Abstract:
A transmission is provided which includes a fixed housing or support, an input part moveable relative to the support and a torque shaft, a first one-way clutch between the torque shaft and the driven shaft, linkage elements rotatable about the axis of rotation of the driven shaft under the influence of the input parts and an inertial body mounted on the linkage elements to be cyclically angularly deflected in response to the input part, the reaction forces generated by the inertial body as it cyclically deflected being applied to the torque shaft as a positive and negative torque and the torque shaft being connected over a second one-way clutch opposite to the first one-way clutch either to the support or to the driven shaft over a rotation reversal system whereby the driven shaft can be rotated by the torque shaft in one sense of rotation only.

Description:
FIELD OF THE INVENTION 
     This invention relates to a continuously variable transmission and more particularly to a continuously variable transmission in which primarily inertial reactions on a suitably arranged mass distribution are employed as coupling forces and torques to enable net transfer of energy from an input to an output. The time integral of the output torque and, if applicable, the input torque resulting from these inertial reactions is balanced by the time integral of a reaction torque resulting from these inertial reactions. The reaction torque is applied to the fixed surrounding or the transmission housing or otherwise so as to enable the transmission process to take place in a cyclic manner. In some cases during the cyclic movements of the transmission mechanisms, forces and moments other than the aforesaid inertial reactions may be additionally or otherwise employed to cause transfer of energy from the input to the output of the transmission. Even those cyclic movements of the transmission mechanisms themselves required to cause transfer of energy from the input to the output by other than the aforesaid inertial reactions, may be caused or assisted by means other than inertial reactions. 
     BACKGROUND ART 
     Transmissions which have fixed input/output speed ratios are not suitable for a wide variety of operating conditions. In order to match the input/output variables, namely the torque and speed, so that transmission losses are reduced and to allow optimum operating conditions at the input/output and to avoid excessive stresses developing in the transmission under transient conditions at the input/output, variable transmissions are necessary. 
     Using discretely variable transmissions, the speed ratio is changed in a finite number of steps. The above said benefits of a variable transmission are achieved only partially by this method. 
     Further, the number of steps are limited by economic and practical reasons. 
     A variety of continuously variable transmissions are known. In the main they use frictional elements, hydraulic elements (motor or turbine/pump) or electro-magnetic elements (motor/generator) to transmit power. With the exception of electro-magnetic methods, these transmissions are inefficient due to slip under transient conditions of acceleration and deceleration due to limited response capacity, especially under rapidly changing input/output conditions. Electro-magnetic systems to avoid such inefficiencies can be very costly and not practical under many circumstances due to space and weight conditions. 
     The applicant is aware of a number of prior proposals which endeavour to utilize gyroscopic rotors to achieve continuously variable transmission. 
     The device disclosed in U.S. Pat. No. 4,169,391 relied on varying the moment of inertia of the rotors by hydraulic means to generate a net output torque and to match the input/output conditions. This is extremely difficult to achieve especially under rapidly varying input/output conditions. Furthermore, the hydraulic system described is complex. 
     The device disclosed in the U.S. Pat. No. 3,851,545 on the other hand relied on maintaining appropriate spin orientations by external power input. This adds significant complexity to the invention disclosed especially under rapidly varying input/output conditions. 
     The applicant under the International Application PCT/NZ92/00004, disclosed a device based on gyroscopic rotors. This device relied on pumping action by Coulomb damped oscillation (“vibration”) of the gyroscopic rotors about the spin axis. A hydraulic system capable of a fraction of the total power transmission was required to cause the vibration and the “vibration” is unpredictable under high damping ratios. Further, spring elements are required to cause the “vibration” and hence hysteresis losses. An additional speed controller device was required to achieve a useful operating range. 
     The applicant is also aware of another proposal in which a gyroscopic rotor is mounted on the inner frame of a gimbal support and the outer frame of the gimbal is oscillated to cause gyroscopic torque alternating in direction. Here again with a spring system, the proposal was to cause effectively a coulomb damped vibration and from this vibration, the total power transmission was to have occurred either through hydraulic means or through an equivalent of a complex coulomb damping that would result from the resistance at the output through one-way clutches. The unpredictability of the proposed oscillation in this system is thus very high and the spring system will result in greater hysteresis losses since total power transmitted resulted directly from the “vibration”. Further, only small amplitudes of oscillation were allowed, thus requiring high forces to cause a given power transmission. 
     OBJECT 
     Accordingly, it is an object of the present invention to provide a continuously variable transmission in which such disadvantages are reduced. 
     STATEMENTS OF THE INVENTION 
     In accordance with the present invention there is provided a transmission comprising a fixed housing or support, input means moveable relative to said support, a torque shaft rotatable about its longitudinal axis, a driven shaft arranged to be rotated about its longitudinal axis by the torque shaft, a first one way clutch between the torque shaft and driven shaft, linkage means rotatable about the axis of rotation of the driven shaft under the influence of said input means and an inertial body mounted on the linkage means to be cyclically angularly deflected in response to the input means, the reaction forces generated by the inertial body as it is cyclically deflected being applied to the torque shaft as positive and negative torque and the torque shaft being connected over a second one-way clutch opposite to the first one-way clutch either to said support or to the driven shaft over a rotation reversal system whereby the driven shaft can be rotated by the torque shaft in one sense of rotation only. 
     The inertial body preferably comprises a rotor. 
     In one embodiment of the invention the linkage may comprise an outer frame rotatable about a first frame axis and an inner frame rotatable relative to the outer frame about a frame axis perpendicular to the first frame axis, the inner frame carrying said inertial body. The outer frame may be fixed to the input means for rotation therewith. The inertial body may be a rotor rotating about an axis orthogonal to the second frame axis. The torque shaft may be connected by gearing to the inner frame such that torque applied by the inertial body to the inner frame, when deflected by rotation of the inner frame, will be transmitted to the torque shaft. 
     In another embodiment of the invention the input means may comprise a drive shaft reciprocable along an axis generally coincident with or parallel to that of the output shaft, the inertial body being arranged on the linkage means so as to be angularly deflected in a plane containing or parallel with the axis of the driven shaft as the drive shaft reciprocates. The linkage may be an elbow linkage pivotally connected at one end to the drive shaft and at its other end being immovable relative to the driven shaft along the axis of the latter, the inertial body being mounted on one arm of the elbow linkage so as to be angularly deflected as the drive shaft reciprocates. The linkage may comprise a gimbal the outer frame of which is fixed relative to the torque shaft and rotatable relative to the drive shaft, the inertial body being mounted on the inner frame of the gimbal and means being provided to rotate the inner frame of the gimbal in response to reciprocation of the drive shaft. The inner frame may be connected to the drive shaft so as to be oscillated as the drive shaft reciprocates. The connection between the drive shaft and the inner frame may be connecting rod means or rack-and-pinion means. In this arrangement if the inertial body is a rotor, means may be provided between the inner frame and the rotor whereby the input also causes rotation of the rotor. 
     Means may be provided whereby the speed of rotation of the rotor can be varied relative to the input. 
     Two meshing gears may be interposed between the first one-way clutch and the driven shaft and three meshing gears may be interposed between the second one-way clutch and the driven shaft such that whichever clutch is not free-wheeling will drive the driven shaft in the same sense of rotation. 
     The input means may be additionally coupled to the output means via a third one way clutch such that the input means is driven by the output means when the speed of the latter exceeds that of the input means, in all other conditions the third one way clutch freewheeling. The third one way clutch may be coupled to the input means via a variable ratio gear system. 
     In yet another embodiment of this invention the output means may be a body rotatable about a fixed support, the input means may be a drive shaft reciprocable toward and away from said fixed support, the linkage may comprise an elbow linkage pivotally connected at one end to the drive shaft and at its other end to a frame rotatable with said body and the torque shaft may be connected over said first one-way clutch with said support and over said second one-way clutch with the frame. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Various embodiments of the present invention are described, by way of example only, with reference to the accompanying drawings, in which: 
     FIG. 1 illustrates schematically the principles relating to gyroscopic torque on a rotor due to applied precession, 
     FIG. 2 shows diagrammatically a preferred embodiment of the invention utilizing the principles shown in FIG. 1, 
     FIG. 3 is a scrap view in the direction of the arrow G in FIG. 2, when the frames  6  and  8  lie in the same plane, 
     FIG. 4 is a scrap view in the direction of the arrow H in FIG. 2, 
     FIG. 5 is a cross-section through the upper part of FIG. 2, 
     FIG. 6 shows diagrammatically an embodiment based on an alternative type of operation of the invention, 
     FIG. 7 shows diagrammatically an alternative arrangement to part of FIG. 2, 
     FIG. 8 is a cross-section in a vertical plane through the lower part of FIG. 6, 
     FIGS. 9 and 10 are theoretical diagrams, 
     FIG. 11 shows diagrammatically another embodiment, 
     FIG. 12 shows diagrammatically a further embodiment, 
     FIG. 13 shows diagrammatically part of another embodiment, 
     FIG. 14 illustrates schematically the application of FIG. 1 to the embodiments shown in FIG.  2  and FIG. 6, and 
     FIG. 15 schematically illustrates a further modification of the invention. 
    
    
     DESCRIPTION 
     Referring firstly to FIG. 1, the general principles related to gyroscopic torque generation are described as follows: 
     A rotor A spinning about the Y-axis has an angular momentum M=Iw 1  where I=moment of inertia of the rotor and w 1 =its angular velocity. This rotor may be driven by the input, output or an independent source. 
     If this rotor A is rotated about the X-axis with angular velocity w 2  then a gyroscopic precession torque T UM  about the Z-axis is generated. The torque T is given by the relationship: 
     
       
         
           T=M×w 
           2 
           =Iw 
           1 
           w 
           2 
         
       
     
     In the following description, two of the possible types of transmissions, referred to as Type A and Type B are explained. Basically, the operation of the transmissions takes place in a cyclic manner generating the output torque and the reaction torque over a cycle. 
     Type A: One of the two-and-fro input motions results in the coupling of the torque shaft to an output shaft through a one-way clutch while the other of the two-and-fro motions of the input results in the coupling of the torque shaft to the ground or to another output shaft through another opposite one-way clutch. 
     Type B: Substantially each of the input motions in either direction results in output torque being applied to the output shaft and the reaction torque being applied to the ground. This form of operation requires output rotation at a speed greater than the input frequency for smooth operation. 
     In FIG. 14, X, Y, Z are a set of fixed mutually perpendicular axes and i, j, k are a set of mutually perpendicular vectors attached to DQ so that vector M is always coincident with vector j. T NM  is the reaction torque due to the precession N, given by T NM =M×N in the direction k. 
     n is the rotational speed of the shaft DQ about the axis of PR and S is the rotational speed of DQ about its own axis. 
     Referring to FIG. 14, reaction torque T NM  is generated along the axis of the shaft DQ due to the rotation N of the angular momentum vector M. If the rotation N is now reversed so that the apex angle of the cone described by DQ is decreasing, the reaction T NM  will be generated canceling the previously generated torque T NM  and the net torque on the shaft DQ will be zero over a cycle when the vector M is restored to its original dynamically equivalent position. 
     Referring to one form of the Type A transmission shown in FIG.  2 : 
     Clutch D couples shaft DQ to shaft DP in one sense of rotation and free-wheels in the other so that only torque T NM  is transmitted to shaft PR. Clutch E couples shaft DQ to a fixed support in the other sense of rotation and free-wheels in the said one sense of rotation so that only T′ NM  is transmitted to the support. 
     Thus torque T NM  is transmitted to the shaft PR and the reaction torque is transmitted to the fixed frame by applying reciprocating precessions. This is the essence of the operation of the Type A transmission provided by the invention. 
     T SM  is the reaction torque due to the precession S given by T SM =M×S and in this case equal to zero since S=0, in Type A transmissions. 
     T nM  is the reaction torque due to the precession n given by T nM =M×n Cos ZPQ in the direction −j. 
     When n=0, no power is transmitted to the shaft PR although net torque is transmitted to the a shaft PR and T nM =0. Thus pivoting of the shaft PQ to increase the angle ZPQ requires no input effort. 
     However when n is greater than zero, T nM  is greater than zero and therefore input effort is required to increase the value of ZPQ and net power is transmitted to shaft PR. 
     During the application of the Torque T′ NM  the shaft DQ initially free-wheels and when synchronised, T′ NM  is transmitted to the swivel shaft support through the one-way clutch E. Likewise during the application of T NM  the shaft DQ initially freewheels and when synchronised T NM  is transmitted to the output shaft PR. 
     In the Type B transmission, shown in FIG. 6, S=0 only during the power transmission phase of the cycle and otherwise S does not equal zero. 
     Considering n&gt;0, at the beginning of the cycle, let the precession N be in the opposite direction to that shown and S=0. 
     As the input precession N is applied the shaft DQ will be decelerated and S will increase until equal to a positive value n Cos ZPQ, reaction torque will be applied to the now fixed shaft PR through the one-way clutch D due to the dominant output rotation over the input precession causing the vector M to swing to a dynamically equivalent direction opposite to that shown in FIG.  14 . 
     Continued application of this input precession will cause the shaft DQ to accelerate back to synchronise with the output, resulting in S=0 and transmission of the output torque through the one-way clutch E to the shaft support. At the end of this input precession the cycle is completed whereby the vector M and the precession N will appear as shown in FIG. 14, as the shaft DQ is precessed twice the initial angle ZPQ. A similar sequence of events will occur even if the angle precessed is less. 
     The cycle will be repeated as the vector M is precessed, as before, in the opposite direction ie. N &lt;0. 
     During the freewheeling which occurs preceding the reaction torque, some loss of vector orientation would occur and during the freewheeling that occurs preceding the output torque this would be corrected. 
     In FIG. 2 an output shaft  4  is rotatably mounted on a transmission housing  5 . An outer frame  6  is rotatably supported on the housing  5  by means of co-axial shafts  7 . An inner frame  8  is rotatably supported on the outer frame by means of co-axial shafts  9 . A mis-alignment joint  10  such as a constant velocity joint is coupled to the shaft  4  so that the pivot point of the mis-alignment joint is preferably coincident with the intersection point of the pivot axes of the inner and outer frames. A flexible joint  11  capable of relatively small degrees of linear and angular mis-alignment may be provided between the shaft  4  and the mis-alignment joint  10  to accept any deviation between the intersection points. A shaft  12  is rotatably supported on a shaft support  3 . 
     The shaft  12  is connected to an input link  17  through a pin joint. In its simplest form, the link  17  is a rod with provisions for pin joints at its ends. Attached to an input shaft  21  are grooved flanges  19  and  20  to accept rolling elements  22  and flange  18  is rotatable mounted in between  19  and  20  and to accept the rolling elements  22 . The flange  18  is provided with an extension such as a fork  23  to accept a pin joint with the input link  17  as shown in FIG.  5 . 
     The input shaft  21  is co-axial with the output shaft  4  and a standard mechanism such as a crank/connecting rod may be used to provide a linear reciprocating motion of the input shaft  21  along the axis of the output shaft  4 . 
     The reciprocating motion of the upper end of the input link  17  need not be truly linear. For example, it could be slightly arcuate, where the input is provided by a long horizontal lever. In this case, the link  17  is preferably connected at both ends by swivel joints. 
     Other forms of input drive could be cams, hydraulic or manual means. 
     A first one-way clutch  2  connects the shafts  12  and  4  while a second, opposite one-way clutch  1  connects the shaft  12  to the shaft support  3 . 
     A rotor shaft support  14  is attached to the shaft  12  and a rotor  13  is rotatably mounted on  14  by means of a rotor shaft  16 .  15  is a motor mounted on  14  and coupled to the rotor shaft  16 . 
     The embodiment described above may be identified as a “Type A” transmission. 
     FIG. 7 shows an alternative arrangement for the Type A transmission in which the mis-alignment joint is avoided. 
     The torque shaft  12  in this case is extended past the pivot point and is coupled to one end of a shaft  34  through the one-way clutch  2 . A hollow block  35  has internal splines and is connected to an element  33  by a pin joint. The shaft  34  has external splines engaged in the splines of the block  35 . A plate  32  provides a groove in which the element  33  engages and is free to slide along a radius of the output shaft  4 . The plate  32  is attached to the output shaft  4 . 
     In operation, the torque from the shaft  12  is transmitted to the output shaft  4  through  2 ,  34 ,  35 ,  33  while the shaft  12  is free to pivot about its pivot point. 
     A variation of the Type A transmission described above is Type B transmission shown in FIG.  6  and FIG.  8 . An output body  24  is rotatably mounted on the transmission housing  5 . A fixed shaft  25  is fixed to the transmission housing co-axially with the output body  24 . FIG. 8 shows an arrangement to satisfy the above wherein body  24  is mounted on shaft  25 . 
     Trunnion support brackets  26  are attached to the body  24 . Trunnion pins  28  may be attached to the brackets  26 . Attached to a trunnion  27  is a torque shaft support  3   a.    
     A mis-alignment joint  29  is coupled to the shaft  25  so that the pivot point of the mis-alignment joint lies on the axis of the trunnion pins  28 . A flexible joint may be provided between the shaft  25  and the mis-alignment joint to accept any deviations. 
     The one-away clutch  1  connects the shaft  12  and a shaft  31  of the mis-alignment joint while the opposite one-way clutch  2  connects the shaft  12  to the shaft support  3   a.    
     FIG. 4 applies to the rotor mounting details as for the FIG.  2 . 
     FIG. 5 applies to the input shaft mechanism as for the FIG.  2 . The input link  17  however is connected to  3   a  and not to the shaft  12 . 
     As in FIG. 2, the input shaft  21  is co-axial with the body  24  and shaft  25  and moves linearly along the axis of the output body. The pivot between the input link  17  and the support  3   a  is offset from the axis of the input shaft  21  and output body  24 . 
     A variation to the embodiments described above relating to the Type B transmission is provided by complementing the gyroscopic rotor assembly with a “dead” mass appropriately as illustrated in FIG.  10 . 
     FIG. 9 shows the principle of inertial reaction on a mass “m” moving in the direction “v”. “f” represents the acceleration of the mass and “F” represents the initial reaction of the mass. 
     In FIG. 10 for N&lt;0 the inertial force on the mass “M” and the gyroscopic torque on the vector M will act together on the output of a Type B transmission. The gyroscopic vector M is necessary to cause the cyclic process of the Type B transmission. 
     Further, the work done against the gravitational force on the mass m during the “input stage” is also transmitted to the output during the “reversal stage”, thus providing a further variation to the Type B transmission whereby a force such as gravity other than the inertial reaction is also utilised to transfer energy from the input to the output of the transmission. 
     In FIG. 11 the pivot point for the mass distribution is provided “above” the torque shaft support  5  by a hinge joint  36 . This embodiment is suitable for Type A transmissions. A variation to the Type A transmission described is provided by coupling the one way clutch  1  to another output instead of coupling to the housing, and this output could be combined to the output to the shaft  4  by means of a reversing gear arrangement as shown in FIG.  12 . 
     FIG. 12 shows another preferred embodiment of Type A transmission with many interesting features. A fork  43  is attached to the shaft  12 . The rotor shaft  16  is rotatably mounted on the frame  47 . The frame  47  is rotatably mounted on the fork  43  by means of the shafts  48  attached to the frame  47  co-axially. The shaft  12  is rotatably mounted on the transmission housing  5 . 
     Attached to the end of the input shaft  21  is a flange  37 . Thrust bearings  38  are provided on both sides of this flange  37 . The thrust bearings are housed in  39 . Arms  41  are attached to  39  and to the racks  40  of the rack and pinion arrangement provided by  40  and the pinions  42 . The pinions  42  are attached to the shafts  48 . Thus the reciprocating motion of the input shaft  21  is translated into oscillation of the rotor shaft  16  about the axis of the shafts  48  thus creating the output torque and the reaction torque on the shaft  12 . 
     In FIG. 12 a means of using the input motion to spin the rotor  13  is illustrated. A bevel gear  44  is attached to one of the forks  43  concentric with the shafts  48 . A compound gear  45  is rotatably mounted on the frame  47 . The bevel gear ring of  45  engages the gear  44  while the spur gear ring of  45  engages the gear  46 . The gear  46  is coupled to the rotor shaft  16  through a one-way clutch. Thus the oscillation of the shafts  48  about their axis will cause the rotor  13  to spin in the direction determined by the one-way clutch. 
     The gears  50  and  51  are attached to the output shaft  55 . The torque from the one-way clutch  1  is transmitted to the output gear  50  by the gear  49  attached to the one-way clutch  1 . 
     The idle gear  52  reverses the torque from the other one-way clutch  2  and transmits it to the output shaft  55 , via  53  and  51 . 
     If it is desired that the speed of the rotor  13  should be variable independently of the input frequency this can be achieved by allowing the gear  44  to slip on fork  43 . 
     The present invention may find particular applications in automobile transmissions and in power generation from fluctuating energy sources such as wind and waves. 
     However, the invention is not limited to these applications and several other possible uses are envisaged. 
     In automobile and other applications where output rotation is not always available, Type A transmission is readily applicable. 
     Type B operation is readily applicable where output rotation is available, as in power generation. Gyroscopic rotors have the advantage of being compact and a wide range of characteristics are possible. However in other applications use of a dead mass in conjunction with a gyroscopic rotor may be a cheaper option. 
     Forces and moments other than inertial reactions may be employed in conjunction with these mechanisms in particular by the Type B transmission. By causing the cyclic movements of the torque shaft as in the Type B operation and storing potential energy during the input stage and releasing the stored energy during the reversal stage, a continuously variable transmission can be obtained even without the use of inertial reactions. 
     In the following, examples of modifications are provided. 
     The embodiment shown in FIG. 12 may be modified by substituting the racks  40  and the pinions  42  with a crank and connecting rod mechanism. The pinions  42  would be replaced by cranks attached to the shaft  48  while the racks  40  would be replaced by connecting rods between said cranks and the arms  41 . 
     The Type A transmission can be modified to a versatile variable pump. The one-way clutches  1  and  2  are deleted and the output end of the torque shaft is coupled to a pump such as a swash plate pump or a cam type wobble plate pump to which a rotating input may be applied. In such a pump the stroke length automatically adjusts itself according to the back pressure, without any feed-back control. Feed-back control may still be applied to change the transmission characteristics by changing the relevant variables, such as the gyroscopic rotor speed. 
     Reference was made to the use of gravitational force in the Type B transmission to transfer energy from the input to the output of the transmission. In this case, either of shafts  24 ,  25  can be outputs or one can be coupled to the output while the other is coupled to the housing. In the following, the use of gravitational force is explained with the shaft  25  coupled to the housing. 
     Consider FIG. 10 in conjunction with FIG. 6 with a dead mass m with vector M=0, and assume that the inertial forces on the mass m are not significant in comparison with its weight and assume that the axis of the shaft  25  is substantially vertical. 
     Consider the arm Qm in such a position that the gravity force on the mass m exerts an axial torque on the shaft  25  through the one-way clutch  1 . An equal and opposite torque will be applied by the housing on the shaft  25 . This will result in a balancing torque being applied on the output body  24  due to the mis-alignment of the shafts  12  and  25 . As the output rotates under the action of this balancing force, the mass m drops down to its lowest point giving up its potential energy to the output. At this point the arm Qm is in the plane containing the axes of the shafts  12  and  25 . Continued rotation of the output will result in the mass m being raised, causing the application of a torque on the torque shaft  12  in the opposite direction, by the gravity force on m. This will accelerate the torque shaft  12  until it is synchronised with the output  24  through the one-way clutch  2 . The transmission is now ready for the next input by which the mass m is raised by reversing the angle ZPQ in FIG.  10 . As the angle ZPQ is reversed, the arm Qm will be pointing upwards and the torque on shaft  12  due to the gravity force on m is reversed, causing the shaft  12  to decelerate and synchronise with the shaft  25  through the one-way clutch  1 . The process can be repeated. A typical application of this mode of operation of the Type B transmission is in play equipment. 
     In the following, another form of the transmission is explained with reference to FIG.  13 . In this form, the output torque and the reaction torque are applied to the torque shaft  12  via a differential drive mechanism. In its most basic form, the transmission consists of a pair of co-axial shafts  56 ,  57  one of which is attached to a main fame  58  while the other is rotatable relative to said main frame  58 . A sub-frame  59  carrying a suitable mass distribution is rotatably mounted on the main frame  58  with its axis substantially perpendicular to the axis of said co-axial shafts  56 ,  57 . A right-angled drive train  64 ,  65 ,  66 ,  67  to couple the sub-frame  59  to the shaft  57 , is rotatably mounted on the main frame  58  so that the differential speed between the said co-axial shafts  56 ,  57  is transmitted to the sub-frame  59 . 
     One of these co-axial shafts  56 ,  57  will constitute the torque shaft analogous to the torque shaft  12  of previously described embodiments while the other will be coupled to the input shaft. As before, the torque shaft  57  in the present example will be connected to a driven shaft through one of the one-way clutches and through the other one-way clutch the torque shaft is connected to a rotation reversing mechanism such as shown in FIG. 12 or is connected to a fixed housing  5  of the transmission. 
     The mass distribution may be a gyroscopic rotor rotatably mounted on the sub-frame  59  with the rotor axis  63  substantially perpendicular to the axis of the sub-frame. Alternatively the mass distribution may consist of a dead mass attached to the sub-frame  59  eccentrically about the sub-frame axis, and in this case the main frame  58  must be fixed to the input shaft. 
     The transmitted torque can be adjusted by altering the location of the dead mass or by changing the speed of rotation of the gyroscopic rotor about its axis 
     It can be easily shown that as the input shaft  56  rotates, an alternating inertia torque will act on the torque shaft  57  ( 12 ), thus the output torque and the reaction torque will be generated. In this arrangement, the algebraic sum of the time integrals of the input torque, output torque and the reaction torque equals zero under ideal cyclic conditions. 
     Referring to FIG. 13, one of the co-axial shafts  56  or  57  will be the torque shaft  12 , while the other is driven by the input. The main frame  58  is attached to the shaft  56 , while the shaft  57  is coupled to the shaft  61  differentially through the right angled gear train consisting of the gears  64 ,  65 ,  66  and  67 . Gear wheel  64  is attached to the shaft  57 , which is rotatably mounted on the main frame  58 . The shaft  68  is rotatably mounted on the main frame and the gear wheels  65  and  66  are attached to the shaft  68 . A pair of co-axial shafts  61  and  69  are attached to the sub-frame  59  and rotatably mounted on the main frame as shown. The gear wheel  67  is attached to the shaft  61  and meshes with the gear wheel  66 , while the gear wheel  64  meshes with the gear wheel  65 . 
     The gyroscopic rotor  60  is attached to the shaft  63 , which is rotatably mounted on the sub-frame as shown. The rotor  60  may be driven by a motor  62  or alternatively by the input/output motions as before. Thus, it can be seen that the torque shaft principle can be applied in numerous configurations of continuously variable transmissions employing primarily inertia reactions, but other forces such as gravity are also usefully employed. 
     In the embodiment of FIG. 13 i, j, k are rotating vectors. θ is the angle made by vector j to the centre line of the transmission, in the direction k. 
     Vector i is coincident with rotor axis  63 . Vector k is coincident with the axis of the gear  67 , i.e. axis of rotation of inner frame  70 . Vector j is normal to the vectors i and k so that iΛj =k. N I  is the input speed. N S  is the speed of 70 about k in the direction k. 
     A, B, C are the moments of inertia of the inner frame  70  assembly excluding the rotor in the directions i, j and k respectively. 
     A R , B R  and C R  are the moments of inertia of the rotor in the directions i, j and k respectively. 
     N R  is the speed of the rotor in the direction i. 
     t I , t J  and t K  are the reaction torques in the directions i, j and k respectively. Under steady conditions, 
     
       
           t   I   =i N   I   N   S  Cos θ( B+B   R   −A−C−C   R ) 
       
     
     
       
           t   J   =j{N   I   N   S  Sin θ( B+B   R   +C+C   R   —A )—N S   N   R   A   R } 
       
     
     
       
           t   K   =k{N   I /2  2  Sin 2θ( A−B−B   R )+ A   R   N   R   N   I  Cos θ} 
       
     
     Under free-wheeling conditions the inertia of the gear train and the torque shaft will be considered to determine the relevant factors, such as the cycle period, etc. A cycle consists of one revolution of 70, i.e. θ, 0→360° and during a cycle output, reaction and free-wheeling will occur. 
     In the embodiments of the invention hitherto described reverse transmission of power from the output to the input is not possible. FIG. 15 illustrates an arrangement whereby it is possible for the output shaft  112  to drive the input shaft  101  when the output shaft  112  is rotating faster than the input shaft  101 . This may be advantageous in, for example, automotive applications when it may be desirable to slow down the vehicle without total reliance upon brakes. 
     In FIG. 15 the transmission of power in the forward direction takes place from the shaft  101  to the shaft  112  through the basic transmission  103 . The basic transmission  103  may be any one of those previously described and illustrated, except that a reciprocating input is assumed to be derived from the rotating input  101  with the interposition of a crank and connecting rod system. Input rotation is transmitted from the shaft  101  to the shaft  107  typically by a set of gear wheels such as  104 ,  105 , and  106 . The rotation of the shaft  107  is reduced if required, by a variable gear ratio G by the gear unit  108 . Shaft  109  is coupled to the output shaft  112  typically by a set of gear wheels such as  111 ,  212  and  113  and through the one way clutch  110 . 
     Let N 9  and N 11  be the rotational speeds of the shaft  109  and the gear wheel  111  respectively. In operation when N 9  is greater than N 11  the shaft  109  remains de-coupled from the gear wheel  111  and hence from the shaft  112 . The power transmission takes place from the shaft  101  to the shaft  112  only through the basic transmission  103 . If however when N 9  equals N 11  the gear wheel  111  is coupled to the shaft  109  through the one-way clutch  110 . 
     It may be advantageous to arrange the gear unit  108  so that its gear ratio G can be altered while in operation. In order to do so the gear wheel  111  is conveniently made to free wheel on the shaft  109  by ensuring that N 9  is greater than N 11  thus avoiding the need for a separate clutch unit.