Abstract:
A desmodromic mechanism having transmission elements connected to and supported by an intermediate element and a primary and a secondary cam both in permanent contact with the transmission elements. The transmission elements, the intermediate element, the primary and secondary cams are assembled to one another to compulsorily move in rotation or linearly relative to one another. The various elements are also assembled in such a way as to form sealed variable volume chambers.

Description:
BACKGROUND OF THE INVENTION 
     The present invention has for its object a desmodromic mechanism comprising a primary element and a secondary element mechanically interconnected by a desmodromic connection, which is to say such that the speed of one of said elements precisely determines a speed for the other. 
     Such mechanisms are found in speed changers, speed multipliers or reducers, hydraulic, pneumatic or internal combustion motors, compressors, pumps, jacks, linear actuators, etc. 
     To provide angular or linear drives for mechanisms whose object is to transmit movements permitting changing volumes to obtain pumps, compressors, etc., or to reduce or multiply speed with a certain precision, there is used gearing which has in certain cases major drawbacks, such as problems of lubrication, noise, size, difficulty to obtain movement without play, cost, etc. 
     The object is to provide the mechanisms mentioned above by a simple, precise and robust desmodromic system of a cost lower than that of conventional embodiments. 
     This system permits the use of plastic or ceramic materials under optimum conditions. It is possible to provide mechanisms which can operate without lubrication and have high mechanical resistance. 
     By the reduction of speed between the input shaft and the intermediate element carrying the transmitters, great improvements are enjoyed in the mechanisms relying on variable volume chambers. 
     The object of the present invention is to provide such a desmodromic mechanism which will be inexpensive, robust, easy to produce, which has no gearing and which permits producing linear or rotating motion of the driven element from a rotating movement of the motor element, or vice versa. 
     SUMMARY OF THE INVENTION 
     The present invention has for its object a desmodromic mechanism tending to overcome the mentioned drawbacks and permitting achieving the mentioned objects. This desmodromic mechanism is characterized by the combination of elements set forth in claim  1 . 
     The accompanying drawing shows schematically and by way of example several embodiments of the mechanism of the invention. 
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
     FIG. 1 is a perspective view, partially exploded, of a first embodiment of the mechanism. 
     FIGS. 2 through 6 show the successive positions of the mechanism for successive rotations of 90° of the primary element of the mechanism. 
     FIGS. 7 and 8 show an axial cross-section and a longitudinal cross-section of the mechanism in use in an internal combustion engine. 
     FIGS. 9 to  12  show the positions of the elements of the mechanism for the four cycles, intake, compression, explosion and exhaust, of the motor. 
     FIG. 13 shows an axial cross-section of the mechanism used as a compressor. 
     FIGS. 14 to  18  show the successive positions of the mechanism of FIG. 13, showing the operation of the latter as an air compressor. 
     FIGS. 19 to  23  show the successive positions of a second embodiment of the mechanism for angular increments of 90°, of the primary element; the secondary element is stationary. 
     FIGS. 24 to  28  show the successive positions of the second embodiment of the mechanism, for increments of 30°, of the secondary element, the intermediate element being stationary. 
     FIGS. 29 and 30 show two modifications of a third embodiment of the mechanism comprising five transmission members. 
     FIGS. 31 and 32 show a fourth embodiment of the mechanism in which friction is reduced by the use of rotatable elements. 
     FIG. 33 shows in plan view and schematically, a modification of the embodiment of the mechanism shown in FIGS. 31 and 32. 
     FIGS. 34 and 35 show a fifth embodiment of the mechanism. 
     FIG. 36 is an axial cross-section of a sixth embodiment of the mechanism. 
     FIGS. 37 to  41  show the positions of the elements of the mechanism of FIG. 36 for successive increments of 90°, of the primary element when the secondary element remains stationary. 
     FIG. 42 is a longitudinal cross-sectional view of a seventh embodiment of the mechanism. 
     FIGS. 43 to  47  show the successive positions of the mechanism of FIG. 42 for angular displacements of 90°, of the secondary element, the intermediate element being stationary. 
     FIGS. 48,  49  and  50  are schematic views of the first embodiment of the mechanism shown in FIGS. 1 to  6 , showing a particular fundamental characteristic of the mechanism present in all its embodiments. 
     FIGS. 51 and 52 are axial and longitudinal cross-sections of an eighth embodiment. 
     FIGS. 53 and 54 are developed views of the essential portions of the mechanism shown in FIGS. 51,  52  in two different positions of the mechanism. 
     FIGS. 55,  56  and  57  are longitudinal and axial cross-sections, respectively, of a ninth embodiment of the mechanism. 
     FIGS. 58 to  62  are longitudinal cross-sections and FIGS. 58A to  62 A are axial cross-sections, of a tenth embodiment of the mechanism, showing the successive positions of the latter for increments of 45°, of the primary element, the intermediate element being stationary. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The first embodiment of the desmodromic mechanism according to the invention, shown in FIGS. 1 to  6 , comprises an input shaft  1  whose end is provided with a primary cam  2  here formed by an eccentric with a track. 
     This mechanism also comprises an output shaft  3 , concentric with the input shaft  1 , whose end is provided with a plate  4  comprising axial projections  5  defining between them straight grooves or guides  6 . This assembly constitutes an intermediate element of the mechanism. 
     When mounted in service position, the primary cam  2  is located in the middle of the projections  5  of the intermediate element. 
     A casing  7  comprises bearings  8 ,  9  for the input shaft  1  and output shaft  3  and has an internal cavity  10  in which are disposed the plate  4  and the primary cam  2 . The peripheral wall of this internal cavity  10  of the casing  7  constitutes a secondary cam comprising in this embodiment two tracks  11 ,  12 . 
     Movement transmission members  13  are present in the form of cylindrical rollers and are disposed in each of the guides  6  located between the projections  5  of the plate  4  of the intermediate element  3 . These transmission members  13  slide without play in the guides  6  between the projections  5  and are in contact by their periphery simultaneously with the primary cam  2  and the secondary cam with two tracks  11 ,  12 . Moreover, these transmission members  13  are in permanent bearing relation against at least one of the lateral surfaces of the guides  6  of the intermediate element. Thus, each transmission member  13  is in permanent contact with the primary cam  2 , the secondary cam and the intermediate element. 
     If the casing  7  is held stationary and the input shaft  1  is rotated, there is obtained the successive positioning of the elements of the mechanism. From FIG. 1 to FIG. 2, the primary element  1  has undergone a rotation of 90°, the track of the primary cam forces the transmission member  13   b  outwardly, following the profile of the secondary cam, which gives rise to the rotation, in the same direction, of the intermediate member and the output shaft  3 . 
     A subsequent rotation of 90° (from FIG. 3 to FIG. 4) of the input shaft  1  gives rise, by the primary cam track, to the displacement outwardly of the transmission members  13   b  and  13   c , still in contact with the secondary cam, giving rise again to a rotation of 30° of the intermediate element. From the position of FIG. 4 to that of FIG. 5, force is transmitted from the primary cam  2  to the intermediate member by the transmission members  13   a  and  13   c . When the primary cam has undergone a new displacement of 90°, the intermediate element has undergone a new rotation of 30°. Then by a new rotation of 90° of the primary cam  2  (from FIG. 5 to FIG. 6) the transmission members  13   a  and  13   c  continue to drive the intermediate element through a new movement of 30°. At this time, the initial configuration of FIG. 2 is resumed, the transmission member  13   c  having taken the position of the transmission member  13   a . The input shaft  1  and the primary cam  2  have undergone a rotation of 360° and having done this have driven desmodromically the intermediate element over an angular distance of 120°, namely ⅓ of the angular distance traversed by the primary element  1 . There is thus obtained a speed reduction of 3 to 1 between the input shaft  1  and the output shaft, and this with a gearless mechanism having a minimum of friction, indeed solely rolling movement. The mechanism described is strictly desmodromic, which is to say that the speeds of the elements  1  and  3  are strictly proportional. If the speed of the input shaft  3  is constant, the speed of rotation of the output shaft  3  will also be constant, without any variation, of a value three times less than that of the input shaft  1 . 
     It will be seen that, when the casing is stationary, for an angular movement of the primary cam of 360°, the intermediate element undergoes a rotation in the same direction of 120°, there is thus exactly a ratio of 1 to 3. On the contrary, if it is the intermediate element which is fixed, a rotation of 360° of the primary cam gives rise to a rotation, in the opposite direction, of the casing, of 180°; there is thus in this case a ratio of 1 to 2. 
     In such a mechanism, the demultiplication ratios are always whole numbers. 
     Referring to FIG. 49, it will be seen that the transmission member  13   a  is in contact with the tip of the primary cam  2  and the hollow  11  of the secondary cam. In this position, the tangents to the points of contact of the transmission member  13   a  with the primary and secondary cams, respectively, are parallel to each other. In this position, the transmission member  13   a  cannot transmit any torque or any movement. 
     If the same tangents are traced for the transmission members  13   b  and  13   c , the points of contact of these transmission members with the primary and secondary cams are displaced and are no longer located on a diameter of the transmission member, these tangents then forming an acute angle β, γ between them. It will be noted that these angles β, γ are located one in the clockwise direction and the other in the counterclockwise direction, and hence are opposite. Thus, when the mechanism is stopped, the relative position of the three elements, the primary cam  2 , the secondary cam  11 ,  12  and the intermediate  5 ,  13 , is blocked in one direction by the transmission member  13   c  and in the other direction by the transmission member  13   b . The mechanism accordingly cannot undergo any unintended movement. 
     On the other hand, when the primary cam  2  is driven in rotation, in the clockwise direction, the transmission member  13   b  is pressed outwardly, giving rise to a movement of the intermediate element also in the clockwise direction. This is made possible because simultaneously with the rotation of the primary cam  2 , the angle γ is progressively increased, which permits a passive movement of the transmission member  13   c.    
     Returning to FIGS. 1 to  6 , it will be seen that the transmission members are active, for a rotation of the primary cam  2  in the clockwise direction, when they are located in the quadrants II and IV and passive when they are located in the quadrants I and III. Because in the course of rotation of the intermediate element there is always at least one transmission member located in one of the quadrants II and IV and at least one other in one of the quadrants I and III, there will accordingly always be at least one transmission member that is active during rotation of the mechanism. Upon stopping the mechanism, on the other hand, this arrangement ensures that it is blocked in the two directions no matter what the angular position in which the intermediate member has stopped. 
     It will be seen that the volume of the space  10  contained between the two transmission members  13 , the peripheral surface of the projection  5  and the intermediate element in contact with these transmission members  13  and the portion of the internal peripheral surface of the casing  7 , or secondary cam, is variable as a function of the rotation of the input shaft  1  and the primary cam  2 . This particularity permits designing uses for this mechanism not only as a reducer or multiplier, but also as a motor, a compressor, or a pump. 
     In the case in which the projections  5  do not ensure sealing of the volume  10 , either because the projections comprise passages, or because their height is less than that of the transmission members  13 , variable volume  10  is then determined by two adjacent transmission members and the portions of the primary and secondary cams comprised between these two transmission members. 
     It will be noted that the number of transmission members  13  is equal to the number of tracks of the primary cam  2 , increased by the number of tracks  11 ,  12  of the secondary cam, in this example equal to three. 
     It will also be noted (FIG. 2) that the distance between the high point of the track of the primary cam  2  and the high point  11  of the secondary cam of the secondary element  7 , is equal to the diameter of the transmission member  13 , namely the distance comprised between two end points of contact of this transmission member. 
     The same is true for the distance (FIG. 3) separating the low point of the primary cam  2  and the low point of the secondary cam. 
     The sum of the length y between the center of the transmission member and its contact with the primary cam, and the length z between the center of the transmission member and its contact with the secondary cam, is equal for all the elements of a same mechanism and invariable in all the positions of operation (FIG.  48 ). 
     It will be noted in this arrangement that in the course of the movement of the mechanism, the center O of the three transmission members  13  is permanently located on a circle whose center coincides with the axis X of the primary cam  2 . In this case, the primary cam  2  is constituted by an eccentric whilst the secondary cam is constituted by an oval surface. The primary cam  2  is located within the secondary cam. 
     The frictional or rolling forces are very much reduced, because they are limited to the sliding of the transmission members  13  in their guides  6  and to their rolling against the primary cam  2  and the secondary cam. 
     From the description of this first embodiment of desmodromic mechanism according to the invention, it will be evident that this mechanism is comprised essentially by a primary cam, a secondary cam and an intermediate element defining linear guides in which slide the movement transmission members; the two cams and the intermediate element are moveable relative to each other. 
     For clarity and precision of the description which follows, of the different embodiments of the mechanism, first to define that the primary cam can be located within the secondary cam or vice versa, and that the two cams can oppose axially; but always the intermediate element will be located between the two cams. 
     The two cams can be movable and the intermediate element stationary or one of the cams and the intermediate element can be movable but then the other cam is stationary. One or the other of the cams can be driven, the other cam or the intermediate element being then the driver, or vice versa. 
     By definition, there will always be meant by the primary cam, that one of the two cams which has the fewer tracks. 
     FIGS. 7 and 8 show in transverse and longitudinal cross-section, a use of the mechanism described above for implementing an internal combustion engine. For a better understanding and simplification of the description, the same references numerals as in FIGS. 1 to  6  will be used to indicate the corresponding members. 
     In this use, the casing  7  is maintained stationary and constitutes the motor block. For reasons of construction, it is made of three pieces in this example, two plates  7   a  and  7   b  as well as a ring  7   c . These three pieces  7   a ,  7   b  and  7   c  are secured to each other in stationary. 
     The intermediate element comprises a shaft  3  rotating in the two plates  7   a ,  7   b  of the casing. This shaft  3  is secured to two flanges  20  interconnected by bridges  21  equivalent to the projections  5  of the first embodiment of the mechanism. These flanges  20  turn without play and in a sealed manner relative to the ring  7   c  whose intermediate portion of the internal surface constitutes the secondary cam comprising the two tracks  11 ,  12 . 
     The input shaft  1  is rotatable in the shaft  3  and carries the primary cam  2 . 
     The transmission members  13  are disposed between the bridges  21 , the internal surface or secondary cam of the casing  7   c , the primary cam  2  and the flanges  20 . These transmission members  13  ensure sealed contact between the pieces with which they are in contact and thus delimit three variable volume chambers  10   a ,  10   b ,  10   c . To limit the friction forces between the primary cam  2  and the transmission members  13 , there is provided in this embodiment a needle bearing  22  between an eccentric  23  secured to the shaft  1  and a circular ring constituting the external surface of the primary cam  2 . 
     The ring  7   c  of the casing also comprises an inlet conduit  24  for a combustible mixture, an exhaust conduit  25  for combustion gases and a spark plug  26 , angularly offset by about 120° from each other. 
     The transmission members  13  can be tubular and provided with sealing means guaranteeing good compression and a low coefficient of friction and rolling. 
     The four phases of the cycle of operation of the motor are shown in FIGS. 9 to  12 . FIG. 9 shows the intake of the gaseous mixture into the variable volume chamber  10   c  through the conduit  24 . The primary cam  2  and the intermediate element turn in a clockwise direction. FIG. 10 shows the motor at the moment at which compression is at the point of reaching the maximum in the variable volume chamber  10   c  and at which the ignition is caused by the spark plug  26 . The rotation of the elements continues, and FIG. 11 shows the motor in the expansion phase of the variable volume chamber  10   c ; then FIG. 12 shows the exhaust  25  of the variable volume chamber  10   c . It is evident that the three variable volume chambers pass through the same four-cycle operation, such that for one complete revolution of the intermediate element  3 ,  21  each variable volume chamber  10   a ,  10   b ,  10   c  will have an ignition and expansion phase. This having been done, the shaft  1  and the primary cam  2  will have effected three complete turns. 
     Such a motor therefore has two torque elements: the shaft  1  secured to the primary cam, and the intermediate element  3 , the speed of rotation of this intermediate element  3  being three times less than that of the primary element  1 . 
     FIGS. 13 to  18  show another embodiment of the mechanism and its use as a compressor. 
     The mechanism comprises a casing formed by two flanges  130 ,  131 , of which one comprises a hub  132 , connected by a ring  133  whose internal surface  134  constitutes the secondary cam which here has four tracks. 
     The intermediate element is formed of two flanges  135 ,  136  connected by bridges  137 , provided with air passages  137   a , defining between them rectilinear radial guides in which slide the transmission members  138  formed by tubular elements. The connection between each rotatable flange  135 ,  136  and the fixed ring  133  is sealed. 
     The mechanism again comprises a primary cam  139  with a track formed by an eccentric secured to an input shaft  140  rotatable in the flange  130  and the hub  132  of the casing. 
     The transmission members  138  sealingly slide between the flanges  135 ,  136  but are not sealed in the radial guides and are in permanent and sealed contact with the primary cam  139  and the secondary cam  134 . These transmission members thus define with the primary and secondary cams sealed chambers  150  of variable volume, five in number. 
     This mechanism also comprises at least one inlet opening  141  in the hub  132  of the casing, communicating by a bore  132  in the flange  136  with a distribution sector  143  recessed in one of the side surfaces of the primary cam  139 . 
     This mechanism also comprises an exhaust conduit  144  in the hub  132  of the casing, communicating with a hole  145  provided in the end of the shaft  140  and the primary cam  139 , opening toward the periphery of this primary cam. 
     The distribution sector  143  extends over an angular extent substantially equal to 90°, and one of its ends is diametrically opposite the axis of the hole  145 . 
     In such an arrangement of the mechanism, the casing is stationary, and for a complete revolution of 360° of the input shaft  140  secured to the primary cam  139 , the intermediate element undergoes a rotation of 72°, namely ⅕ of a turn. 
     The operation of the compressor thus produced by the mechanism is the following, with reference to FIGS. 14 to  18 . In FIG. 14, the variable volume chamber  150   a  is at its least volume, isolated from the intake  143  and the exhaust  145 . The variable volume chamber  150   b  is connected to the exhaust  145  whilst the variable volume chambers  150   d  and e are connected to the intake. Rotation of the input shaft  140  and of the primary cam  139  by 45° gives rise to a rotation of the intermediate element and of the variable volume chambers  150 , of 9°, bringing the mechanism into the position shown in FIG.  15 . 
     The variable volume chamber  150   a  is connected to the intake and the variable volume chamber  150   b  to the exhaust. The volume of the chamber  150   a  increases whilst the volume of the chamber  150   b  decreases, emptying the gas which it contains into the exhaust conduit  144 . 
     Upon further rotation by 45° of the shaft  140 , the position shown in FIG. 16 is reached, wherein the chamber  150   b  is at its smallest volume and it is no longer connected to the exhaust but it is the chamber  150   c  which is connected also to the exhaust whilst the chambers  150   d  and e are connected to the intake. Upon a further rotation of the primary cam by 90°, to arrive at the position shown in FIG. 17, the variable volume chamber  150   c  decreases in volume and expels its contents through the exhaust. Upon a further rotation of the primary cam by 90°, to reach the position shown in FIG. 18, the variable volume chamber  150   d  expels its contents to the exhaust whilst the chambers  150   c  and  150   b  refill because they are connected to the intake. 
     Due to the rotation of the input shaft  140 , the exhaust is connected successively to each variable volume chamber while there volume decreases and the chambers refill during increase of their volume. The mechanism thus constitutes a continuous compressor. The torque necessary for the input shaft  140  to obtain a high rate of compression is reduced by the demultiplication of 5 to 1 of the rotative movement between the input shaft and the intermediate element which defines with the secondary cam the variable volume chambers. 
     It will therefore be seen that the mechanism according to the invention can be used as a mechanical reducer or multiplier (FIGS. 1 to  6 ), as an internal combustion engine (FIGS. 7 to  12 ) or as a compressor or hydraulic or pneumatic motor (FIGS. 13 to  18 ). It is also used to carry out linear movements for example of jacks, linear actuators of the displacement of elements of indefinite length by replacing racks, chains, etc. Thus, by using the same mechanical principle, several very different applications can be carried out, which renders this mechanism particularly polyvalent. 
     In what follows, there will be described several more embodiments and variations of the mechanism which, although they refer to the use as a speed reducer or multiplier, can of course be used in the concepts mentioned above. 
     The embodiment of the desmodromic mechanism according to the invention shown in FIGS. 19 to  23  comprises an input shaft  1  secured by a primary cam  2  to a track and a fixed casing  7  having a secondary cam with three tracks formed by the internal peripheral wall of the casing  7 . 
     The intermediate element in this case comprises an output shaft secured to a plate  4  having four projections  5  uniformly spaced about its circumference and defining between them four guides  6  receiving the transmission members  13 , sliding without play in these guides and bearing against the primary cam  2  and the secondary cam and these projections  5 . 
     In this embodiment, if the casing  7  is maintained stationary and successive rotations of 90° are imposed on the primary cam  2 , there are obtained the successive positions illustrated in FIGS. 19 to  23 . When the primary cam  2   a  performs one complete revolution, passing from FIG. 19 to FIG. 23, the intermediate element  4 ,  5  has carried out a rotation of 90° as shown by the position of projection  5   a  and the transmission member  13   a.    
     The sum of the tracks of the primary cam  2  and of the tracks of the secondary cam  7  is four, equal to the number of transmission members  13 . 
     In this example, there is a demultiplication ratio of 4:1 between the angular movements of the input shaft  1  secured to the primary cam  2  and the intermediate element  3 ,  5 . The two shafts  1 ,  3  turn in the same direction. 
     In FIGS. 24 to  28 , there are shown the successive positions of a mechanism identical to that of FIGS. 19 to  23  but in which it is the intermediate element  4 ,  5  which is maintained stationary. Thus, for each rotation of 90° of the input shaft  1  and of the primary cam  2  in the direction of the arrow F, it will be seen that the casing  7  performs a rotation in the reverse direction of 30°. Thus, for one turn of the primary cam  2  in the clockwise direction there is obtained a rotation of 120° of the casing  7  in the counterclockwise direction, the track A of this casing passing from its position shown in FIG. 24 (noon) to that shown in FIG. 28 (8 a.m.). 
     For one complete revolution of the primary cam  2 , the casing performs a rotation of ⅓ of a turn in the reverse direction. There is thus carried out a demultiplication of 3 to 1. 
     In the embodiment shown in FIG. 29, the input shaft  1  has an eccentric  30  on which is idly mounted a tubular primary cam  31  via a needle bearing  32 . This primary cam  31  has a single track. 
     The intermediate element, secured to the output shaft  3 , comprises a plate  4  provided with five projections  5  uniformly disposed about the axis of said plate  4  and defining five rectilinear radial guides  6  each receiving one transmission member  13  sliding without play in these guides and the transmission members  13  are tubular to reduce the inertia and deform slightly during rotation of the system and prevent play upon stopping. 
     The internal peripheral wall of the casing  7  has four tracks  33  which constitute the secondary cam. 
     The number of transmission members  13  is equal to the sum of the tracks of the primary cam  31  and the tracks  33  of the secondary cam, namely five. If the casing  7  is maintained stationary, there is obtained for each complete revolution of the primary cam  30 ,  31  an angular displacement in the same direction of the intermediate element  4 ,  5  of 72°, namely ⅕ of a turn. 
     In the modification of this third embodiment shown in FIG. 30, the shape of the secondary cam is different although it also comprises four tracks  34 . The rule of the sum of the values y, z applies to these two variations. 
     In these two variations also, the distance separating the low point of the primary cam  2  from each low point of the secondary cam is equal to the diameter of a transmission member, as is also the distance separating the high point of the primary cam from each high point of the secondary cam when these points are aligned across a diameter of the mechanism. 
     Here again, the center of the transmission members  13  is always located on a circle whose center coincides with the axis of the eccentric and hence of the primary cam  30 . 
     FIGS. 31 and 32 show an embodiment of the mechanism comprising an input shaft  41  secured to a central drum  42  carrying at each of its axial ends a primary cam with one track  43 , these cams  43  being exactly aligned angularly. This input shaft  41  rotates in an intermediate element comprising two flanges  44  each secured to a bearing  45 , located on opposite sides of the primary cams  43 . These bearings freely pivot in the casing formed by two lateral flanges  46  interconnected by a ring  47  whose central section  48  of the internal surface constitutes the secondary cam. 
     The primary cam  43  is constituted by an eccentric comprising one track and the secondary cam  48  by a casing having seven tracks uniformly distributed about the axis of the mechanism. 
     This mechanism also comprises eight transmission members, each constituted by an axle  49  bearing a central roller  50  coacting with the secondary cam  48  and two lateral rollers  51  coacting respectively each with one of the primary cams  43 . The axles  49  slide without play in radial slots  52  of the flanges  44  of the intermediate element and serving as guides to the transmission members. 
     There will be found in this embodiment the same criteria regulating the number of transmission members  49 ,  50 ,  51  which is equal to the sum of the tracks of the primary cam  43  and the seven tracks of the secondary cam  48 , namely, in this case, eight. 
     The same is true for the separating distances, taken on the radius of the mechanism, the high and low points respectively of the primary and secondary cams are equal to the diameter of the transmission members. The axles  49  of the transmission members are disposed about a circumference whose center coincides with the axis of the eccentric  43 . 
     In this embodiment, the intermediate element and its output shaft  45  perform ⅛ of a turn when the primary cam  43  and its input shaft  41  carry out one complete revolution. There is therefore a ratio of 8 to 1. This embodiment permits transmitting high torque, almost all the friction being avoided by the rotation of the assembly of the rollers forming the transmission members. 
     FIG. 33 shows a modification of this embodiment in which one of two transmission members  51  has been omitted. The secondary cam  48  again comprises seven tracks, the primary cam  42  one track, but the number of transmission members  52  is four. This does not modify the demultiplication ratio, which again is equal to ⅛. This solution permits simplifying the production for uses in which the cost is important and the input torque low. 
     In this embodiment, the intermediate member is of the type of that shown in FIGS. 1 to  6  for example, and comprises a plate  4  provided with projections  5  constituting the linear guides. The transmission members  52  are constituted by cylindrical rollers. 
     In the embodiment shown in FIGS. 34 and 35, the mechanism comprises an input shaft  61  comprising two angularly opposite eccentrics  62  forming together a primary cam with two tracks. 
     The intermediate element comprises an output shaft  63  carrying a plate  64  provided with three projections  65  defining between them the radial rectilinear guides for the transmission members  66  juxtaposed two by two in each of these guides and each coacting with one of the eccentrics  62 . One of the ends of the input shaft  61  is journelled in the output shaft  63  whilst the other is journelled in a half  67  of the casing  67 ,  68 . 
     The casing  67 ,  68  has on its internal surface of each of its halves  67 ,  68  a secondary cam  69 ,  70  each with two tracks. The secondary cams  69 ,  70  are offset by 90° so as to form a secondary cam with four tracks total. 
     The sum of the tracks of the primary cam  62  and of the tracks of the secondary cam  69 ,  70  is six, equal to the number of transmission members  66 . 
     When the primary input shaft  61  carries out one complete turn, the output shaft  63  of the intermediate element performs a rotation of 120° as in the first embodiment described, the demultiplication ratio being three. 
     It will be seen from the description of the preceding embodiments and of their operation, that the ratio of the speeds of movement, for a mechanism whose casing is fixed, is equal to the number of tracks of the secondary cam increased by the number of tracks of the primary cam, divided by the number of tracks of the primary cam, namely (3+1):1=4 in the example of FIGS. 19 to  23  and (7+1):1=8 in the example of FIGS. 31,  32 ,  33  and (6+2):2=3 in the example of FIGS. 34,  35 . The input and output shafts turn in the same direction. For a secondary cam with four tracks=360°:4=90°; six transmission members 360°:6=60°; 90°−60°=30°; 90°:30°=3; demultiplication 1:3; 60°:30°=2, demultiplication 1:2. 
     On the contrary, when it is the intermediate element which is maintained fixed, a rotation of one complete turn of the casing gives rise to a rotation of the primary cam or of the input shaft equal to the number of tracks of the secondary cam divided by the number of tracks of the primary cam, namely three in the example of FIGS. 24 to  28 . In this case, the casing rotates in the reverse direction from the input shaft. 
     It will also be seen that the number of transmission members is generally equal to the number of tracks of the secondary cam increased by one. 
     In the embodiment shown in FIGS. 36 to  41 , the input shaft  1  carries a primary cam  2  with two tracks. The intermediate element or output shaft  3  comprises a plate  4  provided with projections  5  defining eight guides  6  for the transmission members  13 , which are eight in number. The casing  7  has an internal peripheral surface forming the secondary cam which has six tracks. The casing  7  being maintained fixed, the output shaft  3  turns four times less quickly than the input shaft  1 , which corresponds to the number eight, divided by the number of tracks of the primary cam, two. The two shafts  1  and  3  turn in the same direction. 
     In the embodiment shown in FIGS. 42 to  47 , the shaft  1  is provided with a secondary cam  2  with four tracks disposed symmetrically about this axis. The intermediate element is constituted by a housing  80  pivoted on the input shaft  1  on opposite sides of the secondary cam  2 . This housing  80  has five holes  81  provided in its peripheral wall, uniformly spaced about the axis of this housing  80  and constituting recesses or guides for the transmission members constituted by the spherical balls  82 . 
     The primary cam is in this instance formed by a ring  83  pivoted on the housing  80  and of which the internal surface  84 , which is eccentric, constitutes the primary cam which in this case has a single track. 
     If the intermediate element  80  is maintained stationary, one complete revolution of the ring  83  in a clockwise direction gives rise to the rotation of ¼ of a turn in the reverse direction, of the shaft  1 . There is thus precisely achieved a demultiplication ratio of 1 to 4, namely, in this case, equal to the number of tracks of the secondary cam divided by the number of tracks of the primary cam. The number of transmission members  82  is equal to the number of tracks of the secondary cam increased by the number of tracks of the primary cam, namely five. If the input shaft  1  provided with the four tracks of the secondary cam  2  is maintained fixed, the intermediate element  80  will turn five times less rapidly than the primary cam  83  but in the same direction. The ratio will accordingly be 1 to 5. 
     In all the embodiments of the mechanism, the transmission members are always permanently in contact with the primary and secondary cams and with the intermediate element in which they slide radially. 
     This mechanism, which therefore has no play, permits a perfect desmodromic transmission of the movement of one element on another. There is a continuous sliding or rolling of the transmission members which have a perfectly smooth contact surface, circular or spherical, on the primary cam and simultaneously on the secondary cam. It should be noted that this arrangement of the cams permits providing coaxial speed reducers whose housing turns more rapidly than the central shaft, which is the reverse of all known existing systems. 
     The form of the transmissions can vary. They generally have, however, a spherical or cylindrical peripheral portion of circular cross-section which is in contact with each of the primary and secondary cams. 
     It will be noted that in all the embodiments described up to now, the transmission members slide radially and perpendicularly relative to the axis of the mechanism. 
     The embodiment of the desmodromic mechanism described with respect to FIGS. 51 to  54  operates again according to the same principle but this embodiment is original and is particularly suitable for reducers of small diameter having high demultiplication ratios. 
     This mechanism is inscribed within a tube or tubular envelope  90  closed at its two ends by flanges  91  giving passage to an input shaft  92  and respectively an output shaft  93 . 
     In this embodiment, the primary and secondary cams are no longer disposed one within the other but axially in alignment one behind the other within the tubular envelope  90 . This arrangement permits providing several stages of reduction one after the other and obtaining with three stages for example a reduction of 1 to 1000 and this in a diameter less than 8 mm and a length less than 25 mm. 
     The input shaft  92  is secured to a cylindrical element  94  pivoted in the envelope  90  having on its front surface a surface  95  constituting the primary cam comprising a track. 
     A tubular partition  96  positions a fixed secondary cam  97  constituted by an annular bell cam comprising four tracks. A first intermediate element  98  is pivoted coaxially on the envelope  90 . This intermediate element  98  passes through the central opening of the bell cam  97  and has a hub grooved in the direction of the primary cam  95 . This hub comprises five throats or grooves  99  in which are disposed five balls  100  constituting the transmission members. The axial position of the secondary cam  97  and of this intermediate element  98 , defined by the tubular partition  90 , are such that when one ball  100  is in contact with the top of the track of the primary cam  95 , this ball will be in contact with the secondary cam  97  in the deeper one of its tracks. 
     FIGS. 53 and 54 show schematically the primary cam  95  and secondary cam  97  as well as the five balls  100  in a linear development in two different positions of the mechanism. 
     The demultiplication ratio of such a stage is equal to the number of tracks of the secondary cam increased by the number of tracks of the primary cam, divided by the number of tracks of the primary cam, in this case (4+1):1=5; or according to the formula: secondary cam 360°:4=90°; transmission members 360°:5=72°; 90°−72°=18°; 90°:18°=5. 
     The free front surface of the intermediate element  98  itself also has a primary cam  95   a  acting on the balls  100   a  sliding axially in a second intermediate element  98   a  and coacting with the four tracks of the second secondary cam  97  thereby forming a second demultiplication stage identical to the first. 
     A third demultiplication stage of the mechanism is constituted by a third primary cam  95   b  disposed on the front surface of the second intermediate element acting on the balls  100   b  sliding axially in a hub  101  of the output shaft and coacting with the tracks of a third secondary cam  97   b.    
     In this embodiment, the primary and secondary cams are coaxial and facing, the secondary cams  97  are fixed, whilst the primary cams  95  turn about the axis of the assembly and of the input shaft  92  and output shaft  93 . 
     In a modification, it is evident that the number of tracks of the secondary cams  97 ,  97   a ,  97   b  of the different stage of demultiplication can be different, the number of grooves  99  of the intermediate element  98  and of the transmission members  100  varying as a result. Thus, a very large choice of ratios, always whole numbers, is available. 
     It will also be noted here that the tangents to the points of contact of at least two balls  100  with the primary cam  95  and secondary cam  97  form angles β, γ extending in opposite directions, preventing any movement of the mechanism when it is stopped. 
     The embodiment of the mechanism according to the invention shown in FIGS. 55 to  57  constitutes a jack or a linear mechanical actuator, again based on the same principle of actuation and of demultiplication. 
     This mechanism comprises a fixed body  110  forming an intermediate element on which is journalled a ring  111  whose eccentric internal surface  112  constitutes the primary cam and one track of the mechanism. A linear actuating rod  113 , cylindrical or polygonal, slides in the body  110  and comprises at its end portion disposed in the body, at least one hourglass-shaped portion  114  constituting the secondary cam. 
     Holes  114 , four in the illustrated example, pass through the body radially. These holes are angularly offset by 90° from each other and axially by a distance equal to ¼ of the length L of the secondary cam  114  of hourglass shape. The arrangement of these holes  115  relative to the secondary cam  114  is such that the latter comprises by analogy three tracks. 
     Transmission members constituted by spherical balls  116  are slidably mounted in the holes  115  and are in permanent contact with the body  110  and each of the primary cam  112  and secondary cam  114 . 
     For one complete revolution of the ring  112  and hence of the primary cam, there is obtained a linear displacement of the actuating rod  113  of a length L of the secondary cam of hourglass shape. 
     There are in this embodiment acute angles β and γ between the tangents to the points of contact of two balls  116  with the primary cam  112  and secondary cam  114 , ensuring blocking of the mechanism when it is stopped. 
     FIG. 57 shows the mechanism when the ring  111  has carried out ¼ of a turn from the position shown in FIG.  54 . The two balls have advanced relative to the rod  113  by a quarter of the length of the hourglass-shaped cam. 
     This embodiment of the mechanism is particularly interesting because the actuating rod  113  can, independently of its linear movements controlled by the ring  111 , carry out movements of rotation about itself without changing its axial position. 
     The final embodiment of the mechanism, shown in FIGS. 58 to  62 A, is also a linear displacement mechanism. It comprises a frame  120  constituting the intermediate element, in this case H-shaped in longitudinal cross-section. In the upper portion of the frame, between the legs of the H, is journalled an input shaft  121  secured to the primary cam, here comprised by four eccentrics  122   a, b, c, d  angularly offset by 90° relative to each other and representing the track of the primary cam. The horizontal bar of the H of frame  120  comprises four holes  123  each aligned with one of the eccentrics  122   a, b, c, d , constituting the guides for the balls  124  comprising the transmission members. 
     In the lower portion of the frame  120  is provided a space in which slides longitudinally, parallel to the axis of the input shaft  121 , a portion of,a rod or bar  125  that is displaceable linearly on the rollers  126 . The upper surface of this bar  125  facing the holes  123  of the frame  120  has a secondary cam  127  formed by successive hollows which constitute the tracks of this secondary cam. The distance D corresponding to the length of three successive tracks is equal to four times the interaxial distance of the holes  123 . 
     The smooth balls  124  are permanently in contact each with one of the eccentrics  122   a, b, c, d  of the primary cam and with the secondary cam and bear on the frame  120 . This assembly corresponds to a mechanism comprising one primary cam with one track and one secondary cam with three tracks. 
     For one complete revolution of the input shaft  121  and hence of the primary cam  122 , there is obtained a linear movement of the bar equal to ⅓ of the distance D, namely equal to the extent of one track of the secondary cam. 
     In this embodiment also, the tangents to the point of contact of two balls  124  with the primary cam  122  and secondary cam  125  form opposite acute angles β and γ such that the elements  120 ,  121  and  125  of the mechanism are blocked when the input shaft  121  is not driven in rotation. 
     In modifications, the transmission members can comprise a cylindrical body and rounded ends. This transmission members can also be formed by the juxtaposition of several rotating elements to limit friction. 
     In all of the embodiments of the mechanism, the primary cam is the one of the two cams which has the fewer tracks. In all embodiments of the mechanism, except the one shown in FIGS. 52 to  54 , the guide axles of the rectilinear guides of the intermediate element are disposed radially and/or perpendicularly to the axis of the mechanism. 
     In the embodiment shown in FIGS. 52 to  54 , by contrast, the guide axles of the guides of the intermediate element are disposed parallel to the axis of the mechanism. 
     In embodiments of the mechanism not shown, it can be provided that the transmission members are connected to the intermediate element or to the body of this intermediate element by other means than the rectilinear guides in which they slide. Thus, each transmission member can be connected to the body of the intermediate element by a rod articulated on the body of the intermediate element and carrying the transmission member. In such an arrangement, there is no friction but only rolling of the transmission members on the primary and secondary cams and on the body of the intermediate element. In such an arrangement, the movement of the transmission members relative to the body of the intermediate element takes place along an arc of a circle, namely, along an curvilinear and nonrectilinear path.