Patent Publication Number: US-2021172481-A1

Title: Plunging type constant velocity universal joint for propeller shaft

Description:
TECHNICAL FIELD 
     The present invention relates to a plunging type constant velocity universal joint dedicated to propeller shafts. 
     BACKGROUND ART 
     Plunging type constant velocity universal joints capable of axial displacement and angular displacement are used for propeller shafts used in automobiles such as four-wheel drive vehicles (4WD vehicles) and front-engine, rear-wheel drive vehicles (FR vehicles). The plunging type constant velocity universal joints include a double-offset plunging type constant velocity universal joint (DOJ), a tripod plunging type constant velocity universal joint (TJ), a cross-groove plunging type constant velocity universal joint (LJ), etc. 
     In recent years, along with the improvement in fuel efficiency of automobiles, the propeller shafts are required to be smaller and lighter. Conventionally, from the viewpoint of component commonality, components (such as an outer joint member, an inner joint member, and a cage) used for plunging type constant velocity universal joints for drive shafts have been directly used for plunging type constant velocity universal joints for propeller shafts except for a modified shape of the attachment portion of the outer joint member. 
     The plunging type constant velocity universal joints used for propeller shafts include a double-offset plunging type constant velocity universal joint (hereinafter also referred to as DOJ). Patent Literature 1 below proposes a DOJ designed to have eight balls to achieve size reduction and weight reduction. 
     CITATIONS LIST 
     Patent Literature 
     Patent Literature 1: JP H10-73129 A 
     SUMMARY OF INVENTION 
     Technical Problems 
     The DOJ can slide a relatively large distance in the axial direction, has a good track record of use and stable performance, and further, can be designed to have eight balls to achieve size reduction and weight reduction. The present inventors have studied various existing DOJs used for propeller shafts in order to meet the demands for further improvement in fuel efficiency of automobiles and size reduction, weight reduction, and increase in rotation speed of propeller shafts. 
     It is an object of the present invention to provide a plunging type constant velocity universal joint dedicated to propeller shafts with a reduced size and weight, which can contribute to the demands for further improvement in fuel efficiency of automobiles and increase in rotation speed of propeller shafts. 
     Solutions to Problems 
     The present inventors have conducted various studies in order to achieve the above-mentioned objective and arrived at the present invention based on the following findings and ideas. 
     (1) An existing 8-ball type DOJ for propeller shafts as shown in  FIGS. 11A, 11B, and 12  has a maximum operating angle of about 25° so that it can also be used for drive shafts. The present inventors have focused on the fact that the function of the DOJ can be limited by specializing the DOJ to required characteristics for use with propeller shafts. Specifically, it has been found that by making the DOJ dedicated to propeller shafts, the maximum operating angle can be limited to a low value (e.g., 15° or less), and size reduction and weight reduction of the DOJ can thereby be achieved. 
     (2) By limiting the maximum operating angle of the propeller shaft-dedicated DOJ to a low value, the following specific technical effects can be obtained. 
     (a) Radial size reduction and weight reduction by reducing the wall thickness of each component (outer joint member, inner joint member, cage) 
     (b) Axial size reduction and weight reduction of the inner joint member by reducing the amount of axial movement of the balls 
     (c) Radial size reduction and weight reduction of the cage by reducing the amount of circumferential movement of the balls 
     (d) Axial size reduction and weight reduction of the cage by reducing pocket load 
     (3) In addition, the possibility of further size reduction and weight reduction has been studied by focusing on the dynamic factors that the DOJ for propeller shafts has a small and substantially constant operating angle and a high rotation speed. As a result, the idea to reduce the offset of the cage has been conceived, and it has been found that this dramatically enhances the technical effects of (2) mentioned above, and size reduction and weight reduction that are qualitatively different than in the conventional technique can be achieved. 
     (4) Further, in terms of performance, the idea of the combined use of an axial pocket clearance δ1 between a pocket of the cage and a ball and an axial clearance δ2 between spherical surfaces of the cage and the inner joint member has been conceived. And the advantageous arrangement of the present invention has been reached as a result verifying the effects of improvement in life, increase in rotation speed, reduction of sliding resistance, and vehicle vibration characteristics as a propeller shaft-dedicated DOJ. 
     As technical means for achieving the above-mentioned objective, the present invention is a plunging type constant velocity universal joint for a propeller shaft, including: an outer joint member having eight straight track grooves formed along an axial direction on a cylindrical inner surface; an inner joint member having eight straight track grooves formed along the axial direction on a spherical outer surface and opposing the straight track grooves of the outer joint member and a connecting hole in which female splines are formed; eight torque transmitting balls disposed between the straight track grooves of the outer joint member and the straight track grooves of the inner joint member; a cage having pockets accommodating the torque transmitting balls, a spherical outer surface guided in contact with the cylindrical inner surface of the outer joint member, and a spherical inner surface guided in contact with the spherical outer surface of the inner joint member, and is characterized in that a center of curvature of the spherical outer surface and a center of curvature of the spherical inner surface of the cage each have an equal and axially opposite offset (f) with respect to a center of the pockets, and a ratio f/PCD BALL  between the offset (f) of the cage and a pitch circle diameter (PCD BALL ) of the torque transmitting balls is 0.07 or more and 0.09 or less. 
     With the above arrangement, it is possible to realize a plunging type constant velocity universal joint dedicated to propeller shafts that has a reduced size and weight, is qualitatively different from conventional one, and can contribute to the demands for further improvement in fuel efficiency of automobiles and increase in rotation speed of propeller shafts. 
     In the above plunging type constant velocity universal joint for the propeller shaft, it is desirable to provide an axial pocket clearance δ1 between axially opposing wall surfaces of the pockets of the cage and the torque transmitting balls and to provide an axial clearance δ2 between the spherical inner surface of the above cage and the spherical outer surface of the inner joint member. This suppresses temperature rise due to the sliding between the cage and the balls and the sliding between the cage and the inner joint member, which is effective for improvement in life and increase in rotation speed of the joint, as well as resulting in reduction of the sliding resistance. Further, the vibration from the engine can be absorbed by the above pocket clearance δ1 and axial clearance δ2, and thus the vibration characteristics of the vehicle can be improved. In particular, it is desirable to set the pocket clearance δ1 to 0 to 0.050 mm and the axial clearance δ2 to 0.5 to 1.5 mm. 
     By setting the maximum operating angle of the above plunging type constant velocity universal joint for the propeller shaft to 15° or less to specialize it to the required function for use with propeller shafts, the function of the plunging type constant velocity universal joint can be limited. And the size reduction and weight reduction of the plunging type constant velocity universal joint can be achieved. 
     By setting the ratio Ti/Db between the wall thickness Ti of the inner joint member and the ball diameter Db of the torque transmitting balls to 0.30 or more and 0.45 or less, radial size reduction and weight reduction can be achieved. 
     By setting the ratio Wi/Db between the width Wi of the inner joint member and the ball diameter Db of the torque transmitting balls to 1.2 or more and 1.4 or less, axial size reduction and weight reduction can be achieved. 
     By setting the ratio Wc/Db between the width Wc of the cage and the ball diameter Db of the torque transmitting balls to 1.8 or more and 2.0 or less, axial size reduction and weight reduction can be achieved. 
     Further, as technical means for achieving the above-mentioned objective, the present invention is a plunging type constant velocity universal joint for a propeller shaft including: an outer joint member having eight straight track grooves formed along an axial direction on a cylindrical inner surface; an inner joint member having eight straight track grooves formed along the axial direction on a spherical outer surface and opposing the straight track grooves of the outer joint member and a connecting hole in which female splines are formed; eight torque transmitting balls disposed between the straight track grooves of the outer joint member and the straight track grooves of the inner joint member; a cage having pockets accommodating the torque transmitting balls, a spherical outer surface guided in contact with the cylindrical inner surface of the outer joint member, and a spherical inner surface guided in contact with the spherical outer surface of the inner joint member, and is characterized in that a center of curvature of the spherical outer surface and a center of curvature of the spherical inner surface of the cage each have an equal and axially opposite offset (f) with respect to a center of the pockets, a ratio Ti/Db between a wall thickness Ti of the inner joint member and a ball diameter Db of the torque transmitting balls is 0.30 or more and 0.45 or less, and a ratio PCD BALL /Db between a pitch circle diameter PCD BALL  of the torque transmitting balls and the diameter Db of the torque transmitting balls is 3.3 or more and 3.6 or less. 
     In the case of a ball type constant velocity universal joint that transmits torque via balls, while each ball is evenly loaded when the operating angle is 0°, uneven loads are applied to the balls when an operating angle is taken, and the difference increases at a higher operating angle. Accordingly, the maximum load applied to one ball is also increased at a high operating angle. And the inner joint member, the outer joint member, and the cage, which contact the balls, are thus required to have a large wall thickness sufficient to withstand the load applied from the balls. 
     Thus, by making the DOJ dedicated to propeller shafts, it is possible to limit the maximum operating angle to a low value, so that the maximum load applied to one ball is reduced. Accordingly, the load applied to the inner joint member and the outer joint member from the balls is reduced, and it is thus possible to reduce their wall thickness and achieve the axial size reduction and weight reduction of the DOJ. 
     Further, by limiting the maximum operating angle of the DOJ to a low value, the amount of circumferential movement of the balls in the pockets of the cage is reduced, and it is thus possible to shorten the circumferential length of the pockets. This allows the cage to have a smaller diameter, and it is thus possible to reduce the pitch circle diameter PCD BALL  of the balls and hence the outer diameter of the outer joint member, so that further radial size reduction and weight reduction of the DOJ can be achieved. 
     Further, by limiting the maximum operating angle of the DOJ to a low value, allowance can be made for the strength of the inner joint member. It is thus possible to increase the inner diameter of a connecting hole of the inner joint member into which the shaft is connected, that is, the pitch circle diameter of the female splines. This allows the shaft, which is the weakest component at a low operating angle, to have a larger diameter and thus an increased strength, so that the durability of the propeller shaft is improved. 
     In the DOJ, the center of curvature of the spherical outer surface of the cage and the center of curvature of the spherical inner surface of the cage are axially offset to maintain the balls on the bisector plane of the operating angle at any operating angle, so that the constant-speed torque transmission is achieved. Since the propeller shaft DOJ has a small and substantially constant operating angle, smooth torque transmission can be achieved even if the offset (f) between the center of curvature of the outer surface and the center of curvature of the inner surface of the cage is reduced. The present inventors have found that by reducing the offset (f) of the cage, it is possible to reduce the axial dimension and radial wall thickness of the cage without impairing the function and durability of the DOJ, and have thereby achieved further size and weight reduction of the DOJ. Further, by reducing the offset (f) of the cage, the force acting on the pockets of the cage and the inner surface of the outer joint member is reduced, so that the heat generation of the DOJ for propeller shafts, which is used at high rotation speed, can be suppressed. 
     Further, as technical means for achieving the above-mentioned objective, the present invention is a plunging type constant velocity universal joint for a propeller shaft including: an outer joint member having eight straight track grooves formed along an axial direction on a cylindrical inner surface; an inner joint member having eight straight track grooves formed along the axial direction on a spherical outer surface and opposing the straight track grooves of the outer joint member and a connecting hole in which female splines are formed; eight torque transmitting balls disposed between the straight track grooves of the outer joint member and the straight track grooves of the inner joint member; a cage having pockets accommodating the torque transmitting balls, a spherical outer surface guided in contact with the cylindrical inner surface of the outer joint member, and a spherical inner surface guided in contact with the spherical outer surface of the inner joint member, and is characterized in that a center of curvature of the spherical outer surface and a center of curvature of the spherical inner surface of the cage each have an equal and axially opposite offset (f) with respect to a center of the pockets, a ratio Wi/Db between an axial width Wi of the inner joint member and a ball diameter Db of the torque transmitting balls is 1.2 or more and 1.4 or less, and a ratio PCD BALL /Db between a pitch circle diameter PCD BALL  of the torque transmitting balls and the diameter Db of the torque transmitting balls is 3.3 or more and 3.6 or less. 
     By making the DOJ dedicated to propeller shafts, it is possible to limit the maximum operating angle to a low value, so that the amount of axial movement of the balls relative to the inner joint member is reduced. Accordingly, it is possible to reduce the axial length of the track grooves of the inner joint member and hence the axial width Wi of the inner joint member, so that the axial size reduction and weight reduction of the DOJ can be achieved. 
     Further, by limiting the maximum operating angle of the DOJ to a low value, the amount of circumferential movement of the balls in the pockets of the cage is reduced, and it is thus possible to shorten the circumferential length of the pockets. This allows the cage to have a smaller diameter, and it is thus possible to reduce the pitch circle diameter PCD BALL  of the balls, so that the radial size reduction and weight reduction of the DOJ can be achieved. 
     Further, by limiting the maximum operating angle of the DOJ to a low value, the load applied to the axially opposing wall surfaces of the pockets of the cage is reduced, and it is thus possible to reduce the axial widths of the portions of the cage to which axial load is applied from the balls (specifically, the annular portions provided on both axial sides of the pockets). In this manner, the axial width of the cage is reduced, and further axial size reduction and weight reduction of the DOJ can be achieved. 
     Further, as technical means for achieving the above-mentioned objective, the present invention is a plunging type constant velocity universal joint for a propeller shaft including: an outer joint member having eight straight track grooves formed along an axial direction on a cylindrical inner surface; an inner joint member having eight straight track grooves formed along the axial direction on a spherical outer surface and opposing the straight track grooves of the outer joint member and a connecting hole in which female splines are formed; eight torque transmitting balls disposed between the straight track grooves of the outer joint member and the straight track grooves of the inner joint member; a cage having pockets accommodating the torque transmitting balls, a spherical outer surface guided in contact with the cylindrical inner surface of the outer joint member, and a spherical inner surface guided in contact with the spherical outer surface of the inner joint member, and is characterized in that a center of curvature of the spherical outer surface and a center of curvature of the spherical inner surface of the cage each have an equal and axially opposite offset (f) with respect to a center of the pockets, a ratio To/Db between a wall thickness To of the outer joint member and a ball diameter Db of the torque transmitting balls is 0.25 or more and 0.29 or less, and a ratio PCD BALL /Db between a pitch circle diameter PCD BALL  of the torque transmitting balls and the diameter Db of the torque transmitting balls is 3.3 or more and 3.6 or less. 
     In the case of a ball type constant velocity universal joint that transmits torque via balls, while each ball is evenly loaded when the operating angle is 0°, uneven loads are applied to the balls when an operating angle is taken, and the difference increases at a higher operating angle. Accordingly, the maximum load applied to one ball is also increased at a high operating angle, and the inner joint member, the outer joint member, and the cage, which contact the balls, are thus required to have a large wall thickness sufficient to withstand the load applied from the balls. 
     Thus, by making the DOJ dedicated to propeller shafts, it is possible to limit the maximum operating angle to a low value, so that the maximum load applied to one ball is reduced. Accordingly, the load applied to the inner joint member and the outer joint member from the balls is reduced, and it is thus possible to reduce their wall thickness and achieve the axial size reduction and weight reduction of the DOJ. 
     Further, by limiting the maximum operating angle of the DOJ to a low value, the amount of circumferential movement of the balls in the pockets of the cage is reduced, and it is thus possible to shorten the circumferential length of the pockets. This allows the cage to have a smaller diameter, and it is thus possible to reduce the pitch circle diameter PCD BALL  of the balls and hence the outer diameter of the outer joint member, so that further radial size reduction and weight reduction of the DOJ can be achieved. 
     Further, by limiting the maximum operating angle of the DOJ to a low value, allowance can be made for the strength of the inner joint member. It is thus possible to increase the inner diameter of a connecting hole of the inner joint member into which the shaft is connected, that is, the pitch circle diameter of the female splines. This allows the shaft, which is the weakest component at a low operating angle, to have a larger diameter and thus an increased strength, so that the durability of the propeller shaft is improved. 
     Advantageous Effects of Invention 
     According to the present invention, it is possible to realize a plunging type constant velocity universal joint dedicated to propeller shafts that has a reduced size and weight, is qualitatively different from conventional one, and can contribute to the demands for further improvement in fuel efficiency of automobiles and increase in rotation speed of propeller shafts. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a diagram showing a propeller shaft equipped with a plunging type constant velocity universal joint for a propeller shaft according to an embodiment of the present invention. 
         FIG. 2A  is a longitudinal sectional view taken along line B-N-B in  FIG. 2B , showing a plunging type constant velocity universal joint for a propeller shaft according to an embodiment of the present invention. 
         FIG. 2B  is a cross sectional view taken along line A-A in  FIG. 2A . 
         FIG. 3A  is a diagram showing on the upper side a longitudinal section of the upper half of the plunging type constant velocity universal joint of  FIG. 2A  with respect to axis line N-N, and on the lower side a longitudinal section of the upper half of the plunging type constant velocity universal joint of  FIG. 11A  with respect to axis line N-N in a reversed orientation. 
         FIG. 3B  is a diagram showing on the upper side a longitudinal section of the lower half of the plunging type constant velocity universal joint of  FIG. 2A  with respect to axis line N-N in a reversed orientation, and on the lower side a longitudinal section of the lower half of the plunging type constant velocity universal joint of  FIG. 11A  with respect to axis line N-N. 
         FIG. 4  is a sectional view of the plunging type constant velocity universal joint of  FIG. 2A  (upper half) and the plunging type constant velocity universal joint of  FIG. 11A  (lower half), comparing them with regard to the axial movement of an inner joint member and a ball. 
         FIG. 5  is a longitudinal sectional view showing the inner joint member, cage, and ball of  FIG. 2A  at an enlarged scale. 
         FIG. 6A  is an enlarged view of portion C of  FIG. 5 . 
         FIG. 6B  is an enlarged view of portion D of  FIG. 5 . 
         FIG. 7A  is a longitudinal sectional view showing an inner joint member, a cage, and a ball in a standard design in which a pocket clearance δ1 and an axial clearance δ2 are not provided. 
         FIG. 7B  is a longitudinal sectional view showing an inner joint member, a cage, and a ball in a design in which the pocket clearance δ1 and the axial clearance δ2 are provided. 
         FIG. 7C  is a longitudinal sectional view showing an inner joint member, a cage, and a ball in another design in which the pocket clearance δ1 and the axial clearance δ2 are provided. 
         FIG. 8  is a longitudinal sectional view showing the maximum operating angle of the plunging type constant velocity universal joint of  FIGS. 2A and 2B . 
         FIG. 9  is a longitudinal sectional view showing an operating angle that can be taken by the plunging type constant velocity universal joint of  FIGS. 2A and 2B  when equipped with a boot. 
         FIG. 10  is a diagram comparing the cross section of the plunging type constant velocity universal joint in  FIG. 2B  and the cross section of the plunging type constant velocity universal joint in  FIG. 11B . 
         FIG. 11A  is a longitudinal sectional view taken along line F-N-F in  FIG. 11B , showing an existing plunging type constant velocity universal joint. 
         FIG. 11B  is a cross sectional view taken along line E-E in  FIG. 11A . 
         FIG. 12  is a longitudinal sectional view showing the plunging type constant velocity universal joint of  FIG. 11  when assembled. 
         FIG. 13  is a plan view showing an outline of the drive system of an FF-based 4WD vehicle. 
         FIG. 14  is a plan view showing an outline of the drive system of an FR-based 4WD vehicle. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Embodiments of the present invention will be described with reference to the drawings. 
     First, an outline of the drive system of an example four-wheel drive vehicle (hereinafter also referred to as a 4WD vehicle) using a propeller shaft will be described with reference to  FIGS. 13 and 14 . 
     As shown in  FIG. 13 , in the drive system of an FF (front-engine, front-wheel drive)-based 4WD vehicle, the driving force is transmitted in the order of an engine  100 , a transaxle  113 , a differential  111 , a transfer  112 , a propeller shaft (rear propeller shaft)  102 , a differential  103 , drive shafts  104 , and rear wheels  105 . On the front side, the driving force is transmitted in the order of the engine  100 , the transaxle  113 , the differential  111 , drive shafts  109 , and front wheels  110 . 
     As shown in  FIG. 14 , in the drive system of an FR (front-engine, rear-wheel drive)-based 4WD vehicle, the driving force is transmitted in the order of an engine  100 , a transmission  101 , a propeller shaft (rear propeller shaft)  102 , a differential  103 , drive shafts  104 , and rear wheels  105 . Also, on the front side, the driving force is transmitted in the order of the engine  100 , the transmission  101 , a transfer  106 , a propeller shaft (front propeller shaft)  107 , a differential  108 , drive shafts  109 , and front wheels  110 . 
     In both of the FF-based and FR-based 4WD vehicles, constant velocity universal joints  45 ,  46 , and  47  used for the drive shafts  104  and  109  placed after the differentials  103 ,  108 , and  111 , which are final reduction gears, have a maximum rotational speed of about 2000 min −1  and a normal maximum operating angle of about 15°. The operating angles of the constant velocity universal joints  45 ,  46 , and  47  used for the drive shafts  104  and  109  are required to follow the vertical movement of the wheels  105  and  110 , and constantly fluctuate. In addition, the fixed type constant velocity universal joints  46  attached to the front wheels  110  require large operating angles for steering. In the present embodiment, the fixed type constant velocity universal joints  46  attached to the front wheels  110  have a maximum operating angle of about 45°, and the other constant velocity universal joints  45  and  47  have a maximum operating angle of about 20 to 25°. 
     On the other hand, the propeller shafts  102  and  107  are arranged before the differentials  103 ,  108  and  111 , which are final reduction gears, and are thus used at high rotation speed. Specifically, the maximum rotation speed is about 8000 min −1 . Since in the case of an independent suspension vehicle, the differentials  103 ,  108 , and  111  are mounted on the vehicle body side, and the propeller shafts  102  and  107  have large total lengths, a constant velocity universal joint  1  used for the propeller shafts  102  and  107  has a small and substantially constant operating angle. Specifically, the constant velocity universal joint  1  has a normal maximum operating angle of 10° or less and a maximum operating angle of about 15°. Further, the transmission torque of the constant velocity universal joint  1  used for the propeller shafts  102  and  107  is much smaller than that of the constant velocity universal joints  45 ,  46 , and  47  used for the drive shafts  104  and  109 . Although  FIGS. 13 and 14  illustrates an example in which universal joints  43 ,  44 ,  48 , and  49  used for the propeller shafts  102  and  107  are cross joints, constant velocity universal joints may be used as at least one of these universal joints  43 ,  44 ,  48 , and  49 . 
     Using the propeller shaft of the FF-based 4WD vehicle as an example, an outline of the propeller shaft will be described with reference to  FIG. 1 . The propeller shaft  102  is composed of a first propeller shaft  41  located on the front side (the right side in the figure, the engine  100  side in  FIG. 13 ) and a second propeller shaft  42  located on the rear side (the left side in the figure, the differential  103  side in  FIG. 13 ). 
     The first propeller shaft  41  has a main part composed of a hollow pipe  64  and one end (front end) connected to the output side (the transfer  112 , see  FIG. 13 ) of the engine  100  via the cross joint  43 . The plunging type constant velocity universal joint  1  is connected to the other end (rear end) of the hollow pipe  64  of the first propeller shaft  41 . The plunging type constant velocity universal joint  1  is the plunging type constant velocity universal joint for the propeller shaft according to the present embodiment. 
     The second propeller shaft  42  has a main part composed of a hollow pipe  65  and one end (front end) rotatably supported by a bearing support  60 . Specifically, the bearing support  60  consists of a bracket  61 , an elastic member  62 , and a rolling bearing  63 . An outer ring  62   a  of the elastic member  62  is fitted to the bracket  61 , and an inner ring  62   b  of the elastic member  62  is fitted to the rolling bearing  63 . A shaft  20  is provided at one end of the second propeller shaft  42 , and the outer periphery of the shaft  20  is fitted to the rolling bearing  63  and elastically supported in the radial direction. One end (front end) of the shaft  20  is connected to a connecting hole of an inner joint member of the plunging type constant velocity universal joint  1 . The other end (rear end) of the second propeller shaft  42  is connected to the differential  103  (see  FIG. 13 ) via the cross joint  44 . As described above, the first propeller shaft  41  and the second propeller shaft  42  are connected in the axial direction. 
     The overall arrangement of the plunging type constant velocity universal joint  1  for the propeller shaft according to the present embodiment will be described with reference to  FIGS. 2A and 2B . 
     The plunging type constant velocity universal joint  1  for the propeller shaft (hereinafter also simply referred to as a plunging type constant velocity universal joint  1 ) according to the present embodiment is a so-called double-offset plunging type constant velocity universal joint (hereinafter also referred to as DOJ), and mainly includes an outer joint member  2 , an inner joint member  3 , torque transmitting balls  4 , and a cage  5 . Eight straight track grooves  7  are formed on a cylindrical inner surface  6  of the outer joint member  2  at equal intervals in the circumferential direction and along the axial direction. Eight straight track grooves  9  opposing the track grooves  7  of the outer joint member  2  are formed on a spherical outer surface  8  of the inner joint member  3  at equal intervals in the circumferential direction and along the axial direction. The torque transmitting balls (hereinafter also simply referred to as balls)  4  are individually disposed between the straight track grooves  7  of the outer joint member  2  and the straight track grooves  9  of the inner joint member  3 . The balls  4  are accommodated in pockets  5   a  of the cage  5 . 
     The cage  5  has a spherical outer surface  12  and a spherical inner surface  13 , the spherical outer surface  12  is fitted to and guided in contact with the cylindrical inner surface  6  of the outer joint member  2 , and the spherical inner surface  13  is fitted to and guided in contact with the spherical outer surface  8  of the inner joint member  3 . The spherical outer surface  12  of the cage  5  has a center of curvature O 1 , and the spherical inner surface  13  has a center of curvature O 2 . The centers of curvature O 1  and O 2  have equal and axially opposite offsets f with respect to a center O 3  of the pockets  5   a  of the cage  5 . Here, the center O 3  of the pockets  5   a  refers to the intersection point of the plane including the respective axial direction-centers of the eight pockets  5   a  and joint axis line N-N. In this manner, when the joint has an operating angle, the balls  4  are always guided on the plane that bisects the angle formed by the two axis lines of the outer joint member  2  and the inner joint member  3 , and the rotational torque is transmitted between the two axes at the constant speed. 
     As shown in  FIG. 2A , a large diameter portion  2   a  joined to the hollow pipe  64  of the first propeller shaft  41  is formed at one end (right end in  FIG. 2A ) of the outer joint member  2 , and a seal cover  16  is attached to an inner hole near the large diameter portion  2   a . Female splines (including serrations)  11  are formed in a connecting hole  10  passing through the axial center of the inner joint member  3 , and male splines  21  of the shaft  20  (see  FIGS. 1 and 8 ) are fitted and connected thereto and fixed in the axial direction by a retaining ring  22 . 
     A retaining ring groove  14  is provided on the inner periphery of the other end (opening-side end) of the outer joint member  2 . A retaining ring  23  (see  FIG. 8 ) mounted in the retaining ring groove  14  prevents an inner assembly consisting of the inner joint member  3 , the balls  4 , and the cage  5  from coming out from the opening-side end of the outer joint member  2 . A cylindrical surface-shaped notch  5   c  for disposing the inner joint member  3  is provided on the inner periphery of the large-diameter-side end (right end in  FIG. 2A ) of the cage  5 . A boot mounting groove  15  is provided on the outer periphery of the opening-side end of the outer joint member  2 . As shown in  FIG. 9 , a boot  25  is mounted in the boot mounting groove  15  of the outer joint member  2  and a boot mounting groove  20   a  of the shaft  20 , and is tightened and fixed with boot bands  27  and  26 . The boot  25  and the seal cover  16  function together to prevent the grease sealed inside the joint from leaking out and foreign matter from entering from outside the joint. 
     The overall structure of the plunging type constant velocity universal joint  1  of the present embodiment is as described above. Next, characteristic arrangements will be described. The findings and ideas in the development process leading to the characteristic arrangements of the plunging type constant velocity universal joint  1  of the present embodiment are as follows. 
     (1) The double-offset plunging type constant velocity universal joint (DOJ) can slide a relatively large distance in the axial direction, have a good track record of use and stable performance, and further, can be designed to have eight balls to achieve size reduction and weight reduction. Focusing on these points, various DOJs used for the existing propeller shafts as shown in  FIGS. 11 and 12  have been studied in order to meet the demands for further improvement in fuel efficiency of automobiles and size reduction, weight reduction, and increase in rotation speed of propeller shafts. As a result, the focus has been put on the fact that although the existing DOJs have a maximum operating angle of about 25° so that they can also be used for drive shafts, the function of the DOJ can be limited by specializing it to required characteristics for use with propeller shafts. Specifically, it has been found that by making the DOJ dedicated to propeller shafts, the maximum operating angle can be limited to a low value (e.g., 15° or less), and size reduction and weight reduction of the DOJ can thereby be achieved. 
     (2) By limiting the maximum operating angle of the propeller shaft-dedicated DOJ to a low value, the following specific technical effects can be obtained. 
     (a) Radial size reduction and weight reduction by reducing the radial wall thickness of each component (outer joint member, inner joint member, cage) 
     (b) Axial size reduction and weight reduction of the inner joint member by reducing the amount of axial movement of the balls 
     (c) Radial size reduction and weight reduction of the cage by reducing the amount of circumferential movement of the balls 
     (d) Axial size reduction and weight reduction of the cage by reducing pocket load 
     (3) In addition, the possibility of further size reduction and weight reduction has been studied by focusing on the dynamic factors that the DOJ for propeller shafts has a small and substantially constant operating angle and a high rotation speed. As a result, the idea to reduce the offset of the cage has been conceived, and it has been found that this enhances the technical effects of (2) mentioned above, and further size reduction and weight reduction of the DOJ can be achieved. 
     The above characteristic arrangements will be described in comparison with an existing plunging type constant velocity universal joint shown in  FIGS. 11 and 12 . As shown in  FIGS. 11 and 12 , an existing plunging type constant velocity universal joint  201  is a double-offset plunging type constant velocity universal joint using eight torque transmitting balls  204 , mainly includes an outer joint member  202 , an inner joint member  203 , the torque transmitting balls  204 , and a cage  205 , and has a maximum operating angle of about 25°. A diameter Db of the torque transmitting balls  4  of the plunging type constant velocity universal joint  1  according to the present embodiment is equal to a diameter Db′ of the torque transmitting balls  204  of the existing plunging type constant velocity universal joint  201 . The basic internal arrangement is the same as that of the plunging type constant velocity universal joint  1  for the propeller shaft of the present embodiment, and portions having the same functions as those of the plunging type constant velocity universal joint  1  for the propeller shaft of the present embodiment are provided with reference numerals obtained by adding 200 to the reference numerals given in the present embodiment, and the center of the pockets, the centers of curvature, the offsets, and the like are provided with the alphabet reference characters obtained by adding a prime (′) to the characters of the present embodiment. 
     The respective longitudinal sections of the plunging type constant velocity universal joint  1  according to the present embodiment and the existing plunging type constant velocity universal joint  201  will be described in comparison with reference to  FIGS. 3A and 3B .  FIG. 3A  is a diagram showing on the upper side a longitudinal section of the upper half of  FIG. 2A  with respect to axis line N-N, and on the lower side a longitudinal section of the upper half of  FIG. 11A  with respect to axis line N-N in a reversed orientation.  FIG. 3B  is a diagram showing on the upper side a longitudinal section of the lower half of  FIG. 2A  with respect to axis line N-N in a reversed orientation, and on the lower side a longitudinal section of the lower half of  FIG. 11A  with respect to axis line N-N. 
     The maximum operating angle of the plunging type constant velocity universal joint  1  of the present embodiment shown on the upper side of joint axis line N-N in  FIG. 3B  is set to 15°. Accordingly, an inclination angle β of a conical stopper surface  5   d  of the outer periphery of the cage  5  is formed at 7.5°, which is ½ of the maximum operating angle of 15°. Therefore, as shown in  FIG. 8 , the plunging type constant velocity universal joint  1  can take the maximum operating angle θmax=15° before the boot is mounted. However, the maximum operating angle may be set to an appropriate angle of 15° or less. Thus, when an operating angle is taken, the cylindrical inner surface  6  of the outer joint member  2  and the conical stopper surface  5   d  of the outer periphery of the cage  5  abut, so that the maximum operating angle is limited. In this specification, the maximum operating angle has the above meaning. In the completed state in which the boot is attached to the plunging type constant velocity universal joint  1 , as shown in  FIG. 9 , when an operating angle is taken, the available operating angle is limited due to the abutment of the boot  25  and the shaft  20 , and becomes smaller than the above maximum operating angle. 
     In contrast to the above, the maximum operating angle of the existing plunging type constant velocity universal joint  201  shown on the lower side of joint axis line N-N in  FIG. 3B  is set to about 25° so that it can be used for drive shafts, and an inclination angle β′ of a conical stopper surface  205   d  of the outer surface of the cage  205  is formed at 12.5°, which is ½ of the maximum operating angle of 25°. 
     In the case of a ball type constant velocity universal joint, while each ball is evenly loaded when the operating angle is 0°, uneven loads are applied to the balls when an operating angle is taken, and the difference increases at a higher operating angle. Accordingly, the maximum load applied to one ball is also increased at a high operating angle, and the inner joint member, the outer joint member, and the cage, which contact the balls, are thus required to have a large wall thickness sufficient to withstand the maximum load applied from the balls. In contrast, with the plunging type constant velocity universal joint  1  of the present embodiment, by limiting the maximum operating angle to a low value, the required strength of the components of the outer joint member  2 , the inner joint member  3 , and the cage  5  can be reduced, and it is thus possible to reduce their wall thickness. Further, by limiting the maximum operating angle to a low value, the amount of radial movement of the balls  4  in the pockets  5   a  of the cage  5  at the maximum operating angle is also reduced, and it is thus possible to reduce the wall thickness of the cage  5 . 
     Specifically, as shown in  FIGS. 3A and 3B , a wall thickness To of the outer joint member  2  (specifically, the radial distance between the groove bottom of the track grooves  7  and the outer surface of the outer joint member  2 ) and a wall thickness Ti of the inner joint member  3  (specifically, the radial distance between the groove bottom of the track grooves  9  and the pitch circle of the female splines  11  of the inner joint member  3 ) of the plunging type constant velocity universal joint  1  in the present embodiment are thinner than a wall thickness To′ of the outer joint member  202  and a wall thickness Ti′ of the inner joint member  203  of the existing plunging type constant velocity universal joint  201 , respectively. As an optimum value, the ratio Ti/Db between the wall thickness Ti of the inner joint member  3  and the ball diameter Db is 0.30 to 0.45. Also, the ratio To/Db between the wall thickness To of the outer joint member  2  and the ball diameter Db is 0.25 to 0.29. 
     In the case of a ball type constant velocity universal joint, the amount of circumferential movement of the balls relative to the cage increases at a higher operating angle. In the existing 8-ball-based plunging type constant velocity universal joint  201 , since the maximum operating angle is set to about 25°, the amount of circumferential movement of the balls  204  relative to the cage  205  is large, and the circumferential length of the pockets  205   a  of the cage  205  accommodating the balls  204  needs to be increased. Further, in order to obtain a sufficient strength of a pillar portion  205   b  (see  FIG. 11B ) of the cage  205 , there is a limit to the reduction of the circumferential dimension of the pillar portion  205   b . As a result, the outer diameter of the cage  205  is increased, and it has not been possible to achieve sufficient size reduction of the plunging type constant velocity universal joint  201 . Accordingly, the wall thickness Ti′ of the inner joint member  203  has been unnecessarily large. 
     In contrast, by limiting the maximum operating angle of the plunging type constant velocity universal joint  1  to a low value as described above, the amount of circumferential movement of the balls  4  in the pockets  5   a  of the cage  5  is reduced, and it is thus possible to shorten the circumferential length of the pocket  5   a , which enables the reduction of the diameter of the cage  5  and hence the radial size reduction of the plunging type constant velocity universal joint  1 . Further, by reducing the diameter of the cage  5 , it is possible to optimize the wall thickness of the inner joint member  3  and reduce the pitch circle diameter PCD BALL  of the balls  4 . Accordingly, an outer diameter Do of the outer joint member  2  can be reduced. As an optimum value, the ratio PCD BALL /Db between the pitch circle diameter PCD BALL  of the ball  4  and the diameter Db of the balls  4  is 3.3 or more and 3.6 or less. 
       FIG. 10  shows in comparison the respective cross sections of the plunging type constant velocity universal joint  1  of the present embodiment and the existing plunging type constant velocity universal joint  201 . The plunging type constant velocity universal joint  1  of the present embodiment has achieved a size reduction of 5% or more in the outer diameter Do of the outer joint member  2  over the existing plunging type constant velocity universal joint  201 . The optimum value of the ratio Do/Db between the outer diameter Do of the outer joint member  2  and the diameter Db of the balls  4  is 2.7 or more and 3.0 or less. 
     Further, by limiting the maximum operating angle of the plunging type constant velocity universal joint  1  to a low value as described above, allowance can be made for the strength of the inner joint member  3 , and it is possible to increase the strength of the shaft  20 , which is the weakest part at a low operating angle. That is, it is possible to increase the pitch circle diameter (PCD SPL ) of the female splines  11  of the inner joint member  3 , and as a result, the strength of the propeller shaft at a low operating angle can be improved. As an optimum value, the ratio PCD SPL /Db between the pitch circle diameter PCD SPL  of the female splines  11  and the diameter Db of the balls  4  is 1.75 or more and 1.85 or less. However, it is also possible to maintain the pitch circle diameter (PCD SPL ) of the female splines  11  as it currently is to facilitate the radial size reduction of the inner joint member  3 . 
     Further, by limiting the maximum operating angle of the plunging type constant velocity universal joint  1  to a low value as described above, it is possible to reduce the axial widths of the inner joint member  3  and the cage  5 , so that the weight and axial size reduction of the plunging type constant velocity universal joint  1  can be achieved. As shown in  FIGS. 3A and 3B , an axial width Wi of the inner joint member  3  and an axial width Wc of the cage  5  of the plunging type constant velocity universal joint  1  are significantly reduced as compared to an axial width Wi′ of the inner joint member  203  and an axial width Wc′ of the cage  205  of the existing plunging type constant velocity universal joint  201 . 
     In the above plunging type constant velocity universal joint  1 , since the amount of axial movement of the ball  4  is determined by the maximum operating angle, the axial width Wi of the inner joint member  3  may be set accordingly. The relationship between the amount of axial movement of the balls  4  and the axial width Wi of the inner joint member  3  will be specifically described with reference to  FIG. 4 .  FIG. 4  is a diagram comparing the plunging type constant velocity universal joint  1  according to the present embodiment and the existing plunging type constant velocity universal joint  201  used for propeller shafts with regard to the axial movement between the inner joint member and the balls. The amount of axial movement of the ball  4  of the plunging type constant velocity universal joint  1  is Zi, and the amount of axial movement of the ball  204  of the existing plunging type constant velocity universal joint  201  is Zi′. The amount of axial movement Zi is shorter than the amount of axial movement Zi′ because of the lower maximum operating angle. Since the axial width Wi of the inner joint member  3  and the axial width Wi′ of the inner joint member  203  are set in accordance with the respective amounts of axial movement Zi and Zi′, the axial width Wi of the inner joint member  3  of the plunging type constant velocity universal joint  1  is significantly reduced as compared to the axial width Wi′ of the inner joint member  203  of the existing plunging type constant velocity universal joint  201 . 
     If the axial width Wi of the inner joint member  3  is too short, the spline fitting length between the female splines  11  of the inner joint member  3  and the male splines  21  of the shaft  20  becomes insufficient, and lack of joint strength between the inner joint member  3  and the shaft  20  occurs. However, by limiting the maximum operating angle of the plunging type constant velocity universal joint  1  to a low value as described above, allowance can be made for the strength of the inner joint member  3 , so that it is possible to set the pitch circle diameter (PCD SPL ) of the female splines  11  to be larger than usual. This has advantageous effects on the torsional strength of the shaft  20 , which is the weakest component at a low operating angle, and on the spline tooth surface pressure, and it is thus possible to shorten the spline fitting length, so that the axial width Wi of the inner joint member can be shortened to achieve weight reduction. As an optimum value, the ratio Wi/Db between the axial width Wi of the inner joint member  3  and the ball diameter Db is 1.2 to 1.4. 
     By limiting the maximum operating angle of the plunging type constant velocity universal joint  1  as described above, the ball load applied to the pockets  5   a  of the cage  5  is reduced. This can reduce the axial wall thickness between the axially opposing wall surfaces of the pockets  5   a  and the end surfaces of the cage  5  (that is, the axial wall thickness of the annular portions provided on both axial sides of the pockets  5   a ), leading to weight reduction. Specifically, as shown in  FIG. 3B , the axial width We of the cage  5  of the plunging type constant velocity universal joint  1  is significantly reduced as compared to the axial width Wc′ of the cage  205  of the existing plunging type constant velocity universal joint  201 . As an optimum value, the ratio Wc/Db between the axial width Wc of the cage  5  and the ball diameter Db is 1.8 to 2.0. 
     The reduction of the offset of the cage, which dramatically enhances the technical effects of the weight reduction and size reduction of the plunging type constant velocity universal joint  1  of the present embodiment described above, will be described with reference to  FIG. 3B . In the process of development, the possibility of size and weight reduction has been drastically studied by focusing on the dynamic factors that the plunging type constant velocity universal joint  1  for the propeller shaft has a small maximum operating angle, a substantially constant angle, and a high rotation speed. As a result, the idea that it is possible to reduce the offset f of the cage  5  has been conceived, and it has been found that this dramatically enhances the above-described technical effects so that further size reduction and weight reduction of the plunging type constant velocity universal joint  1  can be achieved. 
     As shown in  FIG. 3B , the offset f of the cage  5  of the plunging type constant velocity universal joint  1  is set to be smaller than an offset f′ of the cage  205  of the existing plunging type constant velocity universal joint  201 . In the plunging type constant velocity universal joint  1 , as a dedicated design for use with propeller shafts, the ratio f/PCD BALL  between the offset f of the cage  5  and the pitch circle diameter PCD BALL  of the balls  4  (see  FIG. 3A ) is set to be 0.07 or more and 0.09 or less. By reducing the offset of the cage  5  in this manner, further size reduction and weight reduction of the plunging type constant velocity universal joint  1  can be achieved. Further, by reducing the offset f of the cage  5 , the force acting on the pockets  5   a  of the cage  5  and the inner surface  6  of the outer joint member  2  is reduced, so that the heat generation of the plunging type constant velocity universal joint  1  for the propeller shaft, which is used at high rotation speed, can be suppressed. The ratio f′/PCD BALL ′ between the offset f′ of the cage  205  of the existing plunging type constant velocity universal joint  201  and the pitch circle diameter PCD BALL ′ of the balls  204  (see  FIG. 3A ) is set to a value more than 0.09. 
     Table 1 shows dimensional ratios of the plunging type constant velocity universal joint  1  of the present embodiment and the existing plunging type constant velocity universal joint  201 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Invented Product 
                 Existing Product 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 Cage offset f/ball PCD (PCD BALL ) 
                 0.07-0.09 
                 more than 0.09 
               
               
                 Inner joint member wall thickness 
                 0.30-0.45 
                 more than 0.45 
               
               
                 Ti/ball diameter Db 
               
               
                 Outer joint member wall thickness 
                 0.25-0.29 
                 more than 0.29 
               
               
                 To/ball diameter Db 
               
               
                 Inner joint member width 
                 1.2-1.4 
                 1.6-1.8 
               
               
                 Wi/ball diameter Db 
               
               
                 Cage width Wc/ball diameter Db 
                 1.8-2.0 
                 more than 2.0 
               
               
                 Ball pitch circle diameter 
                 3.3-3.6 
                 more than 3.6 
               
               
                 (PCD BALL )/ball diameter Db 
               
               
                 Spline pitch circle diameter 
                 1.75-1.85 
                 less than 1.75 
               
               
                 (PCD SPL )/ball diameter Db 
               
               
                 Outer joint member outer diameter 
                 2.7-3.0 
                 more than 3.0 
               
               
                 Do/spline PCD (PCD SPL ) 
               
               
                   
               
            
           
         
       
     
     Next, the performance characteristics of the plunging type constant velocity universal joint  1  for the propeller shaft in terms of vibration characteristics, reduction of heat generation, and increase in rotation speed will be described with reference to  FIGS. 5 to 7 . 
     As shown in  FIG. 5 , an axial pocket clearance δ1 is provided between the axially opposing wall surfaces of the pocket  5   a  of the cage  5  and the ball  4 . Defining the dimension between the axially opposing wall surfaces of the pocket  5   a  of the cage  5  as Lc and the ball diameter of the ball  4  as Db, the pocket clearance δ1 is represented by δ1=Lc−Db. 
     As shown in  FIG. 6 , an axial clearance δ2 is provided between the spherical inner surface  13  of the cage  5  and the spherical outer surface  8  of the inner joint member  3 . For example, the axial clearance δ2 is the amount of relative axial movement between the position where the spherical outer surface  8  of the inner joint member  3  abuts the spherical inner surface  13  of the cage  5  by moving the inner joint member  3  toward one side in the axial direction and the position where the spherical outer surface  8  of the inner joint member  3  abuts the spherical inner surface  13  of the cage  5  by moving the inner joint member  3  toward the other side in the axial direction, with the cage  5  fixed. 
     By providing the pocket clearance δ1 and the axial clearance δ2 as described above, the sliding resistance of the plunging type constant velocity universal joint  1  is reduced, the vibration characteristics of the vehicle can be improved, and the improvement in life of the plunging type constant velocity universal joint  1  can be expected due to the effect of temperature reduction. In particular, the use with propeller shafts is effective because they are used at a higher speed than drive shafts. 
     The pocket clearance δ1 is preferably set to 0 to 0.05 mm. The pocket clearance δ1 can exhibit its effect even if it is small. If the pocket clearance δ1 is larger than 0.05 mm, the amount of deviation of the ball  4  from the bisector plane of the operating angle is increased, which may lead to decrease in the constant speed property and durability of the plunging type constant velocity universal joint  1 . 
     The axial clearance δ2 is preferably set to about 0.5 to 1.5 mm. If the axial clearance δ2 is smaller than 0.5 mm, the amount of vibration (axial amplitude) from the engine cannot be absorbed by the amount of relative axial movement between the inner joint member  3  and the cage  5 , and the vibration may be propagated. On the other hand, if the axial clearance δ2 is larger than 1.5 mm, the amount of deviation of the ball  4  from the bisector plane of the operating angle is increased, which may lead to decrease in the constant speed property and durability of the plunging type constant velocity universal joint  1 . 
     Designs of the pocket clearance δ1 and the axial clearance δ2 will be described with reference to  FIGS. 7A, 7B, and 7C . In the standard design shown in  FIG. 7A , the axial pocket clearance δ1 is not provided between the axially opposing wall surfaces of the pocket  5   a  of the cage  5  and the ball  4 . Regarding a radius of curvature Rc of the spherical inner surface  13  of the cage  5  and a radius of curvature Ri of the spherical outer surface  8  of the inner joint member  3 , although there is a slight spherical clearance for sliding guide, substantially Rc≈Ri and no axial clearance δ2 is provided. 
     The plunging type constant velocity universal joint  1  according to the present embodiment has a design in which the pocket clearance δ1 and the axial clearance δ2 are provided (see  FIG. 5 ) as shown in  FIGS. 7B and 7C . In the design shown in  FIG. 7B , the pocket clearance δ1 is provided, and the radius of curvature Rc′ of the spherical inner surface  13  of the cage  5  is made larger than the radius of curvature Ri of the spherical outer surface  8  of the inner joint member  3 , and the center of curvature of the radius of curvature Rc′ is radially offset from the axial center of the cage  5 . In this manner, the spherical outer surface  8  of the inner joint member  3  and the spherical inner surface  13  of the cage  5  abut at the axial direction-center of the inner joint member  3 , while the axial clearance δ2 is formed on both sides of the inner joint member  3  (see  FIG. 5 ). 
       FIG. 7C  shows another design in which the pocket clearance δ1 and the axial clearance δ2 are provided. In this design, while the spherical outer surface  8  of the inner joint member  3  is formed of a single spherical surface having a radius of curvature Ri, the spherical inner surface  13  of the cage  5  has a cylindrical portion  13   a  formed in area S at a position corresponding to the axial direction-center of the inner joint member  3 , and spherical surfaces having a radius of curvature Rc are smoothly connected to both ends of the cylindrical portion  13   a . Regarding the radius of curvature Rc of the spherical inner surface  13  of the cage  5  and the radius of curvature Ri of the spherical outer surface  8  of the inner joint member  3 , although there is a slight spherical clearance for sliding guide, substantially Rc Ri. In this design, when the cage  5  and the inner joint member  3  relatively move in the axial direction, the axial direction-center of the spherical outer surface  8  of the inner joint member  3  is slidably guided by the cylindrical portion  13   a , so that smooth relative movement can be achieved. 
     It is apparent that the present invention is not limited to the embodiments described above and can be implemented in various forms without departing from the spirit of the present invention, and the scope of the invention is defined by the claims and encompasses meanings equivalent to those recited in the claims and any modifications that fall within the scope. 
     REFERENCE SIGNS LIST 
     
         
         
           
               1  plunging type constant velocity universal joint for propeller shaft 
               2  outer joint member 
               3  inner joint member 
               4  torque transmitting ball 
               5  cage 
               102  propeller shaft 
               107  propeller shaft 
             O 1  center of curvature of spherical outer surface of cage 
             O 2  center of curvature of spherical inner surface of cage 
             O 3  center of pocket of cage