Abstract:
A self-retaining ball-worm and gear mechanism is provided to facilitate the rotational transmission of motion between two orthogonal but non-intersecting axes. A circuit of balls introduced as rolling elements indirectly couples the worm and gear, and eliminates the sliding friction characteristic of classical worm and gear mechanisms. The mechanism comprises a ball-worm ( 200 ), gear ( 202 ), and axial supports or housing ( 204 ). The ball-worm defines the ball circulation path. The worm helix is designed to retaining the balls such that no additional ball-retaining components are necessary. Magnetism may optionally or additionally be employed to attract the metal balls to the worm body, further enhancing ball self-retention. The gear comprises a plurality of grooves designed to engage the helix of balls on the worm. The path of the worm helix is mathematically accurate so that balls simultaneously engage multiple gear grooves, increasing the torque load capabilities of the device.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Field of Invention  
         [0002]     The present invention relates to mechanical rotational-to-rotational transmissions, specifically to worm and gear transmissions.  
         [0003]     2. Prior Art  
         [0004]     The classical worm and gear mechanism represented in  FIG. 1  is commonly used for speed reduction, rotational positioning, motion control, and other rotational-to-rotational transmission applications. The classic mechanism consists of a worm  100 , gear  102 , and axial support components (not shown) such as bearings or bushings. Sliding motion between the helix of worm  100  and teeth of gear  102  cause the gear to rotate as the worm is rotated. The sliding friction causes the mechanism to suffer from premature wear and inefficient power conversion. Backlash has also been especially problematic in such mechanisms. Several approaches that utilize dual gearing and anti-backlash springs only eliminates the backlash for a narrow torque range. The motion of the mechanism is also irreversible; that is, the worm can drive the gear, but the gear cannot drive the worm.  
         [0005]     To overcome the limitations of the classical worm and gear mechanism, several solutions have been proposed that replace the sliding friction with rolling friction via a circuit of rolling spherical balls.  FIGS. 2 and 3  provide typical examples of such devices known as ball-worm and gear mechanisms, or simply ball-worm transmissions. In the modified mechanism a ball-worm  120  is indirectly coupled to a gear  122  via a plurality of circulating balls  124 .  
         [0006]     The introduction of balls has caused the assembly process of ball-worm transmissions to be cumbersome or awkward. Because balls tend to scatter when unconstrained, ball installation during assembly is difficult. Special tooling or skilled labor is often required. The awkward assembly process also causes replacement of worn-out balls and other parts to be likewise burdensome. Consequently, the ball-worm transmission is more costly to manufacture and maintain.  
         [0007]     The introduction of balls as rolling elements also necessitated a means for constraining, retaining, confining, or otherwise preventing them from straying during normal operation. A ball-retainer  126 , or similar mechanism, was introduced to at least partially fulfill this need. As shown in  FIGS. 2 and 3 , ball-retainer  126  externally surrounds the ball-worm preventing the balls from straying or scattering. In some prior-art ball-worm transmissions, the ball-retainer  126  also provided the recirculation path for the balls. Subsequently, the ball-worm transmission is more complex than its classical predecessor, which needed no such ball-retaining mechanism. The classical mechanism was also simple to assemble. The ball-retainer also increases overall weight and size. In certain applications, such as vehicle transmission systems, increased weight and size can be a considerable disadvantage. Providing a reliable and simple means for ball installation, retention, containment, and recirculation has been arguably one of the greatest challenges of attaining a robust ball-worm transmission.  
         [0008]     All known prior-art ball-worm transmissions have utilized a ball-retainer component  126  of some kind. Although different inventors use different nomenclature to designate the ball-retainer, their function and purpose has remained constant: to constrain, retain, or otherwise confine the balls and prevent them from straying from their circuit path. U.S. Pat. No. 5,090,266 to Otsuka (1992) discloses a “rotation transmitter” that uses “ball guides” in combination with an “outer guide” to achieve an improvement in ball circulation path. U.S. Pat. No. 5,373,753 to Toyomasa (1994) describes a power transmission device that uses “frame rings” mounted on the worm at both ends to prevent the balls from floating out of the groove of the worm. U.S. Pat. No. 5,816,103 to Huang (1998) discloses a ball-worm and gear device with a “housing” that is encased externally to constrain the balls to the helical channel of the worm. The prior-art suggests that an external ball-retaining mechanism surrounding the ball-worm is necessary for the proper functioning of the ball-worm transmission. This suggestion is consistent even in more recent publications. U.S. Patent Application Publication 2003/0115981 (European Patent EP1454078) to Stoianovici et al (2003) discloses a ball-worm transmission that comprises an “outer race” with “internal revolute hyperboloidal surface” to constrain and maintain contact with the balls along the passive path.  
         [0009]     Increased complexity, cost, weight, and size are not the only disadvantages of introducing the ball-retainer component. The ball-retainer also accelerates wear. Surfaces of the balls will wear only when in contact with other surfaces. The ball-retainer must maintain contact with the balls in order to constrain them, thereby wearing the balls and reducing the useful life of the device. It would be greatly advantageous if ball installation, retention, confinement, and recirculation could be accomplished without the use of an extraneous ball-retaining component.  
       OBJECTS AND ADVANTAGES  
       [0010]     Accordingly, in addition to the advantages of ball-worm and gear transmissions in general, several objects and advantages of the present invention are: 
        (1) To eliminate the sliding friction characteristic of the classical worm and gear mechanism, and replace it with rolling friction via a circuit of rolling balls.     (2) To provide a durable and power efficient worm and gear transmission.     (3) To provide a worm and gear transmission with minimal or no backlash.     (4) To provide a worm and gear mechanism that can be easily converted to reverse-drivable and non-reverse-drivable configurations.     (5) To provide an improved ball-worm and gear transmission that obviates the need for any extraneous ball-retaining components, or similar mechanisms, to reduce complexity, production cost, weight, and size.     (6) To provide an improved ball-worm and gear transmission requiring fewer parts than the prior art, but without loss of capability or functionality.     (7) To provide a ball-worm and gear transmission with the ball circuit path entirely defined by the ball-worm.     (8) To provide a ball-worm and gear transmission with a ball circuit path that is smooth and reliable, facilitating ball circulation and reducing wear.     (9) To provide a ball-worm and gear transmission with a ball-worm that is self-retaining; that is, capable of constraining the balls to itself without the assistance of any additional components or mechanisms.     (10) To provide an improved ball-worm and gear transmission with reduced cumulative ball contact surface area to reduce wear and prolong the device&#39;s useful life.     (11) To provide an improved ball-worm and gear transmission that is convenient to assemble, disassemble, and reassemble, minimizing assembly and maintenance costs. 
 
 Further objects and advantages of the present invention will become apparent from a consideration of the drawings and ensuing description. 
       
 
       SUMMARY  
       [0022]     In accordance with the present invention, a ball-worm transmission comprises a self-retaining ball-worm, gear, and axial supporting mechanisms. In the drawings, closely related figures have the same numeric prefix but different alphabetic suffixes.  
     
    
     DRAWINGS—FIGURES  
       [0023]      FIG. 1  shows a representative classical worm and gear mechanism of the prior art.  
         [0024]      FIG. 2  shows a typical ball-worm transmission of the prior art, reproduced from U.S. Pat. No. 5,090,266 to Otsuka (1992).  
         [0025]      FIG. 3  provides a more recent example of a ball-worm transmission of the prior art, reproduced from European Patent EPI 454078 to Stoianovici (2003).  
         [0026]      FIGS. 4A  to  4 C show several overall views of the present invention.  
         [0027]      FIGS. 5A  to  5 C show several views of the present invention with its housing omitted.  
         [0028]      FIG. 6  shows an enlarged view of the ball-worm and gear.  
         [0029]      FIG. 7  shows the gear with circuit of balls. All other components are omitted.  
         [0030]      FIGS. 8A  to  8 C show the gear and circuit of balls, with  FIG. 8C  pointing out the balls in their various active, passive and recirculating states denoted by the letters X, P, and C respectively.  
         [0031]      FIGS. 9A  to  9 B illustrate the assembly of and various subcomponents of the ball-worm.  
         [0032]      FIGS. 10A and 10B  show 3-dimensional views of the worm collar.  
         [0033]      FIGS. 11A  to  11 C reveal the cross-sectional profile of the worm helix.  
         [0034]      FIGS. 12A and 12B  provide alternative cross-sectional profiles for the worm helix.  
         [0035]      FIG. 13  shows a general outline of the ball-worm and defines its reference coordinate system.  
         [0036]      FIG. 14  shows a top-down view with general outline of the ball-worm and gear to define its crucial parameters and variables.  
         [0037]      FIG. 15  provides a representative plot of the path of the worm helix.  
         [0038]      FIGS. 16A  to  16 B illustrate how balls transition to/from passive and recirculating states.  
         [0039]      FIG. 17  shows an enlarged view of the worm shaft and balls in the recirculating state.  
         [0040]      FIG. 18  shows an enlarged view of the worm shaft.  
         [0041]      FIGS. 19A  to  19 C provide cross-sectional profile of the gear grooves.  
         [0042]      FIG. 20  shows an alternative cross-sectional profile for the gear grooves. 
     
    
     DRAWINGS—REFERENCE NUMBERALS  
     Reference Numerals for the Prior Art  
       [0000]    
       
         
           
               100  Worm of classical worm and gear mechanism of the prior art  
               102  Gear of classical worm and gear mechanism the prior art  
               120  Ball-worm of the prior art  
               122  Gear of ball-worm transmission of the prior art  
               124  Balls of the prior art  
               126  Ball-retainer component of the prior art  
           
         
       
     
       Reference Numerals for the Present Invention  
       [0000]    
       
         
           
               200  Self-retaining ball-worm  
               202  Gear  
               204  Housing  
               220  Worm shaft  
               222  Worm collar  
               224  Ball(s)  
               226  Plug  
               240  Gear groove(s)  
               242  Dashed circular curve  
               260  Ball installation port  
               262  Worm helix  
               264  Alignment pocket  
               266  Transitional fillet  
               268  Precision rolling surface(s)  
               270  Clearance surface(s)  
               272  Undercut surface(s)  
               274  Transitional port  
               276  Hourglass shaped surface of ball-worm  
               278  Worm axis  
               300  Alignment boss  
               302  Recirculation channel  
               320  Active ball(s)  
               322  Passive ball(s)  
               324  Recirculating ball(s)  
           
         
       
     
       DETAILED DESCRIPTION  
       [0073]      FIGS. 4A  to  4 C present several overall views of the self-retaining recirculating ball-worm and gear device. The device comprises a self-retaining ball-worm  200 , gear  202 , and housing  204 . Housing  204  is designed to enclose and axially support the internal components of ball-worm  200  and gear  202 . Bearings, bushings, or other support mechanisms may be included in housing  204  to axially support and restrict ball-worm  200  and gear  202  to their respective axes of rotation.  
         [0074]      FIGS. 5A  to  5 C and  FIG. 6  show several views of the device with housing  204  omitted. The axis of ball-worm  200  and axis of gear  202  are orthogonal but non-intersecting. The ball-worm comprises a worm shaft  220 , worm collar  222 , plug  226 , and plurality of balls  224 . The gear has a plurality of gear grooves  240  separated at periodic angular intervals which are designed to engage the balls  224  of the ball-worm. Worm shaft  220  and worm collar  222  are rigidly fastened together so that rotation of one causes the same rotation of the other. Worm shaft  220  and worm collar  222  together define the circuit path for the balls. The ball-worm is designed to retain the balls without requiring any additional or external components. Hence, ball-worm  200  is said to be self-retaining. That is, the balls will adhere to the body of the ball-worm even when the worm is removed from the rest of the assembly. Thus, the ball-worm can be conveniently replaced as a complete unit without the possibility of inadvertently scattering the balls during assembly or disassembly.  
         [0075]     The self-retaining feature of ball-worm  200  is crucial for its low-cost production and maintainability. Prior-art ball-worm transmissions are not self-retaining, and require external components to constrain the balls. Therefore, the balls easily scatter during assembly or disassembly, causing replacement of worn-out parts to be cumbersome. Self-retention allows for convenient assembly and replacement of parts.  
         [0076]     Rotation of the ball-worm causes its helix of balls to circulate. Balls firmly engaged or meshed between the worm helix and gear groove serve to couple the gear to the worm. In  FIG. 6  the rotational displacement of the ball-worm and gear are denoted as θ and φ respectively. Each complete turn of the ball-worm causes the gear to advance by one gear groove. Hence 
 
θ=Nφ
 
 where N is the total number of gear grooves. N is also the transmission ratio, or gear ratio, of the device. The helix of the ball-worm is mathematically accurate so that multiple balls engage multiple gear grooves simultaneously. Simultaneous engagement of multiple grooves enhances the gear-to-worm coupling rigidity. Increased gear-to-worm coupling rigidity means that the device can endure greater applied torques without sustaining permanent damage to its internal components. The use of balls to indirectly couple the gear and worm eliminates, or otherwise dramatically reduces, backlash. Its non-backlash characteristics are maintained when at least one or more balls are firmly engaged between the worm helix and gear groove. As the balls wear through prolonged use, they will no longer be able to firmly engage the worm helix and gear grooves. If one of the balls wears faster than the others, simultaneous multiple groove engagement ensures that there are “backup” balls that are firmly locked between the gear groove and worm helix. Thus, the mathematically accurate worm helix is also intended to prolong the useful life of the device. 
 
         [0077]      FIG. 7  shows gear  202  with closed circuit of balls  224 . For clarity, all other parts have been omitted. A ball traversing along the closed circuit path is said to be in one of three states: 1) active, 2) passive, or 3) recirculating.  FIGS. 8A and 8B  show front and top views of the balls with gear.  FIG. 8C  points out the balls with their various states. In  FIG. 8C , active balls  320  are marked with an “X”, passive balls  322  are marked with a “P”, and recirculating balls  324  are labeled “C”. Some of the balls in the  FIG. 8C  are hidden behind other balls. Only balls that are not hidden are labeled with “X”, “P”, or “C”. Balls that are engaged between the worm helix and gear groove are defined to be in the active state. Active balls  320  serve to couple the gear to the ball-worm. Balls located along the worm helix but not currently engaged with any of the gear groves are defined to be passive. Balls located inside the ball-worm serve to close the circuit of balls and are said to be recirculating. Recirculating balls traverse in the opposite direction than the rest of the balls, and would normally otherwise be hidden from view. Note that the majority of balls at any instant are passive. In prior-art ball-worm transmissions, these passive balls must maintain contact with a ball-retaining component that surrounds the worm. Hence, eliminating the ball-retainer would significantly reduce the cumulative ball contact surface area and decrease wear and tear.  
         [0078]     A fully-assembled self-retaining ball-worm is shown in  FIG. 9A . An exploded view with its necessary subcomponents is shown in  FIG. 9B . The ball-worm comprises worm shaft  220 , worm collar  222 , plurality of balls  224 , and plug  226 . Worm shaft  220  and worm collar  222  are concentrically and rigidly fastened. An alignment pocket  264  on worm collar  222  and alignment boss  300  on worm shaft  220  are used for mating and aligning purposes during fastening. Although alignment pocket  264  and boss  300  are depicted as hexagonal in the Fig, they can alternatively be of any geometry that will adequately mate and align the two parts. Additional fasteners such as pins, screws, or dowels may optionally be used if more fastening strength is required. A helical channel  302  on the worm shaft defines the ball recirculation path. A ball installation port  260  on worm collar  222  provides an opening for balls to be conveniently installed into the ball-worm. Balls are inserted serially. The worm helix located on collar  222  is designed to be self-retaining. Therefore, the balls will not fall out of the helix as they are inserted into the ball-worm. After all balls have been inserted, plug  226  seals installation port  260 , preventing any balls from traveling back out of the port. The plug can be a dowel, set screw, or any appropriate component that will adequately seal the entrance of ball installation port  260 .  
         [0079]     Enlarged 3-dimensional views of worm collar  222  are shown in  FIGS. 10A and 10B . Worm helix  262 , ball installation port  260 , and alignment pocket  264  are particularly pointed out in these figures.  
         [0080]     The cross-sectional profile of the worm helix is shown in  FIGS. 11A through 11C .  FIG. 11C  shows an enlarged detailed cross-sectional view of the worm helix with representative ball  224 . The cross-sectional profile comprises a precision rolling surface  268 , clearance surfaces  270 , and undercut surfaces  272 . Precision rolling surface  268  provides the rolling surface for the balls to engage the worm helix. Clearance surfaces  270  provide a small but finite amount of space (usually between 0.002 to 0.0010 inches from the ball surface) around the ball so that the balls are able to roll freely as they traverse the helix. If there were no clearance, the balls would be jammed or have great difficulty traversing the helix. Undercut surfaces  272  partially enclose around the balls to retain and constrain them to the ball-worm. The undercut surfaces provide the ball-worm its self-retaining capabilities. A small but finite amount of clearance also exists between the undercut surfaces and the balls. In  FIG. 11C , G is the groove gap of the worm helix, and D B  is the ball diameter. The relationship 
 
0&lt;G&lt;D E  
 
 is one of several conditions that must be satisfied for a properly functioning ball-worm. Additionally, the centers of the balls must be embedded below the outer surface of worm collar  222 . Yet, the balls must also partially protrude out of the ball-worm so that they can engage the gear grooves. Self-retention obviates the need for any extraneous ball-retaining components, reducing complexity and production cost. A ball-retaining component that externally surrounds the worm must maintain contact with the balls in order to retain them. Eliminating such a component decreases the cumulative ball contact surface area, which leads to decreased wear of the balls. Thus, the self-retaining ball-worm has improved durability characteristics over its non-self-retaining predecessors. 
 
         [0081]      FIGS. 12A and 12B  show alternative cross-sectional helix profiles that also satisfy the conditions necessary for self-retention. The cross-sectional profile shown in  FIG. 12B  is presently preferred because of its minimized helix-to-ball contact surface area.  
         [0082]     A variety of methods exists for fabricating a ball-worm with helix comprising undercut surface profiles as described above. One method is to use a 4-Axis CNC milling machine with custom undercutting end mills. The 4 th  axis of the milling machine is required to be a rotary axis. Harvey Tool Company of Topsfield, Mass. (web: www.harveytool.com) is among one of the custom toolmakers capable of supplying the necessary undercutting end mills. If more precision is required, the ball-worm may be rough-milled initially with additional post-grinding process. Other approaches may entail a combination of metal injection or casting with a post-machining process.  
         [0083]     Magnetism may additionally be used to assist the self-retention of balls. If balls  224 , for instance, are composed of a ferromagnetic material, worm collar  222  and/or worm shaft  220  may optionally be made of a permanently magnetic material to attract the balls. A combination of magnetism and a self-retaining helix profile design is presently preferred.  
         [0084]     For balls to simultaneously engage multiple gear grooves, the path of the worm helix must be mathematically computed.  FIG. 13  shows a general outline of the ball-worm and defines its Cartesian x, y, z, and angular θ coordinates. The origin of the coordinate system is located at the geometric center of the ball-worm. In this coordinate system, worm axis  278  is also the z-axis.  FIG. 14  provides a top-down outline view of the ball-worm and gear, and defines the essential parameters necessary to mathematically describe the worm helix. The distance from the center of the gear to center of representative ball  224  along the central plane of the gear is given by R G . R G  is also the radius of dashed circular curve  242 , which is concentric with the gear and intersects the center of representative ball  224 . The worm has an hourglass-shaped outer surface  276  with radius R H . L designates the distance between the gear center and worm axis  278 . R H  is the distance between worm axis  278  and representative ball  224 , and is a function of θ that is given by  
           R   H     ⁡     (   θ   )       =       L   -       R   G     ⁢     cos   ⁡     (   ϕ   )           =     L   -       R   G     ⁢     cos   ⁡     (     θ   N     )                 
 
 The path of the worm helix Has a function of θ can then be written as  
         H   ⁡     (   θ   )       =       [             H   x     ⁡     (   θ   )                   H   y     ⁡     (   θ   )                   H   z     ⁡     (   θ   )             ]     =       [             R   H     ⁢     cos   ⁡     (   θ   )                     R   H     ⁢     sin   ⁡     (   θ   )                     R   G     ⁢     sin   ⁡     (   θ   )               ]     =     [             (     L   -       R   G     ⁢     cos   ⁡     (     θ   N     )           )     ⁢     cos   ⁡     (   θ   )                     (     L   -       R   G     ⁢     cos   ⁡     (     θ   N     )           )     ⁢     sin   ⁡     (   θ   )                     R   G     ⁢     sin   ⁡     (     θ   N     )               ]             
 
 where H x , H y , and H z  are the x, y, and z components of helix equation H, and where N is the transmission ratio.  FIG. 15  provides a representative plot of the above helix equation. 
 
         [0085]     As the balls circulate, passive balls will eventually transition to the recirculating state. Likewise, recirculating balls will eventually transition to the passive state. As shown in  FIG. 11B , a transitional port  274  provides a smooth path for balls to enter/exit the passive and recirculating states. The path of transitional port  274  has no sudden turns or sharp edges.  FIGS. 16A and 16B  provide cross-sectional views of transitional ports  274 . The transitional ports comprise a transitional fillet  266  to provide a smooth and stable trajectory for balls to transition to/from the passive and recirculating states.  
         [0086]     An enlarged view of worm shaft  220  with recirculating balls  324  is shown in  FIG. 17 .  FIG. 18  shows the worm shaft alone. Recirculation channel  302  on worm shaft  220  provides a recirculation path for balls to be recycled. Although the recirculation channel is shown with a U-shaped profile, it can optionally be of any cross-sectional profile or path suitable for balls to smoothly and stably be recycled. Balls in direct contact with the recirculation channel are defined to be in the recirculating state.  
         [0087]     Details of gear  202  are shown in  FIGS. 19A through 19C . The cross-sectional profile of the gear grooves is semicircular or partial-circular. The grooves may optionally comprise a slight chamfer (not shown) near the top and bottom faces of the gear to provide the balls a smoother transition to the active state.  FIG. 20  shows a gear with alternative V-shaped, or V-notched, profiled gear groove. Any groove profile that will firmly engage the balls while providing a precision rolling surface will suffice. The gear groove profile depicted in  FIG. 19C  is presently preferred.  
       Operation  
       [0088]     The manner of using the present invention is identical to prior-art ball-worm transmissions. Rotational motion is exerted on ball-worm  200 , which causes gear  202  to rotate as its gear grooves engages the rotating helix of balls. Balls that roll between the worm and the gear become firmly engaged between them, coupling the gear to the worm. Each complete turn of the ball-worm advances the gear by one gear teeth. The circuit of rolling balls significantly reduces frictional forces. Thus, the device is inherently reverse-drivable. That is, rotational motion exerted on the gear can also cause the worm to rotate. If a non-reverse-drivable configuration is desired, additional elements may be added to increase frictional resistance. Sufficient frictional resistance will cause the device to be non-reverse-drivable. The self-retaining feature of the ball-worm greatly simplifies ball installation. The device does not suffer from cumbersome assembly or disassembly that prior-art ball-worm transmissions experience. Rendering all extraneous or external ball-retaining components unnecessary causes the device to be less complex, yet with enhanced durability and wear characteristics.  
       ADVANTAGES  
       [0089]     From the description above, a number of advantages of the present invention are evident: 
        (1) The use of balls as rolling elements greatly reduces, or altogether eliminates, sliding friction, and enhances transmission efficiency.     (2) The use of precision balls as rolling elements minimizes, or altogether eliminates, backlash.     (3) The non-backlash characteristics of the device is not bound to a narrow torque range.     (4) The use of rolling elements to replace sliding elements reduces wear and improves durability.     (5) The device is inherently reverse-drivable, but can be configured for non-reverse-drivable applications.     (6) The self-retaining ball-worm obviates the need for any extraneous ball-retaining mechanisms found in prior-art ball-worm transmissions; thus, it requires fewer parts and is less complex than prior-art ball-worm transmissions.     (7) The elimination of extraneous ball-retaining mechanisms that require contact with the balls improves durability and wear characteristics.     (8) The elimination of all extraneous ball-retaining mechanisms reduces cost, weight, and size.     (9) The ball installation process is greatly simplified and convenient, decreasing assembly and maintenance costs.     (10) Simultaneously engagement of multiple gear grooves enhances coupling rigidity between the gear and ball-worm, which increases the torque load capability of the device.        
 
         [0100]     Although the description above contains many specifics, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments of the invention. The scope of the invention should be determined by the appended claims and their legal equivalent, rather than by the examples given.