Epicyclic transmission having free rolling roller driving elements
BACKGROUND OF THE INVENTION 
     Speed reducing mechanisms of the epicyclic type are well known mechanical transmission mechanisms, which typically include an orbiting internal pinion gear which is provided with teeth on its external periphery. The number of teeth on the pinion gear is typically one or a few less than the number of teeth on an outer ring gear, such that a large speed reduction can be obtained between the orbital input and an output appropriately coupled to the internal pinion gear. 
     Such epicyclic transmissions have been provided in single, double and multiple stages in order to obtain any desired speed transmission ratio. However, gear systems of the type just described suffer from a number of disabilities. Firstly, such gearing systems are not particularly efficient in terms of the amount of torque which can be transmitted, and secondly, the gears are expensive to produce, inasmuch as each toothed member must be precisely cut. Such devices can transmit only a limited amount of torque due to the fact that only some small fraction of the gear teeth are in contact at any given instant. It will be appreciated that it is impossible to design an internal pinion type speed reducing mechanism so that a large percentage of the torque transmitting elements (teeth) are in torque transmitting engagement at all times. 
     SUMMARY OF THE INVENTION 
     The present invention relates to a speed reduction transmission mechanism wherein the drive system includes a pair of conjugate epitrochoidal and hypotrochoidal surfaces disposed on driving and driven disks, with a plurality of rolling elements disposed between and transmitting torque from driving to driven member. The rolling elements are provided in the form of cylindrical rollers, which rollingly transmit torque while remaining engaged with the opposed trochoidal surfaces at all times. The hypotrochoidal and epitrochoidal surfaces have a plurality of &#34;lobes&#34; thereon, where the number of hypotrochoidal &#34;lobes&#34; is greater by two than the number of epitrochoidal lobes. The number of rollers is equal to the number of epitrochoidal lobes, plus one. The speed reduction ratio obtainable with the present invention depends upon the number of reduction stages, while the speed reduction for a given stage is dependent only upon the numbers of lobes of the opposed surfaces. The basic mechanical movement employed by the device is one in which a member is made to orbit about its axis while rotating at a reduced speed, while the rolling torque transmitting rollers circulate following a substantially trochoidal path while maintaining in contact with the trochoidal surfaces of the member and a further gearing element. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a sectional view of a two stage speed reduction device according to the present invention; 
     FIG. 2 is a sectional view of a speed reducer according to a second embodiment of the invention where either double or triple stage reduction can be achieved; 
     FIG. 3 is a sectional view of a transmission according to a third embodiment of the invention, where single stage reduction is obtained; 
     FIGS. 4, 5 and 6 are schematic views of the opposed hypotrochoidal and epitrochoidal surfaces according to the invention, with the rollers shown engaged therebetween; 
     FIGS. 7 and 8 are sectional views depicting modifications of the basic design of FIG. 1; and 
     FIG. 9 is a longitudinal view of an example of a speed reducing mechanism according to the invention illustrating various relationships among the rollers and the driving and driven elements. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Turning now to the drawing figures, and in particular to FIG. 1, a first example of a speed reducing mechanism according to the invention is illustrated. The present transmission achieves a double speed reduction by means of two conjugate sets of epitrochoidal and hypotrochoidal surfaces, as will become more apparent hereafter. 
     An input shaft 10 is received within a stationary housing 20 and is journaled for rotation therein by means of roller bearings 11 which separate the input shaft 10 from an extension of an output shaft 60. The shaft 10 includes a pair of eccentric portions 30, which may be formed integrally with or separately from the shaft. Also provided on the shaft opposite the most highly eccentric portion of the cams 30 are a pair of counterweights 40, which will be described in more detail hereafter. Journaled upon the eccentric cams 30 by means of a ring of bearings 32 or the like is an idler member 50. As is apparent from FIG. 1, as the input shaft 10 is rotated, the idler member 50 is made to undergo orbital motion at a speed determined by that of the input shaft. Due to the presence of the intermediate bearings 32, the idler 50 is capable of rotation about its axis independently of the orbital motion imparted thereto by means of the shaft 10. 
     The idler 50 is a generally disk-shaped element which is bifurcated at its radially outer periphery to form two gear elements 52, 54. The outer surface of the gear 52 is formed with trochoidal curvature, as is a coacting, a conjugate gear element 70 which is in engagement with the former gear element by means of intermediate caged cylindrical rollers 80. In FIG. 1, the gear element 70 is suitably fixed to the housing 20, so as to form a stator therewith. 
     As noted, the surface of the stator 70 is formed with trochoidal curvature, conjugate to that of the gear element 52. By &#34;conjugate&#34; is meant that the curvature of these two surfaces are related in such a way that the rollers will be in substantially continuous contact with both surfaces. One method of producing conjugate epitrochoidal and hypotrochoidal surfaces is taught in copending patent application Ser. No. 313,442, filed Oct. 20, 1981 by the present inventors, the disclosure of which is hereby incorporated by reference. In FIG. 1, the gear element 52 may be provided with epitrochoidal curvature, while that of the stator is hypotrochoidal. 
     FIGS. 4, 5 and 6 schematically show a hypotrochoidal outer member 100 engaged with an inner, epitrochoidal gear element 102 by means of the intermediate rollers 80. FIGS. 4, 5 and 6 show the cases where the number of intermediate rollers are 46, 47 and 34, respectively. The engagement between the stator 70 and the idler gear member 52 is similar to that shown in FIGS. 4 through 6, but may be different in terms of the actual numbers of lobes and roller elements. As can be seen from FIGS. 4-6, the positions of the rollers with respect to the trochoidally formed surfaces range from a position in which a roller is nearly entrained within opposed recesses of the gears, to a position where the roller passes over the confronting crests of the two gear elements. It will be observed from these figures that as the inner member is made to orbit about its axis, assuming that the outer member is stationary, it will be caused to rotate about its axis at a speed determined by the relative number of lobes on the two gears, as the rollers circulate, or rollingly engage both gear elements. Specific formulae for determining the output speed ratio will be presented hereafter. 
     Due to the engagement between idler gear member 52 and stator 70, the idler 50 will be caused to rotate about its own axis in a direction opposite that of the input rotation, at a reduced speed dependent upon the number of lobes on the opposed trochoidal surfaces, as noted above. The idler 50 rotates reversely to the input due to the fact that the stator member 70 has a greater pitch diameter and a larger number of trochoidal lobes than does the gear element 52. Since the first gear element 52 is integral with the second idler gear member 54, these two gears rotate/orbit as a unit. 
     As can be seen from FIG. 1, the second idler gear element 54 is in engagement with an output gear member 90 having a hypotrochoidally lobed surface 92, via an intermediate second set of caged cylindrical rollers 80. The surface 92 of the output gear 90 is formed substantially identically to the gear surface 72 of the idler 70, but the pitch diameter thereof is slightly larger, e.g., it contains one more hypotrochoidal lobe than does the stator surface 72. As the difference in the number of lobes within a conjugate set of hypotrochoidal and epitrochoidal elements is always equal to two, it will be appreciated that the surface 56 of the second idler gear element 54 has one more epitrochoidal lobe than does the surface 53 of the first idler gear 52. It should be noted that whether the stator or the output gear has the greater number of lobes is of no consequence, so that the arrangement could easily be the reverse of that just described. 
     Since the idler 50 is orbiting at a speed determined by the input shaft 10, and is rotating in the direction opposite thereto at a reduced speed, the output obtained at the gear 90 will be at a further reduced speed, in the direction opposite the input direction so long as the pitch diameter of the surface 92 times that of the surface 52 is less than the pitch diameter of the surface 72 times that of the surface 56. 
     The speed reduction ratio obtained with the device of FIG. 1 may be determined from the following formula: ##EQU1## where: n 1  is equal to the number of hypotrochoidal lobes on the stator surface 72, 
     n 2  equals the number of lobes on the coacting epitrochoidal idler surface 53, 
     n 3  equals the number of lobes on the surface 56 of the epicycling idler 50, and 
     n 4  equals the number of lobes on the output gear surface 92. 
     As an example, if the number of lobes of the trochoidal surfaces of the stator, first and second idler gears 52, 54 and output gear 90 are 17, 15, 16 and 18, respectively, it can readily be calculated from the above formula that the speed reduction ratio of the transmission is equal to -135:1, where the negative sign indicates that the output rotation is in the direction opposite that of the input. It goes without saying that the output speed ratio may be easily raised or lowered by merely replacing conjugate gear sets with others having different numbers of lobes formed thereon. For example, with any of the constructions illustrated in FIGS. 4 through 6, the output speed ratio could be made substantially higher. 
     As the pinion member 50 is driven in an orbital fashion by the cam members 30, the system developes a dynamic imbalance which must be effectively cancelled in order for the unit to be usable at high speeds. For this purpose, the counterweights 40 are provided on either side of the idler member 50, and as can be seen from FIG. 1, the counterweights may be made integral with the eccentric cams 30. The counterweights 40 are of course selected as regards their weight and radial length so as to dynamically balance the system. Since the counterweights are arranged opposite the cam members 30, it will be observed that they will always remain at a position opposite the point of maximum eccentricity of the idler 50. The counterweights, as well as the shaft 10 itself, are supported against the housing 20 by means of bearing elements 31, 32. The bearing elements 33 also serve to support the output gear 90 within the housing 20, along with a set of bearings 29. 
     As noted previously, the rollers 80 of the present embodiment are caged, in a manner similar to that commonly found in ball bearings or universal joints. In particular, a pair of annular cage elements are provided on either side of the sets of rollers. The purpose of the cage is to maintain the rolling elements 80 at prescribed distances from each other, and to this end, the cages are provided as simple circular disks having suitably sized apertures therein. The cage elements do not ordinarily act as torque transmitting elements, but merely allow the rollers to cooperate effectively with the respective gear surfaces. A more specific discussion of the interrelationships of the torque transmitting surfaces, the rollers and the cages will be presented hereafter. 
     Shown in FIG. 2 is a second embodiment of the invention which is substantially similar to the first embodiment except that the transmission in FIG. 2 is counterbalanced instead of counterweighted. For ease of description, the elements in FIG. 2 have been numbered similarly to the like elements in FIG. 1. 
     In the embodiment of FIG. 2, the previously unitary idler 50 is divided into two separate disk elements 50a and 50b, which are driven 180° out of phase with respect to each other by means of eccentric cam members 30a, 30b  provided on the input shaft 10. Since the first and second idler disks are maintained oppositely directed, the device of FIG. 2 is thus self-balancing, so that no counterweight elements are required. 
     Although the idler elements 50a, 50b orbit oppositely to each other, they are maintained rotationally coupled by means of a constant velocity coupling consisting of elements 106, 107 and 108. More specifically, each of the idler elements is provided with a series of circular recesses 106, 108, respectively, formed therein. Operating between the two idler elements and transmitting torque from one to the other are a series of balls 107, one for each opposed pair of recesses 106, 108. The diameter of the recesses is selected so that the coupling may accommodate the combined eccentricities of the cam elements 30a, 30b, as is seen in FIG. 2. It will be appreciated that the constant velocity coupling serves to join the members 50a, 50b for joint rotary movement, while allowing independent orbital movement. Constant velocity couplings such as the type shown in FIG. 2 are discussed in more detail in the above-noted copending application Ser. No. 313,442, and are thus not further discussed herein. 
     The embodiment of FIG. 2 otherwise operates identically to the FIG. 1 embodiment, with the first idler 50a being rotated while orbiting due to its engagement with the stator 70 through the rollers 80, while the idler member 50b rotates therewith while being in contact with the output gear 90. A double stage reduction is thus realized, and equation (1) given above is applicable to this embodiment. 
     It should be noted that the conjoint rotation of the idler members 50a, 50b is not necessarily required, as long as these members are maintained orbitally out of phase by 180°. Thus, the constant velocity coupling may be replaced, if desired, with opposed epitrochoidal and hypotrochoidal grooves, such as those found in the above-noted copending application. In this manner, a further speed reduction may be obtained between the idler member 50a and idler member 50b, so that the overall speed reduction ratio is made much larger. In this case, the embodiment of FIG. 2 should be regarded as a three stage reduction transmission, whose ratio may be determined by the following equation, which is analogous to equation (1). ##EQU2## 
     Where: 
     n 1  through n 4  are the same as above, and 
     n 5  and n 6  are equal to the number of lobes on the opposed epitrochoidal and hypotrochoidal surfaces formed in the confronting surfaces of the idlers 50a, 50b, respectively. 
     FIG. 3 discloses an analogous speed reduction mechanism wherein a single stage reduction is achieved. In particular, in FIG. 3, the input shaft 10 is provided with an eccentric cam 30, as in the previous embodiments, which initiates orbital movement on the part of the idler member 50. 
     Attached to the housing 20 is the stator 70 which is provided with surface 72 of hypotrochoidal curvature. The surface 52 of the idler 50 is, as in the previous embodiments, provided with epitrochoidal curvature conjugate to that of the hypotrochoid, and is in engagement therewith through the intermediary of a series of rollers 80. Accordingly, as the idler member 50 is caused to orbit by means of the cam 30, it is also caused to rotate reversely at a speed dependent upon the numbers of lobes on the respective surfaces 52, 72. 
     Joining the idler member 50 to the output member 90 in this embodiment is a constant velocity coupling consisting of elements 120-124. Specifically, cup-shaped recesses are formed in the output member 90 and the idler member 50 in a manner similar to that provided on the two idlers in the embodiment of FIG. 2. As is seen in FIG. 3, one of a series of balls 122 joint each confronting recess 120, 124, of which a plurality are provided. The constant velocity coupling formed as just described operates to transmit the rotational component of the compound motion of the idler 50 to the output shaft 60, such that a single speed reduction is obtained overall. 
     The speed reduction obtainable with the single stage transmission of FIG. 3 may be determined from the following formula, which is completely analogous to previous expressions (1), (2). ##EQU3## 
     Where: 
     n 1  equals the number of lobes on the stator, and 
     n 2  equals the number of lobes on the idler surface 52. 
     The transmission of FIG. 3 is maintained in dynamic balance by means of a single counterweight 40. 
     FIGS. 7 and 8 illustrate further exemplitive embodiments of the invention, each of which is a variant of the device according to FIG. 1. Each of these further embodiments achieves a two stage reduction, and thus equation (1) given above will be applicable in determining the overall speed ratio. 
     In the embodiment of FIG. 7, the various bearing functions are now assumed by more conventional ball and tapered roller bearings. The input shaft 10 is provided integrally with a cam portion 30 which operates via a set of bearings upon a unitary idler member 50 having trochoidal surfaces 53, 56 of different lobe numbers. A pair of conjugate trochoidal surfaces 72, 92 are provided on the stator 70 and output member 90, respectively. A plurality of rollers 80 operate between the respective conjugate surfaces, as before. 
     In this embodiment, the rollers 80 are caged by means of cylindrical retainer members 132, 134, which are generally provided in the form of cylindrical shells having substantially rectangular apertures formed therein at the positions for the rollers. The two cage members 132, 134 are prevented from rubbing against one another by means of an intermediate separating disk 133. Although shown as being in contact with the disk 133, the cage members actually are separated therefrom by a very small distance. 
     The output shaft 60 is integral with output disk or gear member 90. As shown, the shaft 60 and the gear member 90 are joined by means of an intermediate portion 146, which seats a first output bearing 148, along with housing 20. The housing 20 is also provided with an additional extension member 136, a portion which extends axially of the shaft 60. 
     The extension member 136 itself seats a bearing 140, which bears against the output shaft 60. As is obvious from FIG. 7, the additional output bearing 140 is of assistance when substantial transverse loads are applied to the transmission. 
     FIG. 8 discloses a gear box substantially similar to that just discussed in connection with FIG. 7. The primary difference between the two embodiments in that the FIG. 8 construction is designed specifically for construction with a large axial preloading. An annular thrust bearing 160 is arranged between the stator member 70 and the output member 90 within the housing 20. The annular thrust bearing 160 is seated by the respective members 70 and 90 by means of annular recesses formed therein. The thrust bearing 160 enables a large preload force to be exerted upon radially outward portions of the respective gear members, which may be achieved by any conventional means, including screws or the like bearing upon either the stator or the output member. 
     The operation of the embodiment of FIG. 8 is otherwise identical to that discussed in connection with FIGS. 1 and 7, and thus will not be further discussed herein. 
     FIG. 9 is an end view through a transmission according to the present invention, useful for discussing various gearing relations of the speed reduction gears. 
     As can be seen from this figure, the curvature of the outer surface of the inner member is epitrochoidal, while that of the inner surface of the outer member is hypotrochoidal. Nine lobes are formed on the inner member, while eleven such lobes are formed on the outer member, which is presumed to be the stator in FIG. 9. Ten rolling elements rollingly transmit torque between the inner and the outer members, the rollers being separated by the prescribed distances by means of an intermediate retainer member. As is evident from FIG. 9, the centers of the inner and outer members are offset by a distance E, which is equal to the eccentricity of the driving cam. 
     Illustrated on the inner member 162 is an arc length AB, which is measured from peak to peak or from trough to trough of adjacent lobes. For a very precise gear box, the distance AB will be equal to CD, this latter distance being the corresponding arc length on the hypotrochoidal outer member 180. Of course, the arc lengths do not have to be precisely equal, and in practice will vary within limits. 
     Owing to the higher number of lobes on the hypotrochoidal member, the path length along the outer member 180 is 11/9 that of the inner member 162. 
     The dimensions of the epitrochoid, the hypotrochoid and retainer or cage member for the construction of FIG. 9 are given below. It should be noted that these expressions are general in nature, and are applicable to all of the presently disclosed embodiments. 
     Epitrochoid: 
     
         Major Diameter=B/O+1/P.sub.E -U 
    
     
         Minor Diameter=B/O-1/P.sub.E -U 
    
     Hypotrochoid: 
     
         Major Diameter=B/O+1/P.sub.H +U 
    
     
         Minor Diameter=B/O-1/P.sub.H +H 
    
     Retainer: 
     
         Minimum I.D.=B/O+2/P.sub.E -U 
    
     
         Maximum O.D.=B/O-2/P.sub.H +U 
    
     
         Average diameter=B/O+1/P.sub.E -1/P.sub.H 
    
     Where: 
     B=number of rollers 
     O=basic pitch 
     P E  =theoretical epitrochoidal pitch 
     P H  =theoretical hypotrochoidal pitch, and 
     U=roller diameter 
     As discussed previously, as the inner member 162 is made to orbit, it will also be made to rotate recessionally due to the engagement thereof with the outer member 180 via the rollers 80. During this motion, the rollers circulate in the direction of the recession, while maintaining contact with both the inner and outer members. The formulae for the center line of the roller path may be described by the following parametric equations: 
     
         X=(A+B/2xP) sin (T(1-N/B))+(N-B/2P) sin (T)                (4) 
    
     
         Y=(A+B/2xP) cos (T(1-N/B))+(N-B/2P) cos (T)                (5) 
    
     where: 
     A=(B/O-B/P)/2 
     N=number of lobes 
     B=number of rollers 
     O=roller diametral pitch 
     P=theoretical pitch* 
     T=crank angle 
    
    
     Finally in FIG. 9, force vectors have been drawn in and resolved for an individual roller 80, in order to demonstrate how accelerations may be placed on the rollers during operation of the device. In particular, the force vectors show that the roller can be controlled by &#34;tilting&#34; the two roller-lobe contact surfaces to affect accelerations on the rollers. Previously, the accelerations of the rolling element could only be caused by contact friction or the &#34;push&#34; of the cage or retainer device. 
     The roller accelerations as just described are made possible by slightly varying the inner and outer trochoidal shapes. Specifically, the theoretical pitches P E  and P H  of the gears are varied slightly to produce the &#34;tilt&#34; mentioned above. 
     As seen in FIG. 9, a pair of lines tangent to the roller surface and passing through the lines of contact between the roller and the inner and outer surfaces intersect in an angle α, which may be termed the &#34;squeeze angle&#34;, as the roller can be visualized as being urged forward from its illustrated position. Force vectors E and F are the driving forces exerted on the ball, and force vectors J and K extend through the roller center. Vectors E and F are perpendicular to the lines forming the angle α described above. The vectors as illustrated in FIG. 9 may be resolved to yield vectors I and H, which, when combined, produce the vector G which represents the acceleration or deceleration of a particular roller. It should be noted that the vectors I and H represent averaged values, and are not necessarily representative. For example, assuming the outer member to be the stator, the vector J would be colinear with the vector E, and the vector H would be approximately twice as large, the value of G of course being the same. Of course, the same would be true of vectors F and K if the inner member were to be selected as the stator, rather than the outer member 180. The value of the vector G is, of course, unchanged, regardless of which element is the stator, or whether average values are employed as above. 
     While the foregoing embodiments are presently preferred, it will be understood that numerous additional modifications may be made by those skilled in the art, and it is intended to cover in the appended claims all such modifications as fall within the true spirit and scope of the invention.