BACKGROUND OF THE INVENTION 
     Often an engine or motor will operate at speeds different from the required speed of a driven device. Thus, some form of transmission is used to bridge this speed difference (e.g., gears, pulleys etc). Furthermore, the desired speed of the driven device may change substantially while the desired operating speed range of the power supply is narrow (e.g., the internal combustion engine (ICE) in a car operates most efficiently between 1000-3000 rpm, while the driving speeds can vary between −30 mph and 100+ mph). To address such situations the transmission can be designed so that one of several gear ratios is selected at any particular time. In cars these are usually accomplished with manual transmissions (MT) or automatic transmissions (AT). Adding additional gears to a discrete transmission (MT or AT) allows the ICE to operate in a more efficient regime more often, but this is a case of diminishing returns (each additional gear adds less to the total efficiency) and makes the transmission more complicated and expensive. 
     However, it is still desirable to have the power supply operating at its most efficient operating point regardless of the speed of the driven device. A continuously variable transmission or variator can be used for this purpose. There are many ways to design a variator (e.g., two tapered rollers mounted on parallel rotating shafts pointing in opposite directions and coupled with a belt. Changing the position of the belt alters the speed ratio between the two shafts.) However, there are two shortcomings of variators which prevent them from being widely used in automotive applications; (a) mechanical variators transmit forces via friction and therefore the maximum torque that they can transmit is less than geared transmissions, and (b) variators are typically less efficient than a similarly scaled and well designed geared system. 
     It is known (U.S. Pat. No. 5,055,094, U.S. Pat. No. 2,955,477, U.S. Pat. No. 3,023,277, U.S. Pat. No. 4,402,237, U.S. Pat. No. 4,864,889, etc) that a variator can be coupled with one or more epicyclic gears to create an infinitely variable transmission (i.e., if the power supply is operating in a constant forward regime, the speed of the powered device can continuously change from forward through zero to reverse.) However, some power (and torque) must always cross the variator. US2011201470 discloses a device that includes a variator that controls the intermediate shafts. However, a need remains for transmissions with large speed ranges and high efficiency. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  depicts an embodiment of the invention showing how the various shafts connect to the generic differential gear trains and the variator. 
         FIG. 2  shows an example of how a generic differential gear train can be replaced with a kinematically equivalent differential epicyclic gear train with an additional mechanic gearing. 
         FIG. 3  depicts an embodiment of the invention where the generic differential gear trains of  FIG. 1  have been replaced with differential epicyclic gear trains with two additional mechanical gearings. 
         FIG. 4  depicts an embodiment of the invention where an inner device (like the one shown in  FIG. 3 ) replaces the variator of an outer device (like the one depicted in  FIG. 3 ). 
     
    
    
     DETAILED DESCRIPTION OF INVENTION 
       FIG. 1  depicts an embodiment of the invention. A first shaft  12  (A) is connected to a first differential gear train  13  at connection  13 A. A second shaft  14  (C) and a third shaft  15  (B) are also connected to said first differential gear train  13  at connections  13 B and  13 C, respectively. Shafts  12 ,  15 , and  14  rotate with speeds ω A , ω B , and ω C , respectively. Said first differential gear train  13  is a general differential gear train and is characterized by two constants p1 and q1 such that ω A =p 1 ω B +q 1 ω C . 
     The relative speeds of shafts  14  and  15  can be controlled with a “variator”  16  such that nω C =ω B  where n is both adjustable and controllable. A value of n can be selected either manually or automatically in order to achieve superior powertrain performance (e.g., maximize fuel economy; minimize 0-60 acceleration time). The ratio of variator  16  may be controlled by some mechanical means (e.g., hydraulic actuator). A number of different types of variators exist that can continuously adjust the relative speeds of two rotating shafts. Such variators are commonly referred to as continuously variable transmissions (CVTs). Examples of CVTs include a pair of adjustable radius pulleys connected by a belt. In a CVT the value of n can have any value in a range between a maximum and minimum value but the maximum and minimum values of n must either both be positive or both be negative. In other words the range of n in a CVT cannot pass through zero or infinity. 
     The variator can also be comprised of an infinitely variable transmission (IVT). IVTs can have a wider range of n than for CVTs. For an IVT, n can have any maximum and minimum value and can pass through zero and/or infinity. IVTs are typically constructed by connecting a CVT with one or more differential gear trains. This invention is an example of an IVT. 
     Shafts  14  and  15  also connect with a second differential gear train  17  at  17 B and  17 C respectively. The third connection of the second differential gear train  17  is shaft  18  (D) connected at  17 D. Said second differential gear train  17  is a general differential gear train and is characterized by two constants p2 and q2 such that ω D =p 2 ω B +q 2 ω C . The ratio q2/p2 must be different from q1/p1 for the described device to be of any use. 
     By controlling the ratio of the variator  16  the speed ratio of the entire device, R, may be controlled and is a function of p1, p2, q1, q2 and n: 
     
       
         
           
             R 
             = 
             
               
                 
                   ω 
                   D 
                 
                 
                   ω 
                   A 
                 
               
               = 
               
                 
                   
                     q 
                     2 
                   
                   + 
                   
                     
                       p 
                       2 
                     
                     ⁢ 
                     n 
                   
                 
                 
                   
                     q 
                     1 
                   
                   + 
                   
                     
                       p 
                       1 
                     
                     ⁢ 
                     n 
                   
                 
               
             
           
         
       
     
     When this device is used as an automotive transmission shaft  12  is connected to a prime mover (e.g., engine) and shaft  18  is connected to the wheels. The rotational speed of shaft  18  relative to the rotational speed of shaft  12  can span an infinite and continuous range. These ratios include forward speeds, reverse speeds and a geared neutral state where the prime mover can rotate while the output is fixed (e.g., while idling). All of these speed ratios can be achieved without the use of clutches or brake mechanisms. This range of R can be obtained if the range of n includes −q2/p2. For such applications the range of n should not include −q1/p1 as that would prevent the engine from rotating. 
     This device could also be used as a continuous brake pair. In such a configuration this device could hold one rotating member of some larger device connected to shaft  12  and a second rotating member of some larger device connected to shaft  18 . The first rotating member of the larger device can be held fixed (i.e., braked) while the second rotating member of the larger device can rotate freely when n=−q1/p1. Furthermore, the second rotating member of the larger device can be held fixed (i.e., braked) while the first rotating member of the larger device can rotate freely when n=−q2/p2. The range of n should thus include both −q1/p1 and −q2/p2. For all other values of n the speed ratio of the output to input shafts are coupled and described by the ratio R. 
     A general differential gear train (e.g.,  13  and  17 ) can be constructed in a variety of ways and could include the use of a differential epicyclic (or planetary) gear train, a differential cycloidal drive or a differential harmonic drive; wherein said differential gear train is connected to each of the three shafts with a direct connection or by mechanical gearing. 
       FIG. 2  illustrates kinematic and mathematically equivalency of different differential gear train arrangements. A general differential gear train  30  can be constructed as an equivalent system  30 ′ with a differential epicyclic gear train  13 ′ (characterized by a single ratio k1) with one addition mechanical gearing  11 ′ (characterized by the ratio K1) such that an input shaft  12  and two output shafts  14 ,  15  have the same kinematic relationship for both  30  and  30 ′. This simplifies the design process. All possible designs (combinations of p1, q1, p2 and q2) can be considered for a single topology (e.g.,  FIG. 1 ). The topology can then be changed afterwards into systems with equivalent kinematics but may be superior for manufacturing or efficiency reasons. p1, q1, p2 and q2 can then be converted into an equivalent set of k1, K1, k2 and K2.  FIG. 3  illustrates this case. Consider the device  30 ′. It has the same input  12  as device  30  and the same outputs  14 ,  15 . However, in device  30 , input shaft  12  connects to directly to differential gear train connection  13 A while in device  30 ′, input shaft  12  connects to the epicyclic carrier gear  13   c  via mechanical gearing  11 ′ (K1). In device  30 , output shaft  14  is connected directly to differential gear train connection  13 C while in device  30 ′ output shaft  14  is connected to the epicyclic gear train ring gear  13 ′ r . Finally, in device  30 , output shaft  15  is connected directly to differential gear train connection  13 B while in device  30 ′ output shaft  15  is connected to the epicyclic gear train sun gear  13 ′ s.    
     The kinematics of device  30  can be described as follows:
 
ω A   =p   1 ω B   +q   1 ω C  
 
where ω A , ω B , and ω C  are the rotational speeds of shafts  12 ,  15  and  14  respectively.
 
     The kinematics of device  30 ′ can be described as follows:
 
 K   1 ( k   1 +1)ω A   =k   1 ω B +ω C.  
 
     Thus the kinematics of device  30  will be the same as those of device  30 ′ when 
               k   1     =       p   1       q   1             
and
 
     
       
         
           
             
               K 
               1 
             
             = 
             
               1 
               
                 
                   p 
                   1 
                 
                 + 
                 
                   q 
                   1 
                 
               
             
           
         
       
     
     Thus only a single design topology needs to be considered when designing a device with an input shaft, output shaft, two generic differential gear trains, and a variator that controls the speed ratio of the intermediate shafts  14  and  15 . Furthermore, any device of this type can be designed for a pair of generic differential gear trains (a selection of p1, q1, p2, and q2) and converted to a kinematically equivalent set of design variables (e.g., k1, K1, k2, K2). 
       FIG. 3  depicts an embodiment of the invention where the generic differential gear trains  13 ,  17  depicted in  FIG. 1  have been replaced with differential epicyclic gear trains  13 ″,  17 ″ and two additional mechanical gearings  11 ″,  19 ″. 
       FIG. 4  depicts an embodiment of the invention. The variator  16  shown in  FIG. 3  is replaced by the device depicted in  FIG. 3 . Thus, in the implementation shown in  FIG. 4 , shaft  14  serves as the input shaft to the inner device and drives a third epicyclic gear  23  by means of mechanical gearing  21  and connecting shaft  22 . The outputs of epicyclic gear  23  drive shafts  24  and  25  which are connected to the inputs of epicyclic gear  27  and connect to opposite ends of variator  26 . The output of epicyclic gear  27  drives the connecting shaft  28  which is coupled to shaft  15  by means of mechanical gearing  29 . 
     The inner mechanism  21 - 29  should be designed as a continuous brake pair. This allows behavior and operating conditions that would not be available with a CVT type variator. When the ratio of variator  26  is n=−k3 shaft  14  is held fixed (effectively braked) while shaft  15  can rotate freely. In this scenario all the power of the prime mover is directed along shaft  15 , no power flows through the inner device  21 - 29  and the output speed ratio is: 
             R   =             K   1     ⁡     (       k   1     +   1     )       ⁢     k   2             K   2     ⁡     (       k   2     +   1     )       ⁢     k   1         .           
When the ratio of variator  26  is n=−k4 shaft  15  is held fixed (effectively braked) while shaft  14  can rotate freely. In this scenario all the power of the prime mover is directed along shaft  14 , no power flows through the inner device  21 - 29  and the output speed ratio is:
 
             R   =           K   1     ⁡     (       k   1     +   1     )           K   2     ⁡     (       k   2     +   1     )         .           
For any other value of n the ratio of the overall system is:
 
             R   =           K   1     ⁡     (       k   1     +   1     )       ⁢     (       k   2     +     R   ′       )             K   2     ⁡     (       k   2     +   1     )       ⁢     (       k   1     +     R   ′       )               
where
 
     
       
         
           
             
                 
             
             ⁢ 
             
               
                 R 
                 ′ 
               
               = 
               
                 
                   
                     
                       K 
                       3 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           k 
                           3 
                         
                         + 
                         1 
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         k 
                         4 
                       
                       + 
                       
                           
                       
                       ⁢ 
                       n 
                     
                     ) 
                   
                 
                 
                   
                     
                       K 
                       4 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           k 
                           4 
                         
                         + 
                         1 
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         k 
                         3 
                       
                       + 
                       
                           
                       
                       ⁢ 
                       n 
                     
                     ) 
                   
                 
               
             
           
         
       
     
     The closest devices to this invention are US2011201470 and U.S. Pat. No. 5,643,121 as well as derivatives of U.S. Pat. No. 5,643,121 including WO2005047736, CN10044917, and US20120142477. This invention is distinguished from US2011201470 primarily in that US2011201470 does not have a variator controlling the ratio of the two intermediate shafts. This invention is distinguished from the other four inventions in several ways which as described by the above description of the invention: a) this invention makes no use of clutches—simplifying the design, b) this invention proposes the use of a generalized differential gear trains instead of only epicyclic gear trains, c) this invention can be used as an alternative to a pair of brake mechanisms in certain situations by selecting the range of n to include −q1/p1 and −q2/q2, d) this invention describes a compound IVT where an inner IVT replaces the variator component in an outer IVT allowing for a wider range of operation including additional regimes of high efficiency.
An infinitely variable speed amplifier comprising a continuously variable unit ("variator"), two differential gear trains, and four shafts. Two of the shafts connect to opposite ends of the variator and to two connections of each differential gear train, respectively. The third connections of the first and second differential gear trains are connected to the input and output shafts respectively. Ratios and other parameters are chosen so that an acceptable range of transmission speeds can be achieved without the use of clutches while also minimizing the power crossing the variator. Furthermore, this invention includes a variant that is a compound infinitely variable speed amplifier that provides a wider performance range.