Abstract:
A one-way clutch, including: a load rotor, a driving member, and at least one self-locking gripper. The load rotor is spool-shaped and includes two circular contact races, one race at each end of the rotor. The driving member includes a plurality of inward facing cams on an inner circumference arranged to rotate co-axially with the load rotor. The cams rotate within the space separating the two load rotor races. When in a locking position each gripper presses against both load rotor races and a cam over area-to-area contacting surfaces. Rotation of the load rotor and driving member are locked in the first direction when one or more grippers are in the locking position. The driving member is rotatable independent of the load rotor in the second, free-wheeling direction. During free-wheeling rotation centrifugal force acts to disengage the grippers from the load rotor, thus reducing or eliminating friction.

Description:
TECHNICAL FIELD 
     The present invention relates generally to a one-way clutch, and more specifically to a one-way clutch capable of sustaining a high number of high torque lock-and-unlock cycles while operating with reduced freewheeling friction. 
     BACKGROUND 
     Roller-ramp and sprag clutches are one-way clutches that operate automatically and are capable of supporting high torque loads. However, metal fatigue limits the cycle life of roller-ramp and sprag clutches in high torque uses. The ramp angle in roller-ramp clutches and the strut angle in sprags must be shallow to achieve locking action. These shallow angles produce very high compressive force on the sprags or rollers, also called “grippers.” Because the force on these grippers is focused along narrow line contacts, high torque loading causes extreme pressure at the contacts. As a result, even the hardest steel alloys suffer metal fatigue after some number of high torque lock and release cycles. Cycle lifetimes of current technologies range from a few hundred thousand to a few million high torque cycles. 
     An advantage of roller-ramp and sprag clutch technologies is that the gripper elements are “self-locking.” That is, once friction contact is established the grippers lock automatically without need of any external forces or mechanisms. Biasing springs are commonly present in these clutches but only function to initiate friction contact between the grippers and the surfaces of the clutch races. When used in an application in which inertial forces reliably initiate friction contact no springs are required for the function of self-locking grippers. The Langen Overrunning Clutch (U.S. Pat. No. 67,659 August 1867), shown in  FIG. 29 , is an example of a roller-ramp clutch using no biasing springs. 
     Numerous attempts have been made to replace the rollers and sprags of conventional one-way clutches with wedge shaped gripper elements so as to increase the contact area and thereby decrease pressure and stress, thus minimizing metal fatigue. For example U.S. Pat. No. 8,020,681 includes an embodiment with large contact surfaces on wedge shaped grippers. But wedge grippers are not generally self-locking and require springs to press the wedges against the ramp surfaces to hold the torque load. The necessary spring force for maintaining high torque grip produces exceedingly high freewheeling friction. In addition, if the torque load momentarily exceeds the spring force the wedges lose grip, producing a dangerous runaway clutch failure. Runaway clutch failures do not occur in a one-way clutch with self-locking grippers. 
     U.S. Pat. No. 3,202,250 by Bertram Fulton discloses a wedge clutch with self-locking grippers. The patent reveals that application of a low-friction coating at the ramp surface can make a wedge-shaped gripper self-locking if the ramp angle is sufficiently small.  FIG. 28  shows an embodiment of Fulton&#39;s disclosure in which the ramp surfaces are placed on the outer race for the expressed purpose of reducing freewheeling friction. With radially inward facing ramps centrifugal force urges the wedges away from the inner race during freewheeling rotation, reducing friction or even lifting the wedge off the counter-rotating race. The following friction analysis of Fulton&#39;s model is necessary for disclosure of the present invention&#39;s innovations. 
       FIG. 22  is a diagram of the forces acting on wedge  41  in a clutch of the same configuration as the model in  FIG. 28 . Fo is the sum of the pressure on the wedge from contacting ramp surface  45  of outer race  43 . Fi is the sum of the pressure on the wedge from contacting circular inner race  42 . During the locked state Fi and Fo must be equal in magnitude, opposite in direction and co-linear, and therefore angle θo is equal to θi. To produce self-locking action the wedge must slip at the ramp surface when the wedge slips against the inner race. For the wedge to slip at the ramp surface the ratio Fto/Fno must be greater than the coefficient of friction μo at the ramp, where Fto is the frictional component and Fno is the normal component of force Fo. Therefore angle φo must be greater than the friction angle arctan(μo) for locking action to occur. During slip at the inner race the ratio Fti/Fni is the kinetic coefficient of friction μi, where Fti is the frictional component and Fni is the normal component of Fi. Therefore the sum of angles (θi+φi) is equal to friction angle arctan(μi). It can be shown that combining these conditions leads to the following requirement for self-locking action:
 
arctan(μ o )&lt;arctan(μ i )−α−φ i   (1)
 
where α is the slope angle of the ramp. The larger the magnitude of φi the more difficult it is to comply with condition (1). But φi increases as the ratio Ro/Ri increases, where Ro is the rotational radius of Fo and Ri is the rotational radius of Fi. That is, the magnitude of φi increases with the thickness of the wedge. In practice φi often reaches a value that makes satisfying requirement (1) unattainable, or attainable for only small values of α. Therefore wedge-clutch designs with outer race ramps use thin spiral wedges and very shallow ramp angles. However a shallow ramp angle is known to lead to “lock up,” a state in which a wedge permanently jams between the races. Substantial force may be necessary to free up a locked up wedge. Additionally, wedge-clutch designs typically specify a circular ramp curvature or leave the ramp curvature unspecified. But a circular or undefined ramp curve does not distribute pressure evenly along the contacting surfaces, especially in spiral-type ramps. Instead these curvatures focus most of the compressive force on a small section of the wedge, leading to lock ups and fatigue processes.
 
     Placement of the ramps on the inside race in a wedge-clutch design reverses the effect of the φi term in equation (1) and makes self-locking action more easily attainable. Most all wedge-clutch designs therefore use inner race ramps. But inner race ramps put the wedges in constant friction contact with the outer race during freewheeling rotation. This effect generates undesirable wear and friction, especially during long periods of high speed counter-rotation. High speed freewheeling is also known to cause freewheeling lockup in operation of inner ramp wedge-clutch designs. U.S. Pat. No. 9,016,451 discloses an inner ramp wedge-clutch with reduced freewheeling friction by use of a spring mechanism built into a wedge ring. Though reduced the design still requires significant freewheeling friction to initiate locking action and is still subject to freewheeling lockup. Other designs, for example U.S. Pat. No. 9,353,802, use an external actuator to disengage the wedges from the outer race during freewheeling operation. These designs do not operate automatically, however, and require additional and complex external mechanisms for operation of the clutch. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention broadly comprises a one-way clutch including a driving member, a load rotor, and at least one gripper element. The load rotor includes two radially outward facing circular contact races and an inner shaft. The load rotor inner shaft and contact races are arranged for rotation about the axis of rotation of the clutch, with the two contact races separated at a fixed longitudinal distance and rigidly connected to the inner shaft. The rotational radius of the load rotor inner shaft is smaller than the radius of the contact races, forming a spool-shaped rotor. The load rotor is arranged for rotational connection to a torque load in most embodiments, or to a power source in others. 
     The clutch driving member includes an inner circumference with a plurality of radially inward facing cam surfaces on the inner circumference. The driving member is arranged co-axially to the load rotor with the cam surfaces rotatable around the load rotor inner shaft and within the longitudinal distance separating the two load rotor races. A space is provided between the driving member inner circumference and the load rotor inner shaft and races. The driving member is arranged for rotational connection to a source of torque in most embodiments, or to a rotating load in others. 
     The clutch gripper elements are disposed in the space provided between the load rotor and the driving member. Each gripper includes three contact surfaces: two gripping surfaces and one slipping surface, with the slipping surface disposed between the two gripping surfaces. The gripper element contact surfaces are arranged to provide a locking position in which one gripping surface presses against one load rotor race, the second gripping surface presses against the other load rotor race, and the slipping surface presses against a driving member cam surface. The driving member includes a stop for each gripper element. Movement of the grippers relative the driving member in the first rotational direction is limited by the stops. In some embodiments the stops are made of an impact absorbing material; in other embodiments the stop includes an elastic element, such as a spring. 
     When in a locked mode of operation at least one gripper element is disposed in its locking position. In locked mode torque is transferred from the driving member to the load rotor through the gripper element(s) and rotation of the driving member and load rotor are locked in the first rotational direction. In a freewheeling mode of operation the driving member is free to rotate independently relative the load rotor in the second rotational direction, opposite the first direction of rotation. During freewheeling rotations of the driving member centrifugal forces urge the grippers to move radially outward, acting to disengage the grippers from the load rotor races. 
     Some embodiments of the present invention include aligning surfaces on the driving member and gripper elements arranged to limit motion of the grippers in the longitudinal, pitching and yawing directions during clutch operation. In some embodiments the curvature of the driving member cams follows a logarithmic spiral. 
     In the present invention the rotational radius of the forces at the clutch driving member cams, Ro, is adaptable in relation to the rotational radius of forces at the load rotor races, Ri. Specifically the ratio Ri/Ro can be made to approach or exceed unity. Friction physics discloses that increasing the ratio Ri/Ro also increases the cam surface ramp angle at which self-locking action of the clutch grippers can be achieved. Increasing the cam surface ramp angle decreases pressure and stress at the clutch contact surfaces, thereby increasing fatigue life and preventing clutch lock-ups. Some embodiments of the present invention include a means for decreasing friction at the interface between the gripper slipping surfaces and driving member cams, thereby further increasing the attainable cam surface ramp angle. Low-friction materials such as polyfluorotetraethylene are used in some embodiments and lubricating grease or oil is used in others. In some embodiments of the present invention the load rotor races are beveled at an angle to the axis of rotation so as to form a conical surface, a method which further acts to increase the attainable cam surface ramp angle. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various embodiments are disclosed, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, in which: 
         FIG. 1  is a perspective view of coordinate system  50 , demonstrating the spatial terminology used in the disclosure; 
         FIG. 2  is a sectional view of an exemplary embodiment of the invention, clutch  100 , with the section taken along the rotational axis of the invention; 
         FIG. 3  is a sectional view of clutch  100  taken along the line  3 - 3  of  FIG. 2 ; 
         FIG. 4  is a partial sectional view of clutch  100  taken generally along the line  4 - 4  of  FIG. 2 ; 
         FIG. 5  is an exploded view of load rotor  20  of clutch  100 ; 
         FIG. 6  is a perspective view of load rotor  20  of clutch  100 ; 
         FIG. 7  is a perspective view of driving member  30  of clutch  100 ; 
         FIG. 8  is a perspective view of main gear  31  of clutch  100 ; 
         FIG. 9  is an exploded view of gripper element  10  of clutch  100 ; 
         FIG. 10  is a perspective view of gripper element  10  of clutch  100 ; 
         FIG. 11  is a longitudinal view gripper element  10  of clutch  100 ; 
         FIG. 12  is a sectional view of a gripper element  10  of clutch  100  taken along line  12 - 12  of  FIG. 11 . 
         FIG. 13  is a bottom view of pad  2  of gripper element  10  in which the extent of expansion slots  11  is visible; 
         FIG. 14  is a perspective view of cradle  1  of gripper element  10 ; 
         FIG. 15  is a perspective view of an alternative embodiment of gripper element  10 ; 
         FIG. 16  is a perspective view of load rotor  20  and a single gripper element  10 , with the gripper element located in its locking position; 
         FIG. 17  is a perspective view of clutch  100 ; 
         FIG. 18  is schematic longitudinal view of load rotor races  26   a ,  26   b , and gripper element  10  with the gripper located in a recessed position; 
         FIG. 19  is a schematic longitudinal view of load rotor races  26   a ,  26   b , and gripper element  10  in its locking position, with a diagram of the forces acting upon the gripper projected onto the illustration; 
         FIG. 20  is a perspective view of gripper  10  with a diagram of the forces acting upon the gripper projected onto the illustration; 
         FIG. 21  is a front view of gripper  10  with a diagram of the forces acting upon the gripper projected onto the illustration; 
         FIG. 22  is a schematic front view of a prior art one-way wedge clutch with a diagram of the forces acting upon the wedge projected onto the illustration; 
         FIG. 23  is a schematic front view cam surface  35  depicting the variables used to calculate the curvature of the surface; 
         FIG. 24  is a perspective view of an alternative embodiment of driving member  30 ; 
         FIG. 25  is longitudinal sectional view of an alternative embodiment of the present invention, clutch  200 ; 
         FIG. 26  is longitudinal sectional view of an alternative embodiment of the present invention, clutch  300 ; 
         FIG. 27  is a partial front sectional view of an alternative embodiment of the present invention illustrating the inclusion of elastic elements  44 ; 
         FIG. 28  is a front view of a prior art one-way wedge clutch; 
         FIG. 29  is a front view of a prior art one-way roller-ramp clutch; 
     
    
    
     DETAILED DESCRIPTION 
     At the outset, it should be understood that the drawings of the disclosure are schematic in nature and may not be to scale. Features such as proportions, sizes, lengths, spacing, widths, and gaps may be exaggerated or otherwise altered for the sake of clarity. For example the size of gap g in  FIG. 18  will likely be much smaller in practice than depicted, and the length of gripper  10  as depicted in  FIG. 11  and other figures may be longer or shorter relative to other features in testing and practice. Additionally, the number of grippers, stops, and cam surfaces of the disclosure is not limited to the number depicted in these drawings. 
       FIG. 1  is a perspective view of coordinate system  50  used for demonstrating the spatial terminology used in the present invention. System  50  has orthogonal axes X, Y and Z and also includes elements of a cylindrical coordinate system. Axis Z is the invention&#39;s axis of rotation and the term “longitudinal” refers to the direction of the Z axis. A plane containing the Z axis will be termed an “axial plane.” The origin Po is located approximately equidistant between the invention&#39;s load rotor races (described later). Any plane that is parallel to the X-Y plane is designated a “radial plane.” A radial is a line extending from the Z axis and lying on a radial plane. The term radial motion and radial distance will refer to motion and distance respectively along a radial. P 1  is a point on the X-Y plane and RR 1  is the radial of P 1 . Circle C 1  is the path of P 1  as it rotates about axis Z and is termed the “rotational circle” of P 1 . R 1  is the radius of C 1  and is called the “rotational radius” of P 1 . D 1  is the first direction of rotation and D 2  is the second direction of rotation. 
     To demonstrate the terminology used for describing the orientation of various forces, lines and surfaces  FIG. 1  includes objects V 2  and V 3 . Point P 2  lies on surface S 2  of V 2 . Line N 2  is the normal to surface S 2  at point P 2 . Because the normals of S 2  point away from the X-Y plane S 2  is termed “longitudinally outward” facing. C 2  is the rotational circle of P 2  and N 2 . Because the normals of S 2  are directed inside their rotational circles S 2  is termed “radially inward” facing. Referring to object V 3 , N 3  is the surface normal at point P 3  of surface S 3 . Surface S 3  is “longitudinally inward” facing and is “radially outward” facing. The terms “front” and “rear” will refer to the positive and negative directions of axis Z. For example, object V 2  is in front of object V 3 . F 2  is a force impinging on surface S 2  at point P 2 . Force F 2   n  is the normal component of F 2 . That is, F 2   n  is the component of F 2  that is perpendicular to the surface at P 2 . Line T 2  is the tangent of C 2  at P 2 . Line T 2 ′ is tangent T 2  translated to the tail of F 2  for diagrammatic purposes. Force F 2   t  is the component of force F 2  parallel to T 2  and will be called the rotational component of F 2 . Line RR 2  is the radial at point P 2 . Force F 2   r  is the radial component of F 2  and lies on RR 2 . Force F 2   a  is the component of F 2  that is parallel to axis Z and will be called the longitudinal component of F 2 . Force F 2  is the sum of F 2   t , F 2   a  and F 2   r . If F 2   n  lies on an axial plane then F 2  is also the sum of F 2   t  and F 2   n . Referring to object V 3 , RR 2 ′ is the radial of P 2  translated along the Z axis to the radial plane of P 3 . The angle between radials RR 3  and RR 2 ′ will be called the rotational angle between point P 3  and P 2  and is marked β in  FIG. 1 . Rotation of an object about a radial passing through the object will be termed a rotation in the “yaw” direction. Rotation Y 3  of object V 3  is a yawing rotation. Rotation of an object about the tangent to a rotational circle passing through the object will be termed rotation in the “pitch” direction. Rotation Q 2  of object V 2  is a pitching rotation. Rotation of an object about an axis parallel to the Z axis, but not the Z axis, will be termed a rotation in the “roll” direction. In  FIG. 1  line L 3  is a line parallel to axis Z that passes through V 3 . Rotation U 3  of V 3  is a rolling rotation. An object that remains motionless in a frame of reference that is rotating about axis Z has no pitching, yawing or rolling motion in that frame of reference. 
       FIG. 2  is a longitudinal sectional view of an exemplary embodiment of the present invention, one-way clutch  100 , with the section taken along the axis of rotation AX. Following standard practice, like drawing numbers on different drawing views of clutch  100  and the drawing views of other embodiments of the invention will identify identical, or functionally similar, structural elements. Load rotor  20  of clutch  100  includes front disc  21   a , rear disc  21   b  and inner shaft  22 . Driving member  30  includes main gear  31  and cam blocks  32 . Grippers  10  include cradles  1 , pad holders  3  and pads  2 . The load rotor is arranged for rotation about axis AX and is arranged for rotational connection to a torque load (not shown). The driving member is arranged to be rotatable co-axially to the load rotor and is arranged in a manner that limits longitudinal displacement in relation to the load rotor. The driving member is arranged for rotational connection to a source of power, that is, a source of rotating torque (not shown). 
       FIG. 3  is a sectional view of clutch  100  taken along line  3 - 3  of  FIG. 2 . Grippers  10  are movable in the radial and rotational directions relative driving member  30 . The grippers are shown in their recessed position and the position of pad  2  is shown in hidden lines. When in the recessed position the grippers rest against both cam blocks  32  and stops  33 . Stops  33  limit the rotation of the grippers in the D 1  direction relative the driving member. 
       FIG. 4  is a partial sectional view of clutch  100  taken along line  4 - 4  of  FIG. 2 . Three grippers  10  are shown and the gripper marked  10 ′ is shown in its recessed position. Surfaces  36  of stops  33  contact surfaces  8  of grippers  10  when the grippers are in recessed position. Surfaces  36  are raked at angle θs to the radial as shown. During operation of the clutch reversal of rotation of the driving member from direction D 1  to D 2  may cause the stops to collide with the grippers. Rake angle θs of stop surfaces  36  direct the impact rebound of the grippers radially outward. Surfaces  6  and  8  of grippers  10  are arranged to make area-to-area contact with surfaces  35  and  36  respectively when the grippers are in recessed position. 
       FIG. 5  is an exploded view of load rotor  20  of clutch  100 . Disc  21   a  and disc  21   b  are attached in a rotationally and longitudinally ridged manner to inner shaft  22  so that a fixed longitudinal distance separates contact races  26   a  and  26   b . Inner shaft  22  is fashioned to present a smaller rotational radius than races  26   a  and  26   b . Any means known in the art may be selected for rigid attachment of the discs to the inner shaft. For example hex plugs  29  may be fashioned at the ends of inner shaft  22 , and may be fitted to hex sockets  49  in the discs using bolt  23 , nut  24  and washers  25 . 
       FIG. 6  is a perspective view of load rotor  20  of clutch  100 . Contact races  26   a  and  26   b  are conical surfaces facing radially outward and longitudinally inward. Load rotor  20  can be rotationally connected to the torque load by any means known in the art. For example splines  28  may be used. Any means known in the art can be used to arrange the load rotor to be rotatable about axis AX. For example, surfaces  27   a  and  27   b  may be used as bushing surfaces or bearing races for mounting the load rotor into a housing (not shown). In some embodiments connection of the load rotor to the torque load may fix the load rotor to the axis of rotation. In such cases surfaces  27  are not needed for mounting purposes. Alternative configurations for surfaces  27  and  28  and are not precluded. For example, splines or gear teeth may be placed on surfaces  27   a  or  27   b , or the radius of surface  27   a  may be expanded to merge with surface  27   c.    
       FIG. 7  is a perspective view of driving member  30  of clutch  100 . Driving member  30  includes main gear  31 , cam blocks  32  and stops  33 . The driving member provides radially inward facing cam surfaces  35 . Stop surfaces  36  protrude from the inner circumference of the driving member. In some embodiments front and back surfaces  52  of cam blocks  32  may be arranged to serve as guide slides for the clutch grippers. Driving member  30  can be rotationally connected to the source of rotating torque by any means known in the art. For example gear teeth  37  may be used. Any means known in the art can be used to arrange the driving member to be rotatable about axis AX in a manner that limits longitudinal movement relative load rotor  20 . For example rim  34  may be used for attachment to a bearing race. Stop blocks  33  are composed of an impact absorbing material such as a visco-elastic polymer, and cam blocks  32  are made of a strong, hard material such as steel. 
       FIG. 8  is a perspective view of main gear  31  of clutch  100 . Main gear  31  includes slots  38  and  39  for holding cam blocks  32  and stops  33 , respectively. The cam blocks and stop blocks may be press fit into their respective slots or they may be attached to the main gear using other methods known in the art. 
       FIG. 9  is an exploded view of gripper  10  of clutch  100 . Cradle  1  and pad holder  3  are made of hard, high strength materials such as steel. Pad  2  is made of a polytetrafluoroethylene (PTFE) composite material. Expansion slots  11  of pad  2  provide stress relief from the difference in thermal expansion of the pad and holder materials. Pad  2  and slot  12  may be arranged for a dove-tail fit or other means may be used to attach the pad to the holder, such as using adhesive. Any means known in the art may be used for attaching pad holder  3  to cradle  1 . For example bolts  53  may be used.  FIG. 10  is a perspective view of gripper  10  of clutch  100 . In some embodiments surfaces  9  may be arranged to slide against guide surfaces  52  of driving member  30  in the rotational and radial directions. 
       FIG. 11  is a longitudinal view of gripper  10  of clutch  100 . Surfaces  7   a ,  7   b  and  6  are shaped and arranged so that when grippers  10  are disposed in a locking position in relation to load rotor  20  and driving member  30 , surfaces  7   a  make area-to-area contact with race  26   a , surfaces  7   b  make area-to-area contact with race  26   b , and surfaces  6  make area-to-area contact with a driving member cam surface  35 .  FIG. 12  is a sectional view of gripper  10  taken along line  12 - 12  of  FIG. 11 . A partial boundary of contact surface  7   b  is shown with hidden lines.  FIG. 13  is a bottom view of pad  2  showing the extent of expansion slots  11 .  FIG. 14  is a perspective view of cradle  1  showing contact surface  7   a  and showing surface  7   b  with hidden lines. Surfaces  9  are also shown. 
       FIG. 15  is a perspective view of an alternative embodiment of gripper  10 . In this alternative embodiment surfaces  6 ,  7   a ,  7   b  and surfaces  9  are all formed on a single block and low-friction coating  2 , consisting of a material such as PTFE, is deposited on surface  6 .  FIG. 16  is a perspective view of load rotor  20  and a single gripper  10 , with the gripper disposed in its locking position in relation to the load rotor. 
       FIG. 17  is a perspective view of the one-way clutch  100 . 
       FIG. 18  is a schematic longitudinal view of load rotor races  26   a ,  26   b  and gripper  10  with gripper  10  shown in a recessed position. Load rotor races  26   a  and  26   b  are angled at a bevel angle θw to the axis of rotation AX. When the grippers are in recessed position a gap g separates surfaces  7   a  and  7   b  of the grippers from races  26   a  and  26   b .  FIG. 19  is a schematic longitudinal view of the load rotor races and a gripper with the gripper  10  shown in locking position. 
     The operation of the present invention is now described in light of  FIGS. 1 through 19 . Referring to  FIG. 3 , ω i  identifies the speed of rotation of load rotor  20  and inner shaft  22 . The speed of rotation of driving member  30  is labeled ω o . For this discussion ω i  and ω o  are referenced to the stationary frame of reference and direction D 1  is chosen for the positive rotational direction. When the gripper elements are in a recessed position, with no contact made with the load rotor, the load rotor and driving member are free to rotate independently of one another. When one or more grippers are in locking position the driving member is free to rotate in direction D 2  relative the load rotor, and the load rotor is free to rotate in the D 1  direction relative the driving member. That is, the driving member and load rotor are allowed to freewheel when ω o  is less than ω i . In some embodiments of the invention, for example clutch  100 , centrifugal forces during freewheeling rotation of the driving member move the gripper(s) into their recessed position and the grippers cause no frictional resistance to freewheeling. In alternative embodiments using biasing springs, such as illustrated in  FIG. 27 , the grippers may make contact with the load rotor during freewheeling but in a manner that causes little frictional resistance, depending on spring length and stiffness. 
     Referring again to  FIG. 3 , when one or more grippers are situated in the locking position the gripper(s) perform a self-locking action that prevents rotational speed ω o  from exceeding ω i . When torque is applied in direction D 1  to the driving member, torque is transmitted through the grippers to the load rotor, counter-torque is transmitted from the load rotor to the driving member, and rotation of the load rotor and driving member is locked. A gripper which is locked and transferring torque will be said to be in locking mode. If the clutch is in an unlocked state, torque applied in direction D 1  to the driving member urges the grippers into their locking position. In embodiments such as illustrated in  FIG. 27 , elastic elements  44  may be employed to urge the grippers into locking position in addition to the force generated by torque applied to the driving member. 
     The forces impinging on the contact surfaces of the grippers  10  during locking mode are now described.  FIG. 19  includes a longitudinal diagram of the forces acting on gripper  10  during locking mode. Fro is the radial component of the total force on surface  6 . Forces Fni-a and Fni-b are the normal components of the forces on gripper surfaces  7   a  and  7   b  from contacting surfaces  26   a  and  26   b . Force Fri-a is the radial component and Fai-a is the longitudinal component of the force on surface  7   a . Force Fri-b is the radial component and Fai-b is the longitudinal components of the force on surface  7   b . Fai-a is equal in magnitude and opposite in direction to Fai-b so the total longitudinal force on gripper  10  is null. The angle between Fni-a and Fri-a is angle θw, as is the angle between Fni-b and Fri-b. We observe that the relationship at both surfaces  7   a  and  7   b  of the normal to radial force components is:
 
 Fni=Fri /cos(θ w )  (2)
 
     Referring again to  FIG. 19 , the rotational radius of force Fro is Ro, and the rotational radius of forces Fni-a and Fni-b is Ri. The configuration of surfaces  26   a ,  26   b ,  6 ,  7   a  and  7   b  is arranged so that Ri approaches the value of Ro. Specifically, because surfaces  6 ,  7   a  and  7   b  are separated longitudinally the ratio Ri/Ro can be made close to or equal to unity. 
       FIG. 20  is a perspective view of the contact forces impinging on gripper  10  when in locking mode. Fo is the summation of pressure on surface  6  from contact with cam surface  35  of the driving member. Fi-a is the total force on surface  7   a  from contacting load rotor race  26   a . Fni-a is the normal component of Fi-a (also shown in  FIG. 19 ). Fti-a is the frictional force on surface  7   a  and is also the rotational component of Fi-a. The angle between Fi-a and Fni-a is angle θi. Surface  7   b  is impinged by corresponding forces Fi-b, Fni-b and Fti-b of near or equal magnitude to forces Fi-a, Fni-a and Fti-a, respectively. 
       FIG. 21  diagrams the forces acting on gripper  10  in locking mode from a front view. Fo is the total force acting on gripper surface  6 . Fto is the frictional component and Fno is the normal component of Fo. Force Fti is the total frictional force from contacting the load rotor races and is the sum of the forces Fti-a and Fti-b described in  FIG. 20 . Fri is the total of the radial component of the forces from contacting the load rotor races and is the sum of the forces Fri-a and Fri-b shown in  FIGS. 19 and 20 . Fj is the sum of Fti and Fri.  FIG. 21  illustrates the case when rotational radius Ro of force Fo is equal to rotational radius Ri of force Fj. 
     The self-locking action of grippers  10  is now described in terms of the forces diagrammed in  FIGS. 19, 20 and 21 . First we examine an initial condition in which grippers  10  are in locking position and the load rotor races are slipping in direction D 2  against the grippers. This initial condition will be referred to as the lash condition. During the lash condition the force angle θi shown in  FIG. 20  is the arctangent of μi, the kinetic coefficient of friction at the interface. The relation of Fti and Fni is therefore:
 
 Fti=μi*Fni.   (3)
 
Substituting equation (2) for Fni in equation (3) reveals:
 
 Fti=μi *( Fri /cos(θ w ))  (4)
 
and therefore:
 
 Fti/Fri=μi /cos(θ w ).  (5)
 
     Referring to  FIG. 21  we observe that the ratio Fti/Fri is the tangent of angle θj, so the value of θj during the lash condition is known:
 
θ j =Arctan(μ i /cos(θ w )).  (6)
 
Again referring to  FIG. 21 , when forces Fo and Fj are equal and opposite in magnitude and co-linear gripper  10  will remain stationary relative the driving member with no slipping at surface  6 . In this case angles θo is equal to angle θj and, because the sum of angles φo and angle α is equal to θo, we have:
 
φ o+α=θj,   (7)
 
and therefore:
 
φ o=θj−α.   (8)
 
However if φo exceeds the friction angle arctan(μo) during the lash condition, where μo is the static coefficient of friction at surface  6 , gripper  10  will slip against the driving member in direction D 2 . This slip at surface  6  increases compression on the gripper until ratio Fti/Fni drops below the coefficient of friction at the load rotor races. Therefore during the lash condition the grippers will grab and lock the load rotor if angle φo exceeds arctan(μo). Inserting this condition into equation (8) gives us the requirement for self-locking action of the grippers:
 
arctan(μ o )&lt;θ j−α   (9)
 
Substituting equation (6) for θj in equation (9) the conditions for self-locking action is expressed in terms of angle α, θw, and μi μo:
 
α&lt;arctan(μ i /cos(θ w ))−arctan(μ o ).  (10)
 
     The difference between requirements (10) and (1) should be noted. Requirement (1) describes the self-locking requirement of the conventional wedge-clutch configuration illustrated in  FIG. 22  and includes the term φi. But φi goes to zero as the ratio Ri/Ro approaches unity. Therefore the negative effect of φi on the maximum ramp angle is negligible or absent in the self-locking action of the grippers in the present invention. 
       FIG. 23  is a schematic front view of cam surface  35  demonstrating the curvature of the cam surfaces of clutch  100 . RR(0) is the radial at the leading edge of surface  35  of driving member  30 . R 35 (0) is the rotational radius of surface  35  at the leading edge. R 35 (0) is also the point of maximum rotational radius of the surface and will be designated R max . R 35 (β) is the rotational radius of surface  35  at rotational angle β, measured in radians, from RR(0) in direction D 2 . In the preferred embodiments of the present invention the curvature of surface  35  follows a logarithmic spiral according to the polar co-ordinate formula:
 
 R   35 (β)= R   max *exp(−tan(α)*β)  (11)
         for: 0≦β≦β max  
 
where β max  is the value of β at the trailing edge of surface  35  and signifies the angular span of the surface. The value α is the chosen ramp angle of cam surface  35  selected according to requirement (10).
       

     It is now shown that logarithmic curve (11) produces even pressure over surface  6  of grippers  10  when the grippers are in locked position and transferring torque. In the invention&#39;s preferred embodiments the curvature of surface  6  matches or closely approximates the curvature of surface  35  when the gripper is in locking position. During the lash condition described above the gripper slides a differential distance dS across surface  35  until lock is achieved. The gripper is compressed against the load rotor races as the gripper is forced radially inward during this lash motion. The pressure at each point on surface  6  is proportional to the differential ratio dR/dS at the point, where dR is the radial displacement caused by motion dS. But the differential dR 35 (β)/dS of curve (11) is a constant value for all points along the surface:
 
 dR   35 (β)/ dS =−tan(α).  (12)
 
Therefore during torque transfer the pressure is constant or nearly constant over the span of gripper surface  6 .
 
     During the operating life of the clutch it is expected that surface wear and temperature variations will change the distance that the grippers slide across cam surfaces  35  as they move from their recessed position to their locking position. The logarithmic nature of curve (11) maintains alignment of the grippers in the roll direction as this sliding distance changes. Referring again to  FIG. 23 , Cr is the rotational circle of point R 35 (β) on surface  35 . Tr is the tangent to Cr and T 35  is the tangent to the surface at R 35 (β). For curve (11) the angle between Tr and T 35  is constant and is equal to ramp angle α at all values β across the span. Therefore the roll alignment of the grippers in relation to load rotor races is constant as the angle β of the locking position changes. 
     When the curvature of the cam surfaces of the invention is made according to curve (11) the performance of the clutch is generally maximized. In embodiments that include gripper elements that span a large rotational angle implementation of curve (11) is recommended. It should be appreciated, however, that various embodiments of the invention may implement other curvatures as long as the curvature produces self-locking action of the clutch grippers. For example, a circular curvature or even a flat cam surface may be used especially with gripper elements spanning a small rotational angle. 
     Various alternative embodiments of the current invention are now described. Referring to expression (10), clutch  100  achieves a high ramp angle α and low compression pressures in part by implementing load rotor races with bevel angle θw. A low coefficient of friction μo at the interface between gripper surfaces  6  and cam surfaces  35  also increases the attainable ramp angle. Clutch  100  provides a low μo value by fabricating gripper pad  2  of a PTFE material. Alternative methods of providing a low μo value may be used. For example cam block  32  of the driving member may be composed of a PTFE composite, or cam surface  35  of the driving member may be coated with a low-friction material. In these cases gripper surface  6  may be formed on a material other than PTFE, such as steel. 
       FIG. 24  is a perspective view of an alternative embodiment of driving member  30 . In this embodiment cam surfaces  35  are formed directly on the inner circumference of the driving member. Although the stops in clutch  100  are made of an impact absorbing material the stop surfaces may be formed on other materials in alternative embodiments. For example, stop surfaces  36  in  FIG. 24  are formed directly on the driving member inner circumference. It should also be appreciated that other embodiments of the invention may implement stop surfaces of various curvatures other than the surface implemented in clutch  100 . 
       FIG. 25  is a longitudinal sectional view of clutch  200 , an additional embodiment of the current invention. Clutch  200  includes an alignment means for limiting longitudinal, pitching and yawing movement of grippers  10  during operation of the clutch. Surfaces  52  of driving member  30  are arranged to form guide slides for the grippers. Contact between surfaces  9  and  52  limit yawing, pitching and longitudinal motion but allow the grippers to slide in the radial and rotational directions relative to the driving member. Low-friction coating  51  may be applied to cam blocks  32 , or to gripper surfaces  9 , to promote easy sliding of the surfaces. Clutch  200  load rotor races  26   a  and  26   b  are not beveled, therefore the term cos(θw) in expression (10) is unity and does not assist in maximizing α. However the clutch  200  races are arranged so that rotational radius Ri is greater than Ro. This introduces the term φi, described above, in a manner that assists in maximizing ramp angle α. In this case the conditions for self-locking action of the grippers is expressed as:
 
α&lt;arctan(μ i )−arctan(μ o )+φ i   (13)
 
       FIG. 26  is a longitudinal sectional view of clutch  300 , a further embodiment of the current invention. Clutch  300  includes a lubricating substance, such as oil or grease, to lower friction at the cam surfaces, thus providing a low value μo. Channel  61  provides means for ejecting the lubricant to the cam surfaces  35 . Alternatively lubricant may be directed to the cam surfaces by other means, for example with an external spray nozzle or jet (not shown). Sump cavity  63  provides a means for catching the splash of lubricant that may occur during clutch operation. Channel  62  provides a means for evacuating lubricant splash from the sump cavity. Clutch  300  load rotor races  26   a  and  26   b  are radially outward facing and longitudinally outward facing conical surfaces. The bevel angle of the races serves to spin any lubricant splash, with the influence of centrifugal forces, away from the race surfaces. 
       FIG. 27  is a partial front sectional view of another embodiment of the present invention. This embodiment includes elastic elements  44  attached to either main gear  31  or grippers  10 , or both. The elastic elements serve to limit rotation of the grippers in direction D 1  as do the stops of previous described embodiments. The elastic elements may be employed to serve in the manner of biasing springs used in conventional technologies. Used as biasing springs the elastic elements are placed to urge the grippers into locking position in addition to or in the absence of inertial forces. But the elastic elements may be employed for other purposes. For example, elements  44  can be employed to pull grippers  10  out of contact with the load rotor races and into a slightly recessed position when the driving member is motionless and centrifugal forces are absent. 
     In yet another embodiment of the present invention the values for ramp angle α of driving member surfaces  35 , bevel angle θw of load rotor contact races, and the ratio Ri/Ro are selected so that self-locking action of the grippers  10  is achieved without use of lubrication or low friction materials to lower the value of μo. This type of embodiment may be useful in some applications, for example when torque loading is relatively light. 
     It should be noted that for clarity the direction of torque transmission described for clutch  100  corresponds to the expected use of the present invention in most common circumstances. However, the disclosure is not limited to these circumstances and may be used in a manner that reverses the direction of torque transmission described above. That is, the load rotor may be connected to a source of rotating power, or may be held stationary in cases where the clutch is used as a break or backstop. In these uses the driving member may be arranged for rotational connection to a torque load.