Annular rotary element for transmitting rotary motion

Abstract

An annular rotary element (R) has at least one internal helical track 12, 13. The helical track having a helical surface defining an internal envelope. In use with an internal rotary element (e.g. PL)

Description

The present invention relates to an annular rotary element for positively transmitting rotary motion in a drive arrangement comprising a further rotary element engaging the inner periphery of the annular rotary element. The invention also relates also to such a rotary drive arrangement. Reference is made to UK patent application GB2406449.5 which is being published as GB2627593A. That application 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. In the rotary element of the above UK patent application, the inclined profile of the helical peripheral engaging surface enables the helical radial projection of one such rotary element to push the helical radial projection of another such rotary element and thus achieve positive drive. In accordance with the present invention, an annular rotary element for a rotary transmission comprises at least one internal helical track disposed about a rotary axis thereof, the helical track having a helical surface which defines an internal envelope of the annular rotary element, the helical surface having a profile in a radial plane which is inclined to a tangent to the internal envelope, whereby in use with an internal rotary element having a corresponding external helical radial projection of opposite sense and a profile in a radial plane of complementary inclination, the helical surfaces of the respective rotary elements engage to positively transmit rotary drive at regions of rolling contact between them. An annular rotary element having an internal helical track has the advantage that it can bear the radially outward forces generated in use by torque between sun and planet elements within the annular rotary element. In a preferred embodiment the annular rotary element has at least first and second internal helical tracks disposed coaxially about a rotary axis thereof, the helical tracks being axially spaced apart and having respective first and second helical surfaces which define a common envelope of the annular rotary element, each helical surface having a profile in a radial plane which is inclined to a tangent to the common envelope and the inclinations of the first and second helical surfaces to the tangent being of opposite sense, whereby in use with an internal rotary element in a rotary transmission, the helical surfaces of the annular rotary element engage with helical peripheral surfaces of complementary inclination of the internal rotary element to positively transmit bidirectional rotary drive between the rotary elements at regions of rolling contact of their respective helical surfaces. Preferably a said helical surface has a convex profile in said radial plane. This feature facilitates rolling motion and reduces sliding friction in use. Optionally said profile is elliptical. In a preferred embodiment the at least one internal helical track has a transverse cross-section comprising two flank sides on either side of said helical peripheral engaging surface. Unlike the flank sides of a gear tooth, the flank sides of such an embodiment are not required to engage with the flank sides of any other rotary element in use, and can optionally be inclined inwardly towards the helical surface eg to maximise the strength of the helical track. They can optionally be left unfinished in order to reduce manufacturing costs. Preferably the helical surface is selectively treated by hardening or polishing or both to reduce rolling friction. For example, a steel radial projection can have its helical surface hardened by carburising. In low cost applications, the or each rotary element can optionally be formed of plastics material, eg polyamide. The invention also provides a rotary drive arrangement comprising: a) an annular rotary element having at least one internal helical track disposed about a rotary axis thereof, the helical radial track having a helical surface which defines an internal envelope of the annular rotary element, the helical surface having a profile in a radial plane which is inclined to a tangent to the internal envelope, and b) an internal rotary element having a corresponding external helical radial projection of opposite sense and a profile in a radial plane of complementary inclination, whereby in use the helical surfaces of the respective rotary elements engage to positively transmit rotary drive at one or more regions of rolling contact between them. In a preferred embodiment the annular rotary element has at least first and second internal helical tracks disposed coaxially about a rotary axis thereof, the helical tracks being axially spaced apart and having respective first and second helical surfaces which define a common internal envelope of the annular rotary element, each helical surface having a profile in a radial plane which is inclined to a tangent to the common envelope and the inclinations of the first and second helical surfaces to the tangent being of opposite sense, whereby in use the helical surfaces of the annular rotary element engage with helical peripheral surfaces of complementary inclination of the internal rotary element to positively transmit bidirectional rotary drive between the rotary elements at regions of rolling contact of their respective helical surfaces. In a preferred embodiment the internal rotary element b) is a planet rotary element and the rotary drive arrangement further comprises: c) a sun rotary element whose axis is coaxial with that of the annular rotary element, the sun rotary element having an external helical radial projection of opposite sense to that of the planetary rotary element and having a profile in a radial plane of complementary inclination to that of the planetary rotary element, whereby in use the respective helical surfaces of the sun and planet rotary elements engage each other to positively transmit rotary drive at regions of rolling contact between them. Preferably: the annular rotary element a) has at least first and second internal helical tracks disposed coaxially about a rotary axis thereof, the helical tracks being axially spaced apart and having respective first and second helical surfaces which define a common internal envelope of the annular rotary element, each helical surface having a profile in a radial plane which is inclined to a tangent to the common envelope and the inclinations of the first and second helical surfaces to the tangent being of opposite sense, the planetary rotary element b) has at least first and second helical projections disposed coaxially about a rotary axis thereof, the helical projections being axially spaced apart and having respective first and second helical surfaces which define a common external envelope of the planetary rotary element, each helical surface having a profile in a radial plane which is inclined to a tangent to its common external envelope and the inclinations of the first and second helical surfaces to the tangent being of opposite sense, and the sun rotary element c) has at least first and second helical projections disposed coaxially about a rotary axis thereof, the helical projections being axially spaced apart and having respective first and second helical surfaces which define a common external envelope of the sun rotary element, each helical surface having a profile in a radial plane which is inclined to a tangent to its common external envelope and the inclinations of the first and second helical surfaces to the tangent being of opposite sense, whereby in use the helical surfaces of the annular rotary element a) engage with helical peripheral surfaces of complementary inclination of the planetary rotary element b) and the helical surfaces of the planetary rotary element b) engage with helical peripheral surfaces of complementary inclination of the sun rotary element c) to positively transmit bidirectional rotary drive between the sun, planetary and annular rotary elements at regions of rolling contact of their respective helical surfaces. Preferably there are three or more such planetary rotary elements. Preferably the rotary elements are as defined above. In some embodiments the ratio of the radii from the respective rotary axes of the annular and internal and 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 annular and internal rotary elements to a point of rolling contact is D such that D is an irrational number. Preferably the respective helical surfaces 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 surfaces is maintained throughout multiple revolutions of the 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. In a preferred embodiment the helical surface of the or each helical projection of the internal rotary element has an elliptical profile. Optionally said helical surfaces are unlubricated. Other preferred features are defined in dependent claims. Preferred embodiments of the invention are described below by way of example only with reference to Figures 1 to 8 of the accompanying drawings, wherein: Figure 1 is a side elevation of an assembly of sun and planet rotary elements used in a planetary drive arrangement 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 diagrammatic cross-section similar to that of Figure 3, showing the elliptical profiles in the radial plane of the helical surfaces of the radial projections of the rotary elements and their inclination to a tangent; Figure 6 is a schematic side elevation partly in axial cross-section, showing the engagement of sun, planetary and annular rotary elements in a planetary drive arrangement in accordance with the invention, and Figure 7 is a diagrammatic end elevation taken on VII-VII of Figure 8 showing a planetary drive arrangement in accordance with the invention, and Figure 8 is a side elevation, partly broken away and partly in axial cross-section, showing the planetary drive arrangement of Figure 7. In the following description generally, what in practice will be a small region of rolling contact will be described as a point of rolling contact because that is consonant with the geometry of the described embodiments when the helical peripheral surfaces are not compressed by a transmitted torque. Figures 1 to 5 show a bidirectional rotary drive arrangement of two rotary elements 1E and 2E. Referring to Figure 1, a rotary element 1E comprises a shaft 3 mounted for rotation about its axis and two axially spaced-apart oppositely-handed helical radial projections 40A and 40B secured to the shaft. The helical radial projections 40A and 40B are each parallel-sided. The helical radial projections in this embodiment 40A and 40B each form one and a half turns, helical radial projection 40A being right-handed and helical radial projection 40B being left-handed. Each helical radial projection 40A and 40B has a helical peripheral radial surface 5 formed between its leading and trailing edges 4A and 4B, each helical peripheral radial surface 5 being inclined radially inwardly from leading edge 4A towards the trailing edge 4B, as best shown in Figure 2. The angle of inclination A of the tangent to the mid-point of peripheral radial surface 5 relative to the surface of envelope E, as shown in Figure 1, is preferably in the range 5° to 45°, more preferably in the range 10° to 30°. If A is too small, there is a risk in high torque applications of the radial projections of one rotary element sliding over those of the other radial element. If on the other hand A is too large, there may be undue friction between the engaging helical surfaces 5. Each helical peripheral radial surface 5 is convex in the axial plane as shown in Figure 1. In this embodiment, envelope E of rotary element 1E corresponds to the envelope of the leading edges 4A but in other embodiments (not shown) in which the radial inclination of the helical peripheral surfaces is lower and / or the convexity of the helical peripheral surfaces 5 is more pronounced it could correspond to a radial extremity of the helical peripheral surfaces intermediate leading and trailing edges 4A and 4B. In the rotary drive arrangement shown in Figure 1, rotary element 2E is identical to rotary element 1E but reversed in the axial direction whereby each of its helical peripheral surfaces 5 engages a complementary helical peripheral surface 5 of rotary element 1E. Thus the helical peripheral surfaces 5 of the first rotary element 1E engage with helical peripheral surfaces 5 of the second rotary element 2E of complementary inclination in the radial plane. This is best seen in Figures 3 and 4, which show oppositely inclined helical peripheral surfaces 5 engaging at contact points P which lie in the common plane of the axes of shafts 3. Accordingly, referring to Figure 3, anticlockwise rotation (indicated by arrow a) of upper rotary element 1E will cause its helical projection 40Ato drive helical projection 40B and hence lower rotary element 2E clockwise. Similarly, referring to Figure 4, clockwise rotation (indicated by arrow b) of upper rotary element 1E will cause its helical projection 40B to drive helical projection 40A and hence lower rotary element 2E anticlockwise. Thus upper rotary element 1E can be used to drive lower rotary element 2E bidirectionally, or vice versa, with no rotational play, unlike the situation with conventional gearing. However if a degree of lost motion between the upper and lower rotary elements 1E and 2E is required, one or both of helical projections 40A and 40B may be angularly offset. Referring now to Figure 1, the loci PT of the contact points P during rotary drive run along the helical peripheral surfaces 5. It should be noted that loci PT are helices and lie midway between the leading and trailing edges 4A and 4B of the helical peripheral radial surface 5 over the entirety of the length of loci PT. Rolling rather than sliding friction occurs between two mutually engaging rotary elements 1E and 2E. 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 results in appreciable sliding friction. 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 point P will in practice be a region of contact. Referring now to Figure 5, the tangent T to the envelope E (closely adjacent contact point P) of upper rotary element 1E and the common tangent TA to the helical peripheral surfaces of the helical projections subtend an angle 0 in the radial plane. 0 is preferably in the range 5° to 45°, more preferably in the range 10° to 30°. If 0 is too small, there is a risk in high torque applications of one or other of the helical radial projections distorting and slipping over the other under load, whereas if 0 is too large, undue friction may occur between the helical peripheral surfaces. In the embodiment of Figures 1 to 5, the inclinations of the tangents (TA in Figure 5) of the helical peripheral surfaces 5 relative to the tangent (T in Figure 5) to the envelope are equal and opposite. However in a variant, the inclinations may be opposite but unequal. As shown in Figure 5, the helical peripheral surfaces of the upper and lower rotary elements 1E and 2E are preferably elliptical, ie defined by identical ellipses E1 and E2 respectively. The spacing between centres c of the rotary axes of the upper and rotary elements is equal to half the sum of the major and minor diameters of ellipses E1 and E2, which corresponds to a contact point P located on the line joining centres C. This location of contact point P on the line joining centres c is optimal for reducing friction. It will be noted that the inclination of the common tangent TA relative to envelope tangent T can be varied by varying the eccentricity of the ellipses E1 and E2, ie the ratio of their major and minor diameters. However an elliptical profile of helical peripheral surfaces 5 is not essential. Optionally, in view of the virtual absence of sliding friction, the helical peripheral surfaces 5 may be unlubricated. Figure 6 shows, in cross-section, a planetary drive arrangement comprising an annular rotary element R in accordance with the invention mounted for rotation about an axis X1 and having a first internal helical track in the form of a helical radial projection 12 and a second internal helical track in the form of a helical radial projection 13. Each helical radial projection 12 and 13 forms a complete turn with a lead L3 (the dimension L3 / 2 being shown) and each has an internal peripheral surface 5 which is inclined in the axial plane of the drawing, the inclinations being opposite. The internal peripheral surfaces 5 define a common internal envelope of the annular rotary element R, each helical surface having a profile in a radial plane which is inclined to a tangent to the common envelope as best seen in Figure 7. Figure 7 shows tangent T to the internal envelope of annular rotary element R, inclination line TA which is a continuation of peripheral surface 5 of rotary element R in the radial plane and is tangential to the peripheral surface 5 of projection 40 of a planetary rotary element PL, and angle 0 between T and TA. 0 is preferably in the range 5° to 45°, more preferably in the range 10° to 30°. If 0 is too small, there is a risk in high torque applications of one or other of the helical radial projections distorting and slipping over the other under load, whereas if 0 is too large, undue friction may occur between the helical peripheral surfaces. The profile of each surface 5 in the axial plane is flat, as shown. The senses of the helices of the internal radial projections 12 and 13 are opposite and they are axially spaced apart. Planetary rotary element PL is mounted for rotation about an axis X2 and has two helical radial projections 40 which are axially spaced apart and whose helices are of opposite sense so as to engage in rolling fashion the helical radial projections 12 and 13 respectively. The peripheral surfaces of the helical radial projections 40 of planetary rotary element PL have complementary inclinations in the axial plane (cf angle A in Figure 1) and the radial plane (angle 0 in Figure 7) to the respective engaging helical surfaces 5 of projections 12 and 13, and their profiles are similar to that shown in Figure 5. Thus the planetary rotary element is similar to eg rotary element 1E of Figure 1, but has more turns and the lead L2 is smaller. Referring to Figure 7, 0 is preferably in the range 5° to 45°, more preferably in the range 10° to 30° The ratio R2 / R3 of the radii R2 and R3 of planetary rotary element PL and annular rotary element R is equal to the ratio L2 / L3 of the leads of their helical radial projections 40 and 12 / 13. (The radii are measured from the axis of rotation to the contact point P of the helical peripheral surfaces.) Accordingly, planetary rotary element PL can roll without slippage around the interior of annular rotary element R with the peripheral helical surfaces of its helical radial projections 40 in continuous rolling contact with the internal peripheral surfaces 5 of helical radial projections 12 and 13. The ratio R1 / R2 and / or R2 / R3 may optionally have an irrational value. A sun rotary element S is mounted for rotation about axis X1 of the annular rotary element R and has helical radial projections 40 which are axially spaced apart and whose helices are of opposite sense so as to engage in rolling fashion the respective helical radial projections 40 of planetary rotary element PL. The peripheral surfaces of the helical radial projections 40 of sun rotary element PL have complementary inclinations in the axial plane (cf angle A in Figure 1) and the radial plane (cf angle 0 in Figure 7) to the respective engaging helical peripheral surfaces of helical radial projections40 of the planetary rotary element PL, and their profiles are similar to that shown in Figure 5. Thus the sun rotary element S is similar to eg rotary element 1E of Figure 1, but has a larger radius R1 and the lead L1 is smaller. The ratio R1 / R2 of the radii R1 and R2 of sun planetary rotary element S and planetary rotary element PL is equal to the ratio L1 / L2 of the leads of their respective helical radial projections 40. (The radii are measured from the axis of rotation to the contact point P of the helical peripheral surfaces, as shown in Figure 6.) Accordingly, if the axis X2 of planetary rotary element PL is maintained at a distance of R1 + R2 from common axis X1 of the sun and annular rotary elements, it can roll without slippage around sun rotary element S with the peripheral helical surfaces of its helical radial projections 40 in continuous rolling contact with those of the helical radial projections 40 of the sun rotary element S. Bidirectional positive drive can thus be achieved between sun rotary element S, planetary rotary element PL and annular rotary element R. During the rotation of the rotary elements of Figure 6, the contact points P of the tracks 12 and 13, the peripheral helical surfaces of the helical projections 40 of planetary rotary element PL and the peripheral helical surfaces of the helical projections 40 of sun rotary element S remain in the common plane of axes X1 and X2. This minimises friction and nearly eliminates sliding friction. During this rotation, the contact points P follow continuous helical tracks similar to tracks PT shown in Figure 1. Preferably there are a plurality, eg three or four planetary rotary elements PL rather than one as shown in Figure 6. Figures 7 and 8 show an embodiment comprising the sun rotary element S of Figure 6, three planetary rotary elements PL like that of Figure 6, and the annular rotary element R of Figure 6. Referring to Figures 7 and 8, three planetary rotary elements PL having shafts 3 mounted on bearings B are held in a regular circumferential array within a carrier 20A, 20B so as to engage sun rotary element S and annular rotary element R in the manner shown in Figure 6. Referring to Figure 8, carrier 20A, 20B is fixed, ie it cannot rotate. Figure 7 shows the engagement of helical radial projections 40 of the sun and planetary rotary elements of the top right planetary rotary element PL. It will be apparent that anticlockwise rotation of this planetary element will drive sun rotary element S clockwise. In this regard, Figure 7 is analogous to Figure 3. A similar cross-section to Figure 7 through projection 13 at the lower right hand side of Figure 8 would show a configuration similar to Figure 4, ie the reverse of the situation shown in Figure 7 whereby clockwise rotation of the top right planetary element PL of Figure 7 will drive sun rotary element anticlockwise. In this manner, this planetary rotary element PL (and likewise the other two planetary rotary elements) is bidirectionally coupled to sun rotary element S by the two axially spaced sets of oppositely inclined engaging surfaces of helical projections 40. Figure 7 also shows the engagement of the helical radial projection 40 of the lower planetary radial element PL with the helical radial projection 12 of annular rotary element R. This is similar to the configuration shown in Figures 3 and 5, except that the inwardly-facing helical surface of projection 12 is flat in radial profile rather than elliptical. Anticlockwise rotation of lower planetary element PL will drive annular rotary element R clockwise. A similar cross-section to Figure 7 through projection 13 at the lower right hand side of Figure 8 would show the reverse of the situation shown in Figure 7 whereby clockwise rotation of the lower planetary element PL of Figure 7 will drive annular rotary element rotary element R clockwise. In this manner, this planetary rotary element PL (and likewise the other two planetary rotary elements) is bidirectionally coupled to annular rotary element R by the two axially spaced oppositely inclined engaging surfaces of its helical projections 40 continuously engaging projections 12 and 13 respectively. To sum up, sun rotary element S is bidirectionally coupled to annular rotary element R via the set of three planetary rotary elements PL which are mounted on fixed carrier 20A, 20B. Referring to Figures 5 and 7, the angle 0 in the radial plane defined by the engaging helical peripheral surfaces of the sun and planetary rotary elements and the planetary and annular rotary elements implies that any torque transmitted between these rotary elements will generate radially outward forces. In principle, it is undesirable that such forces should be borne by the bearings of the planetary rotary elements PL. In order to alleviate this potential problem, the carrier 20A, 20B of Figures 7 and 8 is preferably made resilient (eg by choice of the material of the carrier, or by employing cushioning elements between the carrier and the bearings) to allow limited radial outward movement of the bearings B of the shafts 3 of the planetary radial elements PL, such that the planetary radial elements PL bear against the projections 12 and 13 and thereby transfer the radial load to the annular rotary element R. Annular rotary element R may be made more substantial than eg a ring gear of a typical conventional planetary gear in order to bear this radial load. Referring further to Figure 8, it will be seen that annular rotary element R is mounted on bearings B and can be coupled in conventional fashion to external machinery (not shown). Shaft 3 of sun rotary element S is likewise mounted on bearings B and can be coupled in conventional fashion to eg a prime mover (not shown). The tracks 12 and 13 of annular rotary element R are also shown in Figure 8, and it will be apparent that the left hand helical projections 40 of each planetary rotary element PL run continuously on track 12 and the right hand helical projections 40 of each planetary rotary element PL run continuously on track 13. In a variant, tracks 12 and 13 could be recessed rather than projecting, provided that the recess was sufficiently wide to accommodate the pitch of helical projections 40 of the planetary rotary elements. However such a variant is not preferred. Optionally, in view of the virtual absence of sliding friction, the helical peripheral surfaces 5 and / or tracks 12 and 13 may be unlubricated.

Claims

1. An annular rotary element for a rotary transmission comprising at least one internal helical track disposed about a rotary axis thereof, the helical track having a helical surface which defines an internal envelope of the annular rotary element, the helical surface having a profile in a radial plane which is inclined to a tangent to the internal envelope, whereby in use with an internal rotary element having a corresponding external helical radial projection of opposite sense and a profile in a radial plane of complementary inclination, the helical surfaces of the respective rotary elements engage to positively transmit rotary drive at regions of rolling contact between them.

2. An annular rotary element according to claim 1 wherein the annular rotary element has at least first and second internal helical tracks disposed coaxially about a rotary axis thereof, the helical tracks being axially spaced apart and having respective first and second helical surfaces which define a common envelope of the annular rotary element, each helical surface having a profile in a radial plane which is inclined to a tangent to the common envelope and the inclinations of the first and second helical surfaces to the tangent being of opposite sense, whereby in use with an internal rotary element in a rotary transmission, the helical surfaces of the annular rotary element engage with helical peripheral surfaces of complementary inclination of the internal rotary element to positively transmit bidirectional rotary drive between the rotary elements at regions of rolling contact of their respective helical surfaces.

3. An annular rotary element according to claim 1 or claim 2 wherein a said helical surface has a convex profile in said radial plane.

4. An annular rotary element according to claim 3 wherein said profile is elliptical.

5. An annular rotary element according to any preceding claim wherein the internal helical track is selectively treated by hardening or polishing or both to reduce rolling friction.

6. An annular rotary element according to any preceding claim wherein the at least one internal helical track has a transverse cross-section comprising two flank sides on either side of said helical peripheral engaging surface.

7. A rotary drive arrangement comprising:a) an annular rotary element having at least one internal helical track disposed about a rotary axis thereof, the helical radial track having a helical surface which defines an internal envelope of the annular rotary element, the helical surface having a profile in a radial plane which is inclined to a tangent to the internal envelope, andb) an internal rotary element having a corresponding external helical radial projection of opposite sense and a profile in a radial plane of complementary inclination, whereby in use the helical surfaces of the respective rotary elements engage to positively transmit rotary drive at one or more regions of rolling contact between them.

8. A rotary drive arrangement according to claim 7 wherein the annular rotary element has at least first and second internal helical tracks disposed coaxially about a rotary axis thereof, the helical tracks being axially spaced apart and having respective first and second helical surfaces which define a common internal envelope of the annular rotary element, each helical surface having a profile in a radial plane which is inclined to a tangent to the common envelope and the inclinations of the first and second helical surfaces to the tangent being of opposite sense, whereby in use the helical surfaces of the annular rotary element engage with helical peripheral surfaces of complementary inclination of the internal rotary element to positively transmit bidirectional rotary drive between the rotary elements at regions of rolling contact of their respective helical surfaces.

9. A rotary drive arrangement according to claim 6 or claim 7 or claim 8 wherein the internal rotary element b) is a planetary rotary element and the rotary drive arrangement further comprises:c) a sun rotary element whose axis is coaxial with that of the annular rotary element, the sun rotary element having an external helical radial projection of opposite sense to that of the planetary rotary element and having a profile in a radial plane of complementary inclination to that of the planetary rotary element, whereby in use the respective helical surfaces of the sun and planetary rotary elements engage each other to positively transmit rotary drive at regions of rolling contact between them.

10. A rotary drive arrangement according to claim 6 wherein the annular rotary element a) has at least first and second internal helical tracks disposed coaxially about a rotary axis thereof, the helical tracks being axially spaced apart and having respective first and second helical surfaces which define a common internal envelope of the annular rotary element, each helical surface having a profile in a radial plane which is inclined to a tangent to the common envelope and the inclinations of the first and second helical surfaces to the tangent being of opposite sense,the planetary rotary element b) has at least first and second helical projections disposed coaxially about a rotary axis thereof, the helical projections being axially spaced apart and having respective first and second helical surfaces which define a common external envelope of the planetary rotary element, each helical surface having a profile in a radial plane which is inclined to a tangent to its common external envelope and the inclinations of the first and second helical surfaces to the tangent being of opposite sense, andthe sun rotary element c) has at least first and second helical projections disposed coaxially about a rotary axis thereof, the helical projections being axially spaced apart and having respective first and second helical surfaces which define a common external envelope of the sun rotary element, each helical surface having a profile in a radial plane which is inclined to a tangent to its common external envelope and the inclinations of the first and second helical surfaces to the tangent being of opposite sense,whereby in use the helical surfaces of the annular rotary element a) engage with helical peripheral surfaces of complementary inclination of the planetary rotary element b) and the helical surfaces of the planetary rotary element b) engage with helical peripheral surfaces of complementary inclination of the sun rotary element c) to positively transmit bidirectional rotary drive between the sun, planetary and annular rotary elements at regions of rolling contact of their respective helical surfaces.

11. A rotary drive arrangement according to claim 9 or claim 10 comprising three or more such planetary rotary elements.

12. A rotary drive arrangement according to any of claims 7 to 11 comprising an annular rotary element as defined in any of claims 3 to 6.

13. A rotary drive arrangement according to any of claims 7 to 12 wherein a said region of rolling contact remains in a common plane of the rotary axes of two of the rotary elements.

14. A rotary drive arrangement according to claim 11 or claim 12 wherein an engaging surface of a said helical track or helical projection is unlubricated.

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