WO1997007343A1

WO1997007343A1 - Constant velocity joints

Info

Publication number: WO1997007343A1
Application number: PCT/GB1996/001924
Authority: WO
Inventors: John Craven Carden
Original assignee: Lica-Carden (Ipr) Limited
Priority date: 1995-08-11
Filing date: 1996-08-08
Publication date: 1997-02-27

Abstract

A constant velocity ratio joint connects two shafts (2) each having three mutually perpendicular axes (X, Y, Z) intersecting at the joint centre point (20) where the axis (X) of rotation of the shafts intersects. In each shaft end (4) is formed a recess (6) cylindrical about the Y axis, receiving a corresponding part cylindrical portion (8) of a spider (10), which also has a portion (13) cylindrical about the Z axis, received in a corresponding part cylindrical recess of a central member (16) whose axis of symmetry (18) is maintained in the joint bisector plane, e.g. by teeth (22) on the spider portion (12) engaging spur gears (26), which in turn engage rack teeth (34) on a balancer plate (32). Needle roller bearings (70) are provided between the facing flat end surfaces of the spider portion (12) and the central member (16) recess. To carry load between the flat facing surfaces of the shaft recesses (6) and the spider portions (8), there may be recirculating balls (70) (figs. 1, 4, 5), which may be retained by a cover (81, 84) (fig. 6).

Description

CONSTANT VELOCITY JOINTS

The present invention relates to constant velocity universal joints for use in drive line applications, that is to say particularly for automotive use, e.g. in the drive shafts of front wheel drive vehicles, but also in any applications in which it is desired to transmit rotational movement between two rotary shafts which are inclined to one another, at least at certain times. The invention is concerned with such joints which comprise two shafts with respective opposed ends in which respective part-cylindrical recesses are formed, the axes of which intersect at the geometrical centre of the joint, two spiders, each including an outer portion of part-cylindrical shape slidably received in a respective part-cylindrical recess and an inner portion affording a cylindrical surface which is opposed to a corresponding cylindrical surface of a central member and whose axis is perpendicular to that of the outer portion, the axes of the two cylindrical surfaces of the inner portions being coincident and constituting the axis of the central member which passes through the geometrical centre.

A joint of the type referred to above is known from German Patent No.914208 which discloses a constant velocity joint in which two part-cylindrical recesses are formed in the opposed end of the two shafts. Slidably received in each recess is a part-cylindrical portion of a respective member or spider of generally U shape, at the end of each of whose limbs is an aperture defined by a cylindrical portion, the axis of which is perpendicular to that of the associated recess . Rotatably received in all four apertures is a central joint pin. Slidably received on the joint pin is a guide member which is keyed to two guide pins which are in sliding engagement with the internal surface of a respective part- cylindrical portion and are rotatably secured to the end of a respective one of the shafts.

Torque is transmitted through this known joint through the engaging surfaces of the joint pin and the spiders. Due to the fact that the engaging surfaces of the spiders are cylindrical the central pin is necessarily relatively small because otherwise the overall size of the joint would become unacceptably large. This means that the engaging surfaces are necessarily of small area which results in high surface loadings which in turn results in lubrication breakdown and in galling and ultimately welding or seizure of the engaging surfaces, if the joint is transmitting significant torque. Furthermore, when the two shafts are inclined, the guide member reciprocates longitudinally on the guide pin which means that the joint is not balanced and this results in unacceptable vibration when the joint rotates at high speed.

A constant velocity joint of this type is disclosed in EP-A-0668452, which was not published by the earliest priority date of the present application. It is desirable for most applications that the joint be self- supporting and the prior specification discloses a number of ways in which this may be achieved. In the first embodiment illustrated in Figures 1 to 5 the outer portion of each spider has two arcuate tongues which are received in corresponding arcuate grooves in the adjacent end of the associated shaft and reciprocate therein along an arcuate path when the joint is rotated in the deflected state. Similarly, the inner portion of each spider has two arcuate tongues which are received, and reciprocate in, corresponding arcuate grooves in the central member. In the second embodiment illustrated in Figures 6 and 7 the tongues and grooves are replaced by cooperating arcuate part-circular ball races, each cooperating pair of ball races together accommodating a plurality of ball bearings which serve to key the components together. The two ends of each ball race are connected together by a respective recirculating passage which passes through the body of the associated spider. In a further embodiment, which is not illustrated, the components are not actively keyed together but the outer casing is strengthened and serves the structural function of holding all the components together.

However, it is relatively expensive to provide the tongues and grooves or the recirculating ball races and their presence adds to the complexity of assembling the joint. The construction in which they are both omitted and the structural integrity of the joint is ensured by the outer casing is therefore to be preferred. However, in certain applications, in particular high speed applications, it is thought that the joint disclosed in the prior application might be subject to excessive wear at the interfaces between the spiders and the surfaces of the recesses in the ends of the shafts and between the spiders and the central member and that premature failure might therefore occur.

Accordingly it is an object of the invention to provide a constant velocity joint which overcomes the problems of the known joints and is cheap and simple to manufacture and which is capable of operating at high speeds and joint angles for an extended period of time without being subject to appreciable wear or the risk of premature failure. It is a further object to provide a constant velocity joint which is at least approximately statically and dynamically balanced at all times. It is a yet further object to provide a constant velocity joint which has the necessary structural integrity but does not have either arcuate tongues and grooves or recirculating ball races but which is nevertheless capable of long term high speed operation without suffering premature wear or failure.

According to the present invention a constant velocity joint of the type referred to above is characterised in that the cylindrical surfaces of the inner portions are only part-cylindrical, that the inner portions are received in a respective part-annular cylindrical recess in the central member, that coupling means are provided which connect the two spiders and are arranged to transmit rotational movement between them such that the two spiders are constrained to rotate through equal distances but in opposite directions about the axis of the central member and that disposed in the interface between each axial end surface of the inner portion of each spider and the central member there is a respective part-annular needle roller thrust bearing.

The joint of the present invention can be considered to be equivalent to two Oldham couplings, the output member of one, namely the central member, constituting the input member of the other, with the crucial difference that all the engaging portions and recesses are of part- cylindrical shape with the^' axes of all the cylinders intersecting at the geometrical centre of the joint. When the two shafts are aligned, the entire joint rotates as a solid body and torque is transmitted from one shaft to the central member via the two rotational couplings constituted by the engagement in the part-cylindrical recess in each shaft of the part-cylindrical portion of the associated spider and by the engagement of the inner portion of the spider in the associated part-annular recess in the central member. The torque is transmitted on from the central member to the other shaft by the two corresponding rotational couplings on the other side of the joint. If the two shafts are now inclined to one another relative reciprocating rotational movement occurs of the part-cylindrical surfaces of each of the couplings about the axis of the surfaces, the sliding motion at the two couplings on each side of the joint being at right angles and out of phase. The fact that the surfaces of the spiders which are opposed to the central member are only part-cylindrical enables them to engage the same portion of the length of the central member and thus to have a substantially greater length in the direction of the axis of the central member. This means in turn that the torque may be transmitted between the spiders and the central member through a much greater surface area than in the prior German patent .

The opposed part-cylindrical surfaces of the inner portions and the central member may be in sliding contact or they may be slightly spaced apart. In any event, whilst a small proportion of the torque may be transmitted through the opposed part-cylindrical surfaces, if they are in engagement, the majority of the torque is transmitted through the engaging pairs of axial end surfaces of the inner portions and the axial end surfaces of the recesses in the central member. Each such pair of engaging surfaces are in force transmitting relationship with one another but are slightly spaced apart by the associated needle roller thrust bearing.

The coupling together of the two spiders so that they rotate in opposite directions but through the same distance may be effected in various ways but it is preferred that the coupling means comprises gear teeth formed on the internal cylindrical surface of each inner cylindrical portion and two spur gears which are rotatably mounted on the central member and which are in mesh with each other and with the gear teeth on a respective one of the inner portions.

The two spur gears may be directly in mesh with one another. However, when the two spiders rotate away from the diametrically opposed position, their mass will be displaced to one side of the axis of the central member and whilst this may be acceptable for low speed applications it is likely to lead to unacceptable vibration at high speeds. It is therefore preferred that the spur gears are indirectly in mesh with one another via an elongate balancer member carrying a substantially linear array of gear teeth on each of two opposed surfaces, each spur gear being in mesh with a respective one of the linear arrays of gear teeth, the balancer member being so arranged that when the two spiders are diametrically opposed with respect to the axis of the central member the balancer member is symmetrically disposed with respect to the axis of the central member and that when the two spiders rotate to positions where they are disposed on one side of the axis of the central member the balancer member moves to the other side of the axis of the central member. In this embodiment the balancer member, which essentially constitutes a double sided rack, fulfils two separate functions. Firstly, it forms part of the coupling between the two spiders and secondly it moves in the opposite direction to the spiders and acts as a counterbalance. If its mass is appropriately matched to that of the spiders it can be ensured that the joint is substantially statically and dynamically balanced at all joint angles.

In the preferred embodiment the opposed ends of the shafts carry respective flanges in which the part- cylindrical recesses are formed and whose external shape is substantially part-spherical, the joint being enclosed in an outer casing whose internal shape is substantially part-spherical and which is formed with openings through which the shafts pass. The joint thus has a generally spherical overall external appearance.

Whilst not essential for all applications, it is desirable that the joint be self-supporting and for this purpose it is preferred that the outer casing constitutes a structural component of the joint and holds it together, that is to say is responsible for its mechanical integrity, by virtue of the sliding engagement of its part-spherical internal surface with the part- spherical external surface of the two flanges on the shafts.

As mentioned above, the joint of the present invention is provided with respective part-annular needle roller thrust bearings in the interfaces between each axial end surface of the inner portion of each spider and the opposed axial end surface of the associated recess in the central member. The "axial end surfaces" of the inner portions of the spider are those two surfaces which extend generally parallel to the radial direction of the inner portion in question. In practice each bearing will constitute a plurality of needle rollers retained in respective equispaced holes in a cage. The surfaces of each needle roller will engage the opposed surfaces defining the interface in question and transmit thrust between them. It will also roll over the two surfaces as they swing relative to one another and this will result in all the needle rollers and the associated cage moving an arcuate distance equal to one half of the relative arcuate distance moved by the two surfaces. In order that the two surfaces are adequately supported at all times, i.e. at all relative positions, this means that the arcuate length of each bearing should be equal to the arcuate length of the two associated surfaces plus one half the maximum possible relative arcuate movement of the two surfaces. Expressed in angular terms, if the two surfaces have an angular extent of, say 90° and their maximum relative angular movement is 44°, the angular extent of the associated bearing should be at least 112°.

As the two surfaces defining an interface reciprocate relative to one another along arcuate paths, the bearing between them will oscillate also along an arcuate path at the same frequency but at half the amplitude. The bearing should inherently be in the correct position at all times but it will be appreciated that if the needle rollers should for some reason slip relative to the two surfaces the bearing will move into an incorrect position and will thereafter always be in the incorrect position. This may not constitute a problem for much of the time, due to the fact that the angular extent of the bearing is greater than that of the associated surfaces, but if the shafts of the coupling should be offset to their maximum angular extent, whereby the amplitude of the oscillation of the two surfaces reaches its maximum value, the two surfaces may be inadequately supported at the ends of their relative travel. This potential problem may be overcome by positively constraining the bearings always to occupy the desired correct position. This may be effected by gearing the bearing cages or one or more of the needle rollers to some other moving component of the joint in a manner analogous to that in which the two spiders are coupled together and are thus constrained always to occupy precisely predetermined relative positions. Thus in one embodiment of the invention one or more needle rollers associated with each bearing is provided with gear teeth along part of its length which are in mesh with teeth formed on the surfaces defining the interface accommodating the bearing such that the bearing is constrained to occupy a position in which it is offset from its centre position, that is to say the position it occupies when the two shafts are aligned, by an angle which is one half of the instantaneous angular offset of the two surfaces defining the associated interface from their centre position.

It is also possible for a similar needle roller thrust bearing to be provided in each interface defined by the axial end surfaces of the outer portions of the spiders and the opposed axial end surfaces of the part- cylindrical recesses in the ends of the shafts. However, in a particularly preferred embodiment of the invention an arcuate ball groove, which is preferably part-circular and also of part-circular cross-section, is provided in each axial end surface of the outer portion of each spider, which ball groove cooperates with a complementary arcuate ball groove, which is preferably also of part- circular cross-section, formed in the opposed axial end surface of the part-cylindrical recess in the associated shaft, each cooperating pair of ball grooves together accommodating a plurality of ball bearings, the two ends of each ball groove in the spider being connected by a respective recirculating passage which extends in the form of a groove over the part-cylindrical surface of the outer portion of the spider. Thus each spider will have a thrust bearing at its inboard end and a recirculating ball race at its outboard end.

This aspect of the present invention is based on the recognition that the area of the inner portion of each spider through which torque is transmitted between the spider and the central member is inherently smaller than the area of the outer portion of each spider through which torque is transmitted between the spider and the associated shaft. This fact coupled with the fact that the lever arm of the inner portion of each spider is inherently less than that of the outer portion means that the inner portion of the spider is always more highly stressed than the outer portion. This means in turn that chere is a much higher need for thrust bearings at the inner portions of the spiders than at the outer portions, particularly if the joint is to operate at high speeds at high deflection angles.

This aspect of the invention is based further on the recognition that much of the expense of the recirculating ball races disclosed in EP-A-0668452 is caused by the necessity of using expensive fabrication techniques for the spiders and boring the recirculating passages through them. However, recirculating passages can be provided in the outer portions of the spiders in the form of open topped grooves extending over the end surfaces of the spiders remote from the central member, that is to say in the part-cylindrical sliding surfaces of the outer portions of the spiders. This opens up the possibility of manufacturing the spiders by the much cheaper techniques of sintering or precision forging, during which process the recirculating grooves are produced. The ends of the ball grooves in the outer portion of the spider must of course be connected to the ends of the associated recirculating groove but thus can be effected by boring short straight connecting passages through the spider.

As mentioned above, the recirculating ball passages provided in the outer portions of the spiders are in the form of open topped grooves in the sliding surfaces of the outer portions. The depth of the recirculating grooves will in practice be equal to at least the diameter of the ball bearings so that they are wholly accommodated in the recirculating grooves. They will normally be retained in the recirculating grooves by virtue of the fact that the part-cylindrical sliding surfaces on the ends of the shafts, that is to say formed in the flanges at the ends of the shafts, cover and close the recirculating grooves. However, if the joint is operated at the maximum deflection angle of the shafts, whereby the amplitude of the arcuate oscillation between the shafts and the outer portions of the spiders reaches its maximum value, there is a risk that the ball bearings could fall out of the recirculating grooves and/or the ball grooves at the end of the relative travel of the outer portions of the spiders and the associated ends of the shafts. In the case of the recirculating grooves this potential problem may be simply cured by providing a first cover over the part-cylindrical sliding surfaces of the outer portions of the spiders which constitutes a roof over the recirculating grooves and positively retains the ball bearings therein. In the case of the ball grooves the problem may be cured by providing a second cover over each axial end surface of the outer portion of each spider in which an arcuate slot is formed through which the balls project into the corresponding ball groove in the end of the associated shaft and whose internal surface is of part-circular section, or at least of decreasing size in the outward direction, and thus partially embraces the ball bearings and again positively retains them in position in the ball grooves. The first cover and two second covers associated with the outer portion of each spider are conveniently integrated into a single end cap secured to the outer portion of the spider by any conventional means, e.g. adhesive or a snap fastening.

Further features and details of the invention will be apparent from the following description of one specific embodiment which is given by way of example with reference to the accompanying diagrammatic drawings, in which:

Figure 1 is a central sectional view through a constant velocity joint with the shafts at an angle in the plane of the drawing;

Figure 2 is a central sectional view similar to that of Figure 1 but on a plane at right angles to that of Figure 1, with the shafts at an angle in the plane of the drawing; Figure 3 is a scrap sectional exploded view on an enlarged scale of one of the interfaces defined by the axial end surfaces of the inner portions of the spiders and the corresponding opposed surface of the associated recess in the central element of the joint showing the associated needle roller thrust bearing;

Figure 4 is a view of one of the spiders in the direction of the part-cylindrical sliding surface afforded by its outer portion;

Figure 5 is a sectional view on the line V-V in Figure 4; and

Figure 6 is a transverse sectional view on an enlarged scale of the retaining end cap for the outer portion of one of the spiders.

The constant velocity joint is generally similar to that illustrated in Figures 1 to 5 of EP-A-0668452 to which reference should be made for details of the construction and its function and advantages.

Very briefly, however, the joint comprises two shafts 2, at whose inner ends, which are spaced from and opposed to one another, there is a respective flange 4 whose external surface is part-spherical, whereby the flanges 4 have an appearance reminiscent of that of a mushroom. Formed in the inner surface of each flange 4 is a part- cylindrical recess or concavity 6, the axes of the two recesses being coincident, when the two shafts 2 are aligned, and intersecting at all times at the geometrical centre 20 of the joint. Slidably received in each recess 6 is an outer, part-cylindrical portion 8 of a respective spider 10, the other, inner portion 12 of each of which is of part-annular cylindrical shape and extends through less than 180°, e.g. 60 to 150°, and is slidably received in a respective part-annular cylindrical recess 14 in a central joint member 16. The two recesses 14 are separate in this embodiment but it will be appreciated that in certain constructions they could be coterminous and thus constitute a single annular recess. The axes of the two part-annular cylindrical portions 12 and the two part-annular cylindrical recesses 14 are coincident and indicated by 18 in Figure 2 and pass through the geometrical centre point 20 of the joint.

The part-cylindrical internal surface of each part- annular cylindrical portion 12 is provided with gear teeth 22 which are in mesh with corresponding gear teeth 24 on a respective spur wheel 26. The two spur wheels 26 are journalled in two spaced end caps 28 which constitute the bulk of the central member 16 and which each carry four equiangularly spaced formations 30. The free end surfaces of the formations 30 on the two end caps 28 engage one another and their external surfaces constitute the internal circular-section surface of the part-annular cylindrical recesses 14.

Located within the central member 20 and extending out of it on both sides in directions perpendicular to the axes of the two shafts 2 is an elongate balancer plate 32. Formed on the opposed surfaces of the balancer plate 32 are respective sets of rack teeth 34 which are in mesh with the spur teeth 24 on a respective spur wheel 26. The part-annular cylindrical portions 12 are free to slide in rotation about the axis 18 within the part- annular cylindrical recesses 14 and as they do so the meshing sets of gear teeth 22,24 result in rotation of the spur wheels 26 and thus in linear movement of the balancer plate 32. The two spiders 10 are thus geared together and constrained always to rotate about the axis 18 in opposite senses and through equal distances. The balancer plate 32 and the spur wheels 26 are so positioned that when the two shafts 2 are axially aligned the balancer plate projects an equal distance on each side of the central member 16. If one shaft is then inclined to the other about the axis 18, the relative movement of the spiders in one direction results in movement of the balancer plate in the other direction. The relative masses and the relative distances of movement are such that even when the shafts are inclined the joint remains substantially statically and dynamically balanced. By appropriately dimensioning the various components it would be possible to increase the mass of the balancer plate at its ends by making it of I section shape.

The joint of the present embodiment does, however, differ from that described in EP-A-0668452 and these are as follows:

The tongues and grooves keying the various components of the joint together have been omitted and the outer casing 48 has been strengthened to permit it to serve a structural function and hold all the components of the joint together. The interfaces between the axial end surfaces of the inner portions 12 of the spiders and the corresponding surfaces of the recesses in the central member 28 are thus defined by smooth, arcuate surfaces. Each associated pair of surfaces is spaced apart to define a gap in which a needle roller thrust bearing is received. This is constituted by a cage 70, comprising a part-annular metallic strip, in which a plurality of rectangular apertures is formed. Rollably received in each aperture is a respective needle roller 72 whose diameter is greater than the thickness of the cage, whereby each needle roller projects out of its associated aperture and engages the two surfaces defining the interface.

In this embodiment each bearing 70,72 is positively constrained always to occupy the correct position between the opposed surfaces of the inner portions 12 of the spiders and the central member 28. This is achieved by providing each needle roller 72 with gear teeth 90 over part of its length which are in mesh with arrays of gear teeth 92 and 94 projecting from the opposed surfaces of the inner portion 12 and the central member 28, respectively. The remainder of each needle roller is in rolling contact with untoothed portions of the opposed surfaces. Accordingly the needle rollers serve a dual function: they not only transmit thrust between the surfaces defining the interface in which they are accommodated over part of their length but are also geared to the said surfaces over the remainder of their length, thereby ensuring that the bearings do not become displaced from their desired positions.

The axial end surfaces of the outer portions 8 of the spiders are provided with a respective part-circular ball groove 74 of semi-circular cross-sectional shape. Each ball groove 74 cooperates with a corresponding similarly shaped ball groove formed in the associated axial end surface of the recess 6 formed in the end of the associated shaft 2. Each associated pair of grooves together receive a plurality of ball bearings 76 which act as a thrust bearing and key the spiders to the associated shafts. The two ends of each groove 74 are connected together by a recirculating passage, the majority of which is constituted by an open topped groove 78 of U shape whose base is of semi-circular shape matching that of the ball bearings 76 and whose height is equal to or greater than the diameter of the ball bearings. The recirculating grooves 78 extend across the part-cylindrical sliding surfaces of the outer portions 8 of the spiders. The ball recirculating loop is completed by the provision of two short bores 80 which connect the adjacent ends of each ball groove 74 with the associated ends of the respective recirculating groove 78.

In order to ensure that the ball bearings cannot fall out of the grooves 74,78, even if the joint is operating at high speed and high deflection angles, each spider may be provided with a part-annular ball retainer, as shown diagrammatically in Figure 4. This comprises a part- annular base 81, whose size and shape match those of the part-cylindrical sliding surface on the outer portions 8 of the spiders and upstanding from the sides of which are side walls 84 in which a respective part-circular slot 86 is formed. In use, the ball retainer cap is pushed onto the outer portion 8 of the associated spider so that the base 81 overlies and closes the recirculating grooves 78. The side walls overlie the axial end surfaces of the outer portion and the slots 86 are aligned with the ball grooves 74 so that the balls 76 extend through them. The edges 87 of the slots are of part-circular cross-section and contact the surfaces of the balls and thus positively retain them in the ball grooves 74.

Claims

1. A constant velocity joint comprising two shafts (2) with respective opposed ends (4) in which respective part-cylindrical recesses (6) are formed, the axes of which intersect at the geometrical centre (20) of the joint, two spiders (10) , each including an outer portion

(8) of part-cylindrical shape slidably received in a respective part-cylindrical recess (6) and an inner portion (12) affording a cylindrical surface which is opposed to a corresponding cylindrical surface of a central member (16) and whose axis is perpendicular to that of the outer portion (8) , the axes of the two cylindrical surfaces of the inner portions (12) being coincident and constituting the axis of the central member (18) which passes through the geometrical centre

(20) , characterised in that the cylindrical surfaces of the inner portions (12) are only part-cylindrical, that the inner portions (12) are received in a respective part-annular cylindrical recess in the central member (16) , that coupling means (22, 24, 34) are provided which connect the two spiders (10) and are arranged to transmit rotational movement between them such that the two spiders (10) are constrained to rotate through equal distances but in opposite directions about the axis (18) of the central member (16) and that disposed in the interface between each axial end surface of the inner portion (12) of each spider (10) and the central member (16) there is a respective part-annular needle roller thrust bearing (70, 72) .

2. A joint as claimed in Claim 1 in which the coupling means comprises gear teeth (22) formed on the internal cylindrical surface of each inner portion (12) and two spur gears (26) which are rotatably mounted on the central member (16) and which are in mesh with each other and with the gear teeth (22) on a respective one of the inner portions (12) .

3. A joint as claimed in Claim 2 in which the spur gears (26) are indirectly in mesh with one another via an elongate balancer member (32) carrying a substantially linear array of gear teeth (34) on each of two opposed surfaces, each spur gear (26) being in mesh with a respective one of the linear arrays of gear teeth (34) , the balancer member (32) being so arranged that when the two spiders (10) are diametrically opposed with respect to the axis (18) of the central member (16) the balancer member (32) is symmetrically disposed with respect to the axis (18) of the central member (16) and that when the two spiders (10) rotate to positions where they are disposed on one side of the axis (18) of the central member (16) the balancer member (32) moves to the other side of the axis (18) of the central member (16) .

4. A joint as claimed in any one of the preceding claims which includes an outer casing (48) which constitutes a structural component of the joint and holds it together.

5. A joint as claimed in any one of the preceding claims in which each needle roller thrust bearing comprises a cage (70) retaining a plurality of rollers (72) and at least one roller (72) is provided with gear teeth along part of its length which are in mesh with teeth formed on the surfaces defining the interface accommodating the bearing such that the bearing is constrained to occupy a position in which it is offset from its centre position, that is to say the position it occupies when the two shafts (2) are aligned, by an angle which is one half of the instantaneous angular offset of the two surfaces defining the associated interface from their centre position.

6. A joint as claimed in any one of the preceding claims in which an arcuate ball groove (74) is provided in each axial end surface of the outer portion (8) of each spider (10) , which ball groove (74) cooperates with a complementary arcuate ball groove formed in the opposed axial end surface of the part-cylindrical recess (6) in the associated shaft (2) , each cooperating pair of ball grooves (74) together accommodating a plurality of ball bearings (76) , the two ends of each ball groove (74) in the spider being connected by a respective recirculating passage which extends in the form of a groove (78) over the part-cylindrical surface of the outer portion (8) of the spider (10) .

7. A joint as claimed in Claim 6 which includes a first cover (81) over the part-cylindrical sliding surfaces of the outer portions (8) of the spiders (10) which constitutes a roof over the recirculating grooves (78) and positively retains the ball bearings (76) therein.

8. A joint as claimed in Claim 6 or 7 which includes a second cover (84) over each axial end surface of the outer portion (8) of each spider (10) in which an arcuate slot (86) is formed through which the balls (76) project into the corresponding ball groove in the end of the associated shaft (2) and the internal surface of which is preferably of decreasing size in the outward direction, and partially embraces the ball bearings and positively retains them in position in the ball grooves (74) .

9. A joint as claimed in Claims 7 and 8 in which the first cover (81) and two second covers (84) associated with the outer portion (8) of each spider (10) are integrated into a single end cap secured to the outer portion of the spider.