Abstract:
A geared continuously variable transmission (GCVT) is provided. The GCVT includes a first set of solar gears having a first solar gear and first plurality of connection components. Power enters the GCVT through the first set of solar gears. The GCVT includes a second set of solar gears having a second solar gear and second plurality of connection components. Power exits the GCVT through the second set of solar gears. Power is transmitted from the first set of solar gears to the second set of solar gears via the first plurality of connection components and the second plurality of connection components. The GCVT includes a hydraulic pump and a hydraulic motor connecting first component from the first plurality of connection components to second component from the second plurality of connection components and providing constant rotation ratio between the first component and the second component.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims the benefit of priority to Iran patent application serial number 139350140003006972 filed on Sep. 22, 2014, which subsequently issued as Iran patent number 85650 on May 13, 2015, and to PCT/IB32015/057273 filed on Sep. 21, 2015, all of which are incorporated by reference herein in their entireties. 
       TECHNICAL FIELD 
       [0002]    The present application relates generally to transmissions and, more particularly, to a geared continuously variable transmission (GCVT) for producing high torque output, high power transmission and efficiency of the transmission. 
       BACKGROUND 
       [0003]    Transmissions are used in transportation, agricultural and construction equipment to transmit power from power sources, such as internal combustion engines to equipment for accomplishing a desired task. For example, transmissions are used to properly transmit power to the wheels of a vehicle, or to a vehicle implement. Various industries use gear mechanisms for transmission and conversion of engine power. Various gearbox types such as, for example, gearboxes with constant or variable transmission rates are used. Gearboxes have multiple advantages such as capability of transmission of high torques, low depreciation rate, constant transmission for a selected rotation rate, and high efficiency. However, despite of multiple advantages, the gearboxes have disadvantages such as, for example, limited number of transmission rates, and stepwise (non-linear) transmission rates, which can lower efficiency and cause difficulty in selection of a suitable torque. 
         [0004]    Continuously variable transmission (CVT) can be used to overcome the above mentioned disadvantages of gearboxes. A continuously variable transmission (CVT) is a transmission that can change through an infinite number of effective gear ratios between a minimum and a maximum range. In contrast, non-CVT transmissions offer a fixed number of gear ratios. Specifically, hydrostatic CVTs may use a variable displacement pump and a hydraulic motor and transmit power using hydraulic fluid. A swash plate may be used within the variable displacement pump to vary the output of the hydrostatic CVT by adjusting the fluid flowing into the hydraulic motor. Thus, the swash plate may enable the hydrostatic CVT to be continuously variable. Some hydrostatic CVTs may be combined with gear assemblies, drive shafts, and clutches to create a hydro-mechanical CVT. It may be appreciated that in certain applications, such as in construction equipment, a high torque output may be utilized by implements of the construction equipment. Further, a high torque output may be beneficial for low speed movement of vehicles, such as construction vehicles or agricultural vehicles. 
         [0005]    In CVTs, transmission rate between an input shaft and an output shaft can be changed continuously in a linear manner such that infinite number of transmission rates is available between predefined lower and upper limits. In a CVT, transmission is provided by friction between parts of the CVT. For example, in a belt driven CVT, friction between a belt and a pulley and in a toroidal CVT, friction between a toroid and disks of the CVT cause the transmission. 
         [0006]    However, using the friction mechanism in CVTs cause problems such as limited transmission capability, high depreciation, low efficiency, and lack of stability in the selected revolution. Hence there is a need for a GCVT to produce efficient transmission with continuous/linear variation and high torque output and high power transmission 
       SUMMARY 
       [0007]    The disclosed subject matter relates to a geared continuously variable transmission (GCVT). The GCVT includes a first set of solar gears having a first solar gear and a first plurality of connection components. Power enters the GCVT through the first set of solar gears. The GCVT includes a second set of solar gears having a second solar gear and a second plurality of connection components. Power exits the GCVT through the second set of solar gears. Power is transmitted from the first set of solar gears to the second set of solar gears via the first plurality of connection components and the second plurality of connection components. The GCVT includes a hydraulic pump and a hydraulic motor connecting a first component from the first plurality of connection components to a second component from the second plurality of connection components and providing constant rotation ratio between the first component and the second component. The hydraulic pump and the hydraulic motor can be connected to each other via a hydraulic pipe. 
         [0008]    Each of the first plurality of connection components and the second plurality of connection components may include a shaft fixed to the respective solar gear, one or more pinion gears, a carrier, and a ring gear. The power transmission from the first set of solar gears to the second set of solar gears can be performed by a geared interface shaft. In some instances, the power transmission from the first set of solar gears to the second set of solar gears can be performed by an interface gear. In some other instances, the power transmission from the first set of solar gears to the second set of solar gears can be performed by direct geared connection between one of the first plurality of connection components to a counterpart component from the second plurality of connection components. 
         [0009]    The power transmission from the first set of solar gears to the second set of solar gears can be performed by direct solid connection between one of the first plurality of connection components to a counterpart component from the second plurality of connection components. In some instances, the power transmission from the first set of solar gears to the second set of solar gears can be performed by direct coupling of the hydraulic motor and the hydraulic pump with one of the first plurality of connection components and a counterpart component from the second plurality of connection components. 
         [0010]    In some instances, the power transmission from the first set of solar gears to the second set of solar gears can be performed by direct coupling of each component form the first plurality of connection components to a counterpart component from the second plurality of connection components. 
         [0011]    The GCVT may further include one or more sensors. The one or more sensors may monitor volume capacity of the hydraulic pump and the hydraulic motor. Moreover, an infinite number of transmission rates can be provided by the GCVT between a predefined lower limit number and a predefined upper limit number. A change in the transmission rates can be continuous in a linear manner. In addition, at least one of the hydraulic pump and the hydraulic motor may have a variable volume flow rate. 
         [0012]    The hydraulic pump may be configured to connect to the first plurality of connection components and the second plurality of connection components via a first geared interface shaft component. The first geared interface shaft component may include a first geared interface shaft, a first gear connected to the first geared interface shaft and a first component from the first plurality of connection components, a second gear connected to the first geared interface shaft and a second component from the second plurality of connection components, and a third gear connected to the first geared interface shaft and a gear of the hydraulic pump. 
         [0013]    The hydraulic motor may be configured to connect to the first plurality of connection components and the second plurality of connection components via a second geared interface shaft component. The second geared interface shaft component may include a second geared interface shaft, a first gear connected to the second geared interface shaft and a third component from the first plurality of connection components, a second gear connected to the second geared interface shaft and a fourth component from the second plurality of connection components, and a third gear connected to the first geared interface shaft and a gear of the hydraulic motor. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]    Features of the subject technology are set forth in the appended claims. However, for purpose of explanation, several implementations of the subject technology are set forth in the following figures. 
           [0015]      FIGS. 1-10  illustrate components of an exemplary Geared Continuously Variable Transmission (GCVT). 
       
    
    
     DETAILED DESCRIPTION 
       [0016]    In the following detailed description, numerous specific details are set forth by way of examples in order to provide a thorough understanding of the relevant teachings. However, it should be apparent to those skilled in the art that the present teachings may be practiced without such details. In other instances, well known methods, procedures, components, and/or circuitry have been described at a relatively high-level, without detail, in order to avoid unnecessarily obscuring aspects of the present teachings. 
         [0017]    A Geared Continuously Variable Transmission (GCVT) is a geared transmission system that benefits from the advantages of gearboxes while solving the disadvantage of stepwise (non-linear) transmission of gearboxes. A GCVT, as disclosed, may include a shell, two sets of solar gears, two sets of connection components and a hydraulic pump and a hydraulic motor. In some instances, at least one of the hydraulic pump and the hydraulic motor may have variable volume capacity (V g ). The GCVT may also include safety hydraulic components. 
         [0018]    A first set of solar gears, from the two sets of solar gears, can be used for inputting power to the GCVT. The power can enter the GCVT via one of the components of the first set of solar gears (e.g., input component) such as, for example, a shaft (e.g., a shaft connected to a solar gear), a ring gear, a carrier (e.g., planetary carrier), etc. A second set of solar gears, from the two sets of solar gears, can be used for outputting the power from the GCVT. The power can exit the GCVT via one of the components of the second set of solar gears (e.g., output component) such as, for example, a shaft (e.g., a shaft connected to a solar gear), a ring gear, a carrier (e.g., a planetary carrier), etc. Power transmission by the GCVT is performed by connection among components of the two sets of solar gears (excluding the input and output components). The components of the two sets of solar gears can be connected to each other by various methods such as, for example, an interface shaft between the gears, an interface gear, direct connection of the components using gears, solid connection of the components, etc. 
         [0019]    For example, when the components of the two sets of solar gears are connected via interface shafts, the connection can be described as follows. A first shaft having connecting gears can connect a first component from the first set of solar gears to a first component from the second set of solar gears such that a constant rotation is maintained between the two components. A second shaft having connecting gears can connect a second component from the first set of solar gears to a second component from the second set of solar gears such that a constant rotation is maintained between the two components. The hydraulic pump and motor can be connected to the first and second shafts respectively using interface gears. A hydraulic pipe can connect an output of the hydraulic pump to an input of the hydraulic motor. In this case, a constant rotation is generated between the hydraulic pump and the hydraulic motor and as a result between the first and the second shafts. 
         [0020]    The GCVT as described can function with a constant transmission rate. By changing the volume capacity of the hydraulic pump and/or hydraulic motor, the rotation ratio of their axes and the rotation ratio of the two interface shafts can change. By changing the rotation ratio of the two interface shafts which carry torque between the components of the two sets of solar gears, the transmission rate of the gearbox can change. Since the change in volume capacity (V g ) of a hydraulic pump and/or hydraulic motor is continuous, the change in transmission rate of the GCVT is also continuous. 
         [0021]    An example connection between the components of the two sets of solar gears is described herein in more detail. Among the main components of the first set of solar gears such as, shaft, ring gear and carrier, the shaft (e.g., first shaft) can be considered as the main input component of power. Similarly, the second shaft from the second set of solar gears can be considered as the output component. In addition, two counterpart components from the two sets are considered to be connected to each other by an interface shaft. For example, the first ring gear from the first set is a counterpart of the second ring gear from the second set and the first carrier from the first set is a counterpart of the second carrier from the second set. A gear can be installed on each of the first and second ring gears and first and second carriers. Interface shafts are used to connect counterpart components from the two sets. 
         [0022]    The first interface shaft may have three fixed gears. A first fixed gear of the first interface shaft can be connected to a gear installed on the first ring gear from the first set. The second fixed gear of the first interface shaft can be connected to a gear installed on the second ring gear from the second set. As a result, the first interface shaft connects the first ring gear from the first set with its counterpart second ring gear from the second set and maintains a constant rotation ratio among the two. Similarly, the second interface shaft may have three fixed gears. A first fixed gear of the second interface shaft can be connected to a gear installed on the first carrier from the first set. The second fixed gear of the second interface shaft can be connected to a gear installed on the second carrier from the second set. As a result, the second interface shaft connects the first carrier from the first set with its counterpart second carrier from the second set and maintains a constant rotation ratio among the two. 
         [0023]    In addition, a gear can be installed on the axis of the hydraulic pump and another gear can be installed on the axis of the hydraulic motor. In this case, the third gear of the first interface shaft can be connected with the gear of the hydraulic pump and the third gear of the second interface shaft can be connected with the gear of the hydraulic motor, such that a constant rotation (K) can be created between rotation of the two axes of the hydraulic pump and the hydraulic motor. Moreover, a constant ratio (H) can be created between rotation of the first interface shaft and the second interface shaft, which are connected to the gears of the hydraulic pump and the hydraulic motor. The ratio H is a function of ratio K. 
         [0024]    The structure of the GCVT can be completed by using a hydraulic valve, a hydraulic relief valve and a hydraulic damper. The GCVT as described, can work with a constant transmission rate. As shown in equations of Table 1 when the ratio H between rotation of the first interface shaft and the second interface shaft is changed, the transmission rate of the GCVT may also change. As previously noted, at least one of the hydraulic pump and hydraulic motor may have variable volume capacity (V g ). In this case, by changing the volume capacity, the ratio K between the axes of the hydraulic pump and the hydraulic motor can change. As a result ratio H, a function of K, may also change and this can cause the transmission rate of the GCVT to change. 
         [0025]    In Table 1, N is the rotation speed of a gear or shaft, G is a number of teeth of a gear, V g  is the volume capacity of the hydraulic pump and motor, and Q is volume flow rate of the hydraulic pump and hydraulic motor. An index shows the component number. For example G 12  is the number of teeth of gear  12  and N 12  is the rotation speed of gear  12 . 
         [0000]    
       
         
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 N 12 *G 12  + N 13 *G 13  = N 15 *(G 12  + G 13 ) 
               
               
                   
                 N 22 *G 22  + N 23 *G 23  = N 25 *(G 22  + G 23 ) 
               
               
                   
                 N 2  = N 13 *G 16 /G 19  = N 23 *G 26 /G 29   
               
               
                   
                 N 3  = N 15 *G 17 /G 18  = N 25 *G 27 /G 28   
               
               
                   
                 Q 7  = Q 8   
               
               
                   
                 Q 7  = N 2 *G 20 *Vg 7 /G 6   
               
               
                   
                 Q 8  = N 3 *G 4 *Vg 8 /G 5   
               
               
                   
                 N 2 /N 3  = G 4 *G 6 *Vg 8 /(G 5 *G 20 *Vg 7 ) 
               
               
                   
                 K = Vg8/Vg7 
               
               
                   
                 H = N 2 /N 3   
               
               
                   
                 H = K*G 4 *G 6 /(G 5 *G 20 ) 
               
               
                   
                   
               
             
          
         
       
     
         [0026]    Since in hydraulic systems variations of volume capacity are continuous, therefore variations in K and H and the transmission rate of the GCVT are continuous as well. The tests and studies show that in the GCVT as described, majority of the power (e.g., torque and angular speed) may be transferred by the two interface shafts, which connect the counterpart components, as previously discussed, and a small part of the power is transferred via the hydraulic pump and hydraulic motor. As a result, the GCVT has advantages such as capability of transferring high and low powers, low depreciation, high efficiency, constant transmission rate based on selection, and low cost. 
         [0027]      FIG. 1  illustrates the first set of solar gears. As shown in  FIG. 1 , the shaft  11  is installed onto the solar gear  12  and the two components may produce an integrated component. One or more pinions  14  can be attached to carrier  15 . In the illustration of  FIG. 1  two pinons  14  are shown. The carrier  15  is installed on shaft  11  and can freely rotate around the shaft&#39;s axis. A ring gear  13  is installed on shaft  11  and can freely rotate around the shaft&#39;s axis 
         [0028]    In  FIG. 2 , two gears  16  and  17  are installed on the first set of solar gears such that gear  16  is installed on ring gear  13  and the two components can produce an integrated component. The gear  17  is installed on carrier  15  and the two components can produce an integrated component. 
         [0029]      FIG. 3  illustrates the second set of solar gears. As shown in  FIG. 3 , the shaft  21  is installed onto the solar gear  22  and the two components may produce an integrated component. One or more pinions  24  can be attached to carrier  25 . The carrier  25  is installed on shaft  21  and can freely rotate around the shaft&#39;s axis. A ring gear  23  is installed on shaft  21  and can freely rotate around the shaft&#39;s axis. 
         [0030]    In  FIG. 4 , two gears  26  and  27  are installed on the second set of solar gears such that gear  26  is installed on ring gear  23  and the two components can produce an integrated component. The gear  27  is installed on carrier  25  and the two components can produce an integrated component. 
         [0031]      FIG. 5  illustrates the two sets of solar gears of  FIGS. 1 and 3 . As shown in  FIG. 5 , the first and the second set of solar gears are placed together such that the two sets facing each other on bearings A and B. In the combined structure of  FIG. 5 , the shaft  11  can be considered as input shaft of power (torque and rotation) and shaft  21  is the output shaft of power. For transferring the torque and rotation from the first set of solar gears to the second set of solar gears two shafts can be used with each shaft having three gears, as shown in  FIG. 6 . 
         [0032]    As shown in  FIG. 6 , the gears  19 ,  20  and  29  are installed on shaft  2 . The shaft  2  and the gears  19 ,  20  and  29  can produce an integrated component. Similarly, gears  4 ,  18  and  28  are installed on shaft  3  and components  3 ,  4 ,  18  and  28  can produce an integrated component. 
         [0033]      FIG. 7  illustrates shaft  2  as shown in  FIG. 6 . The shaft  2  can be placed on two bearings E and F. The gear  19  of shaft  2  is engaged with gear  16  and the gear  29  of shaft  2  is engaged with gear  26 . In this case, shaft  2  can transfer torque and rotation from ring gear  13  (of the first set of solar gears) to ring gear  23  (from the second set of solar gears). The shaft  2  can generate a stable ratio revolution between the two ring gears  13  and  23 . 
         [0034]      FIG. 8  illustrates shaft  3  as shown in  FIG. 6 . The shaft  3  can be placed on two bearings C and D. The gear  18  of shaft  3  is engaged with gear  17  and the gear  28  of shaft  3  is engaged with gear  27 . In this case, shaft  3  can transfer torque and rotation from carrier  15  (of the first set of solar gears) to carrier  25  (from the second set of solar gears). The shaft  3  can generate a stable ratio revolution between the two carriers  15  and  25 . 
         [0035]    As shown in  FIG. 5 , each of the first and second sets of solar gears can have two degrees of freedom. As shown in  FIGS. 7 and 8 , the shafts  2  and  3  provide two connections between components of the two sets of solar gears and balance the two degrees of freedom. In order to achieve one degree of freedom for the GCVT structure, the shafts  2  and  3  can be connected by a hydraulic system as shown in  FIG. 9 . 
         [0036]      FIG. 9  illustrates a hydraulic pump  7  and a gear  6  installed on a shaft of the hydraulic pump  7 . The gear  6  is engaged with gear  20  (installed on shaft  2 ). Furthermore, a gear  5  is installed on a shaft of the hydraulic motor  8 . The gear  5  is engaged with gear  4  (installed on shaft  3 ). A hydraulic pipe  9  connects an output fluid canal of the hydraulic pump  7  to an input fluid canal of the hydraulic motor  8 . The three hydraulic pipes  33  (input to the hydraulic pump  7 ),  32  (output of the hydraulic motor  8 ), and  34  (output of the hydraulic valve  10 ) are connected to a hydraulic oil tank (not shown). Component  31  is a hydraulic damper and component  30  is a hydraulic relief valve. Component  10  is a hydraulic valve for hydraulic connection and disconnection. Connection between the oil output from the hydraulic pump  7  to the input of the hydraulic motor  8  can create an equivalent volume flow rate for the pump and the motor. In this case, the gears  5  and  6  can rotate with a constant ratio and as a result the two shafts  2  and  3  can also have a constant rotation ratio. This may create one degree of freedom for the GCVT mechanism. In this case, the GCVT mechanism has one degree of freedom. 
         [0037]    As discussed with regards to  FIG. 9 , the GCVT mechanism can function with a constant rotation ratio (R). In this case, if the volume flow rate of the hydraulic pump  7  or the hydraulic motor  8  is changed, this change can cause the ratio of rotation speed of shaft  2  to rotation speed of shaft  3  to change. This in return can cause a change in the conversion rate (rotation ratio) R such that a ratio of the rotation of output shaft  21  to the rotation of the input shaft  11  may also change. 
         [0038]    An example discussed below shows the continuity of the changes. As previously described with respect to Table 1, in the following equations N is the rotation speed of a gear or shaft, G is a number of teeth of a gear, V g  is the volume capacity of the hydraulic pump and motor, and Q is the volume flow rate of the hydraulic pump and hydraulic motor. An index shows the component number. For example G 12  is the number of teeth of gear  12  and N 12  is the rotation speed of gear  12 . 
         [0039]    When the hydraulic valve  10  is open (in this case, the pipe  9  is connected to the hydraulic oil tank via hydraulic pipe  34 ), the hydraulic pump is disconnected from the hydraulic motor and therefore shafts  2  and  3  are disconnected. In this case the GCVT mechanism may reach the two degrees of freedom or the GCVT may be in neutral state (the mechanism becomes idle). 
         [0040]    In some instances, sensors can be installed in the power consuming set or in the power producing set such that the volume capacity of the hydraulic pump  7  and motor  8  can be automatically controlled using the sensors. 
         [0041]    In some instances, some of the gears and interface shafts can be omitted such that the counterpart components connect directly to each other. For example, the hydraulic pump  7  and motor  8  can be directly coupled with their counterpart shafts and the gears connecting the hydraulic pump  7  and the hydraulic motor  8  can be omitted. 
         [0042]    In some other instances, the rotation speed of the counterpart components from the two sets of solar gears can be preset to be equal. In such cases, there may be no need for interface shafts and interface gears between the counterpart components, because the two counterpart components can be coupled to each other. 
         [0043]      FIG. 10  is graph representation of the conversion rate R as calculated below. The equations that follow are used to calculate a ratio of rotational speed of the output shaft of the GCVT (shaft  21  coupled to gear G 22  in  FIG. 9 ) to the rotation speed of the input shaft of the GCVT (shaft  11  coupled to gear G 12  in  FIG. 9 ). This ratio represents the conversion rate R of the GCVT. 
         [0044]    Equations 1-4 calculate the rotational speed of the solar gears. Equation 5 is a combination of equations 3 and 4, and equation 7 is resulted when equation 6 is assumed. Equation 10 is a combination of equations 8 and 9, and equation 12 is resulted when equation 11 is assumed. 
         [0045]    Considering that the output of hydraulic pump  7  is connected to the input of the hydraulic motor  8 , the volume flow rate of the pump  7  and motor  8  may be equal (Q 7 =Q 8 ). Following the relation between the volume flow rate, rotational speed and the volume capacity equation 15 is resulted, wherein V g  represents the volume capacity of the hydraulic set in each rotation of its shaft in cubic centimeters per rotation. Equation 16 is resulted from replacing value N 6  from equation 13 into equation 15 and equation 18 is resulted from replacing value N 5  from equation 14 into equation 17. 
         [0046]    Equation 19 is resulted from a combination of equations 16 and 18, and equation 20 is resulted from replacing value N 2  from equation 8 and value N 3  from equation 3 into equation 19. And equation 22 is resulted from equation 21. With equation 22 as an assumption, equation 23 is resulted and equation 24 is resulted from a combination of equations 1 and 23. 
         [0047]    Equation 25 is resulted from equation 2 and equation 26 is a combination of equations 7 and 23. Equation 27 is resulted from replacement of N 25  from equation 26 and N 23  from equation 12 into equation 25. Equation 28 is resulted from replacement of N 13  from equation 24 into equation 27. 
         [0000]        N   12   ×G   12   +N   13   ×G   13   =N   15 ×( G   12   +G   13 )   1)
 
         [0000]        N   22   ×G   22   +N   23   ×G   23   =N   25 ×( G   22   +G   23 )   2)
 
         [0000]        N   3   =−N   15   ×G   17   /G   18    3)
 
         [0000]        N   3   =−N   25   ×G   27   /G   26    4)
 
         [0000]        N   25   =N   15   ×G   17   ×G   28 /( G   27   ×G   18 )   5)
 
         [0000]        A=G   17   ×G   28 /( G   27   ×G   18 )   6)
 
         [0000]        N   25   =A×N   15    7)
 
         [0000]        N   2   =−N   13   ×G   16   /G   19    8)
 
         [0000]        N   2   =−N   23   ×G   26   /G   29    9)
 
         [0000]        N   23   =N   13   ×G   16   ×G   29 /( G   19   ×G   26 )   10)
 
         [0000]        B=G   16   ×G   29 /( G   19   ×G   26 )   11)
 
         [0000]        N   23   =B×N   13    12)
 
         [0000]        N   6   =−N   2   ×G   20   /G   6    13)
 
         [0000]        N   5   =−N   3   ×G   4   /G   5    14)
 
         [0000]        Q   7   =N   6   ×V   g7    15)
 
         [0000]        Q   7   =−N   2   ×G   20   ×V   g7   /G   6    16)
 
         [0000]        Q   8   =N   5   ×V   g8    17)
 
         [0000]        Q   8   =−N   3   ×G   4   ×V   g8   /G   5    18)
 
         [0000]        N   2   ×G   20   ×V   g7   /G   6   =−N   3   ×G   4   ×V   g8   /G   5    19)
 
         [0000]        N   13   ×G   16   ×G   20   ×V   g7 /( G   19   ×G   6 )=− N   15   ×G   17   ×G   4   ×V   g8 /( G   18   ×G   5 )   20)
 
         [0000]        N   15   =−N   13   ×G   16   ×G   20   ×G   18   ×G   5   ×V   g7 /( G   19   ×G   6   ×G   17   ×G   4   ×V   g8 )   21)
 
         [0000]        X=G   16   ×G   20   ×G   18   ×G   5   ×V   g7 /( G   19   ×G   6   ×G   17   ×G   4   ×V   g6 )   22)
 
         [0000]        N   15   =−X×N   13    23)
 
         [0000]        N   13   =−B   12   ×G   12 /( X ×( G   12   +G   13 )+ G   13 )   24)
 
         [0000]        N   22 =( N   25 ×( G   22   +G   23 )− N   23   ×G   23 )/ G   22    25)
 
         [0000]        N   25   =−A×X×N   13    26)
 
         [0000]        N   22 =−( A×X×N   13 ×( G   22   +G   23 )+ B×N   13   ×G   23 )/ G   22    27)
 
         [0000]        N   22   =N   12 ×( A×X×G   12 ×( G   22   +G   23 )+ B×G   23   ×G   12 )/( X×G   22 ×( G   12   +G   13 )+ G   22   ×G   13 )   28)
 
         [0000]        R=N   22   /N   12    29)
 
         [0000]        R =( A×G   12 ×( G   22   +G   23 )× X+B×G   23   ×G   12 )/( G   22 ×( G   12   +G   13 )× X+G   22   ×G   13 )   30)
 
         [0000]        M=G   18   ×G   20   ×G   18   ×G   5   ×V   g7 /( G   19   ×G   6   ×G   17   ×G   4 )   31)
 
         [0000]        L=A×G   12 ×( G   22   +G   23 )   32)
 
         [0000]        F=B×G   23   ×G   12    33)
 
         [0000]        P=G   22 ×( G   12   +G   13 )   34)
 
         [0000]        C=G   22   ×G   13    35)
 
         [0000]        X=M/V   g6    36)
 
         [0000]        R =( L×M+F×V   g6 )/( P×M+C×V   g8 ) R=f ( V   g8 )   37)
 
         [0048]    Equation 29 represents the conversion rate of the GCVT. Equation 30 is resulted from replacement of N 22  from equation 28 into equation 29. As previously discussed, one or both of the hydraulic pump  7  and hydraulic motor  8  may have variable volume flow rate, for example, the volume capacity of the hydraulic motor  8  can be variable. For simplification of the equations, assumptions  31  to  35  are made. Equation 36 is resulted from a combination of equations 31 and 22 and equation 37 is resulted from a combination of equations 32 to 36 into equation 30. The parameters L, M, F, P, and C are all constant positive numbers (L, M, P, F, C&gt;0) and variable V g8  also has a positive value (V g8 &gt;0). Therefore, the circumference of the function R=f(V g8 ) can be a non-zero value. 
         [0049]    The derivative of conversion rate function R with variable V g8  is: 
         [0000]      ( F×P×M−C×L×M )/( P×M+C×V   g8 ) 2    
         [0050]    Considering that (F*P≠C*L) in the design of gears, under predefined conditions, the above derivative may have a non-zero value which shows that the function is either descending or ascending and does not have a maximum point or a minimum point. 
         [0051]    The second derivative of the above function is: 
         [0000]      −2 ×C×M ×( F×P−C×L )/( P×M+C×V   g8 ) 3  
 
         [0052]    Again considering the predefined conditions, the value of the second derivative is non-zero and the function does not have a turning point. Therefore, in a defined interval, the function R is a continuous function. For example, function R can be calculated for a GCVT gearbox with following parameters. 
         [0000]      G 12 =51 
         [0000]      G 13 =87 
         [0000]      G 22 =24 
         [0000]      G 23 =84 
         [0000]      G 18 =70 
         [0000]      G 19 =G 20 =46 
         [0000]      G 26 =105 
         [0000]      G 29 =11 
         [0000]      G 5 =14 
         [0000]      G 17 =G 27 =G 28 =G 18 =G 4 =100 
         [0000]      G 6 =67 
         [0000]      V g7 =10 
         [0000]      V g8 =0.5 . . . 10 
         [0000]        A=G   17   ×G   28 /( G   27   ×G   18 )=1 
         [0000]      B=G 16   ×G   29 /( G   19   ×G   26 )=0.15942 
         [0000]        M=G   15   ×G   20   ×G   18   ×G   5   ×V   g7 /( G   19   ×G   6   ×G   17   ×G   4 )=1.462686 
         [0000]        L=A×G   12 ×( G   22   +G   23 )=5508
 
         [0000]        F=B×G   23   ×G   12 =682.955 
         [0000]        P=G   22 ×( G   12   +G   13 )=3312
 
         [0000]        C=G   22   ×G   13 =2088 
         [0000]      F×P≠C×L 682.955×3312≠2088×5508→2261946.96≠11500704
 
         [0000]        R =( L×M+F×V   g8 )/( P×M+C×V   g8 ) 
         [0000]        R =(5508×1.462686→682.955 ×V   g8 )/(3312×1.462666+2088 ×V   g8 )
 
         [0000]        R =(8056.474+682.955 ×V   g8 )/(4844.416+2088 ×V   g8 ) 
         [0000]      V g8 =0.5 R=1.426182 
         [0000]      V g8 =10 R=0.578674. 
         [0053]    The curve shown in  FIG. 10  displays variations of value of function R based on the values of variable V g8  between 0.5 and 1 (0.5≦V g8 ≦1). 
         [0054]    The separation of various system components in the examples described above should not be understood as requiring such separation in all examples, and it should be understood that the described components and systems can generally be integrated together in a single packaged into multiple systems. 
         [0055]    While the foregoing has described what are considered to be the best mode and/or other examples, it is understood that various modifications may be made therein and that the subject matter disclosed herein may be implemented in various forms and examples, and that the teachings may be applied in numerous applications, only some of which have been described herein. It is intended by the following claims to claim any and all applications, modifications and variations that fall within the true scope of the present teachings. 
         [0056]    Unless otherwise stated, all measurements, values, ratings, positions, magnitudes, sizes, and other specifications that are set forth in this specification, including in the claims that follow, are approximate, not exact. They are intended to have a reasonable range that is consistent with the functions to which they relate and with what is customary in the art to which they pertain. 
         [0057]    The scope of protection is limited solely by the claims that now follow. That scope is intended and should be interpreted to be as broad as is consistent with the ordinary meaning of the language that is used in the claims when interpreted in light of this specification and the prosecution history that follows and to encompass all structural and functional equivalents. Notwithstanding, none of the claims are intended to embrace subject matter that fails to satisfy the requirement of Sections  101 ,  102 , or  103  of the Patent Act, nor should they be interpreted in such a way. Any unintended embracement of such subject matter is hereby disclaimed. 
         [0058]    Except as stated immediately above, nothing that has been stated or illustrated is intended or should be interpreted to cause a dedication of any component, step, feature, object, benefit, advantage, or equivalent to the public, regardless of whether it is or is not recited in the claims. 
         [0059]    It will be understood that the terms and expressions used herein have the ordinary meaning as is accorded to such terms and expressions with respect to their corresponding respective areas of inquiry and study except where specific meanings have otherwise been set forth herein. Relational terms such as first and second and the like may be used solely to distinguish one entity or action from another without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms “comprises,” “comprising,” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by “a” or “an” does not, without further constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element. 
         [0060]    The Abstract of the Disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, it can be seen that various features are grouped together in various implementations for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed implementations require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed implementation. Thus the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separately claimed subject matter.