifth speed at the output shaft  502 A 2 . The reverse speed ratio is established by the engagements of clutch  502 C 1  and synchronizer  502 SR. This results in  502 G 4  driving  502 G 6  through the idler  502 G 5 . Since  502 G 6  and  502 GR 1  are linked through engagement of synchronizer  502 SR,  502 GR 1  drives  502 GR 2  through the idler  502 GI to give a reverse speed in reverse direction at the output shaft  502 A 2 . 
         [0072]    A powertrain system  503 , shown in  FIG. 5 , has a conventional engine  503 E and a five-speed transmission gearbox  503 G. 
         [0073]    The five-speed transmission gearbox  503 G includes a mechanical damper  503 D, which has connection between a main clutch  503 C 0  and an input shaft  503 A 1 , an output shaft  503 A 2  which has a fixed output gearwheel  503 GO to transmit torque to a final drive(not shown) and an intermediate shaft  503 A 3 .  503 A 1  is selectively interconnected with  503 C 0 .  503 G also includes a plurality of forward driving gearwheels  503 G 1 , which is fixed on  503 A 1 ,  503 G 2 ,  503 G 4 ,  503 G 5 ,  503 G 6 ,  503 G 7 ,  503 G 8  and  503 G 9  which are free to rotate and selectively interconnected with input shaft  503 A 1 , the output shaft  503 A 2  and the intermediate shaft  503 A 3  by synchronizers  503 S 1 ,  503 S 2 ,  503 S 3 ,  503 S 4  and  503 S 5 , respectively.  503 G 6  and  503 G 9  are linked with each other and fixed on the intermediate shaft  503 A 3 .  503 G also has a reverse driving gearwheel  503 GR 1  which is free to rotate and selectively interconnected with the intermediate shaft  503 A 3 , a reverse driven gearwheel  503 GR 2  which is fixed on output shaft  503 A 2  and  503 GI which serves as an idler to change rotating direction. The synchronizers allow  503 G 4  and  503 G 7  to be selectively interconnected with the input shaft  503 A 1 , and  503 G 2 ,  503 G 5  and  503 G 8  to be selectively interconnected with the output shaft  503 A 2 , respectively. The engagement and disengagement of torque transmitting mechanisms are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0074]    A static truth table, shown in  FIG. 6 , gives shift sequence of transmission of  FIG. 5  and ratio steps between adjacent drive ratios. 
         [0075]    When a forward speed is accomplished, main clutch  503 C 0  is always engaged. In addition, the following synchronizer engagements are applied. The first forward speed ratio is established by engagement of synchronizers  503 S 1  and  503 S 3 . This results in gearwheel  503 G 4  driving gearwheel  503 G 5  to provide first forward speed ratio. The second forward speed ratio is established by engagement of synchronizers  503 S 2  and  503 S 3 . This results in  503 G 7  driving  503 G 9  through the idler  503 G 8 . Since  503 G 6  and  503 G 9  are linked,  503 G 6  drives  503 G 5  through the synchronizer  503 S 2 &#39;s engagement to give reduced speed at the output shaft  503 A 2 . The third forward speed ratio is established by engagement of synchronizers  503 S 1  and  503 S 5 . This results in  503 G 4  driving  503 G 6  through the idler  503 G 5 . Since  503 G 6  and  503 G 9  is linked,  503 G 9  drives  503 G 8  through the  503 S 5 &#39;s engagement to give third reduced speed at the output shaft  503 A 2 . The fourth forward speed ratio is established by engagement of synchronizers  503 S 4  only. This results in  503 G 1  driving  503 G 2  through the  503 S 4 &#39;s engagement to give fourth speed at the output shaft  503 A 2 . The fifth forward speed ratio is established by engagement of synchronizers  503 S 2  and  503 S 5 . This results in  503 G 7  driving  503 G 8  to give the fifth speed at the output shaft  503 A 2 . The reverse speed ratio is established by the engagements of synchronizer  503 S 1  and synchronizer  503 SR. This results in  503 G 4  driving  503 G 6  through the idler  503 G 5 . Since  503 G 6  and  503 GR 1  are linked through engagement of synchronizer  503 SR,  503 GR 1  drives  503 GR 2  through the idler  503 GI to give a reverse speed in reverse direction at the output shaft  503 A 2 . 
         [0076]    A powertrain system  601 , shown in  FIG. 7 , has a conventional engine  601 E and a six-speed transmission gearbox  601 G using nine forward driving gearwheels. 
         [0077]    The six-speed transmission gearbox  601 G includes a mechanical damper  601 D, which has connection between a main clutch  601 C 0  and an input shaft  601 A 1 .  601 G also includes forward driving gearwheels  601 G 1  and  601 G 3 , which are fixed on the input shaft  601 A 1  and the intermediate shaft  601 A 3 , respectively. A forward driving gearwheel  601 G 2  is free to rotate on the output shaft  601 A 2  to serve as an idler. The forward driving gearwheels  601 G 4 ,  601 G 5 ,  601 G 6 ,  601 G 7 ,  601 G 8  and  601 G 9  are free to rotate on input shaft  601 A 1 , the output shaft  601 A 2  which has a fixed output gearwheel  601 GO to transmit torque to a final drive(not shown) and an intermediate shaft  601 A 3 , respectively. They are also selectively interconnected with input shaft  601 A 1 , output shaft  601 A 2  and intermediate shaft  601 A 3  by clutches  601 C 1 ,  601 C 2 ,  601 C 3 ,  601 C 4 ,  601 C 5  and synchronizer  604 S 1 , respectively. The selective interconnection of  601 G 6  and  601 G 9  to the intermediate shaft  601 A 3  gives two different connections, i.e.  601 G 3  with  601 G 6  and  601 G 9 , and  601 G 6  with  601 G 9 . The synchronizer  601 S 1  is fixed on the intermediate shaft  601 A 3  and selectively interconnected with the linked  601 G 6  and  601 G 9 . The clutches  601 C 1  and  601 C 2  allow  601 G 4  and  601 G 7  to be selectively interconnected on the input shaft  601 A 1  and the clutches  601 C 3  and  601 C 4  also allow  601 G 5  and  601 G 8  to be selectively interconnected on the output shaft  601 A 2 , respectively.  601 G also has reverse gearwheel  601 GR 1  which is free to rotate on the intermediate shaft  601 A 3  and selectively interconnected with the intermediate shaft  601 A 3  through synchronizer  601 SR, gearwheel  601 GR 2  which is fixed on output shaft  601 A 2  and  601 GI which serves as an idler to enable  601 A 2  in the same rotating direction of  601 A 1 . The engagement and disengagement of the clutches are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0078]    A static truth table, shown in  FIG. 8 , gives shift sequence of transmission of  FIG. 7  and ratio steps between adjacent drive ratios. 
         [0079]    When a forward speed is accomplished, main clutch  601 C 0  is always engaged. In addition, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  601 C 3  and  601 S 1 . This results in gearwheel  601 G 1  driving gearwheel  601 G 3  through the idler  601 G 2 . Since  601 G 3  is linked to  601 G 9  by the synchronizer  601 S 1 ,  601 G 8  is driven by  601 G 9  to provide the first forward speed at the output shaft  601 A 2 . The second forward speed ratio is established by engagement of the synchronizer  601 S 1  and the clutch  601 C 4 . This results in gearwheel  601 G 1  driving gearwheel  601 G 3  through the idler  601 G 2 . Since  601 G 3  is linked to  601 G 6  by the synchronizer  601 S 1 ,  601 G 5  is driven by  601 G 6  to provide the second forward speed at the output shaft  601 A 2 . The third forward speed ratio is established by engagement of clutches  601 C 2  and  601 C 3 . This results in  601 G 7  driving  601 G 8  to give third reduced speed at the output shaft  601 A 2 . The fourth forward speed ratio is established by engagement of clutches  601 C 1  and  601 C 3 . This results in  601 G 4  driving  601 G 6  through the idler  601 G 5 . Since  601 G 6  and  601 G 9  are linked,  601 G 8  is driven by  601 G 9  to give fourth speed at the output shaft  601 A 2 . The fifth forward speed ratio is established by engagement of clutches  601 C 2  and  601 C 4 . This results in  601 G 7  driving  601 G 9  through the idler  601 G 8 . Since  601 G 6  and  601 G 9  are linked,  601 G 5  is driven by  601 G 6  to give fifth speed at the output shaft  601 A 2 . The sixth forward speed ratio is established by engagement of clutches  601 C 1  and  601 C 4 . This results in  601 G 4  driving  601 G 5  to give the sixth speed at the output shaft  601 A 2 . The reverse speed ratio is established by engagement of synchronizer  601 SR. This results in  601 G 1  driving  601 G 3  through the idler  601 G 2 . Since  601 G 3  and  601 GR 1  are linked through the engaged synchronizer  601 SR,  601 GR 1  drives  601 GR 2  through idler  601 GI to give a reverse speed at the output shaft  601 A 2 . 
         [0080]    A powertrain system  602 , shown in  FIG. 9 , has a conventional engine  602 E and a six-speed transmission gearbox  602 G using nine forward driving gearwheels. 
         [0081]    The six-speed transmission gearbox  602 G includes a torque converter  602 TC to be connected to an input shaft  602 A 1 .  602 G also includes forward driving gearwheels  602 G 1  and  602 G 3 , which are fixed on the input shaft  602 A 1  and the intermediate shaft  602 A 3 , respectively. A forward driving gearwheel  602 G 2  is free to rotate on the output shaft  602 A 2  to serve as an idler. The forward driving gearwheels  602 G 4 ,  602 G 5 ,  602 G 6 ,  602 G 7 ,  602 G 8  and  602 G 9  are free to rotate on input shaft  602 A 1 , the output shaft  602 A 2  which has a fixed output gearwheel  602 GO to transmit torque to a final drive(not shown) and an intermediate shaft  602 A 3 , respectively. They are also selectively interconnected with input shaft  602 A 1 , output shaft  602 A 2  and intermediate shaft  602 A 3  by clutches  602 C 1 ,  602 C 2 ,  602 C 3 ,  602 C 4 ,  602 C 5  and synchronizer  604 S 1 , respectively. The selective interconnection of  602 G 6  and  602 G 9  to the intermediate shaft  602 A 3  gives two different connections, i.e.  602 G 3  with  602 G 6  and  602 G 9 , and  602 G 6  with  602 G 9 . The synchronizer  602 S 1  is fixed on the intermediate shaft  602 A 3  and selectively interconnected with the linked  602 G 6  and  602 G 9 . The clutches  602 C 1  and  602 C 2  allow  602 G 4  and  602 G 7  to be selectively interconnected on the input shaft  602 A 1  and the clutches  602 C 3  and  602 C 4  also allow  602 G 5  and  602 G 8  to be selectively interconnected on the output shaft  602 A 2 , respectively.  602 G also has reverse gearwheel  602 GR 1  which is free to rotate on the intermediate shaft  602 A 3  and selectively interconnected with the intermediate shaft  602 A 3  through synchronizer  602 SR, gearwheel  602 GR 2  which is fixed on output shaft  602 A 2  and  602 GI which serves as an idler to enable  602 A 2  in the same rotating direction of  602 A 1 . The engagement and disengagement of the clutches are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0082]    A static truth table, shown in  FIG. 10 , gives shift sequence of transmission of  FIG. 9  and ratio steps between adjacent drive ratios. 
         [0083]    When a forward speed is accomplished, main clutch  602 C 0  is always engaged. In addition, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  602 C 3  and  602 S 1 . This results in gearwheel  602 G 1  driving gearwheel  602 G 3  through the idler  602 G 2 . Since  602 G 3  is linked to  602 G 9  by the synchronizer  602 S 1 ,  602 G 8  is driven by  602 G 9  to provide the first forward speed at the output shaft  602 A 2 . The second forward speed ratio is established by engagement of the synchronizer  602 S 1  and the clutch  602 C 4 . This results in gearwheel  602 G 1  driving gearwheel  602 G 3  through the idler  602 G 2 . Since  602 G 3  is linked to  602 G 6  by the synchronizer  602 S 1 ,  602 G 5  is driven by  602 G 6  to provide the second forward speed at the output shaft  602 A 2 . The third forward speed ratio is established by engagement of clutches  602 C 2  and  602 C 3 . This results in  602 G 7  driving  602 G 8  to give third reduced speed at the output shaft  602 A 2 . The fourth forward speed ratio is established by engagement of clutches  602 C 1  and  602 C 3 . This results in  602 G 4  driving  602 G 6  through the idler  602 G 5 . Since  602 G 6  and  602 G 9  are linked,  602 G 8  is driven by  602 G 9  to give fourth speed at the output shaft  602 A 2 . The fifth forward speed ratio is established by engagement of clutches  602 C 2  and  602 C 4 . This results in  602 G 7  driving  602 G 9  through the idler  602 G 8 . Since  602 G 6  and  602 G 9  are linked,  602 G 5  is driven by  602 G 6  to give fifth speed at the output shaft  602 A 2 . The sixth forward speed ratio is established by engagement of clutches  602 C 1  and  602 C 4 . This results in  602 G 4  driving  602 G 5  to give the sixth speed at the output shaft  602 A 2 . The reverse speed ratio is established by engagement of synchronizer  602 SR. This results in  602 G 1  driving  602 G 3  through the idler  602 G 2 . Since  602 G 3  and  602 GR 1  are linked through the engaged synchronizer  602 SR,  602 GR 1  drives  602 GR 2  through idler  602 GI to give a reverse speed at the output shaft  602 A 2 . 
         [0084]    A powertrain system  603 , shown in  FIG. 11 , has a conventional engine  603 E and a six-speed transmission gearbox  603 G using nine forward driving gearwheels. 
         [0085]    The six-speed transmission gearbox  603 G includes a mechanical damper  603 D, which has connection between a main clutch  603 C 0  and an input shaft  603 A 1 .  603 G also includes forward driving gearwheels  603 G 1  and  603 G 3 , which are fixed on the input shaft  603 A 1  and the intermediate shaft  603 A 3 , respectively. A forward driving gearwheel  603 G 2  is free to rotate on the output shaft  603 A 2  to serve as an idler. The forward driving gearwheels  603 G 4 ,  603 G 5 ,  603 G 6 ,  603 G 7 ,  603 G 8  and  603 G 9  are free to rotate on input shaft  603 A 1 , the output shaft  603 A 2  which has a fixed output gearwheel  603 GO to transmit torque to a final drive(not shown) and an intermediate shaft  603 A 3 , respectively. They are also selectively interconnected with input shaft  603 A 1 , output shaft  603 A 2  and intermediate shaft  603 A 3  by synchronizers  603 S 1 ,  603 S 2 ,  603 S 3 ,  603 S 4  and  603 S 5 , respectively. The selective interconnection of  603 G 6  and  603 G 9  to the intermediate shaft  603 A 3  gives two different connections, i.e.  603 G 3  with  603 G 6  and  603 G 9 , and  603 G 6  with  603 G 9 . The synchronizer  603 S 5  is fixed on the intermediate shaft  603 A 3  and selectively interconnected with the linked  603 G 6  and  603 G 9 . The synchronizers  603 S 1  and  603 S 2  allow  603 G 4  and  603 G 7  to be selectively interconnected on the input shaft  603 A 1  and the synchronizers  603 S 3  and  603 S 4  also allow  603 G 5  and  603 G 8  to be selectively interconnected on the output shaft  603 A 2 , respectively.  603 G also has reverse gearwheel  603 GR 1  which is free to rotate on the intermediate shaft  603 A 3  and selectively interconnected with the intermediate shaft  603 A 3  through synchronizer  603 SR, gearwheel  603 GR 2  which is fixed on output shaft  603 A 2  and  603 GI which serves as an idler to enable  603 A 2  in the same rotating direction of  603 A 1 . The engagement and disengagement of the synchronizers are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0086]    A static truth table, shown in  FIG. 12 , gives shift sequence of transmission of  FIG. 11  and ratio steps between adjacent drive ratios. 
         [0087]    When a forward speed is accomplished, main synchronizer  603 C 0  is always engaged. In addition, the following synchronizer and synchronizer engagements are applied. The first forward speed ratio is established by engagement of synchronizers  603 S 3  and  603 S 5 . This results in gearwheel  603 G 1  driving gearwheel  603 G 3  through the idler  603 G 2 . Since  603 G 3  is linked to  603 G 9  by the synchronizer  603 S 5 ,  603 G 8  is driven by  603 G 9  to provide the first forward speed at the output shaft  603 A 2 . The second forward speed ratio is established by engagement of the synchronizer  603 S 4  and the synchronizer  603 S 5 . This results in gearwheel  603 G 1  driving gearwheel  603 G 3  through the idler  603 G 2 . Since  603 G 3  is linked to  603 G 6  by the synchronizer  603 S 5 ,  603 G 5  is driven by  603 G 6  to provide the second forward speed at the output shaft  603 A 2 . The third forward speed ratio is established by engagement of synchronizers  603 S 2  and  603 S 3 . This results in  603 G 7  driving  603 G 8  to give third reduced speed at the output shaft  603 A 2 . The fourth forward speed ratio is established by engagement of synchronizers  603 S 1  and  603 S 3 . This results in  603 G 4  driving  603 G 6  through the idler  603 G 5 . Since  603 G 6  and  603 G 9  are linked,  603 G 8  is driven by  603 G 9  to give fourth speed at the output shaft  603 A 2 . The fifth forward speed ratio is established by engagement of synchronizers  603 S 2  and  603 S 4 . This results in  603 G 7  driving  603 G 9  through the idler  603 G 8 . Since  603 G 6  and  603 G 9  are linked,  603 G 5  is driven by  603 G 6  to give fifth speed at the output shaft  603 A 2 . The sixth forward speed ratio is established by engagement of synchronizers  603 S 1  and  603 S 4 . This results in  603 G 4  driving  603 G 5  to give the sixth speed at the output shaft  603 A 2 . The reverse speed ratio is established by engagement of synchronizer  603 SR. This results in  603 G 1  driving  603 G 3  through the idler  603 G 2 . Since  603 G 3  and  603 GR 1  are linked through the engaged synchronizer  603 SR,  603 GR 1  drives  603 GR 2  through idler  603 GI to give a reverse speed at the output shaft  603 A 2 . 
         [0088]    A powertrain system  604 , shown in  FIG. 13 , has a conventional engine  604 E and a six-speed transmission gearbox  604 G using ten forward driving gearwheels. 
         [0089]    The six-speed transmission gearbox  604 G includes a mechanical damper  604 D, which has connection between a main clutch  604 C 0  and an input shaft  604 A 1 .  604 G also includes forward driving gearwheels  604 G 1  and  604 G 3 , which are fixed on the input shaft  604 A 1  and the intermediate shaft  604 A 3 , respectively. Two linked forward driving gearwheels  604 G 2  and  604 G 2   a  are free to rotate on the output shaft  604 A 2  and they are selectively interconnected with the output shaft  604 A 2  by clutch  604 C 4 . The forward driving gearwheels  604 G 4 ,  604 G 6 ,  604 G 7 ,  604 G 8  and  604 G 9  are free to rotate and selectively interconnected with input shaft  604 A 1 , output shaft  604 A 2  which has a fixed output gearwheel  604 GO to transmit torque to a final drive(not shown) and intermediate shaft  604 A 3  by clutches  604 C 1 ,  604 C 2 ,  604 C 3 ,  604 C 5  and synchronizer  604 S 1 , respectively.  604 G 3 ,  604 G 6  and  604 G 9  are selectively interconnected to generate three different connections, i.e.  604 G 3  with  604 G 9 ,  604 G 3  with  604 G 6  and  604 G 9 , and  604 G 6  with  604 G 9 . The synchronizer  604 S 1  is fixed on the intermediate shaft  604 A 3  and selectively interconnected with  604 G 9 . The clutches  604 C 1  and  604 C 2  allow  604 G 4  and  604 G 7  to be selectively interconnected on the input shaft  604 A 1  and the clutches  604 C 3  and  604 C 4  also allow  604 G 8  and the linked  604 G 2  and  604 G 2   a  to be selectively interconnected on the output shaft  604 A 2 , respectively.  604 G also has a reverse gearwheel  604 GR 1  which is free to rotate and selectively interconnected with the intermediate shaft  604 A 3  through synchronizer  604 SR, gearwheel  604 GR 2  which is fixed on output shaft  604 A 2  and  604 GI which serves as an idler to provide the same rotating direction of  604 A 1 . The engagement and disengagement of the clutches are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0090]    A static truth table, shown in  FIG. 14 , gives shift sequence of transmission of  FIG. 13  and ratio steps between adjacent drive ratios. 
         [0091]    When a forward speed is accomplished, main clutch  604 C 0  is always engaged. In addition, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  604 C 3  and  604 S 1 . This results in gearwheel  604 G 1  driving the linked gearwheels  604 G 2  and  604 G 2   a.  Since  604 G 2   a  drives  604 G 3  and  604 G 3  is interconnected with  604 G 9  through the engagement of synchronizer  604 S 1 ,  604 G 8  is driven by  604 G 9  to provide first forward speed at the output shaft  604 A 2 . The second forward speed ratio is established by engagement of synchronizer  604 S 1  and  604 C 5 . This also results in gearwheel  604 G 1  driving linked gearwheels  604 G 2  and  604 G 2   a.  Since  604 G 2   a  drives  604 G 3  and  604 G 3  is connected with  604 G 6  through the engagements of clutch  604 C 5  and synchronizer  604 S 1 ,  604 G 5  is driven by  604 G 6  to provide the second forward speed at the output shaft  604 A 2 . When shifting from the first gear to the second gear, the relative slippery speed between the driving and driven clutch pads on  604 C 5  is reduced. The reason is that the driving clutch pad speed on intermediate shaft is reduced by the higher gear ratio of  604 G 1 ,  604 G 2 ,  604 G 2   a  and  604 G 3  while the driven clutch pad speed is reduced by lower gear ratio of  604 G 5  and  604 G 6 . This gives the lower relative speed of driving and driven clutch pads before the engagement of  604 C 5 . The third forward speed ratio is established by engagement of clutches  604 C 2  and  604 C 3 . This results in  604 G 7  driving  604 G 8  to give third reduced speed at the output shaft  604 A 2 . The fourth forward speed ratio is established by engagement of clutch  604 C 4  only. This results in  604 G 1  driving  604 G 2  to give fourth speed at the output shaft  604 A 2 . The fifth forward speed ratio is established by engagement of clutch  604 C 2  and  604 C 5 . This results in  604 G 7  driving  604 G 9  through the idler  604 G 8 . Since  604 G 9  is interconnected with  604 G 6  through the engagement of clutch  604 C 5 ,  604 G 5  is driven by  604 G 6  to give fifth speed at the output shaft  604 A 2 . The sixth forward speed ratio is established by engagement of clutches  604 C 1  only. This results in  604 G 4  driving  604 G 5  to give the sixth speed at the output shaft  604 A 2 . The reverse speed ratio is established by engagement of synchronizer  604 SR. This results in  604 G 1  driving  604 G 2  and  604 G 2   a  driving  604 G 3 . Since  604 G 3  and  604 GR 1  are interconnected through the engaged synchronizer  604 SR,  604 GR 1  drives  604 GR 2  through idler  604 GI to give a reverse speed at the output shaft  604 A 2 . 
         [0092]    A powertrain system  605 , shown in  FIG. 15 , has a conventional engine  605 E and a six-speed transmission gearbox  605 G using ten forward driving gearwheels. 
         [0093]    The six-speed transmission gearbox  605 G includes a torque converter  605 TC to be connected to an input shaft  605 A 1 .  605 G also includes forward driving gearwheels  605 G 1  and  605 G 3 , which are fixed on the input shaft  605 A 1  and the intermediate shaft  605 A 3 , respectively. Two linked forward driving gearwheels  605 G 2  and  605 G 2   a  are free to rotate on the output shaft  605 A 2  and they are selectively interconnected with the output shaft  605 A 2  by clutch  605 C 4 . The forward driving gearwheels  605 G 4 ,  605 G 6 ,  605 G 7 ,  605 G 8  and  605 G 9  are free to rotate and selectively interconnected with input shaft  605 A 1 , output shaft  605 A 2  which has a fixed output gearwheel  605 GO to transmit torque to a final drive(not shown) and intermediate shaft  605 A 3  by clutches  605 C 1 ,  605 C 2 ,  605 C 3 ,  605 C 5  and synchronizer  605 S 1 , respectively.  605 G 3 ,  605 G 6  and  605 G 9  are selectively interconnected to generate three different connections, i.e.  605 G 3  with  605 G 9 ,  605 G 3  with  605 G 6  and  605 G 9 , and  605 G 6  with  605 G 9 . The synchronizer  605 S 1  is fixed on the intermediate shaft  605 A 3  and selectively interconnected with  605 G 9 . The clutches  605 C 1  and  605 C 2  allow  605 G 4  and  605 G 7  to be selectively interconnected on the input shaft  605 A 1  and the clutches  605 C 3  and  605 C 4  also allow  605 G 8  and the linked  605 G 2  and  605 G 2   a  to be selectively interconnected on the output shaft  605 A 2 , respectively.  605 G also has a reverse gearwheel  605 GR 1  which is free to rotate and selectively interconnected with the intermediate shaft  605 A 3  through synchronizer  605 SR, gearwheel  605 GR 2  which is fixed on output shaft  605 A 2  and  605 GI which serves as an idler to provide the same rotating direction of  605 A 1 . The engagement and disengagement of the clutches are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0094]    A static truth table, shown in  FIG. 16 , gives shift sequence of transmission of  FIG. 15  and ratio steps between adjacent drive ratios. 
         [0095]    When a forward speed is accomplished, main clutch  605 C 0  is always engaged. In addition, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  605 C 3  and  605 S 1 . This results in gearwheel  605 G 1  driving the linked gearwheels  605 G 2  and  605 G 2   a.  Since  605 G 2   a  drives  605 G 3  and  605 G 3  is interconnected with  605 G 9  through the engagement of synchronizer  605 S 1 ,  605 G 8  is driven by  605 G 9  to provide first forward speed at the output shaft  605 A 2 . The second forward speed ratio is established by engagement of synchronizer  605 S 1  and  605 C 5 . This also results in gearwheel  605 G 1  driving linked gearwheels  605 G 2  and  605 G 2   a.  Since  605 G 2   a  drives  605 G 3  and  605 G 3  is connected with  605 G 6  through the engagements of clutch  605 C 5  and synchronizer  605 S 1 ,  605 G 5  is driven by  605 G 6  to provide the second forward speed at the output shaft  605 A 2 . When shifting from the first gear to the second gear, the relative slippery speed between the driving and driven clutch pads on  605 C 5  is reduced. The reason is that the driving clutch pad speed on intermediate shaft is reduced by the higher gear ratio of  605 G 1 ,  605 G 2 ,  605 G 2   a  and  605 G 3  while the driven clutch pad speed is reduced by lower gear ratio of  605 G 5  and  605 G 6 . This gives the lower relative speed of driving and driven clutch pads before the engagement of  605 C 5 . The third forward speed ratio is established by engagement of clutches  605 C 2  and  605 C 3 . This results in  605 G 7  driving  605 G 8  to give third reduced speed at the output shaft  605 A 2 . The fourth forward speed ratio is established by engagement of clutch  605 C 4  only. This results in  605 G 1  driving  605 G 2  to give fourth speed at the output shaft  605 A 2 . The fifth forward speed ratio is established by engagement of clutch  605 C 2  and  605 C 5 . This results in  605 G 7  driving  605 G 9  through the idler  605 G 8 . Since  605 G 9  is interconnected with  604 G 6  through the engagement of clutch  605 C 5 ,  605 G 5  is driven by  605 G 6  to give fifth speed at the output shaft  605 A 2 . The sixth forward speed ratio is established by engagement of clutches  605 C 1  only. This results in  605 G 4  driving  605 G 5  to give the sixth speed at the output shaft  605 A 2 . The reverse speed ratio is established by engagement of synchronizer  605 SR. This results in  605 G 1  driving  605 G 2  and  605 G 2   a  driving  605 G 3 . Since  605 G 3  and  605 GR 1  are interconnected through the engaged synchronizer  605 SR,  605 GR 1  drives  605 GR 2  through idler  605 GI to give a reverse speed at the output shaft  605 A 2 . 
         [0096]    A powertrain system  606 , shown in  FIG. 17 , has a conventional engine  606 E and a six-speed transmission gearbox  606 G using ten forward driving gearwheels. 
         [0097]    The six-speed transmission gearbox  606 G includes a mechanical damper  606 D, which has connection between a main clutch  606 C 0  and an input shaft  606 A 1 .  606 G also includes forward driving gearwheels  606 G 1 ,  606 G 3  and  601 G 8 , which are fixed on the input shaft  606 A 1 , the intermediate shaft  606 A 3  and output shaft  606 A 2 , respectively. Two linked forward driving gearwheels  606 G 2  and  606 G 2   a  are free to rotate on the output shaft  606 A 2  and they are selectively interconnected with the output shaft  606 A 2  by synchronizer  606 S 4 . The forward driving gearwheels  606 G 4 ,  606 G 5 ,  606 G 6 ,  606 G 7  and  606 G 9  are free to rotate and selectively interconnected with input shaft  606 A 1 , output shaft  606 A 2  and intermediate shaft  606 A 3  by synchronizers  606 S 1 ,  606 S 2 ,  606 S 3 ,  606 S 5  and  606 S 6 , respectively.  606 G 3 ,  606 G 6  and  606 G 9  are selectively interconnected by  606 S 5  and  606 S 6  to generate three different connections, i.e.  606 G 3  with  606 G 9 ,  606 G 3  with  606 G 6  and  606 G 9 , and  606 G 6  with  606 G 9 . The synchronizer  606 S 6  is fixed on the intermediate shaft  606 A 3  and selectively interconnected with  606 G 9 . The synchronizers  606 S 1  and  606 S 2  allow  606 G 4  and  606 G 7  to be selectively interconnected on the input shaft  606 A 1  and the synchronizers  606 S 3  and  606 S 4  also allow  606 G 5  and the linked  606 G 2  and  606 G 2   a  to be selectively interconnected on the output shaft  606 A 2 , respectively.  606 G also has reverse gearwheel  606 GR 1  which is free to rotate and selectively interconnected with the intermediate shaft  606 A 3  through synchronizer  606 SR, gearwheel  606 GR 2  which is fixed on output shaft  606 A 2  and  606 GI which serves as an idler provides the same rotating direction of  606 A 1 . The engagement and disengagement of the synchronizers are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0098]    A static truth table, shown in  FIG. 18 , gives shift sequence of transmission of  FIG. 17  and ratio steps between adjacent drive ratios. 
         [0099]    When a forward speed is accomplished, main synchronizer  606 C 0  is always engaged. In addition, the following synchronizer engagements are applied. The first forward speed ratio is established by engagement of synchronizers  606 S 3  and  606 S 6 . This results in gearwheel  606 G 1  driving linked gearwheels  606 G 2  and  606 G 2   a.  Since  606 G 2   a  drives  606 G 3  and  606 G 3  is interconnected with  606 G 6  through synchronizer  606 S 6 ,  606 G 5  is driven by  606 G 6  to provide first forward speed at the output shaft  606 A 2 . The second forward speed ratio is established by engagement of synchronizer  606 S 5  and  606 S 6 . This also results in gearwheel  606 G 1  driving linked gearwheels  606 G 2  and  606 G 2   a.  Since  606 G 2   a  drives  606 G 3  and  606 G 3  is interconnected with  606 G 9  through the engaged synchronizer  606 S 5 ,  606 G 8  is driven by  606 G 9  to provide the second forward speed at the output shaft  606 A 2 . The third forward speed ratio is established by engagement of synchronizers  606 S 2  and  606 S 3 . This results in  606 G 4  driving  606 G 5  to give third reduced speed at the output shaft  606 A 2 . The fourth forward speed ratio is established by engagement of synchronizer  606 S 4  only. This results in  606 G 1  driving  606 G 2  to give fourth speed at the output shaft  606 A 2 . The fifth forward speed ratio is established by engagement of synchronizer  606 S 2  and  606 S 5 . This results in  606 G 7  driving  606 G 9  through the idler  606 G 8 . Since  606 G 9  is interconnected with  606 G 6  through the engaged synchronizer  606 S 6 ,  606 G 5  is driven by  606 G 6  to give fifth speed at the output shaft  606 A 2 . The sixth forward speed ratio is established by engagement of synchronizers  606 S 1  only. This results in  606 G 7  driving  606 G 8  to give the sixth speed at the output shaft  606 A 2 . The reverse speed ratio is established by engagement of synchronizer  606 SR. This results in  606 G 1  driving  606 G 2  and  606 G 2   a  driving  606 G 3 . Since  606 G 3  and  606 GR 1  are interconnected through the engaged synchronizer  606 SR,  606 GR 1  drives  606 GR 2  through idler  606 GI to give a reverse speed at the output shaft  606 A 2 . 
         [0100]    A powertrain system  607 , shown in  FIG. 19 , has a conventional engine  607 E and a six-speed transmission gearbox  607 G using eleven forward driving gearwheels. 
         [0101]    The six-speed transmission gearbox  607 G includes a mechanical damper  607 D, which has connection between a main clutch  607 C 0  and an input shaft  607 A 1 , a torque converter  607 TC to be connected to an input shaft  607 A 1 .  607 G also includes forward driving gearwheels  607 G 1  and  607 G 3 , which are fixed on the input shaft  607 A 1  and the intermediate shaft  607 A 3 , respectively. Two linked forward driving gearwheels  607 G 2  and  607 G 2   a  are free to rotate on the output shaft  607 A 2  to serve as an idler. The forward driving gearwheels  607 G 4 ,  607 G 5 ,  607 G 5   a,    607 G 6 ,  607 G 7 ,  607 G 8  and  607 G 9  are free to rotate on input shaft  607 A 1 , output shaft  607 A 2  which has a fixed output gearwheel  607 GO to transmit torque to a final drive(not shown) and intermediate shaft  607 A 3 , respectively. They are also selectively interconnected with input shaft  607 A 1 , output shaft  607 A 2  and intermediate shaft  607 A 3  by clutches  607 C 1 ,  607 C 2 ,  607 C 3 ,  607 C 4 ,  607 C 5  and synchronizer  607 S 1 , respectively.  607 G 5  and  607 G 5   a  are linked gearwheels. The selective interconnection of  607 G 3 ,  607 G 6  and  607 G 9  to the intermediate shaft  607 A 3  gives three different connections, i.e.  607 G 3  with  607 G 9 ,  607 G 3  with  607 G 6  and  607 G 9 , and  607 G 6  with  607 G 9 . The synchronizer  607 S 1  is fixed on the intermediate shaft  607 A 3  and selectively interconnected with  607 G 6 . The clutches  607 C 1  and  607 C 2  allow  607 G 4  and  607 G 7  to be selectively interconnected on the input shaft  607 A 1  and the clutches  607 C 3  and  607 C 4  also allow linked  607 G 5  and  607 G 5   a  and  607 G 8  to be selectively interconnected on the output shaft  607 A 2 , respectively.  607 G also has reverse gearwheel  607 GR 1  which is free to rotate on the intermediate shaft  607 A 3  and selectively interconnected with the intermediate shaft  607 A 3  through synchronizer  607 SR, gearwheel  607 GR 2  which is fixed on output shaft  607 A 2  and  607 GI which serves as an idler to enable  607 A 2  in the same rotating direction of  607 A 1 . The engagement and disengagement of the clutches are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0102]    A static truth table, shown in  FIG. 20 , gives shift sequence of transmission of  FIG. 19  and ratio steps between adjacent drive ratios. 
         [0103]    When a forward speed is accomplished, main clutch  607 C 0  is always engaged. In addition, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  607 C 3  and synchronizer  607 S 1 . This results in gearwheel  607 G 1  driving gearwheel  607 G 3  through the linked idlers  607 G 2  and  607 G 2   a.  Since  607 G 3  is linked to  607 G 9  through clutch  607 C 3  and synchronizer  607 S 1 ,  607 G 8  is driven by  607 G 9  to provide the first forward speed at the output shaft  607 A 2 . The second forward speed ratio is established by engagement of synchronizer  607 S 1  and clutch  607 C 5 . This results in gearwheel  607 G 1  driving gearwheel  607 G 3  through the linked idlers  607 G 2  and  607 G 2   a.  Since  607 G 3  is linked to  607 G 6  through synchronizer  607 S 1 ,  607 G 5   a  is driven by  607 G 6  to provide the second forward speed at the output shaft  607 A 2 . When shifting from the first gear to the second gear, the relative slippery speed between the driving and driven clutch pads on  607 C 5  is reduced. The reason is that the driving clutch pad speed on intermediate shaft is reduced by the higher gear ratio of  607 G 1 ,  607 G 2 ,  607 G 2   a  and  607 G 3  while the driven clutch pad speed is reduced by lower gear ratio of  607 G 5  and  607 G 6 . This gives the lower relative speed of driving and driven clutch pads before the engagement of  607 C 5 . The third forward speed ratio is established by engagement of clutches  607 C 2  and  607 C 3 . This results in  607 G 7  driving  607 G 8  to give third forward speed at the output shaft  607 A 2 . The fourth forward speed ratio is established by engagement of clutch  607 C 4  only. This results in  607 G 1  driving  607 G 2  to give fourth speed at the output shaft  607 A 2 . The fifth forward speed ratio is established by engagement of clutches  607 C 2  and  607 C 5 . This results in  607 G 7  driving  607 G 9  through the idler  607 G 8 . Since  607 G 9  is linked to  607 G 6  through clutch  607 C 5 ,  607 G 5   a  is driven by  607 G 6  to give fifth speed at the output shaft  607 A 2 . The sixth forward speed ratio is established by engagement of clutches  607 C 1  only. This results in  607 G 4  driving  607 G 5  to give the sixth speed at the output shaft  607 A 2 . The reverse speed ratio is established by engagement of synchronizer  607 SR. This results in  607 G 1  driving  607 G 3  through the idler  607 G 2 . Since  607 G 3  and  607 GR 1  are linked through the engaged synchronizer  607 SR,  607 GR 1  drives  607 GR 2  through idler  607 GI to give a reverse speed at the output shaft  607 A 2 . 
         [0104]    A powertrain system  608 , shown in  FIG. 21 , has a conventional engine  608 E and a six-speed transmission gearbox  608 G using eleven forward driving gearwheels. 
         [0105]    The six-speed transmission gearbox  608 G includes a torque converter  608 TC to be connected to an input shaft  608 A 1 .  608 G also includes forward driving gearwheels  608 G 1  and  608 G 3 , which are fixed on the input shaft  608 A 1  and the intermediate shaft  608 A 3 , respectively. Two linked forward driving gearwheels  608 G 2  and  608 G 2   a  are free to rotate on the output shaft  608 A 2  to serve as an idler. The forward driving gearwheels  608 G 4 ,  608 G 5 ,  608 G 5   a,    608 G 6 ,  608 G 7 ,  608 G 8  and  608 G 9  are free to rotate on input shaft  608 A 1 , output shaft  608 A 2  which has a fixed output gearwheel  608 GO to transmit torque to a final drive(not shown) and intermediate shaft  608 A 3 , respectively. They are also selectively interconnected with input shaft  608 A 1 , output shaft  608 A 2  and intermediate shaft  608 A 3  by clutches  608 C 1 ,  608 C 2 ,  608 C 3 ,  608 C 4 ,  608 C 5  and synchronizer  608 S 1 , respectively.  608 G 5  and  608 G 5   a  are linked gearwheels. The selective interconnection of  608 G 3 ,  608 G 6  and  608 G 9  to the intermediate shaft  608 A 3  gives three different connections, i.e.  608 G 3  with  608 G 9 ,  608 G 3  with  608 G 6  and  608 G 9 , and  608 G 6  with  608 G 9 . The synchronizer  608 S 1  is fixed on the intermediate shaft  608 A 3  and selectively interconnected with  608 G 6 . The clutches  608 C 1  and  608 C 2  allow  608 G 4  and  608 G 7  to be selectively interconnected on the input shaft  608 A 1  and the clutches  608 C 3  and  608 C 4  also allow linked  608 G 5  and  608 G 5   a  and  608 G 8  to be selectively interconnected on the output shaft  608 A 2 , respectively.  608 G also has reverse gearwheel  608 GR 1  which is free to rotate on the intermediate shaft  608 A 3  and selectively interconnected with the intermediate shaft  608 A 3  through synchronizer  608 SR, gearwheel  608 GR 2  which is fixed on output shaft  608 A 2  and  608 GI which serves as an idler to enable  608 A 2  in the same rotating direction of  608 A 1 . The engagement and disengagement of the clutches are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0106]    A static truth table, shown in  FIG. 22 , gives shift sequence of transmission of  FIG. 21  and ratio steps between adjacent drive ratios. 
         [0107]    When a forward speed is accomplished, main clutch  608 C 0  is always engaged. In addition, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  608 C 3  and  608 S 1 . This results in gearwheel  608 G 1  driving gearwheel  608 G 3  through the linked idlers  608 G 2  and  608 G 2   a.  Since  608 G 3  is linked to  608 G 9  through clutch  608 C 3  and synchronizer  608 S 1 ,  608 G 8  is driven by  608 G 9  to provide the first forward speed at the output shaft  608 A 2 . The second forward speed ratio is established by engagement of synchronizer  608 S 1  and  608 C 5 . This results in gearwheel  608 G 1  driving gearwheel  608 G 3  through the linked idlers  608 G 2  and  608 G 2   a.  Since  608 G 3  is linked to  608 G 6  through synchronizer  608 S 1 ,  608 G 5   a  is driven by  608 G 6  to provide the second forward speed at the output shaft  608 A 2 . When shifting from the first gear to the second gear, the relative slippery speed between the driving and driven clutch pads on  608 C 5  is reduced. The reason is that the driving clutch pad speed on intermediate shaft is reduced by the higher gear ratio of  608 G 1 ,  608 G 2 ,  608 G 2   a  and  608 G 3  while the driven clutch pad speed is reduced by lower gear ratio of  608 G 5   a  and  608 G 6 . This gives the lower relative speed of driving and driven clutch pads before the engagement of  608 C 5 . The third forward speed ratio is established by engagement of clutches  608 C 2  and  608 C 3 . This results in  608 G 7  driving  608 G 8  to give third forward speed at the output shaft  608 A 2 . The fourth forward speed ratio is established by engagement of clutch  608 C 4  only. This results in  608 G 1  driving  608 G 2  to give fourth speed at the output shaft  608 A 2 . The fifth forward speed ratio is established by engagement of clutches  608 C 2  and  608 C 5 . This results in  608 G 7  driving  608 G 9  through the idler  608 G 8 . Since  608 G 9  is linked to  608 G 6  through clutch  608 C 5 ,  608 G 5   a  is driven by  608 G 6  to give fifth speed at the output shaft  608 A 2 . The sixth forward speed ratio is established by engagement of clutches  608 C 1  only. This results in  608 G 4  driving  608 G 5  to give the sixth speed at the output shaft  608 A 2 . The reverse speed ratio is established by engagement of synchronizer  608 SR. This results in  608 G 1  driving  608 G 3  through the idler  608 G 2 . Since  608 G 3  and  608 GR 1  are linked through the engaged synchronizer  608 SR,  608 GR 1  drives  608 GR 2  through idler  608 GI to give a reverse speed at the output shaft  608 A 2 . 
         [0108]    A powertrain system  609 , shown in  FIG. 23 , has a conventional engine  609 E and a six-speed transmission gearbox  609 G using eleven forward driving gearwheels. 
         [0109]    The six-speed transmission gearbox  609 G includes a mechanical damper  609 D, which has connection between a main clutch  609 C 0  and an input shaft  609 A 1 .  609 G also includes forward driving gearwheels  609 G 1 ,  609 G 3  and  601 G 8 , which are fixed on the input shaft  609 A 1 , the intermediate shaft  609 A 3  and output shaft  609 A 2 , respectively. Two linked forward driving gearwheels  609 G 2  and  609 G 2   a  are free to rotate on the output shaft  609 A 2  and they are selectively interconnected with the output shaft  609 A 2  by synchronizer  609 S 4 . The forward driving gearwheels  609 G 4 ,  609 G 5 ,  609 G 6 ,  609 G 7  and  609 G 9  are free to rotate and selectively interconnected with input shaft  609 A 1 , output shaft  609 A 2  which has a fixed output gearwheel  609 GO to transmit torque to a final drive(not shown) and intermediate shaft  609 A 3  by synchronizers  609 S 1 ,  609 S 2 ,  609 S 3 ,  609 S 5  and  609 S 6 , respectively.  609 G 6  and  609 G 9  are selectively interconnected by  609 S 5  and  609 S 6  to generate three different connections, i.e.  609 G 3  with  609 G 9 ,  609 G 3  with  609 G 6  and  609 G 9 , and  609 G 6  with  609 G 9 . The synchronizer  609 S 6  is fixed on the intermediate shaft  609 A 3  and selectively interconnected with  609 G 9 . The synchronizers  609 S 1  and  609 S 2  allow  609 G 4  and  609 G 7  to be selectively interconnected on the input shaft  609 A 1  and the synchronizers  609 S 3  and  609 S 4  also allow  609 G 5  and the linked  609 G 2  and  609 G 2   a  to be selectively interconnected on the output shaft  609 A 2 , respectively.  609 G also has reverse gearwheel  609 GR 1  which is free to rotate and selectively interconnected with the intermediate shaft  609 A 3  through synchronizer  609 SR, gearwheel  609 GR 2  which is fixed on output shaft  609 A 2  and  609 GI which serves as an idler provides the same rotating direction of  609 A 1 . The engagement and disengagement of the synchronizers are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0110]    A static truth table, shown in  FIG. 24 , gives shift sequence of transmission of  FIG. 23  and ratio steps between adjacent drive ratios. 
         [0111]    When a forward speed is accomplished, main clutch  609 C 0  is always engaged. In addition, the following synchronizer engagements are applied. The first forward speed ratio is established by engagement of synchronizers  609 S 3  and  609 S 6 . This results in gearwheel  609 G 1  driving linked gearwheels  609 G 2  and  609 G 2   a.  Since  609 G 2   a  drives  609 G 3  and  609 G 3  is linked with  609 G 6  through the engaged synchronizer  609 S 6 ,  609 G 5   a  is driven by  609 G 6  to provide first forward speed at the output shaft  609 A 2 . The second forward speed ratio is established by engagement of synchronizer  609 S 5  and  609 S 6 . This also results in gearwheel  609 G 1  driving linked gearwheels  609 G 2  and  609 G 2   a.  Since  609 G 2   a  drives  609 G 3  and  609 G 3  is linked with  609 G 9  through the engaged synchronizer  609 S 5 ,  609 G 8  is driven by  609 G 9  to provide the second forward speed at the output shaft  609 A 2 . The third forward speed ratio is established by engagement of synchronizers  609 S 2  and  609 S 3 . This results in  609 G 4  driving  609 G 5  to give third forward speed at the output shaft  609 A 2 . The fourth forward speed ratio is established by engagement of synchronizer  609 S 4  only. This results in  609 G 1  driving  609 G 2  to give fourth speed at the output shaft  609 A 2 . The fifth forward speed ratio is established by engagement of synchronizer  609 S 1  and  609 S 5 . This results in  609 G 4  driving  609 G 6  through the idler  609 G 5 . Since  609 G 6  is interconnected with  609 G 9  through the engaged synchronizer  609 S 5 ,  609 G 8   a  is driven by  609 G 9  to give fifth speed at the output shaft  609 A 2 . The sixth forward speed ratio is established by engagement of synchronizer  609 S 1  only. This results in  609 G 7  driving  609 G 8  to give the sixth speed at the output shaft  609 A 2 . The reverse speed ratio is established by engagement of synchronizer  609 SR. This results in  609 G 1  driving  609 G 2  and  609 G 2   a  driving  609 G 3 . Since  609 G 3  and  609 GR 1  are interconnected through the engaged synchronizer  609 SR,  609 GR 1  drives  609 GR 2  through idler  609 GI to give a reverse speed at the output shaft  609 A 2 . 
         [0112]    A powertrain system  701 , shown in  FIG. 25 , has a conventional engine  701 E and a seven-speed transmission gearbox  701 G using ten forward driving gearwheels. 
         [0113]    The seven-speed transmission gearbox  701 G includes a mechanical damper  701 D, which has connection between a main clutch  701 C 0  and an input shaft  701 A 1 .  701 G also includes forward driving gearwheels  701 G 1  and  701 G 3 , which are fixed on the input shaft  701 A 1  and the intermediate shaft  701 A 3 , respectively. Two linked forward driving gearwheel  701 G 2  and  701 G 2   a  are free to rotate on the output shaft  701 A 2  to serve as an idler. The forward driving gearwheels  701 G 4 ,  701 G 5 ,  701 G 6 ,  701 G 7 ,  701 G 8  and  701 G 9  are free to rotate on input shaft  701 A 1 , the output shaft  701 A 2 , which has a fixed output gearwheel  701 GO to transmit torque to a final drive(not shown), and an intermediate shaft  701 A 3 , respectively. They are also selectively interconnected with input shaft  701 A 1 , output shaft  701 A 2  and intermediate shaft  701 A 3  by clutches  701 C 1 ,  701 C 2 ,  701 C 3 ,  701 C 4 ,  701 C 5  and synchronizer  604 S 1 , respectively.  701 G 6  and  701 G 9  are linked and the synchronizer  701 S 1  is fixed on the intermediate shaft  701 A 3  and selectively interconnected with the linked  701 G 6  and  701 G 9 . The clutches  701 C 1  and  701 C 2  allow  701 G 4  and  701 G 7  to be selectively interconnected on the input shaft  701 A 1  and the clutches  701 C 3  and  701 C 4  allow  701 G 5  and  701 G 8  to be selectively interconnected on the output shaft  701 A 2 , respectively.  701 G also has a reverse gearwheel  701 GR 1  which is free to rotate on the intermediate shaft  701 A 3  and selectively interconnected with the intermediate shaft  701 A 3  through synchronizer  701 SR, gearwheel  701 GR 2  which is fixed on output shaft  701 A 2  and  701 GI which serves as an idler to enable  701 A 2  in the same rotating direction of  701 A 1 . The engagement and disengagement of the clutches are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0114]    A static truth table, shown in  FIG. 26 , gives shift sequence of transmission of  FIG. 25  and ratio steps between adjacent drive ratios. 
         [0115]    When a forward speed is accomplished, main clutch  701 C 0  is always engaged. In addition, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  701 C 3  and  701 S 1 . This results in gearwheel  701 G 1  driving gearwheel  701 G 3  through the linked idlers  701 G 2  and  701 G 2   a.  Since  701 G 3  is linked to  701 G 9  by the synchronizer  701 S 1 ,  701 G 8  is driven by  701 G 9  to provide the first forward speed at the output shaft  701 A 2 . The second forward speed ratio is established by engagement of the synchronizer  701 S 1  and the clutch  701 C 4 . This results in gearwheel  701 G 1  driving gearwheel  701 G 3  through the linked idlers  701 G 2  and  701 G 2   a.  Since  701 G 3  is linked to  701 G 6  by the synchronizer  701 S 1 ,  701 G 5  is driven by  701 G 6  to provide the second forward speed at the output shaft  701 A 2 . The third forward speed ratio is established by engagement of clutches  701 C 2  and  701 C 3 . This results in  701 G 7  driving  701 G 8  to give third speed at the output shaft  701 A 2 . The fourth forward speed ratio is established by engagement of clutches  701 C 1  and  701 C 3 . This results in  701 G 4  driving  701 G 6  through the idler  701 G 5 . Since  701 G 6  and  701 G 9  are linked,  701 G 8  is driven by  701 G 9  to give fourth forward speed at the output shaft  701 A 2 . The fifth forward speed ratio is established by engagement of clutch  701 C 5  only. This results in gearwheel  701 G 1  driving gearwheel  701 G 2  to give fifth speed at the output shaft  701 A 2 . The sixth forward speed ratio is established by engagement of clutches  701 C 2  and  701 C 4 . This results in  701 G 7  driving  701 G 9  through the idler  701 G 8 . Since  701 G 6  and  701 G 9  are linked,  701 G 5  is driven by  701 G 6  to give sixth speed at the output shaft  701 A 2 . The seventh forward speed ratio is established by engagement of clutches  701 C 1  and  701 C 4 . This results in  701 G 4  driving  701 G 5  to give the seventh speed at the output shaft  701 A 2 . The reverse speed ratio is established by engagement of synchronizer  701 SR. This results in  701 G 1  driving  701 G 3  through the idler  701 G 2 . Since  701 G 3  and  701 GR 1  are linked through the engaged synchronizer  701 SR,  701 GR 1  drives  701 GR 2  through idler  701 GI to give a reverse speed at the output shaft  701 A 2 . 
         [0116]    A powertrain system  702 , shown in  FIG. 27 , has a conventional engine  702 E and a seven-speed transmission gearbox  702 G using ten forward driving gearwheels. 
         [0117]    The seven-speed transmission gearbox  702 G includes a torque converter  602 TC to be connected to an input shaft  602 A 1 .  702 G also includes forward driving gearwheels  702 G 1  and  702 G 3 , which are fixed on the input shaft  702 A 1  and the intermediate shaft  702 A 3 , respectively. Two linked forward driving gearwheel  702 G 2  and  702 G 2   a  are free to rotate on the output shaft  702 A 2  to serve as an idler. The forward driving gearwheels  702 G 4 ,  702 G 5 ,  702 G 6 ,  702 G 7 ,  702 G 8  and  702 G 9  are free to rotate on input shaft  702 A 1 , the output shaft  702 A 2 , which has a fixed output gearwheel  702 GO to transmit torque to a final drive(not shown), and an intermediate shaft  702 A 3 , respectively. They are also selectively interconnected with input shaft  702 A 1 , output shaft  702 A 2  and intermediate shaft  702 A 3  by clutches  702 C 1 ,  702 C 2 ,  702 C 3 ,  702 C 4 ,  702 C 5  and synchronizer  604 S 1 , respectively.  702 G 6  and  702 G 9  are linked and the synchronizer  702 S 1  is fixed on the intermediate shaft  702 A 3  and selectively interconnected with the linked  702 G 6  and  702 G 9 . The clutches  702 C 1  and  702 C 2  allow  702 G 4  and  702 G 7  to be selectively interconnected on the input shaft  702 A 1  and the clutches  702 C 3  and  702 C 4  allow  702 G 5  and  702 G 8  to be selectively interconnected on the output shaft  702 A 2 , respectively.  702 G also has a reverse gearwheel  702 GR 1  which is free to rotate on the intermediate shaft  702 A 3  and selectively interconnected with the intermediate shaft  702 A 3  through synchronizer  702 SR, gearwheel  702 GR 2  which is fixed on output shaft  702 A 2  and  702 GI which serves as an idler to enable  702 A 2  in the same rotating direction of  702 A 1 . The engagement and disengagement of the clutches are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0118]    A static truth table, shown in  FIG. 28 , gives shift sequence of transmission of  FIG. 27  and ratio steps between adjacent drive ratios. 
         [0119]    When a forward speed is accomplished, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  702 C 3  and  702 S 1 . This results in gearwheel  702 G 1  driving gearwheel  702 G 3  through the linked idlers  702 G 2  and  702 G 2   a.  Since  702 G 3  is linked to  702 G 9  by the synchronizer  702 S 1 ,  702 G 8  is driven by  702 G 9  to provide the first forward speed at the output shaft  702 A 2 . The second forward speed ratio is established by engagement of the synchronizer  702 S 1  and the clutch  702 C 4 . This results in gearwheel  702 G 1  driving gearwheel  702 G 3  through the linked idlers  702 G 2  and  702 G 2   a.  Since  702 G 3  is linked to  702 G 6  by the synchronizer  702 S 1 ,  702 G 5  is driven by  702 G 6  to provide the second forward speed at the output shaft  702 A 2 . The third forward speed ratio is established by engagement of clutches  702 C 2  and  702 C 3 . This results in  702 G 7  driving  702 G 8  to give third speed at the output shaft  702 A 2 . The fourth forward speed ratio is established by engagement of clutches  702 C 1  and  702 C 3 . This results in  702 G 4  driving  702 G 6  through the idler  702 G 5 . Since  702 G 6  and  702 G 9  are linked,  702 G 8  is driven by  702 G 9  to give fourth forward speed at the output shaft  702 A 2 . The fifth forward speed ratio is established by engagement of clutch  702 C 5  only. This results in gearwheel  702 G 1  driving gearwheel  702 G 2  to give fifth speed at the output shaft  702 A 2 . The sixth forward speed ratio is established by engagement of clutches  702 C 2  and  702 C 4 . This results in  702 G 7  driving  702 G 9  through the idler  702 G 8 . Since  702 G 6  and  702 G 9  are linked,  702 G 5  is driven by  702 G 6  to give sixth speed at the output shaft  702 A 2 . The seventh forward speed ratio is established by engagement of clutches  702 C 1  and  702 C 4 . This results in  702 G 4  driving  702 G 5  to give the seventh speed at the output shaft  702 A 2 . The reverse speed ratio is established by engagement of synchronizer  702 SR. This results in  702 G 1  driving  702 G 3  through the idler  702 G 2 . Since  702 G 3  and  702 GR 1  are linked through the engaged synchronizer  702 SR,  702 GR 1  drives  702 GR 2  through idler  702 GI to give a reverse speed at the output shaft  702 A 2 . 
         [0120]    A powertrain system  703 , shown in  FIG. 29 , has a conventional engine  703 E and a seven-speed transmission gearbox  703 G using ten forward driving gearwheels. 
         [0121]    The seven-speed transmission gearbox  703 G includes a mechanical damper  703 D and a main clutch  703 C 0  to be connected to an input shaft  703 A 1 .  703 G also includes forward driving gearwheels  703 G 1  and  703 G 3 , which are fixed on the input shaft  703 A 1  and the intermediate shaft  703 A 3 , respectively. Two linked forward driving gearwheel  703 G 2  and  703 G 2   a  are free to rotate on the output shaft  703 A 2  to serve as an idler. The forward driving gearwheels  703 G 4 ,  703 G 5 ,  703 G 6 ,  703 G 7 ,  703 G 8  and  703 G 9  are free to rotate on input shaft  703 A 1 , the output shaft  703 A 2 , which has a fixed output gearwheel  703 GO to transmit torque to a final drive(not shown), and an intermediate shaft  703 A 3 , respectively. They are also selectively interconnected with input shaft  703 A 1 , output shaft  703 A 2  and intermediate shaft  703 A 3  by synchronizers  703 S 1 ,  703 S 2 ,  703 S 3 ,  703 S 4 ,  703 S 5  and  604 S 6 , respectively.  703 G 6  and  703 G 9  are linked and the synchronizer  703 S 6  is fixed on the intermediate shaft  703 A 3  and selectively interconnected with the linked  703 G 6  and  703 G 9 . The synchronizers  703 S 1  and  703 S 2  allow  703 G 4  and  703 G 7  to be selectively interconnected on the input shaft  703 A 1  and the synchronizers  703 S 3  and  703 S 4  allow  703 G 5  and  703 G 8  to be selectively interconnected on the output shaft  703 A 2 , respectively.  703 G also has a reverse gearwheel  703 GR 1  which is free to rotate on the intermediate shaft  703 A 3  and selectively interconnected with the intermediate shaft  703 A 3  through synchronizer  703 SR, gearwheel  703 GR 2  which is fixed on output shaft  703 A 2  and  703 GI which serves as an idler to enable  703 A 2  in the same rotating direction of  703 A 1 . The engagement and disengagement of the synchronizers are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0122]    A static truth table, shown in  FIG. 30 , gives shift sequence of transmission of  FIG. 29  and ratio steps between adjacent drive ratios. 
         [0123]    When a forward speed is accomplished, the following synchronizer and synchronizer engagements are applied. The first forward speed ratio is established by engagement of synchronizers  703 S 3  and  703 S 6 . This results in gearwheel  703 G 1  driving gearwheel  703 G 3  through the linked idlers  703 G 2  and  703 G 2   a.  Since  703 G 3  is linked to  703 G 9  by the synchronizer  703 S 6 ,  703 G 8  is driven by  703 G 9  to provide the first forward speed at the output shaft  703 A 2 . The second forward speed ratio is established by engagement of the synchronizers  703 S 6  and  703 S 4 . This results in gearwheel  703 G 1  driving gearwheel  703 G 3  through the linked idlers  703 G 2  and  703 G 2   a.  Since  703 G 3  is linked to  703 G 6  by the synchronizer  703 S 6 ,  703 G 5  is driven by  703 G 6  to provide the second forward speed at the output shaft  703 A 2 . The third forward speed ratio is established by engagement of synchronizers  703 S 2  and  703 S 3 . This results in  703 G 7  driving  703 G 8  to give third speed at the output shaft  703 A 2 . The fourth forward speed ratio is established by engagement of synchronizers  703 S 1  and  703 S 3 . This results in  703 G 4  driving  703 G 6  through the idler  703 G 5 . Since  703 G 6  and  703 G 9  are linked,  703 G 8  is driven by  703 G 9  to give fourth speed at the output shaft  703 A 2 . The fifth forward speed ratio is established by engagement of synchronizers  703 S 5  only. This results in  703 G 1  driving  703 G 2  to give fifth speed at the output shaft  703 A 2 . The sixth forward speed ratio is established by engagement of synchronizers  703 S 2  and  703 S 4 . This results in  703 G 7  driving  703 G 9  through the idler  703 G 8 . Since  703 G 6  and  703 G 9  are linked,  703 G 5  is driven by  703 G 6  to give sixth speed at the output shaft  703 A 2 . The seventh forward speed ratio is established by engagement of synchronizers  703 S 1  and  703 S 4 . This results in  703 G 4  driving  703 G 5  to give the seventh speed at the output shaft  703 A 2 . The reverse speed ratio is established by engagement of synchronizer  703 SR. This results in  703 G 1  driving  703 G 3  through the idler  703 G 2 . Since  703 G 3  and  703 GR 1  are linked through the engaged synchronizer  703 SR,  703 GR 1  drives  703 GR 2  through idler  703 GI to give a reverse speed at the output shaft  703 A 2 . 
         [0124]    A transmission gearbox  901 G, shown in  FIG. 31 , uses nine forward driving gearwheels for seven, eight and nine speeds.  901 G are driven by a conventional engine through either a torque converter, not shown, or through a mechanical damper with a main clutch, not shown, to the input shaft  901 A 1 . 
         [0125]    The transmission gearbox  901 G for seven, eight and nine speeds includes forward driving gearwheels,  901 G 1 ,  901 G 4  and  901 G 7  which are free to rotate on the input shaft  901 A 1 ,  901 G 2 ,  901 G 5  and  901 G 8  which are free to rotate on the output shaft  901 A 2 , and  901 G 3 , which is fixed on the intermediate shaft  901 A 3 .  901 G 2  is selectively interconnected with the output shaft  901 A 2  by clutch  901 C 5 . The forward driving gearwheels  901 G 1 ,  901 G 4  and  901 G 7  are selectively interconnected with input shaft  901 A 1  by clutches  901 C 1 ,  901 C 2  and  901 C 6 , respectively.  901 G 5  and  901 G 8  are selectively interconnected with output shaft  901 A 2  by clutches  901 C 4  and  901 C 3 , respectively.  901 G 6  and  901 G 9  are linked and the synchronizer  901 S 1  is fixed on the intermediate shaft  901 A 3 . The linked  901 G 6  and  901 G 9  are selectively interconnected with intermediate shaft  901 A 3  by synchronizer  901 S 1 .  901 G also has reverse gearwheel  901 GR 1  which is free to rotate and selectively interconnected with the intermediate shaft  901 A 3  through synchronizer  901 SR, gearwheel  901 GR 2  which is fixed on output shaft  901 A 2  and  901 GI which serves as an idler to provide the same rotating direction of  901 A 1 . The engagement and disengagement of the clutches are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0126]    A static truth table, shown in  FIG. 32 , gives shift sequence of seven-speed transmission gearbox of  FIG. 31  and ratio steps between adjacent drive ratios. 
         [0127]    When a forward speed is accomplished, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  901 C 5  and  901 C 6 . This results in gearwheel  901 G 1  driving linked gearwheels  901 G 2  to provide the first forward speed at the output shaft  901 A 2 . The second forward speed ratio is established by engagement of clutches  901 C 2 ,  901 C 5  and synchronizer  901 S 1 . This also results in gearwheel  901 G 7  driving  901 G 9  through the idler  901 G 8 . Since  901 G 9  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 2  is driven by  901 G 3  to provide the second forward speed at the output shaft  901 A 2 . The third forward speed ratio is established by the engagement of clutches  901 C 1 ,  901 C 5  and synchronizer  901 S 1 . This results in  901 G 4  driving  901 G 6  through the idler  901 G 5 . Since  901 G 6  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 2  is driven by  901 G 3  to provide the third forward speed at the output shaft  901 A 2 . The fourth forward speed ratio is established by engagement of clutches  901 C 3 ,  901 C 6  and synchronizer  901 S 1 . This results in  901 G 1  driving  901 G 3  through the idler  901 G 2 . Since  901 G 9  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 8  is driven by  901 G 9  to provide the fourth forward speed at the output shaft  901 A 2 . The fifth forward speed ratio is established by engagement of clutches  901 C 4 ,  901 C 6  and synchronizer  901 S 1 . This results in  901 G 1  driving  901 G 3  through the idler  901 G 2 . Since  901 G 6  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 5  is driven by  901 G 6  to provide the fifth forward speed at the output shaft  901 A 2 . The sixth forward speed ratio is established by engagement of clutches  901 C 2  and  901 C 3 . This results in  901 G 7  driving  901 G 8  to give the sixth speed at the output shaft  901 A 2 . After shifting from fifth to sixth gears, or shifting from sixth to fifth gears, the synchronizer  901 S 1 &#39;s engagement and disengagement do not affect the resulting gear ratio. The seventh forward speed ratio is established by engagement of clutches  901 C 1  and  901 C 3 . Since  901 G 4  drives  901 G 6  through the idler  901 G 5  and  901 G 9  is linked with  901 G 6 ,  901 G 8  is driven by  901 G 9  to provide seventh forward speed at the output shaft  901 A 2 . The reverse speed ratio is established by engagement of synchronizer  901 SR. This results in  901 G 1  driving  901 G 2  and  901 G 2   a  driving  901 G 3 . Since  901 G 3  and  901 GR 1  are interconnected through the engaged synchronizer  901 SR,  901 GR 1  drives  901 GR 2  through idler  901 G 1  to give a reverse speed at the output shaft  901 A 2 . 
         [0128]    A static truth table, shown in  FIG. 33 , gives shift sequence of eight-speed transmission gearbox of  FIG. 31  and ratio steps between adjacent drive ratios. 
         [0129]    When a forward speed is accomplished for eight-speed transmission gearbox, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  901 C 5  and  901 C 6 . This results in gearwheel  901 G 1  driving linked gearwheels  901 G 2  to provide the first forward speed at the output shaft  901 A 2 . The second forward speed ratio is established by engagement of clutches  901 C 2 ,  901 C 5  and synchronizer  901 S 1 . This also results in gearwheel  901 G 7  driving  901 G 9  through the idler  901 G 8 . Since  901 G 9  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 2  is driven by  901 G 3  to provide the second forward speed at the output shaft  901 A 2 . The third forward speed ratio is established by the engagement of clutches  901 C 1 ,  901 C 5  and synchronizer  901 S 1 . This results in  901 G 4  driving  901 G 6  through the idler  901 G 5 . Since  901 G 6  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 2  is driven by  901 G 3  to provide the third forward speed at the output shaft  901 A 2 . The fourth forward speed ratio is established by engagement of clutches  901 C 3 ,  901 C 6  and synchronizer  901 S 1 . This results in  901 G 1  driving  901 G 3  through the idler  901 G 2 . Since  901 G 9  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 8  is driven by  901 G 9  to provide the fourth forward speed at the output shaft  901 A 2 . The fifth forward speed ratio is established by engagement of clutches  901 C 4 ,  901 C 6  and synchronizer  901 S 1 . This results in  901 G 1  driving  901 G 3  through the idler  901 G 2 . Since  901 G 6  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 5  is driven by  901 G 6  to provide the fifth forward speed at the output shaft  901 A 2 . The sixth forward speed ratio is established by engagement of clutches  901 C 2  and  901 C 3 . This results in  901 G 7  driving  901 G 8  to give the sixth speed at the output shaft  901 A 2 . After shifting from fifth to sixth gears, or shifting from sixth to fifth gears, the synchronizer  901 S 1 &#39;s engagement or disengagement do not affect the resulting gear ratio. The seventh forward speed ratio is established by engagement of clutches  901 C 1  and  901 C 3 . Since  901 G 4  drives  901 G 6  through the idler  901 G 5  and  901 G 9  is linked with  901 G 6 ,  901 G 8  is driven by  901 G 9  to provide seventh forward speed at the output shaft  901 A 2 . The eighth forward speed ratio established by engagement of clutches  901 C 2  and  901 C 4 . This results in  901 G 7  driving  901 G 9  through the idler  901 G 8 . Since  901 G 6  and  901 G 9  are linked,  901 G 5  is driven by  901 G 6  to provide eighth forward speed at the output shaft  901 A 2 . The reverse speed ratio is established by engagement of synchronizer  901 SR. This results in  901 G 1  driving  901 G 2  and  901 G 2   a  driving  901 G 3 . Since  901 G 3  and  901 GR 1  are interconnected through the engaged synchronizer  901 SR,  901 GR 1  drives  901 GR 2  through idler  901 GI to give a reverse speed at the output shaft  901 A 2 . 
         [0130]    A static truth table, shown in  FIG. 34 , gives shift sequence of nine-speed transmission gearbox of  FIG. 31  and ratio steps between adjacent drive ratios. 
         [0131]    When a forward speed is accomplished for nine-speed transmission gearbox, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  901 C 5  and  901 C 6 . This results in gearwheel  901 G 1  driving linked gearwheels  901 G 2  to provide the first forward speed at the output shaft  901 A 2 . The second forward speed ratio is established by engagement of clutches  901 C 2 ,  901 C 5  and synchronizer  901 S 1 . This also results in gearwheel  901 G 7  driving  901 G 9  through the idler  901 G 8 . Since  901 G 9  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 2  is driven by  901 G 3  to provide the second forward speed at the output shaft  901 A 2 . The third forward speed ratio is established by the engagement of clutches  901 C 1 ,  901 C 5  and synchronizer  901 S 1 . This results in  901 G 4  driving  901 G 6  through the idler  901 G 5 . Since  901 G 6  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 2  is driven by  901 G 3  to provide the third forward speed at the output shaft  901 A 2 . The fourth forward speed ratio is established by engagement of clutches  901 C 3 ,  901 C 6  and synchronizer  901 S 1 . This results in  901 G 1  driving  901 G 3  through the idler  901 G 2 . Since  901 G 9  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 8  is driven by  901 G 9  to provide the fourth forward speed at the output shaft  901 A 2 . The fifth forward speed ratio is established by engagement of clutches  901 C 4 ,  901 C 6  and synchronizer  901 S 1 . This results in  901 G 1  driving  901 G 3  through the idler  901 G 2 . Since  901 G 6  and  901 G 3  are interconnected through the engagement of synchronizer  901 S 1 ,  901 G 5  is driven by  901 G 6  to provide the fifth forward speed at the output shaft  901 A 2 . The sixth forward speed ratio is established by engagement of clutches  901 C 2  and  901 C 3 . This results in  901 G 7  driving  901 G 8  to give the sixth speed at the output shaft  901 A 2 . After shifting from fifth to sixth gears, or shifting from sixth to fifth gears, the synchronizer  901 S 1 &#39;s engagement or disengagement do not affect the resulting gear ratio. The seventh forward speed ratio is established by engagement of clutches  901 C 1  and  901 C 3 . Since  901 G 4  drives  901 G 6  through the idler  901 G 5  and  901 G 9  is linked with  901 G 6 ,  901 G 8  is driven by  901 G 9  to provide seventh forward speed at the output shaft  901 A 2 . The eighth forward speed ratio established by engagement of clutches  901 C 2  and  901 C 4 . This results in  901 G 7  driving  901 G 9  through the idler  901 G 8 . Since  901 G 6  and  901 G 9  are linked,  901 G 5  is driven by  901 G 6  to provide eighth forward speed at the output shaft  901 A 2 . The ninth forward speed ratio established by engagement of clutches  901 C 1  and  901 C 4 . This results in  901 G 4  driving  901 G 5  to provide ninth forward speed at the output shaft  901 A 2 . The reverse speed ratio is established by engagement of synchronizer  901 SR. This results in  901 G 1  driving  901 G 2  and  901 G 2   a  driving  901 G 3 . Since  901 G 3  and  901 GR 1  are interconnected through the engaged synchronizer  901 SR,  901 GR 1  drives  901 GR 2  through idler  901 GI to give a reverse speed at the output shaft  901 A 2 . 
         [0132]    A powertrain system  902  with a transmission gearbox  902 G, shown in  FIG. 35 , uses nine forward driving gearwheels for seven, eight and nine speeds.  902 G is driven by a conventional engine through a mechanical damper  902 D with a main clutch  902 C 0  to the input shaft  902 A 1 . 
         [0133]    The clutches are replaced with synchronizers as torque transmitting mechanisms in the transmission gearbox  901 G in  FIG. 31  to become automated manual transmission gearbox  902 G, shown in  FIG. 35. 902G  is driven by a conventional engine  902 E through a mechanical damper  902 D with a main clutch  902 C 0  to the input shaft  902 A 1 . 
         [0134]    A static truth table, shown in  FIG. 36 , gives shift sequence of seven-speed transmission gearbox of  FIG. 35  and ratio steps between adjacent drive ratios. 
         [0135]    A static truth table, shown in  FIG. 37 , gives shift sequence of eight-speed transmission gearbox of  FIG. 35  and ratio steps between adjacent drive ratios. 
         [0136]    A static truth table, shown in  FIG. 38 , gives shift sequence of nine-speed transmission gearbox of  FIG. 35  and ratio steps between adjacent drive ratios. 
         [0137]    A transmission gearbox  903 G, shown in  FIG. 39 , uses ten forward driving gearwheels for seven, eight and nine speeds.  903 G are driven by a conventional engine through a torque converter, not shown, or through a mechanical damper with a main clutch, not shown, to the input shaft  903 A 1 . 
         [0138]    The transmission gearbox  903 G for seven, eight and nine speeds includes forward driving gearwheels,  903 G 1 ,  903 G 4  and  903 G 7  which are free to rotate on the input shaft  903 A 1 ,  903 G 2 ,  903 G 2   a,    903 G 5  and  903 G 8  which are free to rotate on the output shaft  903 A 2 , and  903 G 3 , which is fixed on the intermediate shaft  903 A 3 .  903 G 2  and  903 G 2   a  are linked and are selectively interconnected with the output shaft  903 A 2  by clutch  903 C 5 . The forward driving gearwheels  903 G 1 ,  903 G 4  and  903 G 7  are selectively interconnected with input shaft  903 A 1  by clutches  903 C 1 ,  903 C 2  and  903 C 6 , respectively.  903 G 5  and  903 G 8  are selectively interconnected with output shaft  903 A 2  by clutches  903 C 4  and  903 C 3 , respectively.  903 G 6  and  903 G 9  are linked and the synchronizer  903 S 1  is fixed on the intermediate shaft  903 A 3 . The linked  903 G 6  and  903 G 9  are selectively interconnected with intermediate shaft  903 A 3  by synchronizer  903 S 1 .  903 G also has reverse gearwheel  903 GR 1  which is free to rotate and selectively interconnected with the intermediate shaft  903 A 3  through synchronizer  903 SR, gearwheel  903 GR 2  which is fixed on output shaft  903 A 2  and  903 GI which serves as an idler to provide the same rotating direction of  903 A 1 . The engagement and disengagement of the clutches are controlled by conventional electro-hydraulic mechanism, not shown, which includes a programmable digital computer. Such control mechanisms are well known to those skilled in the art. 
         [0139]    A static truth table, shown in  FIG. 40 , gives shift sequence of seven-speed transmission gearbox of  FIG. 39  and ratio steps between adjacent drive ratios. 
         [0140]    When a forward speed is accomplished, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  903 C 3 ,  903 C 6  and  903 S 1 . This results in gearwheel  903 G 1  driving linked gearwheels  903 G 2  and  903 G 2   a.  Since  903 G 2   a  drives  903 G 3  and  903 G 3  is interconnected with  903 G 9  through synchronizer  903 S 1 ,  903 G 8  is driven by  903 G 9  to provide first forward speed at the output shaft  903 A 2 . The second forward speed ratio is established by engagement of clutches  903 C 4 ,  903 C 6  and synchronizer  903 S 1 . This also results in gearwheel  903 G 1  driving linked gearwheels  903 G 2  and  903 G 2   a.  Since  903 G 2   a  drives  903 G 3  and  903 G 3  is interconnected with  903 G 6  through clutches  903 C 2  and  903 C 3 ,  903 G 5  is driven by  903 G 6  to provide the second forward speed at the output shaft  903 A 2 . The third forward speed ratio is established by engagement of clutches  903 C 2  and  903 C 3 . This results in  903 G 7  driving  903 G 8  to give the third forward speed at the output shaft  903 A 2 . After shifting from second to third gear or from third to second gear, the synchronizer  903 S 1 &#39;s engagement or disengagement do not affect the resulting gear ratio. The fourth forward speed ratio is established by engagement of clutches  903 C 1  and  903 C 3 . Since  903 G 4  drives  903 G 6  through the idler  903 G 5  and  903 G 9  and  903 G 6  are linked,  903 G 8  is driven by  903 G 9  to provide fourth forward speed at the output shaft  903 A 2 . The fifth forward speed ratio is established by engagement of clutches  903 C 5  and  903 C 6 . This results in  903 G 1  driving  903 G 2  to give fifth speed at the output shaft  903 A 2 . The sixth forward speed ratio is established by engagement of clutches  903 C 2  and  903 C 4 . This results in  903 G 7  driving  903 G 9  through the idler  903 G 8 . Since  903 G 9  and  903 G 6  are linked,  903 G 5  is driven by  903 G 6  to give the sixth speed at the output shaft  903 A 2 . The seventh forward speed ratio is established by engagement of clutches  903 C 1  and  903 C 4 . This results in  903 G 4  driving  903 G 5  to provide seventh forward speed at the output shaft  903 A 2 . The reverse speed ratio is established by engagement of synchronizer  903 SR. This results in  903 G 1  driving  903 G 2  and  903 G 2   a  driving  903 G 3 . Since  903 G 3  and  903 GR 1  are interconnected through the engaged synchronizer  903 SR,  903 GR 1  drives  903 GR 2  through idler  903 GI to give a reverse speed at the output shaft  903 A 2 . 
         [0141]    A static truth table, shown in  FIG. 41 , gives shift sequence of eight-speed transmission gearbox of  FIG. 39  and ratio steps between adjacent drive ratios. 
         [0142]    When a forward speed is accomplished, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  903 C 3 ,  903 C 6  and  903 S 1 . This results in gearwheel  903 G 1  driving linked gearwheels  903 G 2  and  903 G 2   a.  Since  903 G 2   a  drives  903 G 3  and  903 G 3  is interconnected with  903 G 9  through synchronizer  903 S 1 ,  903 G 8  is driven by  903 G 9  to provide first forward speed at the output shaft  903 A 2 . The second forward speed ratio is established by engagement of clutches  903 C 4 ,  903 C 6  and synchronizer  903 S 1 . This also results in gearwheel  903 G 1  driving linked gearwheels  903 G 2  and  903 G 2   a.  Since  903 G 2   a  drives  903 G 3  and  903 G 3  is interconnected with  903 G 6  through clutches  903 C 2  and  903 C 3 ,  903 G 5  is driven by  903 G 6  to provide the second forward speed at the output shaft  903 A 2 . The third forward speed ratio is established by engagement of clutches  903 C 2  and  903 C 3 . This results in  903 G 7  driving  903 G 8  to give the third forward speed at the output shaft  903 A 2 . After shifting from second to third gear or from third to second gear, the synchronizer  903 S 1 &#39;s engagement or disengagement do not affect the resulting gear ratio. The fourth forward speed ratio is established by engagement of clutches  903 C 1  and  903 C 3 . Since  903 G 4  drives  903 G 6  through the idler  903 G 5  and  903 G 9  and  903 G 6  are linked,  903 G 8  is driven by  903 G 9  to provide fourth forward speed at the output shaft  903 A 2 . The fifth forward speed ratio is established by engagement of clutches  903 C 5  and  903 C 6 . This results in  903 G 1  driving  903 G 2  to give fifth speed at the output shaft  903 A 2 . The sixth forward speed ratio is established by engagement of clutches  903 C 2  and  903 C 4 . This results in  903 G 7  driving  903 G 9  through the idler  903 G 8 . Since  903 G 9  and  903 G 6  are linked,  903 G 5  is driven by  903 G 6  to give the sixth speed at the output shaft  903 A 2 . The seventh forward speed ratio is established by engagement of clutches  903 C 1  and  903 C 4 . This results in  903 G 4  driving  903 G 5  to provide seventh forward speed at the output shaft  903 A 2 . The eighth forward speed ratio established by engagement of clutches  903 C 2  and  903 C 5  and synchronizer  903 S 1 . This results in  903 G 7  driving  903 G 9  through the idler  903 G 8 . Since  903 G 9  is interconnected with  903 G 3  through synchronizer  903 S 1 ,  903 G 2   a  is driven by  903 G 3  to provide eighth forward speed at the output shaft  903 A 2 . The reverse speed ratio is established by engagement of synchronizer  903 SR. This results in  903 G 1  driving  903 G 2  and  903 G 2   a  driving  903 G 3 . Since  903 G 3  and  903 GR 1  are interconnected through the engaged synchronizer  903 SR,  903 GR 1  drives  903 GR 2  through idler  903 GI to give a reverse speed at the output shaft  903 A 2 . 
         [0143]    A static truth table, shown in  FIG. 42 , gives shift sequence of nine-speed transmission gearbox of  FIG. 39  and ratio steps between adjacent drive ratios. 
         [0144]    When a forward speed is accomplished, the following clutch and synchronizer engagements are applied. The first forward speed ratio is established by engagement of clutches  903 C 3 ,  903 C 6  and  903 S 1 . This results in gearwheel  903 G 1  driving linked gearwheels  903 G 2  and  903 G 2   a.  Since  903 G 2   a  drives  903 G 3  and  903 G 3  is interconnected with  903 G 9  through synchronizer  903 S 1 ,  903 G 8  is driven by  903 G 9  to provide first forward speed at the output shaft  903 A 2 . The second forward speed ratio is established by engagement of clutches  903 C 4 ,  903 C 6  and synchronizer  903 S 1 . This also results in gearwheel  903 G 1  driving linked gearwheels  903 G 2  and  903 G 2   a.  Since  903 G 2   a  drives  903 G 3  and  903 G 3  is interconnected with  903 G 6  through clutches  903 C 2  and  903 C 3 ,  903 G 5  is driven by  903 G 6  to provide the second forward speed at the output shaft  903 A 2 . The third forward speed ratio is established by engagement of clutches  903 C 2  and  903 C 3 . This results in  903 G 7  driving  903 G 8  to give the third forward speed at the output shaft  903 A 2 . After shifting from second to third gear or from third to second gear, the synchronizer  903 S 1 &#39;s engagement or disengagement do not affect the resulting gear ratio. The fourth forward speed ratio is established by engagement of clutches  903 C 1  and  903 C 3 . Since  903 G 4  drives  903 G 6  through the idler  903 G 5  and  903 G 9  and  903 G 6  are linked,  903 G 8  is driven by  903 G 9  to provide fourth forward speed at the output shaft  903 A 2 . The fifth forward speed ratio is established by engagement of clutches  903 C 5  and  903 C 6 . This results in  903 G 1  driving  903 G 2  to give fifth speed at the output shaft  903 A 2 . The sixth forward speed ratio is established by engagement of clutches  903 C 2  and  903 C 4 . This results in  903 G 7  driving  903 G 9  through the idler  903 G 8 . Since  903 G 9  and  903 G 6  are linked,  903 G 5  is driven by  903 G 6  to give the sixth speed at the output shaft  903 A 2 . The seventh forward speed ratio is established by engagement of clutches  903 C 1  and  903 C 4 . This results in  903 G 4  driving  903 G 5  to provide seventh forward speed at the output shaft  903 A 2 . The eighth forward speed ratio established by engagement of clutches  903 C 2  and  903 C 5  and synchronizer  903 S 1 . This results in  903 G 7  driving  903 G 9  through the idler  903 G 8 . Since  903 G 9  is interconnected with  903 G 3  through synchronizer  903 S 1 ,  903 G 2   a  is driven by  903 G 3  to provide eighth forward speed at the output shaft  903 A 2 . The ninth forward speed ratio established by engagement of clutches  903 C 1  and  903 C 5  and synchronizer  903 S 1 . This results in  903 G 4  driving  903 G 6  through the idler  903 G 5 . Since  903 G 6  is interconnected with  903 G 3  through synchronizer  903 S 1 ,  903 G 2   a  is driven by  903 G 3  to provide ninth forward speed at the output shaft  903 A 2 . The reverse speed ratio is established by engagement of synchronizer  903 SR. This results in  903 G 1  driving  903 G 2  and  903 G 2   a  driving  903 G 3 . Since  903 G 3  and  903 GR 1  are interconnected through the engaged synchronizer  903 SR,  903 GR 1  drives  903 GR 2  through idler  903 GI to give a reverse speed at the output shaft  903 A 2 . 
         [0145]    A powertrain system  904  with a transmission gearbox  904 G, shown in  FIG. 43 , uses ten forward driving gearwheels for seven, eight and nine speeds.  904 G is driven by a conventional engine through a mechanical damper  904 D with a main clutch  904 C 0  to the input shaft  904 A 1 . 
         [0146]    The clutches are replaced with synchronizers as torque transmitting mechanisms in the transmission gearbox  903 G in  FIG. 39  to become automated manual transmission gearbox  904 G, shown in  FIG. 43. 904G  is driven by a conventional engine  904 E through a mechanical damper  904 D with a main clutch  904 C 0  to the input shaft  904 A 1 . 
         [0147]    A static truth table, shown in  FIG. 44 , gives shift sequence of seven-speed transmission gearbox of  FIG. 43  and ratio steps between adjacent drive ratios. 
         [0148]    A static truth table, shown in  FIG. 45 , gives shift sequence of eight-speed transmission gearbox of  FIG. 43  and ratio steps between adjacent drive ratios. 
         [0149]    A static truth table, shown in  FIG. 46 , gives shift sequence of nine-speed transmission gearbox of  FIG. 43  and ratio steps between adjacent drive ratios.