Abstract:
The present invention is an omni traction wheel system, which adopts an integrated differential mechanism to generate longitudinal and lateral traction forces. The omni traction wheel system may include a rotary device that delivers two individually controllable rotational forces, the differential output of which may drive a plurality of peripheral wheels to rotate laterally, and the common output of which may drive a pair of longitudinal plates to rotate longitudinally. Accordingly, the omni traction wheel system may travel in all directions.

Description:
BACKGROUND 
       [0001]    1. Field 
         [0002]    The invention relates to an omni traction wheel system. More particularly, the invention relates to an omni traction wheel system deploying an integrated differential mechanism. 
         [0003]    2. Description of the Related Art 
         [0004]    An omni traction wheel, also known as the omni directional wheel, is a rolling device comprises a main wheel and a set of peripheral wheels distributed along the edge of the main wheel. The main wheel may rotate forward and backward while the set of peripheral wheels may rotate left and right. As such, a transportation system deploying the omni traction wheel may travel laterally or diagonally without actually steering the main wheel. Unlike other wheel systems, the omni traction wheel system provides superb maneuverability because it can change the direction of travelling in a relatively short period of time and in a relatively small amount of space. 
         [0005]    Because of their high maneuverability, the omni traction wheel systems are widely used in the fields of low speed transportation systems, such as electronic wheel chair system and robotic systems. Attempts have been made in the past to implement the omni traction wheel system by powering and controlling each peripheral wheel individually. However, such implementation requires a large number of electronic components, transmission gears, and rotary devices. As a result, the traditional omni traction wheel systems suffer from many drawbacks, such as bulky size, heavy weight, and large power consumption. 
         [0006]    Therefore, a need exists in the art for a smaller size, lighter weight, and less power consuming omni traction wheel system. 
       SUMMARY 
       [0007]    One aspect of the present invention is to improve the traditional omni traction wheel system by deploying an integrated differential mechanism that drives the omni traction wheel in both the longitudinal direction and the lateral direction. The advantages of the integrated differential mechanism include, but are not limited to, reducing the amount of electronic components, rotary devices, and transmission gears and creating an integrated thrust by direct tractions for the longitudinal and lateral directions. An omni traction wheel system may include a pair of longitudinal gears, a rotary device for separately and individually rotating each of the longitudinal gears, a plurality of peripheral wheel assemblies, each having a wheel member and a connecting gear for transferring the differential thrust between the pair of longitudinal gears to the wheel member. 
         [0008]    In one embodiment, the present invention is an omni traction wheel, which may include first and second gears centrally aligned along a first axis, a plurality of peripheral wheel assemblies, each having a wheel member centrally aligned along a second axis, the second axis substantially orthogonal to the first axis, and a connecting gear having a distal end for engaging the first and second gears and a proximal end for engaging the pair of wheels, the distal end and the proximal end defining a radial axis, the radial axis substantially parallel to a common radius of the left and right gears and substantially orthogonal to the first axis and the second axis, and a rotary device for rotating the first gear about the first axis at a first angular velocity and for rotating the second gear about the first axis at a second angular velocity, whereby the connecting gear of each peripheral wheel assembly is configured to rotate its respective wheel member about the respective second axis when the first angular velocity is different from the second angular velocity. 
         [0009]    In another embodiment, the present invention is a transportation system adopting an omni traction wheel, which may include left and right gears centrally aligned along a first axis, the left and right gears defining a cylindrical space therebetween, the cylindrical space having a circumferential region, a plurality of peripheral wheel assemblies distributed along the circumferential region of the cylindrical space, each having a pair of wheels centrally aligned along a second axis, the second axis substantially orthogonal to the first axis, and a connecting gear having a distal end for engaging the left and right gears and a proximal end for engaging the pair of wheels, the distal end and the proximal end defining a radial axis, the radial axis substantially parallel to a common radius of the left and right gears and substantially orthogonal to the first axis and the second axis and a rotary device for rotating the left gear about the first axis at a left angular velocity and for rotating the right gear about the first axis at a right angular velocity, whereby the connecting gear of each peripheral wheel assembly is configured to rotate its respective pair of wheels about the respective second axis at a lateral angular velocity defined by a difference between the left angular velocity and the right angular velocity, and whereby the connecting gear of each peripheral wheel assembly is configured to revolve along the circumferential region at a common angular velocity defined by a combination of the left angular velocity and the right angular velocity. 
         [0010]    In yet another embodiment, the present invention is a method for operating an omni traction wheel, which may include the steps of engaging a plurality of peripheral wheels to first and second gears via a plurality of connection gears, rotating the first gear at a first angular velocity, and rotating the second gear at a second angular velocity, wherein the omni traction wheel travels laterally when the first angular velocity is different from the second angular velocity such that a connecting gear is configured to rotate a peripheral wheel. 
         [0011]    In still yet another embodiment, the present invention is an omni traction wheel, which may include first and second plates centrally aligned along a first axis, a plurality of peripheral wheel assemblies, each having a wheel member centrally aligned along a second axis, the second axis substantially orthogonal to the first axis, and a connecting member having a distal end for engaging the first and second plates and a proximal end for engaging the wheel member, the distal end and the proximal end defining a radial axis, the radial axis substantially parallel to a common radius of the left and right plates and substantially orthogonal to the first axis and the second axis, and a rotary device for rotating the first plate about the first axis at a first angular velocity and for rotating the second plate about the first axis at a second angular velocity, whereby the connecting member of each peripheral wheel assembly is configured to rotate its respective wheel member about the respective second axis when the first angular velocity is different from the second angular velocity. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]    Other systems, methods, features and advantages of the present invention will be or will become apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the present invention, and be protected by the accompanying claims. Component parts shown in the drawings are not necessarily to scale, and may be exaggerated to better illustrate the important features of the present invention. In the drawings, like reference numerals designate like parts throughout the different views, wherein: 
           [0013]      FIG. 1A  shows a perspective view of the omni traction wheel system (OTWS) according to an embodiment of the present invention; 
           [0014]      FIG. 1B  shows an exploded view of the OTWS according to an embodiment of the present invention; 
           [0015]      FIG. 2  shows a side view of the OTWS according to an embodiment of the present invention; 
           [0016]      FIGS. 3A ,  3 B, and  3 C show the side views of the OTWSs having three peripheral wheel assemblies (PWAs), four PWAs, and eight PWAs respectively according to various embodiments of the present invention; 
           [0017]      FIG. 4A  shows a cross-sectional side view of the OTWS according to an embodiment of the present invention; 
           [0018]      FIG. 4B  shows a cross-sectional view of the PWA according to an embodiment of the present invention; 
           [0019]      FIG. 5  shows the cross-sectional front views of the OTWS having several gear configurations according to various embodiments of the present invention; 
           [0020]      FIG. 6  shows the exemplary models of an external gear and a bevel gear according to various embodiments of the present invention; 
           [0021]      FIG. 7  shows the exemplary models of a spear gear, a helical gear, and a double helical gear according to various embodiments of the present invention; 
           [0022]      FIG. 8A  shows a high level conceptual view of the OTWS differential mechanism according to an embodiment of the present invention; 
           [0023]      FIGS. 8A and 8B  show the angular velocities of several components of the OTWS according to various embodiments of the present invention; 
           [0024]      FIG. 9  shows a common mode operation of the OTWS according to an embodiment of the present invention; 
           [0025]      FIG. 10  shows a differential mode operation of the OTWS according to an embodiment of the present invention; 
           [0026]      FIG. 11  shows a forward differential mode operation of the OTWS according to an embodiment of the present invention; 
           [0027]      FIG. 12  shows a backward differential mode operation of the OTWS according to an embodiment of the present invention; 
           [0028]      FIG. 13  shows all the traveling directions of the OTWS with respect to various combinations of the differential angular velocity and common angular velocity according to various embodiments of the present invention; 
           [0029]      FIG. 14  shows a cross-sectional side view of the OTWS with frictional control according to an embodiment of the present invention; and 
           [0030]      FIG. 15  shows a flow diagram showing the method steps for operating the omni traction wheel system according to an embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0031]    Apparatus, systems and methods that implement the embodiments of the various features of the present invention will now be described with reference to the drawings. The drawings and the associated descriptions are provided to illustrate some embodiments of the present invention and not to limit the scope of the present invention. Throughout the drawings, reference numbers are re-used to indicate correspondence between referenced elements. In addition, the first digit of each reference number indicates the figure in which the element first appears. 
         [0032]      FIG. 1A  shows a perspective view of an exemplary omni traction wheel system (OTWS)  100  according to an embodiment of the present invention. In general, the OTWS  100  may include a pair of main wheels formed by a pair of protective plates  102  and a plurality of peripheral wheel assemblies (PWAs)  106  located between the rims of the protective plates  102 . Moreover, the OTWS  100  may be coupled to a leg  120 , which integrates the OTWS  100  to a transportation system that may deploy one or more OTWSs  100 . For example, the transportation system may be a wheel chair deploying four OTWSs  100 , a mobile robot deploying three OTWSs  100 , or a unicycle deploying one OTWS  100 . 
         [0033]      FIG. 1B  shows an exploded view of the OTWS  100  according to an embodiment of the present invention. More specifically, the OTWS  100  may also have a pair of longitudinal gears  108  protected by the protecting plates  102 , a pair of rotary devices  104  for rotating the longitudinal gears  108 , a spacing member  110  that gives structural support to the OTWS  100 . 
         [0034]      FIG. 2  shows a side view of an omni traction wheel system  200  according to an embodiment of the present invention. The OTWS  200 , which is similar to the OTWS  100  of  FIG. 1A , may include two longitudinal gears  202 , each of which has a set of teeth along a circumference region  204 . The two longitudinal gears  202  normally have a common longitudinal radius R, such that their surface areas are substantially the same. Moreover, because the two longitudinal gears  202  have a common longitudinal radius R, the circumferential regions  204  of the two longitudinal gears  202  may be identical in shape and thus hold the same number of teeth. 
         [0035]    As shown in  FIG. 2 , the OTWS  200  may also include a plurality of peripheral wheel assemblies  210 . According to an embodiment of the present invention, each PWA  210  may have a connecting gear  211  and a wheel member  212 . The PWAs  210  may be distributed around the two longitudinal gears  202 . More specifically, the connecting gear  211  of each PWA  210  may be disposed between the circumferential regions  204  of the two longitudinal gears  202  whereas the wheel member  212  of each PWA  210  may be disposed along an outer region  206 . The width of the outer region  206  is defined by a lateral radius r of the wheel member  212 . Accordingly, the main wheel  208  has a longitudinal radius R LONG . 
         [0036]    According to an embodiment of the present invention, the longitudinal radius R LONG  may be ranged from about 10 cm to about 40 cm. More specifically, the longitudinal radius R LONG  can be 15 cm. According to an embodiment of the present invention, the lateral radius r may be ranged from about 2 cm to about 8 cm. More specifically, the lateral radius r can be 3 cm. As such, the circumferential ratio between the longitudinal radius R LONG  and the lateral radius r may be ranged from 1 to 20. More specifically, the circumferential ratio between the longitudinal radius R LONG  and the lateral radius r may about 5. 
         [0037]    Although  FIG. 2  shows that the OTWS  200  has twelve PWAs  210 , the OTWS  200  may also have different numbers of PWAs according to various embodiments of the present invention. For example,  FIG. 3A  shows that the OTWS  200  may have three PWAs  302 ;  FIG. 3B  shows that the OTWS  200  may have four PWAs  303 ; and  FIG. 3C  shows that the OTWS  200  may have eight PWAs  304 . To facilitate smoother rotation of the main wheel, an extra set of peripheral assemblies may be added. For example, as shown in the diagram  312 , an extra set of three extra PWAs  302  is added to the OTWS  200  according to an embodiment of the present invention. For another example, as shown in the diagram  313 , an extra set of four extra PWAs  303  is added to the OTWS  200  according to another embodiment of the present invention. 
         [0038]    The discussion now turns to the internal structure of the OTWS  200 . In  FIG. 4A , which shows a cross-sectional side view of the OTWS  200 , only one longitudinal gear  402  is displayed for the sake of clarity. According to an embodiment of the present invention, the OTWS  200  may have a spacing member  401  disposed between the two longitudinal gears  402 . In general, the spacing member  401  may have a central axle  405  and two parallel discs  403 , such that the central axle  405  is perpendicular to the two parallel discs  403 . 
         [0039]    The spacing member  401  may be operatively coupled to the two longitudinal gears  402  to help provide structural support for the OTWS  200 . On one hand, the two parallel discs  403 , along with the central axle  405 , hold the two longitudinal gears  402  in place by preventing any substantial displacement between the two longitudinal gears  402 . On the other hand, the parallel discs  403  allow the longitudinal gears  402  to freely rotate about the central axle  405 . More specifically, the two longitudinal gears  402  may be rotated independently without interfering each other even though they are both operatively coupled to the spacing member  401 . As such, the angular velocity of one longitudinal gear  402  should not affect the angular velocity of the other longitudinal gear  402  according to an embodiment of the present invention. 
         [0040]    Although the spacing member  401  provides structural support to the longitudinal gears  402 , it may or may not rotate along with the longitudinal gears  402 . For example, if the spacing member  401  is coupled a rotary device (not shown) that rotates the longitudinal gears  402 , it is likely that the spacing member  401  will remain angularly stationary in relative to the two longitudinal gears  402 ; otherwise, the spacing member  401  may rotate along with the longitudinal gears  402 . 
         [0041]    Referring to  FIG. 4A , the OTWS  200  may have several PWAs distributed around the longitudinal gear  402 . For the sake of simplicity,  FIG. 4A  only displays the PWAs  410  and  460 . However, it is understood that the OTWS  200  may include more than two PWAs according to various embodiments of the present invention. In general, each PWA may have a connecting gear  420  and a wheel member, which may include a first wheel  430  and an optional second wheel  440 . For example, the PWA  410  and the PWA  460  are structurally similar to each other except that the wheel member of the PWA  410  has the first wheel  430  and the optional second wheel  440 , whereas the wheel member of the PWA  460  only has the first wheel  430 . In practice, the OTWS  200  may adopt either the PWA  410  or the PWA  460 , or the OTWS  200  may adopt both the PWAs  410  and  460 . 
         [0042]    Referring to  FIG. 4B , which shows a cross-sectional view of the PWAs  410  and  460 , the first wheel  430  may have a circumference  432  defined by a radius r. The first wheel  430  may engage the connecting gear  420  via a receiving gear  434  such that the first wheel  430  may be rotated about the peripheral axle  436  when the connecting gear  420  is rotating. 
         [0043]    The connecting gear  420  of each PWA  410  or  460  may have a distal end  422  and a proximal end  424 . The distal end  422  should be engaged by and sandwiched between the two longitudinal gears  402  along their circumferential regions  404 , and the proximal end  424  should engage the first wheel  430  via the receiving gear  434  of the first wheel  430 . As such, the connecting gear  420  may serve two functions from a high level inventive standpoint. First, the connecting gear  420  may transmit the differential angular velocity between the two longitudinal gears  402  to the respective first wheel  430 , thereby causing the respective first wheel  430  to rotate orthogonally in relative to the rotations of the longitudinal gears  402 . Second, the connecting gear  420  may revolve around the central axle  405  by receiving the common angular velocity of the two longitudinal gears  402 , such that the entire PWA  410  and  460  may also revolve around the central axle  405 . 
         [0044]    According to embodiment of the present invention, the distal end  422  may be coupled to the proximal end  424  via a radial axle  426 , which is substantially parallel to the common radius R of the two longitudinal gears  402 . The radial axle  426  may have an extended section  451  for coupling the entire PWA  410  or  460  to the central axle  405  of the spacing member  401 . Alternatively, the PWA  410  or  460  may be coupled to the spacing member  401  or a pair of protective plates  408  via a brace member  450 . The brace member  450  may have a stabilizer  455  for stabilizing the position of the radial axle  426  to ensure that the receiving gear  434  is properly engaged to the proximal end  424  of the connecting gear  420 . 
         [0045]    Referring again to  FIG. 4A , the OTWS  200  may have protecting plates  406  for protecting the rotary device, the longitudinal gears  402 , and the PWAs  410  and  460 . Particularly, the protecting plates  406  may have an outer region  408  for protecting the PWAs  410  and  460 . According to an embodiment of the present invention, the protecting plates  406  may be coupled to the spacing member  401  via the central axle  405 , which penetrates the centers of the two longitudinal gears  402 . Alternatively, the protecting plates  406  may be coupled to the two longitudinal gears  402  according to another embodiment of the present invention. 
         [0046]    Although  FIG. 4A  shows only one gear configuration of the OTWS  200 , the OTWS  200  may have other gear configurations according to various embodiment of the present inventions. For example,  FIG. 5  shows the cross-sectional front views of the OTWS  200  having several gear configurations  510 ,  520 , and  530 . For the sake of simplicity, only a top and a bottom PWAs  550  are displayed in each gear configuration. However, it is understood that several more PWAs may be included in each gear configuration and that the PWAs  550  are similar to the PWAs  410  and  460  discussed with respect to  FIGS. 4A and 4B . More specifically, the PWA  550  may include the first wheel with the receiving gear  553  and the peripheral axle  551  as well as the connecting gear with the distal end  554  and the proximal end  552 . 
         [0047]    According to an embodiment of the present invention, the gear configuration  510  may adopt a pair of external gears  513  as the longitudinal gears  402 . The external gears  513  may have a set of straight-cut teeth, helical teeth, or double helical teeth. The distal end  554  of the connecting gear may be a bevel gear with a set of teeth matching the external gears  513 . Similarly, the proximal end  552  of the connecting gear may be a bevel gear with a set of teeth matching the receiving gear  553 , which can be a spur gear, a helical gear, or a double helical gear. 
         [0048]    The gear configuration  510  may also include the spacing member  511  and two rotary devices  514  and  515 . The spacing member  511  may have a pair of discs  512  that secure the external gears  513  from the outside and a central axle  516  that penetrates the external gears  513  through their centers. The rotary devices  514  and  515  may be coupled to the central axle  516 , such that the rotary devices  514  and  515  can separately and individually rotate each external gear  513  about the central axle  516 . Although the gear configuration  510  adopts two rotary devices, one rotary device may be sufficient if it can separately and individually rotate each external gear  513 . 
         [0049]    According to another embodiment of the present invention, the gear configuration  520  may adopt a pair of external gears  523  as the longitudinal gears  402 . The external gears  523  may have a set of straight-cut teeth, helical teeth, or double helical teeth. The distal end  554  of the connecting gear may be a bevel gear with a set of teeth matching the external gears  523 . Similarly, the proximal end  552  of the connecting gear may be a bevel gear with a set of teeth matching the receiving gear  553 , which can be a spur gear, a helical gear, or a double helical gear. 
         [0050]    The gear configuration  520  may also include the spacing member  521  and two rotary devices  524  and  525 . The spacing member  521  may have a pair of discs  522  that secure the external gears  523  from the inside and a central axle  526  that penetrates the external gears  523  through their centers. The rotary devices  524  and  525  may be coupled to both ends of the central axle  526 , such that the rotary devices  524  and  525  can separately and individually rotate each external gear  523  about the central axle  526 . Although the gear configuration  520  adopts two rotary devices, one rotary device may be sufficient if it can separately and individually rotate each external gear  523 . 
         [0051]    According to yet another embodiment of the present invention, the gear configuration  530  may adopt a pair of modified external gears  533  as the longitudinal gears  402 . The modified external gears  533  may have a set of straight-cut teeth, helical teeth, or double helical teeth. The distal end  554  of the connecting gear may be a bevel gear with a set of teeth matching the modified external gears  533 . Similarly, the proximal end  552  of the connecting gear may be a bevel gear with a set of teeth matching the receiving gear  553 , which can be a spur gear, a helical gear, or a double helical gear. 
         [0052]    The gear configuration  530  may also include the spacing member  531  and two rotary devices  534  and  535 . The spacing member  531  may have a pair of internal discs  532  embedded in the middle of the modified external gears  533  and a central axle  536  coupled between the internal discs  532 . The rotary devices  534  and  535  may be disposed within the central axle  536  for separately and individually rotating the pair of internal discs  532 . Accordingly, the pair of modified external gears  533  may be rotated separately and individually because they are coupled to the internal discs  532 . Although the gear configuration  530  adopts two rotary devices, one rotary device may be sufficient if it can separately and individually rotate each modified external gear  533 . 
         [0053]    It is understood that the components of each gear configurations may be interchangeable. In an embodiment of the present invention, the spacing member  511  may be used in the gear configuration  520 . In another embodiment of the present invention, the central axle  536  with the embedded rotary devices  534  and  535  may be used in the gear configuration  510 . In yet another embodiment of the present invention, the external gears  523  may be used in the gear configuration  530 . 
         [0054]    For illustrative purposes,  FIGS. 6 and 7  are provided to show the exemplary models of the several gears discussed herein. For example,  FIG. 6  shows the exemplary models of the external gear and the bevel gear. For another example,  FIG. 7  shows the exemplary models of the spur gear, the helical gear, and the double helical gear. It is understood that the longitudinal gears, the connecting gears, and the receiving gears may take other alternative forms, as long as their combinations are consistent with the general principles of mechanics. 
         [0055]    The discussion now turns to the physics of the OTWS. In  FIG. 8A , which shows the high level conceptual view of the OTWS according to an embodiment of the present invention, the pair of longitudinal gears may be represented by a left gear (or interchangeably a first gear)  802  and a right gear (interchangeably a second gear)  804 . Although the terms “left” and “right” are used consistently throughout the rest of the specification, it is to be emphasized that they are interchangeable and are relatively defined such that they should not be construed in the absolute sense. 
         [0056]    The left gear  802  and the right gear  804  are parallel to a first plane Sx and orthogonal to a first axis (interchangeably a longitudinal axis) Ax. The left and right angular velocities V XL  and V XR  represent the angular velocities of the left and right gears  802  and  804  respectively. Both the left and right angular velocities V XL  and V XR  are measured in the clockwise direction about the first axis Ax in radian per second. When the left and right angular velocities V XL  and V XR  are positive, meaning that the left and right gears  802  and  804  are rotating in the clockwise direction, the OTWS  800  travels forward with a positive longitudinal velocity V LONG . When the left and right angular velocities V XL  and V XR  are negative, meaning that the left and right gears  802  and  804  are rotating in the counterclockwise direction, the OTWS  800  travels backward with a negative longitudinal velocity V LONG . 
         [0057]    As defined herein, the term “longitudinal” is associated with the forward and backward directions, whereas the term “lateral” is associated with the left and right directions. Although the terms “forward” and “backward” are used consistently throughout the rest of the specification, it is to be emphasized that they are interchangeable and are relatively defined such that they should not be construed in the absolute sense. 
         [0058]    The left and right gears  802  and  804  define a cylindrical space  806  in between them and the cylindrical space  806  has a circumferential region  808 . According to an embodiment of the present invention, the distal end  822  of the connecting gear  820  of each PWA  810  may be distributed along the circumferential region  808 , such that the connecting gear  820  may be rotated about a radial axis Ay, which is substantially parallel to a radius of the cylindrical space  806 . As such, the radial axis Ay of each PWA  810  should be substantially orthogonal to the first axis Ax and the radial plane Sy of each PWA  810  should be substantially parallel to the side surface of the cylindrical space  806 . 
         [0059]    In an embodiment of the present invention, the distal end  822  of the connecting gear  820  is engaged between both left and right gears  802  and  804 . As such, the angular velocity Vy of the connecting gear  820  is a function of a differential angular velocity V diff  between the left and right gears  802  and  804 . More specifically, the differential angular velocity V diff  is defined as V XL -V XR . For example, if Kxy represents the gear ratio between the longitudinal gear  802  and the connecting gear  820 , the angular velocity Vy equals Kxy*(V diff ). 
         [0060]    Under this differential mechanism, the connecting gear  820  may (1) rotate clockwise about the radial axis Ay at a positive angular velocity Vy when the left angular velocity V XL , is greater than right angular velocity V XR  (i.e., the differential angular velocity V diff  is greater than 0); (2) rotate counterclockwise about the radial axis Ay at a negative angular velocity Vy when the left angular velocity V XL  is less than the right angular velocity V XR  (i.e., the differential angular velocity V diff  is less than 0); and (3) remain angularly stationary (i.e., no rotation) when the left angular velocity V XL  is substantially the same as the right angular velocity V XR  (i.e., the left and right angular velocities V XL  and V XR  are in the same direction and of the same magnitude). 
         [0061]    Referring to  FIG. 8A , the PWA  810  is symmetrical along a plane that is parallel to the first plane Sx and positioned in the middle of the cylindrical space  806 . The receiving gear  830  of the first wheel is engaged by the proximal end  824  of the connecting gear  820 , such that the first wheel may be rotated about a second axis (interchangeably a peripheral axis) Az when the connecting gear  820  rotates. Because the proximal end  824  has the same angular velocity as the distal end  822 , the angular velocity Vz of the first wheel is a function of the angular velocity Vy of the distal end  822 , which ultimately depends on the differential angular velocity V diff  between the left and right angular velocities V XL  and V XR . More specifically, if Kyz represents the gear ratio between the connecting gear  820  and the receiving gear  830 , the angular velocity Vz equals Kyz*Vy, which ultimately equals Kyz*Kxy*(V diff ). 
         [0062]    According to an embodiment of the present invention, the left and right angular velocities V XL  and V XR  may be ranged from about 0 radian per second to about plus or minus 20 radians per second. More specifically, the left and right angular velocities V XL  and V XR  may be about plus or minus 8 radians per second. According to an embodiment of the present invention, the radius of the longitudinal gears  802  and  804  may be about 8 cm, the radius of the connecting gear  420  may be about 0.5 cm, and the radius of the receiving gear  830  may be about 2.5 cm. As such, the gear ratio gear ratio Kxy may be about 16 and the gear ratio Kyz may be about 0.2. 
         [0063]    For example, the first wheel may (1) rotate clockwise about the second axis Az at a positive angular velocity Vz when the left angular velocity V XL  is greater than the right angular velocity V XR  (i.e., the differential angular velocity V diff  is greater than 0); (2) rotate counterclockwise about the radial axis Az at a negative angular velocity Vz when the left angular velocity V XL  is less than the right angular velocity V XR  (i.e., the differential angular velocity V diff  is less than 0); and (3) remain angularly stationary when the left angular velocity V XL  is substantially the same as the right angular velocity V XR . For the sake of clarity,  FIG. 8B  summarizes the rotating directions of the angular velocities Vy and Vz when the left angular velocity V XL  is less than the right angular velocity V XR  (i.e., the differential angular velocity V diff &lt;0); and  FIG. 8C  summarizes the rotating directions of the angular velocities Vy and Vz when the left angular velocity V XL  is greater than the right angular velocity V XR  (i.e., the differential angular velocity V diff &gt;0). 
         [0064]    When the first wheel rotates at a positive angular velocity Vz, the OTWS  800  may travel laterally to the left at a positive lateral velocity V LAT , which equals Vz*r. Conversely, when the first wheel, rotates at a negative angular velocity Vz, the OTWS  800  may travel laterally to the right at a negative lateral velocity V LAT , which equals Vz*r. Moreover, if the left angular velocity V XL  does not substantially cancel out the right angular velocity V XR , the entire PWA  810  may revolve around the first axis Ax by travelling along the circumferential region  808  at a common angular velocity V com . 
         [0065]    The discussion now turns to several operation modes of the OTWS.  FIG. 9  demonstrates a common mode operation of the OTWS  800  according to an embodiment of the present invention. Under the common mode operation, the left and right gears  802  and  804  always rotate at a common angular velocity V com , meaning that the left gear  802  has the same angular speed and the same rotating direction as the right gear  802 . As shown in the diagrams  901  and  903 , both the left and right gears  802  and  804  may rotate clockwise or counterclockwise at the same time with the same angular speed. 
         [0066]    Consequentially, the PWA  810  may revolve around the first axis Ax at the common angular velocity V com . For example, the PWA  810  in the diagram  901  may revolve around the first axis Ax at a negative common angular velocity V com , which is less than 0. Accordingly, the OTWS  800  may travel backward at a negative longitudinal velocity V LONG . For another example, the PWA  810  in the diagram  901  may revolve around the first axis Ax at a positive common angular velocity V com , which is greater than 0. Accordingly, the OTWS  800  may travel forward at a positive longitudinal velocity V LONG . 
         [0067]    Referring to the diagram  902 , which shows the cross-sectional back view of the diagram  901 , the left angular velocity V XL  produces a left thrust T XL  directing the distal end  822  of the connecting gear  820  to rotate counterclockwise about the radial axis Ay, whereas the right angular velocity V XR  produces a right thrust T XR  directing the distal end  822  of the connecting gear  820  to rotate clockwise about the radial axis Ay. However, because the left angular velocity V XL  substantially equals the right angular velocity V XR , the left thrust T XL  substantially cancels out the right thrust T XR  such that the distal end  822  of the connecting gear  820  remains angularly stationary. 
         [0068]    Similarly, in diagram  904 , which shows the cross-sectional back view of the diagram  903 , the left angular velocity V XL  produces a left thrust T XL  directing the distal end  822  of the connecting gear  820  to rotate clockwise about the radial axis Ay, whereas the right angular velocity V XR  produces a right thrust T XR  directing the distal end  822  of the connecting gear  820  to rotate counterclockwise about the radial axis Ay. Again, because the left angular velocity V XL , substantially equals the right angular velocity V XR , the left thrust T XL , substantially cancels out the right thrust T XR  such that the distal end  822  of the connecting gear  820  remains angularly stationary. 
         [0069]      FIG. 10  demonstrates a differential mode operation of the OTWS  800  according to another embodiment of the present invention. Under the differential mode operation, the left and right gears  802  and  804  always rotate at a pair of opposite angular velocities, meaning that the left gear  802  has the same angular speed but the opposite rotating direction as the right gear  802 . As shown in the diagrams  1001  and  1003 , the left and right gears  802  and  804  may rotate at a pair of opposite directions at the same time with the same angular speed. Because the left angular velocity V XL  substantially cancels out the right angular velocity V XR , the PWA  810  will not revolve around the first axis Ax, such that the OTWS  800  will not travel longitudinally. 
         [0070]    Referring to the diagram  1002 , which shows the cross-sectional back view of the diagram  1001 , the left angular velocity V XL , produces a left thrust T XL , directing the distal end  822  of the connecting gear  820  to rotate clockwise about the radial axis Ay, and the right angular velocity V XR  also produces a right thrust T XR  directing the distal end  822  of the connecting gear  820  to rotate clockwise about the radial axis Ay. Consequentially, the connecting gear  820  directs the receiving gear  830  of the first wheel to rotate about the second axis Az at the angular velocity Vz. Because the first wheel rotates clockwise, the OTWS  800  may travel laterally to the left at a positive lateral velocity V LAT . 
         [0071]    Similarly, in diagram  1004 , which shows the cross-sectional front view of the diagram  1003 , the left angular velocity V XL  produces a left thrust T XL  directing the distal end  822  of the connecting gear  820  to rotate counterclockwise about the radial axis Ay, and the right angular velocity V XR  produces a right thrust T XR  also directing the distal end  822  of the connecting gear  820  to rotate counterclockwise about the radial axis Ay. Consequentially, the connecting gear  820  directs the receiving gear  830  of the first wheel to rotate about the second axis Az at the angular velocity Vz. Because the first wheel rotates counterclockwise, the OTWS  800  may travel laterally to the right at a negative lateral velocity V LAT . 
         [0072]      FIG. 11  demonstrates a backward differential mode operation of the OTWS  800  according to yet another embodiment of the present invention. In one embodiment, under the backward differential mode operation, the angular velocity V XL  should be substantially different from the right angular velocity V XR  and the common angular velocity V com  of the left and right gears  802  and  804  will always be negative and in the counterclockwise direction about the first axis Ax. For example, as shown in the diagram  1101 , both the left and right gears  802  and  804  are rotating counterclockwise about the first axis Ax, but the magnitude of the left angular velocity V XL  is substantially greater than the magnitude of the right angular velocity V XR . Accordingly, the common angular velocity V com  is substantially the same as V XR . For another example, as shown in the diagram  1103 , both the left and right gears  802  and  804  are rotating counterclockwise about the first axis Ax, but the magnitude of the left angular velocity V XL  is substantially smaller than the magnitude of the right angular velocity V XR . Accordingly, the common angular velocity V com  is substantially the same as V XL . 
         [0073]    In any event, the longitudinal gear with the dominant angular velocity (i.e., the left angular velocity V XL  in the diagram  1101  and the right angular velocity V XR  in the diagram  1103 ) should be rotating counterclockwise, such that the PWA  810  may revolve counterclockwise around the first axis Ax regardless of the rotating direction of the other longitudinal gear. That is, the right gear  804  in the diagram  1101  may rotate clockwise as long as the magnitude of the right angular velocity V XR  is less than the magnitude of the left angular velocity V XL ; and similarly, the left gear  802  in the diagram  1103  may rotate counterclockwise as long as the magnitude of the left angular velocity V XL  is less than the magnitude of the right angular velocity V XR . 
         [0074]    Referring to the diagram  1102 , which shows the cross-sectional back view of the diagram  1101 , the left angular velocity V XL  produces a left thrust T XL  directing the distal end  822  of the connecting gear  820  to rotate counterclockwise about the radial axis Ay whereas the right angular velocity V XR  produces a right thrust T XR  directing the distal end  822  of the connecting gear  820  to rotate clockwise about the radial axis Ay. Because the left thrust T XL  is stronger than the right thrust T XR , the left thrust T XL  overcomes the left thrust T XR  and thereby causing the distal end  822  of the connecting gear  820  to rotate counterclockwise. Consequentially, the connecting gear  820  directs the receiving gear  830  of the first wheel to rotate counterclockwise about the second axis Az at the angular velocity Vz, such that the OTWS  800  may travel laterally to the right at a negative lateral velocity V LAT . Driven simultaneously by the longitudinal velocity V LONG  and the lateral velocity V LAT , the OTWS  800  may travel diagonally in the back-right direction. 
         [0075]    Similarly, in the diagram  1104 , which shows the cross-sectional back view of the diagram  1103 , the left angular velocity V XL  produces a left thrust T XL  directing the distal end  822  of the connecting gear  820  to rotate counterclockwise about the radial axis Ay, whereas the right angular velocity V XR  produces a right thrust T XR  directing the distal end  822  of the connecting gear  820  to rotate clockwise about the radial axis Ay. Because the left thrust T XL  is weaker than the right thrust T XR , the left thrust T XL  gives way to the right thrust T XR  and thereby causing the distal end  822  of the connecting gear  820  to rotate clockwise. Consequentially, the connecting gear  820  directs the receiving gear  830  of the first wheel to rotate clockwise about the second axis Az at the angular velocity Vz, such that the OTWS  800  may travel laterally to the left at a positive lateral velocity V LAT . Driven simultaneously by the longitudinal velocity V LONG  and the lateral velocity V LAT , the OTWS  800  may travel diagonally in the back-left direction. 
         [0076]      FIG. 12  demonstrates a forward differential mode operation of the OTWS  800  according to yet another embodiment of the present invention. Under the forward differential mode operation, the left angular velocity V XL  should be substantially different from the right angular velocity V XR  and the common angular velocity V com  of the left and right gears  802  and  804  will always be positive and in the clockwise direction about the first axis Ax. For example, as shown in the diagram  1201 , both the left and right gears  802  and  804  are rotating clockwise about the first axis Ax, but the magnitude of the left angular velocity V XL  is substantially greater than the magnitude of the right angular velocity V XR . Accordingly, the common angular velocity V com  is substantially the same as V XR . For another example, as shown in the diagram  1203 , both the left and right gears  802  and  804  are rotating clockwise about the first axis Ax, but the magnitude of the left angular velocity V XL  is substantially smaller than the magnitude of the right angular velocity V XR . Accordingly, the common angular velocity V com  is substantially the same as V XL . 
         [0077]    In any event, the longitudinal gear with the dominant angular velocity (i.e. the left angular velocity V XL  in the diagram  1201  and the right angular velocity V XR  in the diagram  1203 ) should be rotating clockwise, such that the PWA  810  may revolve clockwise around the first axis Ax regardless of the rotating direction of the other longitudinal gear. That is, the right gear  804  in the diagram  1201  may rotate counterclockwise as long as the magnitude of the right angular velocity V XR  is less than the magnitude of the left angular velocity V XL ; and similarly, the left gear  802  in the diagram  1203  may rotate counterclockwise as long as the magnitude of the left angular velocity V XL , is less than the magnitude of the right angular velocity V XR . 
         [0078]    Referring to the diagram  1202 , which shows the cross-sectional back view of the diagram  1201 , the left angular velocity V XL , produces a left thrust T XL  directing the distal end  822  of the connecting gear  820  to rotate clockwise about the radial axis Ay, whereas the right angular velocity V XR  produces a right thrust T XR  directing the distal end  822  of the connecting gear  820  to rotate counterclockwise about the radial axis Ay. Because the left thrust T XR , is stronger than the right thrust T XR , the left thrust T XL  overcomes the left thrust T XR  and thereby causing the distal end  822  of the connecting gear  820  to rotate clockwise. Consequentially, the connecting gear  820  directs the receiving gear  830  of the first wheel to rotate clockwise about the second axis Az at the angular velocity Vz, such that the OTWS  800  may travel laterally to the left at a positive lateral velocity V LAT . Driven simultaneously by the longitudinal velocity V LONG  and the lateral velocity V LAT , the OTWS  800  may travel diagonally in the front-left direction. 
         [0079]    Similarly, in the diagram  1204 , which shows the cross-sectional back view of the diagram  1203 , the left angular velocity V XL , produces a left thrust T XL  directing the distal end  822  of the connecting gear  820  to rotate clockwise about the radial axis Ay, whereas the right angular velocity V XR  produces a right thrust T XR  directing the distal end  822  of the connecting gear  820  to rotate counterclockwise about the radial axis Ay. Because the left thrust T XL  is weaker than the right thrust T XR , the left thrust T XL  gives way to the left thrust T XR  and thereby causing the distal end  822  of the connecting gear  820  to rotate counterclockwise. Consequentially, the connecting gear  820  directs the receiving gear  830  of the first wheel to rotate counterclockwise about the second axis Az at the angular velocity Vz, such that the OTWS  800  may travel laterally to the right at a negative lateral velocity V LAT . Driven simultaneously by the longitudinal velocity V LONG  and the lateral velocity V LAT , the OTWS  800  may travel diagonally in the front-right direction. 
         [0080]      FIG. 13  provides a summary for all traveling directions of the OTWS  800  with respect to various combinations of the differential angular velocity V diff  and the common angular velocity V com . For example, the charts  1301  to  1303  represent the traveling directions of the OTWS  800  when V com  is less than 0 (i.e. the backward mode). For another example, the charts  1304  to  1306  represent the traveling directions of the OTWS  800  when V com  equals 0 (i.e. the pure differential mode). For yet another example, the charts  1307  to  1309  represent the traveling directions of the OTWS  800  when V com  is greater than 0 (i.e. the forward mode). 
         [0081]    Under the differential mechanism, the magnitude of the longitudinal velocity V LONG  and the lateral velocity V LAT  can be adjusted by varying the difference between the left and right angular velocities V XL  and V XR . In general, the magnitude of the lateral velocity V LAT  increases proportionally with the differential angular velocity V diff , whereas the longitudinal velocity V LONG  increases proportionally with the common angular velocity V com . According to an embodiment of the present invention, the magnitudes of the longitudinal velocity V LONG  and the lateral velocity V LAT  may be ranged from about 0 m/s to about plus or minus 10 m/s. More specifically, the magnitudes of the longitudinal velocity V LONG  and the lateral velocity V LAT  may be about plus or minus 2 m/s. 
         [0082]    Various embodiments of the present invention adopt a gear system in actuating the differential mechanism. However, the differential mechanism of the OTSW may be actuated by adopting a frictional system according to an alternative embodiment. For example, referring again to  FIG. 8A , the pair of longitudinal gears  802  and  804  may be replaced by a pair of plates, each of which has a frictional surface facing against each other. As shown in  FIG. 14 , the pair of plates  1402  and  1404  may have the frictional surfaces  1406  and  1408  facing against each other. The frictional surfaces  1406  and  1408  may engage the PWAs  1410  via a connecting member  1420 . 
         [0083]    Similar to the connecting gear  820 , the connecting member  1420  may be rotated about the radial axis Ay when the differential angular velocity V diff  between the pair of plates is greater or less than zero. However, unlike the connecting gear  820 , the connecting member  1420  does not have a teethed surface. Instead, the connecting member  1420  may have a frictional surface similar to the pair of plates  1402  and  1404 . 
         [0084]    The connecting member  1420  may have a distal end for engaging the frictional surfaces  1406  and  1408  of the pair of plates  1402  and  1404 , and a proximal end for engaging the first wheel  1430 , which also has a frictional surface similar to the pair of plates  1402  and  1404 . As such, the PWA  1410  may rotates about the second axis Az when the differential angular velocity V diff  between the pair of plates  1402  and  1404  is greater or less than zero. 
         [0085]      FIG. 15  is a flow chart that illustrates the method steps of operating the omni traction wheel according to an embodiment of the present invention. These method steps are related to the discussion with respect to  FIGS. 2 to 12 . Although these steps might introduce terminologies different from those in the previous discussion, these steps are consistent with the spirit and concept of the previous discussion and should not be construed otherwise. 
         [0086]    In step  1502 , a plurality of peripheral wheels is engaged to first and second gears via a plurality of connection gears. In step  1504 , the first gear is rotated at a first angular velocity. In step  1506 , the second gear is rotated at a second angular velocity, wherein the omni traction wheel: (1) travels laterally when the first angular velocity is different from the second angular velocity such that each connecting gear is configured to rotate the respective peripheral wheel, (2) travels longitudinally when the first and second angular velocities are in a same direction such that each connecting gear, along with the respective peripheral wheel, is configured to revolve around a circular plate positioned between the first and second gears and substantially parallel to the first and second gears, (3) travels diagonally when the first angular velocity is different from the second angular velocity and when the first and second angular velocities are in a same direction, (4) remains laterally stationary when the first angular velocity substantially equals the second angular velocity, and (5) remains longitudinally stationary when the sum of the first and second angular velocities is substantially zero. 
         [0087]    The previous description of the disclosed examples is provided to enable any person of ordinary skill in the art to make or use the disclosed methods or apparatus. Various modifications to these examples will be readily apparent to those skilled in the art, and the principles defined herein may be applied to other examples without departing from the spirit or scope of the disclosed method and apparatus. The described embodiments are to be considered in all respects only as illustrative and not restrictive and the scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.