Abstract:
A gear includes a body defining a portion of a sphere and including at least one curved surface. A plurality of teeth extend from the at least one curved surface. The plurality of teeth are arranged in rows and columns that define a plurality of longitudinal and latitudinal arcuate channels along the curved surface.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a national stage entry under 35 U.S.C. §371 of PCT/US2010/037634, filed on Jun. 7, 2010, which claims priority to U.S. Provisional Patent Application No. 61/185,054 filed on Jun. 8, 2009, the entireties of which are herein incorporated by reference. 
    
    
     FIELD OF DISCLOSURE 
     The disclosed system and methods relate to gears. More specifically, the disclosed system and methods relate to a partial spherical gear enabling the generation of complex motion. 
     BACKGROUND 
     In the growing field of robotics and clean electricity generation, new methods of mechanical actuation will be valuable in developing different types of robotic and power generating systems. Before the advent of optical mice, a traditional mouse generated directional signals for the cursor on the screen via a rubber ball which was in contact with two roll pins mounted perpendicular to one another in the XY plane. This allowed the cursor on the computer screen to move in any direction with respect to the XY plane of the screen. When moving the mouse forward or backwards with respect to the user, only the y-roller pin would be actuated and the mouse on the screen would move up and down. When the mouse was moved from side to side, only the x-roller pin would move and the cursor would move side to side on the screen. 
     However when the mouse was moved at a diagonal with respect to the user, a combination output of the roller pins would allow the cursor to move at various vectors with respect to the XY plane of the computer screen. In this sense, the roller pins of the mouse were passive devices that took “input” from the trackball and then displayed that motion as movement of the cursor on the screen. Furthermore, if these pins were actuated via a motor and “outputted” motion to the trackball, a force feedback mouse could in theory be created. This is an excellent way to create motion in a robot, or in theory to even generate electricity, but is limited by the fact that the rubber on plastic interaction between the track ball, and the rolling pins is unable to generate large amounts of torque. 
     Furthermore, when the x-pin for example is actuated by the track ball, the rubber ball will actually “drag” along the y-roller pin and will generate friction. This is true in the opposite situation as well. When both pins are being actuated (when the mouse is moving for example at a 45 degree angle) there is drag occurring on both pins. Thus, in addition to the inability to create large amounts of torque this device also creates friction between the trackball and the roller pins. This is acceptable in some robotic systems such as those seen in U.S. Pat. No. 5,952,796 entitled “Cobots”, as well as in U.S. Pat. No. 5,923,139 entitled “Passive robotic constraint devices using non-holonomic transmission elements”, the entireties of which are herein incorporated by reference. However in systems that require larger amounts of torque with lower friction, the surface-to-surface trackball system cannot work in its purest form. 
     Accordingly, an improved system and method for generating high-torque and low-friction for two-degree of freedom mechanical applications is desirable. 
     SUMMARY 
     A gear is disclosed that includes a body defining a portion of a sphere and including at least one curved surface. A plurality of teeth extend from the at least one curved surface. The plurality of teeth are arranged in rows and columns that define a plurality of longitudinal and latitudinal arcuate channels along the curved surface. 
     Also disclosed is a gear system that includes a gimbal and first, second, and third gears. The first gear has a body that defines a portion of a sphere and includes a curved surface. The first gear is coupled to the gimbal and includes a plurality of teeth extending from the curved surface. The second gear includes a plurality of teeth and is disposed adjacent to the first gear such that the plurality of teeth of the second gear engage the plurality of teeth of the first gear. The third gear includes a plurality of teeth and is disposed adjacent to the first gear such that the plurality of teeth of the third gear engage the plurality of teeth of the first gear. The second gear rotates about a first axis when the first gear moves in a first direction, and the third gear rotates about a second axis when the first gear moves in a second direction that is substantially perpendicular to the first direction. 
     A gear system is also disclosed that includes a first support structure, a first gear including a body defining a portion of a sphere and including a first curved surface, and first and second spur gears. The first gear is coupled to the first support structure by a first gimbal. A plurality of teeth extend from the first curved surface in a plurality of rows and columns that define a plurality of channels. The first and second spur gears are supported by the first support structure in an approximately orthogonal relationship to one another. The first spur gear includes a plurality of teeth that engage the plurality of teeth of the first gear such that the first spur gear rotates about a first axis when the first gear moves in a first direction. The second spur gear includes a plurality of teeth that engage the plurality of teeth of the first gear such that the second spur gear rotates about a second axis when the first gear moves in a second direction that is approximately orthogonal to the first direction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features and advantages of the present invention will be more fully disclosed in, or rendered obvious by the following detailed description of the preferred embodiments of the invention, which are to be considered together with the accompanying drawings wherein like numbers refer to like parts and further wherein: 
         FIG. 1  is an isometric view of one example of an improved gear assembly; 
         FIG. 2  is a side view of the improved gear assembly illustrated in  FIG. 1 ; 
         FIG. 3A  is a top side view of the gear assembly illustrated in  FIG. 1 ; 
         FIG. 3B  is a top side view of the spur gears and spherical gears illustrated in  FIG. 3A ; 
         FIG. 4  is a front end view of the gear assembly illustrated in  FIG. 1 ; 
         FIG. 5  is an isometric view of the mounting side of a spherical gear in accordance with the gear assembly illustrated in  FIG. 1 ; 
         FIG. 6  is an isometric view of the spur gears and mounting rod in accordance with the gear assembly illustrated in  FIG. 1 ; 
         FIG. 7  is a rear end view of the gear assembly illustrated in  FIG. 1  with the mounting rod having been removed; 
         FIG. 8  is a side view of a plurality of gear assemblies coupled together to form an arm; and 
         FIG. 9  is a side view of a pair of gear assemblies coupled together. 
     
    
    
     DETAILED DESCRIPTION 
     This description of preferred embodiments is intended to be read in connection with the accompanying drawings, which are to be considered part of the entire written description. The drawing figures are not necessarily to scale and certain features of the invention may be shown exaggerated in scale or in somewhat schematic form in the interest of clarity and conciseness. In the description, relative terms such as “horizontal,” “vertical,” “up,” “down,” “top,” and “bottom” as well as derivatives thereof (e.g., “horizontally,” “downwardly,” “upwardly,” etc.) should be construed to refer to the orientation as then described or as shown in the drawing figure under discussion. These relative terms are for convenience of description and normally are not intended to require a particular orientation. Terms including “inwardly” versus “outwardly,” “longitudinal” versus “lateral,” and the like are to be interpreted relative to one another or relative to an axis of elongation, or an axis or center of rotation, as appropriate. Terms concerning attachments, coupling, and the like, such as “connected” and “interconnected,” refer to a relationship wherein structures are secured or attached to one another either directly or indirectly through intervening structures, as well as both movable or rigid attachments or relationships, unless expressly described otherwise. The term “operatively connected” is such an attachment, coupling or connection that allows the pertinent structures to operate as intended by virtue of that relationship. 
     A gear system that can be used to create mechanical motion as an output device or to create electricity when used as an input device is now described. A partial spherical gear is coupled to a two-axis pivot or gimbal that provides for motion in a plurality of directions. The pivot creates a “focal point” at the center and the arrangement allows for full rotation of the partial sphere about the focal point. The angles of the teeth of the partial spherical gears, the arc, and radius of the partial sphere correspond to the focal point of the pivot. 
     The improved gear assembly may be used to generate rotational motion in a plurality of directions by actuating the spherical gear or one of the at least two spur gears that interface with the spherical gear. The spur gears can be mounted to a motor or other device in order to generate electricity. Additionally or alternatively, the gear assembly may be implemented to output motion through the partial spherical gear if the individual spur gears are actuated. Each of the components of the gear assembly may be fabricated from any material such as, for example, metals, ceramics, polymers, or the like. The components may be fabricated by casting, machining, molding, additive manufacturing such as, for example, three-dimensional printing, or other suitable manufacturing techniques as will be understood by one skilled in the art. 
       FIGS. 1-7  illustrate one example of a gear assembly  100 . As shown in  FIGS. 1-7 , gear assembly  100  includes a partial spherical gear  102  having a plurality of teeth  104 , two spur gears  106 - 1  and  106 - 2  (collectively referred to herein as “spur gears  106 ”) each having a plurality of teeth  108 , and a mounting rod  110  coupling spherical gear  102  to a pivot  112 , which is supported by a support structure  114 . Support structure  114  may also be coupled to spur gears  106 . 
     As best seen in  FIGS. 1 and 2 , teeth  104  of partial spherical gear  102  are disposed on a curved surface  116  of the spherical gear  102 . Although the teeth  104  are illustrated in the figures as being disposed on a convex surface, one skilled in the art will understand that teeth  104  may be disposed on a concave surface of spherical gear  102 . Teeth  104  are arranged on curved surface  116  of partial spherical gear  102  such that they correspond to an arc defined by curved surface  116  with respect to the central point  118  of pivot  112 . Teeth  104  may have any variety of cross-sectional shapes including, but not limited to, square, triangular, rectangular, polygonal, or the like. Teeth  104  are quadrilateral pyramids extending from curved surface  116  such that teeth  104  have a greater cross-sectional area at the base  120  and a smaller cross-sectional area at the tip  122  as best seen in  FIGS. 1-3A . 
     The curvature of curved surface  116 , including tips  122  of teeth  104 , corresponds to the distance from the center  118  of pivot  112  to tips  122 . For example, partial spherical gear  102  has a radius of curvature that corresponds to the distance from the center of pivot  112  to the tips  122  such that teeth  104  that mesh with teeth  108  of spur gears  106  remain tangent to the spur gears  106  when the partial spherical gear  102  rotates about the pivot  112 . 
     As best seen in  FIG. 5 , the mounting side  124  of spherical gear may have a concave shape that is complementary to the convex shape of the interface side  126  that includes teeth  104 . In some embodiments, mounting side  124  may be planar or have another geometry as will be understood by one skilled in the art. One or more mounting structures  128  extend from the surface  130  of mounting side  124 . As shown in  FIG. 5 , mounting structures  128  may be fins that extend from the surface  130  of mounting side  124  and each define one or more holes  132  for use in coupling spherical gear  102  to mounting rod  110  as described below. 
     Spur gears  106  each include a plurality of teeth  108  that extend from a central cylindrical body  134  and are configured to be disposed in tangential relationship to the curved surface  116  of spherical gear  102  as best seen in  FIG. 3A . Spur gears  106  are disposed 90 degrees from one another and may each be coupled to a respective motor  136 - 1  and  16 - 2  (collectively referred to herein as “motors  126 ”) as best seen in  FIG. 3B . The teeth  108  of spur gears  106  have a shape configured to be disposed between and engage adjacent teeth  104  of spherical gear  102 . For example, teeth  108  may have a rectangular cross-sectional geometry in a first direction and a triangular or tapered rectangular cross-sectional geometry and in a second direction that is orthogonal to the first direction such that the teeth  108  are tapered and may be received within a gap  138  defined by adjacent teeth  104  of sphere gear  102 . 
     In one embodiment, teeth  108  have a length that is sufficient to engage an adjacent pair of teeth  104  while extending across a gap  188  between the adjacent teeth  104  such that as the spherical gear  102  moves relative to gears  106 , teeth  108  remain disposed within a channel  140  defined by a plurality of teeth  104  extending in the same direction as best seen in  FIG. 3B . Teeth  108  have widths that are less than the distance between adjacent teeth  104  disposed on spherical gear  102 . The height of teeth  108  that radially extend from cylindrical body  134  may vary depending on the position of gears  106  with respect to spherical gear  102 . One skilled in the art will understand that teeth  108  may have other geometries, lengths, widths, and heights. 
     As best seen in  FIG. 6 , mounting rod  110  has an elongate body  142  having a gear mounting end  144  and a second mounting end  146  that each flare out from elongate body  142 . Elongate body defines a through hole  148  adjacent to second mounting end  146  that extends from a top surface  150  to a bottom surface  152 . 
     Gear mounting end  144  may include one or more holes  154  that are sized and arranged to align with holes  132  defined by mounting structures  128 . In some embodiments, holes  154  may be replaced by one or more detents configured to engage holes  132  defined by mounting structures  128  as will be understood by one skilled in the art. In embodiments where spherical gear  102  and mounting rod  110  are monolithic, mounting end  144  may not include holes  154  or detents as will be understood by one skilled in the art. Gear mounting end  144  is dimensioned to be within the space  156  defined by mounting structures  128  of spherical gear  102 . However, one skilled in the art will understand that gear mounting end  144  may be forked such that a single mounting structure  128  may be received therein. 
     Second mounting end  146  may also defined a plurality of holes  158  for coupling to another device or structure. As best seen in  FIG. 6 , second mounting end  146  may include a pair of projections  160  that together define a slot  162  for receiving another device or structure as described below. Each of the projections  160  may include holes  158  that align or correspond to holes disposed on the other projection  160 . 
     Turning now to  FIG. 7 , pivot  112 , which may be a two-axis gimbal, includes a body  164  defining an opening  166  sized and configured to receive elongate body  142  of mounting rod  110  therein. Body  164  may have a rectangular, circular, elliptical, or other shape that defines opening  166 . A pair of extensions  168  the extend from an outer surface  170  of pivot body  164  that are sized and configured to be received in a bearing  172  of support structure  114  as described below. A shaft  174  extends across opening  166  and is sized and configured to be received within hole  148  defined by elongate body  142  of mounting rod  110 . 
     Support structure  114  may include one or more components configured to support spur gears  106 , pivot  112 , and mounting rod  110  such that an engagement is maintained between teeth  104  of spherical gear  102  and teeth  108  of spur gears  106 . In one embodiment, support structure  114  has a substantially ovoid body  176  including a pivot support side  178  disposed opposite a mounting side  180  as best seen in  FIG. 3A . Pivot supporting side  178  may define an aperture  182  for receiving pivot  112  therein. Bearings  172  ( FIG. 7 ) may be disposed on opposite sides of aperture  182  and sized and configured to receive extensions  168  of pivot body  164 . 
     Mounting side  180  includes gear mounting section  184  disposed adjacent to an assembly mounting section  186 . As best seen in  FIGS. 1 and 4 , gear mounting section  184  that defines a pair of openings  188  that are orthogonal to one another and are sized and configured to receive motors  136  coupled to spur gears  106  therethrough. Gear mounting section  184  is spaced apart from pivot support side  178  such that spherical gear  102  may be received in aperture  182 . Assembly mounting section  186  defines a plurality of mounting holes  190  for coupling gear assembly  100  to another gear assembly or to another device in a larger system as described below. 
     Gear assembly  100  is assembled by inserting extensions  168  of pivot body  164  into bearings  172  of support structure  114 . Mounting rod  110  is inserted into opening  166  of pivot body  164  until hole  148  that extends through elongate body  142  of mounting rod  110  aligns with holes (not shown) for receiving shaft  174 . Shaft  174  is received within hole  148  of elongate body  142  to effectively cross-pin mounting rod  110  to pivot  110 . Hole  148  receives shaft  174  with a slip fit such that mounting rod  110  may pivot about shaft  174  as will be understood by one skilled in the art. 
     Spur gears  106  may be coupled to motors  136  by mounting each of the gears  106 - 1 ,  106 - 2  on a shaft (not shown) of a respective motor  136 - 1 ,  136 - 2  or by a transmission (not shown) as will be understood by one skilled in the art. An adapter plate  196  may be used to mount the gears  106  and motors  136  to support structure  114 . Adapter plate  196  may include a pair of holes  198  for receiving screws or bolts (not shown) for securing adapter plate  196 , spur gears  106 , and motors  136  to support structure  114 . Spherical gear  102  is coupled to gear mounting end  144  of mounting rod  110  by aligning holes  132  on mounting side  124  with holes  154  of gear mounting end  144 . Screws and/or bolts (not shown) may be used in connection with nuts (not shown) to secure spherical gear  102  to gear mounting end  144  of mounting rod  110 . In some embodiments, holes  132  may be threaded such that the threads of the screws engage the threads of holes  132  for securing spherical gear  102  to mounting rod  110 . In still other embodiments, gear mounting end  144  may include detents for engaging holes  132  of spherical gear  102 , or spherical gear  102  and mounting rod  110  may be monolithic. One skilled in the art will understand that spherical gear  102  may be coupled to mounting rod  110  using other coupling methods including, but not limited to, using adhesives, cross-pinning soldering, and combinations thereof. 
     In operation, teeth  104  of spherical gear  102  mesh with teeth  108  of the two tangent spur gears  106  each of which is mounted in the XY plane orthogonal to one another in order to create a two-degree of freedom joint for the purpose of power transmission. Spur gears  106  are positioned such that when only spur gear  106 - 1  is actuated, for example, teeth  108  of spur gear  106 - 2  are disposed within channels  140  of spherical gear  102  and do not turn. Conversely, when only spur gear  106 - 2  is actuated, teeth  108  of spur gear  106 - 1  are disposed within channels  140  of spherical gear  102  such that teeth  104  of spherical gear  102  do not engage teeth  108  of spur gear  106 - 1  and spur gear  106 - 1  does not turn. When both spur gears  106  are actuated, teeth  104  of spherical gear  102  engages teeth  108  of both spur gears  106 . Different combinations of outputs from each spur gear  106 - 1 ,  106 - 2  provides different angles of output resulting in an output vector that is a product of the motion of each spur gear  106 - 1 ,  106 - 2 . A specific vector may be created in a plane that is parallel to the central position of spherical gear  106  depending on the rotational speed of each spur gear  106 - 1 ,  106 - 2  with respect to time when outputting to spherical gear  102 . 
     The same is true of the opposite motion when a force is applied by spherical gear  102  resulting in motion of one or both spur gears  106 . For example, motors  136  may act as generators to generate electricity in response to movement by spherical gear  102 . This type of application could be used for generating electricity from various kinds of motion such as wind or constantly shifting ocean currents. 
     In another embodiment, surface  130  of spherical gear  102  may be smooth and spur gears  106  are replaced with a pair of omni-directional wheels (“omni-wheels”), which include a plurality of wheels mated to a surface at different angles. The omni-wheels are frictionally mated to the surface  130  of spherical gear  102  and may be actuated by an attached motor. Alternatively, the motion of the spherical gear about pivot  112  may be translated to one or more wheels of the omni-wheels as will be understood by one skilled in the art. 
     The system may be used as part of a robotic joint, such as a shoulder or an arm. For example,  FIG. 8  illustrates one example of a robotic arm  200  including a plurality of gear assemblies  100 - 1 ,  100 - 2 , and  100 - 3  (collectively referred to as “gear assemblies  100 ”). Although three gear assemblies  100  are illustrated, one skilled in the art will understand that fewer or more gear assemblies may be coupled together. As shown in  FIG. 8 , adjacent gear assemblies, e.g., assemblies  100 - 1  and  100 - 2  and assemblies  100 - 2  and  100 - 3 , may be coupled together by a coupling plate  202 , which may include a plurality of holes (not shown). 
     A first set of holes defined by coupling plate  202  are sized and arranged to align with holes  158  of second mounting end  158  of mounting rod  110  when coupling plate  202  is received within slot  162  defined by projections  160 . A second plurality of holes are defined by a second end of coupling plate  202  and are sized and arranged to align with mounting holes  194  of the assembly mounting section  186  of support structure  114 . Screws may be used to couple together gear assemblies  100  to coupling plate  202 . 
       FIG. 9  illustrates manner in which gear assemblies  100  may be coupled together. As illustrated in  FIG. 9 , gear assemblies  100  are coupled to each other by assembly mounting sections  186  disposed on the mounting side  180 . Screws or bolts may be used in connection with mounting holes  190  to mate gear assembly  100 - 1  and gear assembly  100 - 2 . 
     The disclosed gear assembly  100  is able to generate larger amounts of torque with lower friction compared to conventional systems as the spur gears are able to pass through channels defined by the teeth of the spherical gear when the spherical gear moves in one of two directions. Additionally, the gear assembly may advantageously be coupled together to provide robotic arms having a full range of motion. 
     Although the invention has been described in terms of exemplary embodiments, it is not limited thereto. Rather, the appended claims should be construed broadly, to include other variants and embodiments of the invention, which may be made by those skilled in the art without departing from the scope and range of equivalents of the invention.