Rotary element and rotary drive arrangement

Abstract

A rotary element 1 for use in a rotary drive arrangement has a helical peripheral surface 5 centred on the rotary element's rotary axis X1, the helical peripheral surface 5 being tangential to its env

Description

The present invention relates to a rotary element and to a rotary drive arrangement for positively transmitting rotary motion. In a crude friction wheel arrangement, the rim of one friction wheel frictionally engages the rim of another and the drive ratio D is determined by the ratio of their diameters. D may accordingly be any value, including an irrational number. Since the rims are circular, there is no sliding friction between them, unless they slip under load; the corollary is that they lack the mechanical engagement between non-tangential surfaces which would ensure positive drive. Nevertheless, continuously variable transmissions (CVTs) such as toroidal CVTs have employed rollers disposed between and frictionally transferring rotary motion between facing toroidal discs whose surfaces are profiled to allow the drive ratio to be varied by varying the contact regions between each roller and the toroidal discs. Gears have the opposite combination of advantage and disadvantage, namely sliding friction between the teeth surfaces, but positive drive between the (non-tangential) engaging surfaces of the interdigitating teeth. This is true of both arcuate and cycloidal gear profiles and both spur gears and helical gears. The drive ratio is determined by the numbers of teeth and this can impose design compromises if the number of teeth is limited, eg in calendar complications in horology. In order to avoid mutual scraping between the gear teeth it is conventional to truncate the tips of the gear teeth to form a top land, i.e. a flat, tangential peripheral surface, which defines the tip circle and is designed to avoid contact with any surface, particularly the dedendum, of the meshing gear teeth. Thus the peripheral surface of a gear tooth is normally designed to be non-engaging with any other surface. Reference is made to UK patent GB2627593B, which discloses a rotary element for a rotary transmission, the rotary element having at least one helical radial projection disposed about a rotary axis thereof, the helical radial projection having a helical peripheral surface which defines an envelope of the rotary element, the helical peripheral surface having a profile in a radial plane which is inclined to a tangent to said envelope, whereby in use with another such rotary element of opposite handedness in a rotary transmission, a region of rolling contact of the helical peripheral surface with a helical peripheral surface of the other such rotary element helically traverses the helical peripheral surfaces to positively transmit rotary drive between the rotary elements. The rotary drive arrangement disclosed in GB 262759B is unidrectional, since the inclined peripheral profile of one rotary element bears against the peripheral profile of complementary inclination of the other rotary element. UK patent application GB 2411447.2, published as GB2627344A, discloses a rotary transmission working on the same principle but which is bidirectional. In both the above rotary drive arrangements, there is rolling contact between the mutually engaging helical peripheral surfaces of the respective rotary elements. In preferred embodiments in which the peripheral surfaces have a convex profile in the radial plane, sliding friction is theoretically zero when there is point contact between the two peripheral surfaces. However under load, there will be a finite region of contact owing to compression of the peripheral surfaces at the nominal point of contact. In fact an imaginary line drawn on one helical peripheral surface will rotate relative to an imaginary line drawn on the other peripheral surface about a nominal point of contact at the intersection of the two lines, the rate of relative rotation of the two lines in their common plane being proportional to the sine of the inclination of the peripheral surfaces in the axial plane. Hence some sliding friction will arise. However if the inclination is reduced to zero to eliminate such sliding friction, contrary to the teaching of GB2627593B and GB2627344A, positive drive is lost as in a conventional friction wheel drive. An object of the present invention is to resolve or alleviate the above technical problems. Accordingly the invention provides rotary element for a rotary transmission, the rotary element having at least one helical peripheral surface which is centred on a rotary axis of the rotary element and has a profile in a radial plane which is parallel to a tangent to an envelope of the helical peripheral surface and of lesser curvature than the envelope, whereby in use in a rotary transmission with another such rotary element whose helical peripheral surface has a profile in a radial plane of greater curvature than its envelope and is of opposite handedness, a region of rolling contact of the respective helical peripheral surfaces helically traverses the helical peripheral surfaces to positively transmit rotary drive between the rotary elements. Preferably said profile in the radial plane is symmetrical. Preferably the rotary element has a helical peripheral surface which has a convex arcuate profile in the radial plane and a concave arcuate profile in the axial plane. Preferably the depth of said concave arcuate profile is less than its width. Preferably the depth of said concave arcuate profile is less than 10% (more preferably less than 3%) of the radius of said envelope. Preferably the rotary element has a helical peripheral surface which has a profile in the radial plane which is an arc of an ellipse centred on a minor axis of the ellipse. Preferably the rotary element has a helical peripheral surface which has a substantially parabolic profile in the axial plane. Preferably the rotary element has at least one helical radial projection whose transverse crosssection comprises two flank sides on either side of said helical peripheral surface. Optionally the rotary element has a plurality of such helical peripheral surfaces forming separate turns or separate partial turns. Optionally the helical peripheral surfaces are regularly spaced apart along the rotary axis. Optionally the helical peripheral surfaces are partial turns extending from one end face of a rotary element to another and are regularly spaced around the circumference of the rotary element in circumferentially overlapping fashion. Optionally the rotary element is formed of plastics material, eg polyamide. Optionally the rotary element is frusto-conical. The invention also provides a rotary drive arrangement comprising first and second rotary elements mounted for rotation about respective rotary axes thereof and having helical peripheral surfaces centred on their respective rotary axes, the helical peripheral surfaces of the respective rotary elements being of opposite handedness, the helical peripheral surface of the first rotary element having a profile in a radial plane which is parallel to a tangent to an envelope of its helical peripheral surface but penetrates an envelope of the helical peripheral surface of the second rotary element to positively transmit rotary drive at a region of rolling contact which helically traverses the helical peripheral surfaces. Preferably the helical peripheral surface of the first rotary element has a convex profile in a radial plane whose curvature in the radial plane is less then the curvature of its envelope. Preferably the curvature of the profile of the helical peripheral surface of the second rotary element in the radial plane is greater than the curvature of its envelope. Preferably the radius of the helical peripheral surface of the second rotary element is greater than that of the helical peripheral surface of the first rotary element. Preferably the helical peripheral surface of the first rotary element has a profile in the radial plane which profile is an arc of an ellipse centred on a minor axis of the ellipse and the helical peripheral surface of the second rotary element has a profile in the radial plane which profile is an arc of said ellipse centred on a major axis of said ellipse. Preferably the helical peripheral surfaces of the respective rotary elements have complementary profiles in the axial plane whereby they engage at a line of rolling contact which helically traverses the helical peripheral surfaces. Preferably, under load, the region of contact between the respective helical peripheral surfaces is offset from a common plane of the axes of rotation of the rotary elements. Optionally the spacing between said rotary axes is sufficient to allow a gap between facing regions of the respective helical peripheral surfaces under a zero load condition. Optionally the rotary elements are bevel in form and their rotary axes are inclined towards each other in a common plane. Optionally the rotary elements are bevel in form and the rotary drive arrangement is a differential. Optionally the first rotary element of the rotary drive arrangement is as defined above. In low cost applications, the first rotary element, the second rotary element or both rotary elements can optionally be formed of plastics material, eg polyamide. In some embodiments the ratio of the radii from the respective rotary axes of the first and second rotary elements to a point of rolling contact is D such that D >1.0 or D <1.0. In some embodiments the ratio of the radii from the respective rotary axes of the first and second rotary elements to a point of rolling contact is D such that D is an irrational number. Preferably the respective helical radial projections have leads inversely proportional to the respective radii from their rotary axes to the centre of the region of rolling contact. This feature ensures that engagement between the helical peripheral projections is maintained throughout multiple revolutions of both rotary elements; in general the faster rotation of the smaller diameter rotary element is compensated by the correspondingly greater lead of the helix defining its helical peripheral radial projection. Optionally said helical peripheral surfaces are unlubricated. Preferred embodiments of the invention are described below by way of example only with reference to Figures 1 to 17 of the accompanying drawings, wherein: Figure 1 is a side elevation of a rotary element in accordance with the invention; Figure 2 is a diagrammatic cross-section taken on ll-ll of Figure 1; Figure 3 is a diagrammatic cross-section taken on Ill-Ill of Figure 1; Figure 4 is a diagrammatic cross-section taken on IV-lV of Figure 1; Figure 5 is a side elevation of a rotary drive arrangement in accordance with the invention, showing continuous rolling engagement of the helical peripheral engaging projections of two rotary elements; Figure 6 is a diagrammatic perspective view showing the engagement of the helical radial projections of the rotary drive arrangement of Figure 5; Figure 7 is a diagrammatic cross-section in the common axial plane of Figure 5 showing the engagement of one turn of the helical radial projections thereof; Figure 8 is a diagrammatic radial cross-section taken on VIIl-Vlli of Figure 5; Figure 9 is a similar diagrammatic radial cross-section taken on IX-IX of Figure 5 showing the penetration of the profile of the first rotary element into the envelope of the second rotary element during clockwise rotation of the first (upper) rotary element; Figure 10 is a similar diagrammatic radial cross-section taken on X-X of Figure 5 showing the penetration of the profile of the first rotary element into the envelope of the second rotary element during anticlockwise rotation of the first (upper) rotary element; Figure 11 is a plot of radius: angle of the helical peripheral surface of the first (upper) rotary element in Figure 7; 5 Figure 12 is a diagrammatic cross-section similar to Figure 8 but showing a variant of the drive arrangement of Figure 5 in which there is a gap between the helical peripheral surfaces of the rotary elements in the absence of a load; Figure 13 is an axial cross-section similar to Figure 7 but showing a variant in which the helical peripheral surface of the second (lower) rotary element has a greater curvature then the helical peripheral surface of the first (upper) rotary element; Figure 14 is a diagrammatic perspective view of a further rotary element in accordance with the invention, having multiple helical radial projections; Figure 15 is an end elevation of the rotary element of Figure 14; Figure 16 is a diagrammatic end elevation of a rotary drive arrangement in accordance with the invention showing two rotary elements as shown in Figures 14 and 15 positively engaging without interdigitation, and Figure 17 is a diagrammatic perspective view of four frusto-conical rotary elements of a differential rotary drive arrangement in accordance with the invention. In the following description, the leading edge of a helical projection will be considered to be the right-hand edge (the trailing edge being the left-hand edge). Referring to Figure 1, the rotary element 1 comprises a shaft 3 mounted for rotation about its axis and a parallel-sided helical radial projection 4 secured to the shaft. The helical radial projection 4 forms one and a half turns and its sense is right-handed. The helical radial projection 4 has a helical peripheral surface 5 whose profile is concave in the axial plane as shown in Figure 1 and, as shown in Figure 2, convex in the radial plane. The leading edge 4A and trailing edge 4B of helical radial projection 4 have the same diameter and define a cylindrical envelope E. Thus peripheral surface 5 is parallel to a tangent to envelope E, as shown in Figure 2. As best seen in Figure 2, the curvature in the radial plane of helical peripheral surface 5 is less than the curvature of envelope E. (This feature is shown in more detail in Figure 8, discussed below, and enables the profile of rotary element 1 to penetrate the envelope of rotary element 2 in the rotary drive arrangement of Figure 5.) This contrasts with the arcuate profile FW (shown in phantom in the Figure) of a friction wheel, which has the same radius of curvature as its envelope and thus cannot positively transmit drive. It also contrasts with the profile G of a gear tooth, also shown in phantom in Figure 2; it will be noted that the peripheral surface of a gear tooth is normally a land L as shown, which is specifically designed not to engage any part of the teeth on a meshing gear (not shown) and thus has the opposite function of helical peripheral surface 5 in embodiments of the present invention. Because the curvature in the radial plane of helical peripheral surface 5 is less than the curvature of envelope E, ie its radius is greater than that of envelope E, the radial distance from the rotary axis of the rotary element 1 along centre line AP (Figure 2) to surface 5 is less than the corresponding radial distance to either leading edge 4A or trailing edge 4B. Accordingly, in the axial plane the helical peripheral surface 5 is concave as shown in Figures 1 and 4, and hence it is also concave in transverse cross-section through the helical radial projection as shown in Figure 3. As will be explained below, helical peripheral surface 5 is capable of rolling engagement with a helical peripheral surface 5 of a similar, second, rotary element at, nominally, a line of contact L which, during rotation of the rotary element, runs along the helical peripheral surface 5 in Figure 1. Rolling friction occurs between two mutually engaging rotary elements, as will become apparent from the description of Figures 5 and 6 below. Conversely, in a conventional meshing gear arrangement, the locus of the contact point or contact region moves across the leading edge of a flank surface of a gear tooth of one gear as that tooth ends its engagement with a meshing tooth of the other gear. This interdigitation of the gear teeth 8 results in sliding friction, and is largely avoided in the rotary drive arrangement of Figures 1 to 10 and also in other embodiments. Referring now to Figure 5, the drive arrangement shown comprises a first rotary element 1 as described above with reference to Figure 1, having a radius R1, and a second rotary element 2 having a radius R2. Second rotary element 2 is similar to first rotary element 1 but the profile of its helical peripheral surface 5 is concave in the axial plane as shown in Figure 5 and, as shown in more detail in Figure 7, is complementary to the helical peripheral surface 5 of rotary element 1. The ratio R1 / R2 is substantially equal to the ratio of the leads L1 / L2 of the helical radial projections 4 of the first and second rotary elements 1 and 2, ensuring that at least one pair of turns of the rotary elements 1 and 2 remain in engagement throughout their rotation. The rotary elements are mounted on respective pairs of bearings B which are in turn mounted on fixed frames F. Accordingly the rotary axes X1 and X2 of the first and second rotary elements are maintained at a fixed spacing corresponding to the sum of radii R1 and R2. Figure 6 shows the line of contact L between the helical peripheral surfaces 5 of the respective helical radial projections 4 of the rotary elements 1 and 2 of Figure 5. This line lies in the common plane of the rotary axes of the shafts 3, as shown, and has a slight curvature which follows the curvature of the helical peripheral surfaces 5. Its mid-point P1 has a tangent which is parallel to the rotary axes of shafts 3. As the upper shaft 3 and the upper helical radial projection 4 rotate anticlockwise as shown in Figure 6, the engagement of the latter with the lower helical radial projection 4 at line of contact L positively drives the lower rotary element 2 clockwise, as shown by the arrows a in Figure 6. During this rotation, the engaging regions of the helical radial projections 4 and hence line of contact L move in the upper right direction, parallel to the shaft axes, with line L remaining in or, depending on the load, slightly offset to the right of the plane of the shaft axes. As shown in Figure 5 by bidirectional arrows a, clockwise rotation of upper rotary element 1 drives lower rotary element anticlockwise, and vice versa. Accordingly, shaft 3 of rotary element 1 may be an input shaft and be coupled to eg an engine (not shown) and shaft 3 of rotary element 2 may serve as an output shaft and be coupled to eg road wheels of a vehicle or a propeller (not shown) in eg a marine or aircraft propulsion system. 9 The curvature of line L is also shown in axial cross section in Figure 7 which shows a dimension d which is the radial difference between the mid-point of L and its ends. This discrepancy in radius, which is shown exaggerated for ease of illustration, results in slight sliding friction during rotation. If it were zero then there would no longer be positive drive between the two rotary elements 1 and 2. (The curvature of L and the derivation of d is described in more detail below with reference to Figures 8, 9, 10 and 11.) Despite the fact that the profile of helical peripheral surface 5 of rotary element 2, like that of the helical peripheral surface of rotary element 1, is convex and symmetrical about line AP as shown in Figure 2, the rotary drive arrangement shown in Figure 5 transmits bidirectional positive drive from rotary element 1 to rotary element 2, ie without relying on friction between helical peripheral surfaces 5. Figures 8, 9 and 10 show different cross-sections of the drive arrangement of Figure 5 in the same rotary position. Figure 8 shows the profile of the helical peripheral surface 5 of second rotary element 2 as an arc of an ellipse EL centred on a major axis of the ellipse and the corresponding profile of the helical peripheral surface of first rotary element 1 as an arc of an identical ellipse EL but centred on a minor axis of the ellipse. Thus the ellipses EL are mutually orthogonal and the sum of their minor and major radii R1 + R2 is equal to (or in a variant slightly less than) the spacing between axes X1 and X2. This feature ensures, to a very close approximation, that rotation of the upper rotary element 1 drives lower rotary element 2 with pure rolling motion ie no sliding between their helical peripheral surfaces 5. Figure 8 shows a common tangent T where the helical peripheral surfaces 5 of the first and second helical radial projections of rotary elements 1 and 2 touch at P1. It should be noted that because the curvature of the helical peripheral surface 5 of the upper (first) rotary element 1 is less than the curvature of its envelope E it penetrates the envelope E of the lower (second) rotary element 2 in use under load and positively drives the second rotary element. In particular, an initial slight rotation of first rotary element 1 will apply torque to second rotary element 2 while the latter remains stationary, until the torque is sufficient to rotate the second rotary element. In this state, point P1 will be marginally displace and tangent T will be marginally tilted with respect to its orthogonal orientation shown in Figure 8 in a direction dependent on the 10 sense of the applied torque, and the resultant penetration of the envelope E of the second rotary element 2 will ensure positive drive. Moreover, even under conditions of no applied torque, the profile of the first rotary element 1 penetrates the envelope of the second rotary element 2 at locations axially displaced from that shown in Figure 8. One of these is shown in Figure 9, in which the helical radial projections 4 of the rotary elements are angularly displaced in the clockwise direction by an amount corresponding to their respective pitch angles, such that they make contact at point P2, corresponding to trailing edge 4B (Figure 5). At this location, the ellipses EL are also angularly displaced from the state shown in Figure 8 such that point P2 is a distance R1 + 8 from the axis of the upper shaft 3 and R1 -8 from the axis of the lower shaft 3. Point P2 and offset 8 are also shown in Figure 7. It will be seen from Figure 9 that point P2 lies within the envelope E of the second (lower) rotary element 2; thus the profile of the first rotary element 1 penetrates the envelope of the second rotary element 2 at this axial location. Accordingly, clockwise rotation of first rotary element 1 will force anticlockwise rotation of second rotary element 2 as indicated by arrows a in Figure 9. Accordingly, in a variant of the propulsion system noted in connection with Figure 5, shaft 3 of rotary element 1 may be the output shaft and shaft 3 of rotary element 2 the input shaft. In Figure 10 the helical radial projections 4 of the rotary elements are angularly displaced in the anticlockwise direction by an amount corresponding to their respective pitch angles, such that they make contact at point P3, corresponding to leading edge 4A (Figure 5). At this location, the ellipses EL are also angularly displaced from the state shown in Figure 8 such that point P3 is a distance R1 + 8 from the axis of the upper shaft 3 and R1 -8 from the axis of the lower shaft 3. Point P3 and offset 8 are also shown in Figure 7. It will be seen from Figure 10 that point P3 lies within the envelope E of the second (lower) rotary element 2; thus the profile of the first rotary element 1 penetrates the envelope of the second rotary element 2 at this axial location. Accordingly, anticlockwise rotation of first rotary element 1 will force clockwise rotation of second rotary element 2 as indicated by arrows a in Figure 10. Referring again to Figures 9 and 10, it will be seen that if lower (second) rotary element 2 is considered to be the driving element, Figure 9 shows it will positively drive upper (first) rotary element 2 anticlockwise when rotated clockwise and Figure 10 shows that it will positively drive upper (second) rotary element clockwise when rotated clockwise. In summary, it can be seen from Figures 8, 9 and 10 that either rotary element 1 or 2 can positively drive the other rotary element bidirectionally. During the rotation of the rotary elements 1 and 2 of the drive arrangement of Figure 5, line of contact L will move in the axial direction, together with the cross-sections of Figures 8, 9 and 10. In variants of the embodiment shown in Figures 5 to 10, the drive ratio can be varied by altering the ratio R1 :R2, correspondingly altering the ratio L1 :L2 and adjusting the eccentricity of the ellipses EL to match R2 / R1. The ratio R1 / R2 = D where D is optionally an irrational number. In certain embodiments, D >1.0 or D< 1.0. The preferred profile of each peripheral radial surface 5 in the radial plane is elliptical. This feature is considered to minimise sliding friction, but in less preferred embodiments these profiles need not be elliptical and in still less preferred embodiments need not be arcuate or even convex. Departures from an elliptical profile geometry of the first rotary element 1 and second rotary element 2 shown in Figures 8, 9 and 10 will still achieve positive drive but will result in a degree of sliding friction. In a variant of the embodiment of Figures 5, 8, 9 and 10 the profiles of the helical peripheral surfaces 5 in the radial plane could be convex but not elliptical, eg arcs of a circle. Figure 11 shows a plot of the expressions: y = V(R22cos2x +R12sin2x) (i) and y = -0.20x2 + 0.75 (ii) Expression (i) represents the instantaneous radius of ellipse EL of rotating lower rotary element 2 in the common plane of axes X1 and X2 (where x is in radians and minor axis R1 is unity). It will be seen that the maximum of this expression is at (0, 0.75) where 0.75 is the major radius R2 of ellipse EL, the minor radius being 0.5, corresponding to an eccentricity in this embodiment of 0.75 / 0.5 = 1.5. The values of +0.2 and -0.2 radians correspond to the right and left-hand edges of lower projection 4 in Figures 7, 8, 9 and 10 and thus the profile of line of contact L in Figure 7 corresponds to expression (i) in Figure 11 between x = -0.2 and x = +0.2 radians. These values also correspond to the extreme rotary positions shown in Figures 9 and 10 (Figure 8 corresponding to zero radians) and to the thickness of radial projection 4 (Figure 5) as measured in the axial direction. Referring to Figures 7 and 12, the value 8 in this embodiment is 0.0083 approximately, ie 0.0083R1. Expression (ii) is a parabola and is a close approximation to expression (i) centred on x = 0. It can be derived either by numerical curve-fitting methods or analytically, eg by Maclaurin expansion. Thus the line of contact Lof the helical peripheral surfaces 5 is, to a close approximation, a parabola lying in the axial plane and corresponds to an elliptical profile of each helical peripheral surface 5 in the radial plane. Alternatively, an exactly parabolic profile Lof helical peripheral surfaces 5 in the axial plane will correspond closely to an elliptical profile of each helical peripheral surface 5 in the radial plane. It will be appreciated that in practice when an appreciable torque is being transmitted, there will be some compression of the helical peripheral engaging surfaces 5 and what is nominally a line of contact L will in practice be a region of contact, ie line L will be of finite width. In the embodiment of Figures 5 to 11, as best seen in Figure 7, the helical peripheral surfaces of the respective rotary elements 1 and 2 engage at a line of contact L even under no-load conditions. As shown in Figure 8, minor and major radii R1 and R2 touch at P1. The gear ratio at this point will be R2:R1. At P2 (Figure 9) and P3 (Figure 10) the gear ratio will be R2-8:R1+8. Accordingly, a slight discrepancy in gear ratios arises over the range of cross-sections IX to X in Figure 5 and results in corresponding discrepancies in angular velocity which can only be resolved by relative sliding motion between the helical peripheral surfaces 5. Perfect line contact as shown in Figures 7 and 8 may in some circumstances result in a degree of binding of the helical peripheral surfaces 5. In some applications play in the axial bearings B (Figure 5) will alleviate or eliminate such binding but in high precision applications binding can preferably be prevented by marginally increasing the separation between the axes X1 and X2 as shown in Figure 12. Referring to Figure 12, which shows a variant of the cross-section of Figure 8 under no-load conditions, point P lies on the mid-point of the lower peripheral surface 5 of lower rotary element 2 and between the upper helical peripheral surface 5 of rotary element 1 and the envelope E of upper rotary peripheral element 1. Accordingly, rotation of upper rotary element 1 either clockwise or anticlockwise while lower rotary element 2 is held in a fixed rotary position will bring the helical peripheral surfaces 5 of the rotary elements 1 and 2 into positive driving engagement at the intersection of upper envelope E with lower helical peripheral surface 5. Further driving rotation of either rotary element will drive the other rotary element, albeit with minor sliding friction arising from the slight separation of the elliptical profiles in the radial plane. It is preferred but not essential that the profiles of the helical peripheral surfaces 5 in the radial plane are elliptical. It will be noted that the separation of axes X1 and X2 also reduces the effective value of 8. In summary, the embodiment of Figures 1 to 11 can be modified to prevent binding by increasing the axial separation of axes X1 and X2 as shown in Figure 12. Figure 13 shows a further modification of the embodiment of Figures 1 to 11 which also overcomes or alleviates any binding problem. In the variant of Figure 13, the curvature in the radial plane of the helical peripheral surface 5 of the second rotary element is increased (eg to the profile of an ellipse of greater eccentricity than that of ellipses EL in Figures 8 to 10) whereby the region of contact is at least nominally a point P’ rather than a line L (Figure 7). It follows that 8 is zero in this embodiment and there are no discrepancies in the angular velocity of different regions of helical peripheral surfaces 5. In order to distribute the contact at P’, a film of lubricant 21 is provided at the interface, as shown. It will be noted that in the embodiment of Figures 1 to 11 and the variants of Figures 12 and 13, the larger diameter second rotary element 2 / 2A has more than one turn in order to enable contact throughout multiple revolutions of this rotary element. This has implications for the axial length of the rotary element for a given helix pitch angle of its helical peripheral surface 5. One way of reducing the required axial length of a rotary element is to include more than one helical radial projection 4. 14 Figures 14,15 and 16 show a further embodiment of a drive rotary drive element 10 in which there are multiple helical radial projections 4A, 4B, 4C, 4D, 4E, 4F,.....which are regularly circumferentially distributed and have a common pitch such that there is overlap in the circumferential direction between the termination of each helical radial projection and the start of the immediately adjacent succeeding radial projection, as shown. Each helical radial projection has a helical peripheral surface 5 (Figure 16) having a an elliptical profile in a radial plane which is parallel to a tangent to said envelope and of lesser curvature than the envelope, similar to that shown in Figure 8. Accordingly a rotary drive arrangement as shown in Figure 16 comprises an upper first rotary element 10 as shown in Figures 14 and 15 and a lower second rotary element 20 which is of opposite handedness to the upper rotary element and has a peripheral surface with a smaller radius of curvature in the radial plane than its envelope, similar to the arrangement shown in Figure 8. Rotation of the upper rotary element 10 in the clockwise direction indicated by upper arrow a drives the lower rotary element 20 anticlockwise as indicated by lower arrow a. The helical peripheral radial surfaces 5 are orthogonal to the line joining the centres in Figure 14. In particular, the helical projection 4C of upper first rotary element 10 is shown aligned with a corresponding helical projection 4c of lower second rotary element 20, and the helical projection 4D with the corresponding helical projection 4d. The rotary drive arrangement can be used in any application in which gears are conventionally used, eg in a power transmission. Figure 17 shows a differential arrangement of four frusto-conical rotary elements in accordance with the invention. The rotary elements comprise two identical rotary elements 1C having one or more right-handed helical projections 40A and mounted for independent rotation about a common axis X1, and two identical rotary elements 2C having one or more left-handed helical projections 40B and mounted for independent rotation about axis X2, which intersects axis X1. The helical projections 40Aof both rotary elements 1C both engage the helical projections 40B of both rotary elements 2C. It will be apparent that the frusto-conical envelopes of the four frusto-conical rotary elements are each tapered inwardly in the axial direction ie towards the intersection of axes X1 and X2. The frusto-conical rotary elements 1C are in accordance with the invention and have peripheral surfaces 5 with a concave profile in their axial plane, similar to the profile of the helical radial 15 projection 4 of rotary element 1 as shown in Figure 7. Accordingly they have a profile in their radial plane which is parallel to a tangent to said envelope and of lesser curvature than the envelope. The frusto-conical rotary elements 2C have peripheral surfaces 5 with a convex profile in their axial plane, similar to the profile of helical radial projection 4 of rotary element 2 as shown in Figure 7. Accordingly, in use in a differential, the helical peripheral surface 5 of each rotary element 1C penetrates the envelope of the engaging rotary element 2C to positively transmit rotary drive to the second rotary element at a region of rolling contact which helically traverses the helical peripheral surfaces 5. In this manner, all four frusto-conical rotary elements 1C and 2C are bidirectionally coupled in a manner functionally equivalent to the coupling of bevelled gears in a conventional differential.

Claims

1. A rotary element for a rotary transmission, the rotary element having at least one helical peripheral surface which is centred on a rotary axis of the rotary element and has a profile in a radial plane which is parallel to a tangent to an envelope of the helical peripheral surface and of lesser curvature than the envelope, whereby in use in a rotary transmission with another such rotary element whose helical peripheral surface has a profile in a radial plane of greater curvature than its envelope and is of opposite handedness, a region of rolling contact of the respective helical peripheral surfaces helically traverses the helical peripheral surfaces to positively transmit rotary drive between the rotary elements.

2. A rotary element according to claim 1 wherein said profile in the radial plane is symmetrical.

3. A rotary element according to claim 1 or claim 2 wherein its helical peripheral surface has a convex arcuate profile in the radial plane and a concave arcuate profile in the axial plane.

4. A rotary element according to claim 3 claim wherein the depth of said concave arcuate profile is less than its width.

5. A rotary element according to claim 3 or claim 4 wherein the depth of said concave arcuate profile is less than 10% of the radius of said envelope.

6. A rotary element according to claim 5 wherein the depth of said concave arcuate profile is less than 3% of the radius of said envelope.

7. A rotary element according to any preceding claim wherein its helical peripheral surface has a profile in the radial plane which is an arc of an ellipse centred on a minor axis of the ellipse.

8. A rotary element according to any of claims 1 to 6 wherein its helical peripheral surface has a substantially parabolic profile in the axial plane.

9. A rotary element according to any preceding claim having at least one helical radial projection whose transverse cross-section comprises two flank sides on either side of said helical peripheral surface.

10. A rotary element according to any preceding claim which has a plurality of such helical peripheral surfaces forming separate turns or separate partial turns.

11. A rotary element according to claim 10 wherein the helical peripheral surfaces are regularly spaced apart along the rotary axis.

12. A rotary element according to claim 10 or claim 11 wherein the helical peripheral surfaces are partial turns extending from one end face of a rotary element to another and are regularly spaced around the circumference of the rotary element in circumferentially overlapping fashion.

13. A rotary element according to any preceding claim which is formed of plastics material.

14. A rotary element according to any preceding claim which is frusto-conical.

15. A rotary drive arrangement comprising first and second rotary elements mounted for rotation about respective rotary axes thereof and having helical peripheral surfaces centred on their respective rotary axes, the helical peripheral surfaces of the respective rotary elements being of opposite handedness, the helical peripheral surface of the first rotary element having a profile in a radial plane which is parallel to a tangent to an envelope of its helical peripheral surface but penetrates an envelope of the helical peripheral surface of the second rotary element to positively transmit rotary drive at a region of rolling contact which helically traverses the helical peripheral surfaces.

16. A rotary drive arrangement according to claim 15 wherein the helical peripheral surface of the first rotary element has a convex profile in a radial plane whose curvature in the radial plane is less then the curvature of its envelope.

17. A rotary drive arrangement according to claim 15 or claim 16 wherein the curvature of the profile of the helical peripheral surface of the second rotary element in the radial plane is greater than the curvature of its envelope.

18. A rotary drive arrangement according to any of claims 15 to 17 wherein the radius of the helical peripheral surface of the second rotary element is greater than that of the helical peripheral surface of the first rotary element.

19. A rotary drive arrangement according to any of claims 15 to 18 wherein the helical peripheral surface of the first rotary element has a profile in the radial plane which profile is an arc of an ellipse centred on a minor axis of the ellipse and the helical peripheral surface of the second rotary element has a profile in the radial plane which profile is an arc of said ellipse centred on a major axis of said ellipse.

20. A rotary drive arrangement according to any of claims 15 to 19 wherein the helical peripheral surfaces of the respective rotary elements have complementary profiles in the axial plane whereby they engage at a line of rolling contact which helically traverses the helical peripheral surfaces.

21. A rotary drive arrangement according to any of claims 15 to 20 wherein, under load, the region of contact between the respective helical peripheral surfaces is offset from a common plane of the axes of rotation of the rotary elements.

22. A rotary drive arrangement according to any of claims 15 to 21 wherein the spacing between said rotary axes is sufficient to allow a gap between facing regions of the respective helical peripheral surfaces under a zero load condition.

23. A rotary drive arrangement according to any of claims 15 to 22 wherein the rotary elements are bevel in form and their rotary axes are inclined towards each other in a common plane.

24. A rotary drive arrangement according to claim 23 wherein the rotary elements are bevel in form and the rotary drive arrangement is a differential.

25. A rotary drive arrangement according to any of claims 15 to 24 wherein the first rotary element is as defined in any of claims 1 to 14.

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