Abstract:
A system, methods and apparatus for rapidly and automatically orienting spherical objects, such as game balls, for subsequent downstream processing comprises a series of processing steps that can be performed at four separate, mechanically similar (or even identical) workstations. An imaging sub-system needs only one camera to image the spherical object and image the work process. The method of transposing the spherical object between work stations is simple, requiring an apparatus having only one degree of freedom to simultaneously convey and rotate spherical objects, and the system and method can automatically and rapidly determine the object&#39;s spatial orientation and change the orientation as required for downstream processing.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This nonprovisional patent application is based upon and claims priority from U.S. provisional patent application Ser. No. 60/401,603, filed 07 Aug. 2002, entitled METHOD AND APPARATUS FOR AUTOMATICALLY ORIENTING A SPHERICAL OBJECT, and U.S. provisional patent application Ser. No. 60/402,157, filed 09 Aug. 2002, entitled METHOD AND APPARATUS FOR AUTOMATICALLY ORIENTING A SPHERICAL OBJECT. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   This invention relates to a system and method for automatically orienting a spherical object, particularly a game ball, based on an existing “reference” pattern or indicium on the surface of the spherical object so that additional processing, e.g., printing, inspecting, etc. can take place on the spherical object at a target point that has a predetermined positional relationship with respect to the existing reference pattern or indicium. 
   2. Description of Prior Art 
   A growing segment of the golf ball industry is the manufacturing of balls customized with corporate logos, country club emblems, personal names, etc. These balls are usually produced by taking a finished golf ball and adding the custom printing at a predetermined location relative to the existing trade name or indicium printed on the ball. This is most commonly done by manually orienting the ball and placing it into a printing machine. Some of the problems with this method are: 1) it is labor intensive and therefore expensive, 2) it requires a significant training period for a person to become proficient at it, 3) a person is subject to fatigue and must take frequent breaks, 4) the process requires a great deal of repetitive motion, which can be source of injury, and 5) the accuracy is not as good as the system described herein. 
   U.S. Pat. No. 5,632,205 to Gordon (1997) describes a method of automatically orienting a game ball. This method uses a single station to perform the entire orientation on a single ball at a time. Two conical wheels are used to support the ball and rotate it around two orthogonal axes depending on whether the wheels are rotated in the same or opposite directions. The third axis of rotation is achieved by making two moves using the first two axes. The limitations of this method are: 1) operating rates are low, due to the fact that it performs the orientation on only one ball at a time, 2) the amount of time it takes to orient the ball can vary significantly depending on the initial orientation of the ball, making it difficult to synchronize the ball-orienting apparatus with the printing apparatus, which is usually designed to run at a fixed cycle rate, and 3) the area sensor camera photographs only a limited area of the surface of the ball at one time, therefore more images need to be acquired and, hence more time to process such images. 
   U.S. Pat. No. 5,611,723 to Mitoma (1997) describes another method of automatically orienting a golf ball in two dimensions for the purpose of removing molding burrs and flash from the equator of the ball. The Mitoma method describes a sequential arrangement that allows a different ball to be at each station of the orientation process simultaneously. The limitations of this system are that it requires six stations and three cameras to orient the ball in only two dimensions. The individual stations are mechanically and spatially complex because their orthogonal arrangement requires such stations to be considerably different from one another. Additionally, the conveyance arm that transports the balls from one station to the next adjacent station requires two degrees of freedom, one to lift and place the balls and another to transport them, therefore operating rates are low. 
   BRIEF SUMMARY OF THE INVENTION 
   The apparatus and method according to the present invention, as described herein, is an automatic orientation system and process comprising a series of processing steps that can be performed at four separate, mechanically similar, “work” stations, with spherical objects being simultaneously subjected to different processing operations at each of the individual work stations. The system having such a working configuration facilitates the process that allows higher operating rates to be achieved and for spherical objects having a predetermined required orientation (for additional downstream processing) to be produced at repeatable time intervals. The system and process according to the present invention utilizes an imaging system having only one camera as a necessary element for managing the work-flow process. The method of transposing the spherical objects between work stations is simple, requiring an apparatus that requires only one degree of freedom to simultaneously convey and rotate spherical objects. 
   There are two main objectives of this invention. The first is to provide a system and method that can automatically determine the spatial orientation of a spherical object, such as a game ball, by locating and identifying the position and two-dimensional orientation of an existing reference indicium such as a trade name, e.g., TOP-FLITE or TITLEIST brands for golf balls, or a graphical image or a pattern, such as a dimple pattern on a golf ball, etc., on the spherical object. The second objective of the system and method of the present invention is to manipulate the spatial orientation of the spherical object in the context of the defined position and two-dimensional orientation of the reference indicium so that an additional processing operation, e.g., printing, inspecting, etc., can take place at a predetermined location, i.e., the “target point”, on the spherical object, i.e., the target point has a predetermined positional relationship with respect to the predetermined final position and two-dimensional orientation of the reference indicium. 
   One preferred method according to the present invention for orientating a spherical object, as described herein, utilizes a system having four work stations. Two “locating” work stations, each with an axis of rotation that passes through the center of the spherical object, are used to gather data by means of an imaging system such as a line sensor camera to accurately determine, i.e., “define”, the position and two-dimensional orientation of the reference indicium on the spherical object and, hence the current spatial orientation of the spherical object in terms of the defined reference indicium. Additionally, the described method uses three “orienting” work stations, each with an axis of rotation that passes through the center of the spherical object, to manipulate the spherical object in the context of the defined position and two-dimensional spatial orientation of the reference indicium (as determined by the procedures implemented at the “locating” work stations) to move the reference indicium to the final predetermined position and two-dimensional orientation so that the “target” point on the surface of the spherical object, where an additional processing operation is to be performed, e.g., printing, inspecting, or some other type of operation, is presented in the required location and orientation or perspective for such additional processing. For the described embodiment, the second “locating” work station of the system that is used in determining or defining the position and two-dimensional orientation of the reference indicium on the spherical object also functions as the first “orienting” station used for manipulating the spatial orientation of the spherical object, resulting in the system having total of four work stations for automatically orienting a spherical object according to the present invention. 
   OBJECTS AND ADVANTAGES 
   Accordingly, the objects and advantages of the present invention are:
         a) To orient a spherical object, in the context of the defined position and two-dimensional orientation of an existing reference indicium on the spherical object, at a high operating rate;   b) To orient a spherical object, in the context of the defined position and two-dimensional orientation of an existing reference indicium on the spherical object, at a substantially repeatable time interval;   c) To orient a spherical object, in the context of the defined position and two-dimensional orientation of an existing reference indicium on the spherical object, by performing a minimal number of processing steps over a series of work stations using as few as one imaging device;   d) To transport a spherical object from one work station to a next adjacent work station while simultaneously rotating the spherical object using a mechanism having only one degree of freedom.       

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A more complete understanding of the present invention and the attendant features and advantages thereof may be had by reference to the following detailed description of the invention when considered in conjunction with the accompanying drawings wherein: 
       FIG. 1  is an isometric view of the “orienting” steps performed to orient a spherical object with respect to a reference indicium having a defined location and two-dimensional orientation using three work stations according to the present invention. 
       FIG. 1   a  is a flow chart of the “orienting” steps of  FIG. 1 . 
       FIG. 2  is an isometric view of the “locating” steps performed on a spherical object to accurately determine or define the position and two-dimensional orientation of an existing reference indicium on the object&#39;s surface. 
       FIG. 2   a  is a flow chart of the “locating” steps of  FIG. 2 . 
       FIG. 3  is a pictorial representation of the resulting image of a spherical object produced by an imaging system such as a line sensor camera at a first locating work station ST 1 . 
       FIG. 4  is a pictorial representation of the resulting image of the spherical object produced by an imaging system such as a line sensor camera at the second locating work station ST 2  after being partially oriented at the work station ST 1  of  FIG. 3 . 
       FIG. 5   a  is an isometric view of an imaging system comprising a single camera and system of mirrors that enables the camera to simultaneously image a spherical object at the first and second locating work stations ST 1 , ST 2 . 
       FIG. 5   b  is a camera&#39;s eye view of the resultant image of the spherical object produced by the imaging system of  FIG. 5   a.    
       FIG. 6  is the image produced by the imaging system of  FIG. 5   a  to simultaneously image a spherical object at station ST 1  and station ST 2 . 
       FIG. 7  is the front view of a preferred embodiment of an apparatus utilized in the system according to the present invention for orienting spherical objects, in the context of the defined position and two-dimensional orientation of an existing reference indicium on the surface of such objects. 
       FIG. 8  is a side view showing a single work station and the orientation of the camera of an imaging system in reference to this work station. 
       FIG. 9   a  is a front view of a preferred embodiment of the transposing apparatus utilized in the system according to the present invention. 
       FIG. 9   b  is a side view of the transposing apparatus of  FIG. 9   a.    
       FIG. 10  is a block diagram of the calculating unit used for the present invention. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The system and method according to the present invention for automatically orienting a spherical object utilizes Euler&#39;s rotation theorem that states that any object can be moved from any initial orientation to any desired orientation by rotating it through three angles. These angles are known as the Euler angles .phi., .theta., and .psi. The first angle .phi. is the angle of rotation about a first axis. The second angle .theta. is the angle of rotation about a second axis, wherein the second axis is perpendicular to the first axis. The third angle .psi. is the angle of rotation about a third axis, wherein the third axis is perpendicular to the second axis. 
   Referring now to the drawings wherein like reference characters identify corresponding or similar elements throughout the several views,  FIGS. 1 ,  1   a  depict the processing steps required to orient a spherical object such as a golf ball, in the context of the position and two-dimensional orientation of an existing “reference” indicium on the object&#39;s surface for the purpose of locating a target point (where the target point has a predetermined positional relationship with respect to the existing reference indicium) on the spherical object in a predetermined location and two-dimensional orientation for additional processing, e.g., printing, inspecting. The terminology “reference indicium” as used herein refers to any mark existing on the surface of the spherical object, such as manufacturer&#39;s trade name or logo, player number, and ball type, or a pattern on the surface of the spherical object, such as a dimple pattern on a golf ball. The term two-dimensional orientation refers to the “attitude” of the reference indicium on the surface of the spherical object such that a “word(s)” reference indicium is readable from left to right or a “graphical” reference indicium is right-side up. The spherical object is oriented by rotating it through the three Euler angles, each at a separate “orienting” work station, ST 2 , ST 3 , and ST 4 , respectively, wherein each orienting work station has a single axis of rotation, Z 2 , Z 3 , and Z 4 , respectively, that are parallel and coplanar with one another. The steps described in the following paragraphs assume that the position and two-dimensional orientation of the existing reference indicium has been defined or determined (as discussed in further detail below) and that the predetermined positional relationship of the target point with respect to the defined position and two-dimensional orientation of the reference indicium is known so that orienting the reference indicium to a predetermined final position and two-dimensional orientation concomitantly positions the target point for additional processing. 
   Referring now to the drawings wherein like reference numerals identify corresponding or similar elements throughout the several views, a spherical object O is depicted in  FIG. 1  wherein such spherical object O includes an existing reference indicium I at a defined position  11  at the first orienting work station ST 2 . The indicium I also has a defined two-dimensional orientation represented by the reference arrow I TDO  wherein the direction of the arrow indicates that a “word” indicium is readable from left to right and/or that a graphical indicium is properly positioned for viewing, e.g., right-side up. The method  200  or steps required to orient the spherical object O include a first step  202  wherein the spherical object O is rotated through a predetermined angle .phi about the rotational axis Z 2  at the first orienting work station ST 2 . The resultant location of the reference indicium I as a result of such rotation is identified as a first reference position  12  lying on a circle C. The circle C is defined by the intersection of the surface of the spherical object O with a plane that contains the axis of rotation Z 2  and is perpendicular to the X axis of the reference coordinate system. 
   In a second step  204 , the spherical object O is conveyed (by the apparatus described in further detail below) from the first orienting work station ST 2  to the next adjacent or second orienting work station ST 3  in a manner such that the spherical object O is rotated 90 degrees about an axis passing through the center of the spherical object O coincident with the Y axis of the reference coordinate system (see reference character Y 2  in  FIG. 1 ) such that the circle C is rotated 90 degrees. As a result the circle C coincides with the equator of the spherical object O at the second orienting work station ST 3  and the reference indicium I is now located at a second reference position  14  on the circle C of the spherical object O at the second orienting work station ST 3  and has the two-dimensional orientation indicated by the arrow I TDO . The spherical object O is then rotated, in a third step  206 , through a predetermined angle .theta at the second orienting work station ST 3  to temporarily position the reference indicium I at the intersection of the circle C and the plane passing through the rotational axis Z 3  perpendicular to the X-axis, and is then rotated further through an additional 90 degrees about the axis Z 3  at the second orienting work station ST 3 . The additional 90 degrees of rotation is required to locate the reference indicium I at a third reference position  16  at the intersection of the circle C and the X reference axis at the second orienting work station ST 3 . 
   In a fourth step  208  the spherical object O is then moved or conveyed to the last or third orienting work station ST 4  in such a manner that the spherical object O is rotated 90 degrees about an axis coincident with the Y axis of the reference coordinate system (see reference character Y 3  in  FIG. 1 ) such that the circle C is rotated through 90 degrees. This results in the reference indicium I being moved to a final reference position  18  on the pole of the spherical object O that is coincident with the rotational axis Z 4  at the last orienting work station ST 4  wherein the reference indicium I has the two-dimensional orientation indicated by the arrow I TDO . The spherical object O is then rotated, in a fifth step  210 , through a predetermined angle .psi about the axis Z 4  to bring the two-dimensional orientation I TDO  of the reference indicium I into the desired final position, i.e., the final reference position  20 , wherein the two-dimensional orientation I TDO  of the reference indicium I is aligned with a plane coincident with the X-axis and perpendicular to the equator E of the spherical object O. 
   As an examination of  FIG. 1  indicates, the target point TP is now positioned at the equator E of the spherical object O, and is properly positioned for additional processing. In one preferred embodiment of the present invention, the spherical object O can be subjected to additional processing at this third orienting work station ST 4  due to the configuration of the transposing apparatus according to the present invention (as described in further detail below). In an alternative preferred embodiment, the spherical object O can be transferred to an additional processing work station (not shown). Transference of the spherical object O to the additional processing work station can be achieved in any number of ways. For example, the spherical object O can be conveyed to the additional processing work station in a manner such that the spherical object O retains the spatial orientation that it has at the third orienting work station ST 4  after completion of step  210 . Or, alternatively, for example, a transposing apparatus having the functional capabilities of the transposing apparatus according to the present invention can be used to convey the spherical object O to the additional processing work station. In this embodiment, it will be appreciated that the spherical object O will be subjected to 90 degrees rotation such that the target point TP will have a new spatial location at the additional processing work station (i.e., at the third orienting work station ST 4  illustrated in  FIG. 1  the target point TP is located on the equator E midway between the circle C and a plane perpendicular to the circle C and coincident with the X-axis whereas at the additional processing work station, the target point TP would be located on the surface of the spherical object O at the midpoint of a circle defined by a plane coincident with the Y-axis perpendicular to the X-Y plane (see X, Y 4  in  FIG. 1 ), i.e., the equator E depicted at the final orienting work station ST 4  would be rotated 90 degrees to the position occupied by the circle C as depicted at the third orienting work station ST 4  in  FIG. 1 . One skilled in the art will appreciate that other schemes for transferring the spherical object O from the final orienting work station ST 4  to the additional processing work station could be utilized in conjunction with the present invention. 
   The target point TP described in the preceding paragraphs was selected for the purpose of illustrating and describing the features of the present invention. In particular, this target point TP, which has a predetermined positional relationship with respect to the predetermined final position and two-dimensional orientation of the reference indicium I defined by a 90 degrees arc segment, was selected since it would be visible at the final orienting work station ST 4 , but not visible at the first and second orienting work stations ST 2 , ST 3 . One skilled in the art will appreciate that the invention of the present application will accommodate any predetermined positional relationship between an existing reference indicium and a selected target point, where the selection of the target point is a business consideration outside the scope of the present invention. 
   The Euler angles required to orient the spherical object O, in the context of the predetermined final position and two-dimensional orientation of the existing reference indicium I, are calculated by accurately measuring the position and two-dimensional orientation of the existing reference indicium I on the spherical object O to define or determine the actual position and two-dimensional orientation of the spherical object O at the first orienting work station ST 2  prior to implementing any of the orienting steps described above. This is accomplished by taking images, e.g., two photographs, which together encompass the entire surface area of the spherical object O and using conventional image processing techniques to accurately determine or define the position and two-dimensional orientation of the existing reference indicium I on the spherical object O. The term “image” as used herein refers to using an imaging system such as a line sensor camera and image acquisition device to gather a plurality of line data from the line sensor camera while the spherical object O is rotated at least one revolution about an axis that passes through the center of the spherical object O and is perpendicular to the image axis of the line sensor camera (see, e.g., reference numeral  28  in  FIG. 2  which identifies a line sensor camera and reference character  28   IA  which identifies the image axis of the line sensor camera  28  in  FIG. 2 ). It will be understood by those skilled in the art that other types of imaging systems can be used in the practice of the present invention such as area scan cameras, and other imaging systems of like capability. 
   The plurality of line data is then assembled by an image acquisition device into a two dimensional image representing the surface of the spherical object O from nominally 50 degrees below to nominally 50 degrees above the equator of the spherical object O. This two-dimensional image embodies two image axes (see reference characters  28   IA  and  30   IA  in  FIG. 2 ) that are perpendicular with respect to the frame of reference of the spherical object O (see, e.g., reference axes X, Y 1 , Z 1  and X, Y 2 , Z 2 , respectively, in  FIG. 2 ). 
   In one embodiment, the spherical object is a golf ball and the target point is selected to have a predetermined positional relationship, i.e., a predetermined location, relative to an existing reference indicium imprinted on the golf ball, e.g., manufacturer&#39;s trade name or logo. In order to accurately determine/define the position (and two-dimensional orientation) of the reference indicium, and hence the predetermined location (and two-dimensional orientation) of the target point, the existing reference indicium is first moved so that it is near the equator of the spherical object when photographed by the line sensor camera. The purpose of this move is to prevent the reference indicium from being truncated by the edge of the second image made by the line sensor camera. Moving the reference indicium near the equator of the spherical object has the additional advantage of reducing distortion due to the curvature of the spherical object, hence increasing the accuracy of the definition/determination of the position and two-dimensional orientation of the reference indicium on the surface of a spherical object such as a golf ball. 
   Referring to  FIG. 2 , an image is made at each of two adjacent “locating” work stations ST 1 , ST 2 . The first locating workstation ST 1  serves the purpose of imaging the surface of the spherical object and then positioning the spherical object O based on information extracted from the first image so that the existing reference indicium I will be near the equator when the second image is acquired at the second locating work station ST 2 . The first image extracted at the first locating work station ST 1  serves to identify the coarse position of the reference indicium I by locating the reference indicium I in the image and correlating it with stored reference data representing the spherical object O with its reference indicium I using conventional software known to those skilled in the art, e.g., pattern-matching software. 
     FIGS. 2 ,  2   a  depict the method  300  or steps required to take a randomly oriented spherical object O having an existing reference indicium I on the surface thereof at the first locating workstation ST 1  and move the spherical object O so that the reference indicium I is located near the equator thereof when the spherical object O is conveyed to the second locating work station ST 2  wherein the position and two-dimensional orientation of the indicium can be more accurately defined/determined. In a first step  302 , the spherical object O is rotated approximately one revolution about axis Z 1  at the first locating work station ST 1  while an imaging system, i.e., the first line sensor camera  28  depicted in  FIG. 2 , images the surface of the spherical object O.  FIG. 3  shows an illustrative example of the ST 1  image  32  provided by the first line sensor camera  28  shown in  FIG. 2 . Next, in a step  304  a first or coarse position  22  of the reference indicium  32  (and its two-dimensional orientation) is identified in the ST 1  image  32  using one of the conventional image processing techniques known to those skilled in the art, e.g., pattern matching, blob analysis (using the stored reference data representing the graphical configuration of the spherical object O and its reference indicium I). The first or coarse position  22  of the reference indicium I (and the corresponding two-dimensional orientation thereof as indicated by I TDO ) is exemplarily depicted in  FIGS. 2 ,  3 . An examination of  FIG. 3  shows that the image of the reference indicium I is partially truncated by the edge  32 E of the ST 1  image  32 . Simultaneously in step  304  the conventional image processing techniques are used to determine a predetermined angle of rotation necessary to move the coarse position  22  to coincide with a circle D on the spherical object defined by the intersection of the Y-Z plane (see coordinate axes Y 1 , Z 1  in  FIG. 2 ), which includes the axis of rotation Z 1  and is perpendicular to the X reference axis, with the surface of the spherical object O. 
   Once the coarse position  22  of the reference indicium I and the predetermined angle of rotation have been identified in step  304 , the spherical object O is rotated about the axis Z 1  at the first locating work station ST 1  in a step  306  to move the reference indicium I from the coarse position  22  to a second position  24  on the circle D as illustrated in  FIG. 2 . 
   Next, in a step  308  the spherical object O is conveyed to the next adjacent or second locating work station ST 2  in a manner that causes the spherical object O to be rotated 90 degrees about an axis passing through the center of the spherical object O that is coincident with the Y axis of the reference coordinate system (see reference character Y 1  in  FIG. 2 ). The step  308  rotation moves the circle D, which at the first locating work station ST 1  defined a plane perpendicular to the X-axis, so that it coincides with the equator of the spherical object O at the second locating work station ST 2 , i.e., in the X-Y plane (see coordinate axis Y 2  in  FIG. 2 ). This results in the reference indicium I moving from the second position  24  on the spherical object O at the first locating work station ST 1  to a third reference position  26  near the circle D or equator of the spherical object O at the second locating work station ST 2  as a result of step  108 . The third reference position  26  of  FIG. 2  corresponds to the defined position  11  and two dimensional orientation of the spherical object O at the first orienting work station ST 2  depicted in  FIG. 1 . 
   Then, in step  310 , the spherical object O is imaged at the second locating work station ST 2  using the imaging system, i.e., the second line sensor camera  30  depicted in  FIG. 2  (which has an image axis  30   IA ), while the spherical object O is rotated at least one revolution about the axis Z 2 . The image resulting from step  310 , the ST 2  image  33 , is depicted in  FIG. 4 . The three Euler angles .phi, .theta, and .psi are derived from information in the ST 2  image  33  in step  312  using any conventional technique know to those skilled in the art, e.g., blob analysis, or pattern matching. The first Euler angle .phi is directly related to the X value of the ST 2  image  33 . The second Euler angle .theta is directly related to the Y distance from the equator of the spherical object O of the ST 2  image  33 . The third Euler angle .psi is directly related to the two-dimensional orientation of the reference indicium I (see reference character I TDO  in  FIG. 4 ) which is the angle of the reference indicium I with respect to the X axis of the ST 2  image  33 . 
   While the method  300  or steps described in the preceding paragraphs involve the manipulation and imaging of the spherical object O for the purposes of: (i) identifying the defined position  26  and two dimensional orientation of a reference indicium I on the spherical object O; and (ii) determining three predetermined angles (the Euler angles .phi, .theta+90°, and .psi) required to automatically orient the spherical object using the three “orienting” work stations ST 2 , ST 3 , ST 4 , and steps described above with respect to  FIG. 1 , to enable movement of the reference indicium I to the predetermined final position  20  and two-dimensional orientation so that a target point is prepositioned for further processing, one skilled in the art will appreciate that the method  300  or steps and work stations ST 1 , ST 2  described above can be adapted for other purposes. 
   For example, steps  302 ,  308 , and  310  as described above can be implemented using the work stations ST 1 , ST 2  to generate, using an embodiment of an imaging system described herein, two distinct perspective images (see, e.g., reference numerals  51 ,  52 , in  FIG. 6 ) of the surface of the spherical object O. These individual perspective images  51 ,  52  can be juxtaposed to form a composite image as depicted in  FIG. 6 , which can be converted to a “virtual image” (electronic image) of the surface of the spherical object. This virtual image can then be subjected to further processing, e.g., inspection, by automatically comparing such virtual image to stored reference data representing the standard graphical configuration of the surface of the spherical object O using conventional processing software and techniques such as pattern matching, blob analysis, to identify any discrepancies between the virtual image and the standard graphical configuration of the surface of the spherical object. Such a virtual inspection technique, for example, can be used to ensure that existing reference indicia that are typically found on a golf ball, e.g., manufacturer&#39;s brand name I M , ball type I BT , and player number I PN , have been properly applied to golf balls on a processing line. 
   In one embodiment an image processing technique is implemented as conventional software instructions by a processing unit (see reference numeral  100  in  FIG. 10 ) to manipulate the ST  1 . ST 2  images  32 ,  33 , respectively, to determine the Euler angles as follows: In a first step, the scanned line data representing the original ST 1 , ST 2  images  32 ,  33 , respectively, are converted to binary images (binary images consist of pixels having two intensity values, black or white). If necessary, the processing unit is further operative to invert these binary images by changing the white surface of a spherical object such as a golf ball to black pixels and the black representing the reference indicium to white pixels. Next, the processing unit is operative to fill in the black pixels surrounding the white pixels to eliminate any black spots within the reference indicium and to ensure that the constituent elements comprising a particular reference indicium are all connected. The processing unit is further operative to locate each white subpart in the binary image and compute its centroid, area, and axes of gyration. 
   Then, the processing unit correlates area and relative position information from these binary images with stored reference data representing the graphical image of the spherical object and its reference indicium to identify the particular reference indicium currently being used as the reference standard for orientating the spherical object. The processing unit is then operative to fit the binary images of the imaged reference indicium with a previously stored binary image of the reference indium on the spherical object and computes the three Euler angles from relative positions and two-dimensional orientations of the imaged reference indium and the stored binary image of the reference indicium. The first Euler angle .phi is a function of the X position differential between the imaged and stored reference indiciums, the second Euler angle .theta is a function of the Y position differential between the imaged and stored reference indiciums, and the third Euler angle .psi. is a function of the angular differential of the major radii of gyration of the imaged and stored reference indiciums. It will be understood by those skilled in the art that other types of image processing techniques are also possible, including e.g., pattern matching and others. 
   In another preferred embodiment of the present invention, an imaging system includes a plurality of mirrors, thereby allowing a single line sensor camera to be used to image one spherical object at the first locating workstation ST 1  while simultaneously imaging another spherical object at the second locating work station ST 2 , thereby reducing the system cost and complexity by eliminating one of the two line cameras illustrated in the  FIG. 2  embodiment of the system according to the present invention.  FIG. 5   a  depicts this preferred embodiment of such an imaging system which comprises a single line sensor camera  34  and four mirrors  36 ,  38 ,  40 ,  42 . A first set of mirrors  36 ,  38  is aligned to capture the ST 1  image of the spherical object  44  at the first locating work station ST 1 . More specifically, the secondary mirror  36  reflects the field of view of the line sensor camera  34  towards the primary mirror  38 . The primary mirror  38  reflects the field of view of the line sensor camera  34  towards the spherical object  44  at the first locating work station ST 1 . 
   In a similar manner a second set of mirrors  40 ,  42  is aligned to capture the ST 2  image of a spherical object  46  at the second station ST 2 . More specifically, the secondary mirror  40  reflects the field of view of the line sensor camera  34  towards the primary mirror  42 . The primary mirror  42  reflects the field of view of the line sensor camera  34  towards the spherical object  46  at the second locating workstation ST 2 . 
   The result is a camera view as shown in  FIG. 5   b  consisting of an apparent image  48  of the spherical object  44  at the first locating work station ST 1  positioned above an apparent image  49  of the spherical object  46  at the second locating work station ST 2 . The axis of rotation  50  of the apparent image  48  of the spherical object  44  at the first locating work station ST 1  is positioned along the same line as, i.e., coincident with, the axis of rotation of the apparent image  49  of the spherical object  46  at the second locating work station ST 2 . The merged axes of rotation of the two apparent images  48 ,  49  is then focused onto the line sensor camera  34  allowing both spherical objects  44 ,  46  to be imaged, i.e., line scanned, simultaneously. The resultant line sensor image is depicted in  FIG. 6  and contains the image  51  of the spherical object at the first locating work station ST 1  and the image  52  of the spherical object at the second locating work station ST 2 . Since the exemplary images  51 ,  52  depicted in  FIG. 6  were derived from a golf ball as the spherical object, also depicted in  FIG. 6  are various types of existing reference indicia that are typically found on a spherical object such as a golf ball, to wit the manufacturer&#39;s brand name I M , the ball type I BT , and the player number I PN , any one of which can be selected to function as the reference indicium for orienting the golf ball utilizing the system and method of the present invention. 
   A front view of one preferred embodiment of an apparatus  53  of the system for automatically orienting spherical objects according to the present invention is illustrated in  FIG. 7 . The apparatus  53  comprises one pickup work station ST 0  and four processing work stations ST 1 , ST 2 , ST 3 , and ST 4 , as described above, with all five work stations ST 0 , ST 1 , ST 2 , ST 3 , ST 4 , being disposed in a linear arrangement with equal spacing between adjacent work stations as illustrated in  FIG. 7 . A series of four transposing mechanisms  76 ,  78 ,  80 ,  82 , one located between the pickup work station ST 0  and the first processing work station ST 1  and one between the first and second, second and third, and third and fourth processing work stations ST 1 -ST 2 , ST 2 -ST- 3 , ST 3 -ST 4 , respectively, serve two purposes, i.e., implement two separate and distinct functions. 
   The first purpose or function implemented by the transposing mechanisms  76 ,  78 ,  80 ,  82  is to provide the means to physically convey or transport a spherical object from one work station to the next adjacent work station. The second purpose or function of the transposing mechanisms  76 ,  78 ,  80 ,  82  is to position the spherical object being moved so that the axis of rotation of the spherical object at the new work station is perpendicular to the axis of rotation at the previous work station. The five work stations ST 0 , ST 1 , ST 2 , ST 3 , ST 4  and four transposing mechanisms  76 ,  78 ,  80 ,  82  are all mounted to a support plate  54 . A spherical object starts in a random orientation at the pickup work station ST 0  and is conveyed serially and sequentially through the individual processing work stations ST 1 , ST 2 , ST 3 , ST 4 , to end up with the reference indicium in the predetermined final position and two-dimensional orientation at the last processing work station ST 4  (see reference numeral  20  in  FIG. 1 ) such that the target point is definitively located for additional processing. For this described embodiment, the first two processing work stations ST 1 , ST 2  automatically perform the “locating” function with respect to an existing reference indicium on the spherical object, i.e., define the position and two-dimensional orientation of the reference indicium. The last three processing work stations ST 2 , ST 3 , ST 4  automatically perform the “orientating” function described above with respect to the reference indicium, i.e., sequentially transpose the position and two-dimensional orientation of the “identified” reference indicium by rotating the spherical object O sequentially through a plurality of predetermined angles (the Euler angles .phi, .theta, and .psi as determined and described above) so that the target point is definitively positioned for additional processing. 
   The pickup work station ST 0  is a station to which a randomly-oriented spherical object is supplied from a previous process, e.g., the manufacturing process, the pickup work station ST 0  having a cup  60  on which the spherical object O is placed as shown in  FIG. 7 . In the following discussion, the spherical objects are all identified by the reference character “O” since the spherical objects are fungible (except for the location and two-dimensional orientation of the reference indicium on the individual spherical objects). 
   The first, second, third, and fourth processing work stations ST 1 , ST 2 , ST 3 , ST 4  are mechanically similar and serve the purpose, inter alia, of rotating the spherical object O through a predetermined angle about a vertical axis that passes through the center of the spherical object O at each work station.  FIG. 7  shows the first processing work station ST 1  having a bottom cup  62  on which the spherical object O is placed and a means for rotating the bottom cup  62  that comprises a stepper motor  64  connected to the bottom cup  62  by a coupling  63 . The bottom cup  62  covers an area of the spherical object O that extends to nominally 30 degrees, but no more than 40 degrees, from the bottom pole of spherical object O. The bottom cup  62  has a surface made from nominally low durometer rubber or polyurethane for the purpose of preventing relative movement of the spherical object O with respect to the bottom cup  62  as the bottom cup  62  is rotated. 
   An opposing upper cup  66  is mounted to a shaft  68 , the combination thereof which is operative to move up and down, i.e., away from and towards the spherical object O disposed in the bottom cup  62 . The axis of the shaft  68  passes through the center of the upper cup  66  and the center of the spherical object O. The shaft  68  is concentric with the axis of rotation of the spherical object O and is connected to an actuator  70  that moves the upper cup  66  up and down for the purpose of exerting a force on the spherical object O to hold it securely against the opposing bottom cup  62 . 
   In the preferred embodiment an air cylinder is used as the actuator  70 . Another embodiment would be to use a stepper motor or servomotor as the means for actuating the shaft  68 . Still another embodiment would be to eliminate the upper cup altogether and utilize a vacuum in the bottom cup  62  to hold the spherical object O in place. The upper cup  66  is mechanically coupled to the shaft  68  in such as manner as to freely rotate about the same axis as the spherical object O. When the upper cup  66  is in contact with the surface of the spherical object O the upper cup  66  covers an area of the spherical object O that extends to nominally 30 degrees, but less than 40 degrees, from the upper pole of the spherical object O. Once processing of the spherical object O at the first processing work station TS 1  is complete (see description above), the actuator  70  is operative to retract the upper cup  66  upward, i.e., out of physical contact with the spherical object O, so that the spherical object O can be conveyed to the to the second processing work station ST 2  by operation of the second transposing mechanism  78 . The second, third, and fourth processing stations ST 2 , ST 3 , ST 4  include functional elements corresponding to those described above in connection with the first processing work station ST 1  (see  FIG. 7 ). 
     FIG. 8  depicts the line sensor camera  34  described above used for the purpose of simultaneously imaging spherical objects O at the first processing work station ST 1  and the second processing work station ST 2  while the spherical objects are rotated approximately one complete revolution. The camera  34  is positioned at the same height as the center of the spherical objects O with a line of sight or image axis that is perpendicular to the linear arrangement of the four processing work stations ST 1 , ST 2 , ST 3 , ST 4 . The line sensor camera  34  is parallel to the axis of rotation of the spherical object O at the first processing work station ST 1  and the axis of rotation of the spherical object O at the second processing work station ST 2 . A plurality of lights  74 ,  74   a  can be positioned between the camera  34  and the spherical objects O to illuminate the surfaces of the spherical objects O to facilitate line imaging thereof by the line sensor camera  34 . The lights  74 ,  74   a  are positioned at an angle sufficient to prevent specular glare off the spherical objects O along the band on the surface of the spherical objects O that is imaged by the line sensor camera  34 . 
     FIG. 9   a  depicts in further detail the four transposing mechanisms  76 ,  78 ,  80 ,  82  described above that are operative for the purpose of transposing the spherical objects O from one work station to the immediately-adjacent processing work station while concomitantly causing the spherical objects O to be rotated through an angle of precisely 90 degrees. The transposing mechanisms  76 ,  78 ,  80 ,  82  are mounted to pivot points  84 ,  86 ,  88 ,  90 , respectively, and all four transposing mechanisms  76 ,  78 ,  80 ,  82  are linked together by a beam  92  to a stepper motor  94  that pivots the transposing mechanisms  76 ,  78 ,  80 ,  82  about the pivot points  84 ,  86 ,  88 ,  90 , respectively. The transposing mechanisms  76 ,  78 ,  80 ,  82  are disposed intermediate adjacent work stations (see  FIG. 7  wherein the transposing mechanism  76  is disposed intermediate the pickup work station ST 0  and the first processing work station ST 1 , the transposing mechanism  78  is disposed intermediate the first processing work station ST 1  and the second processing work station ST 2 , the transposing mechanism  80  is disposed intermediate the second processing work station ST 2  and the third processing work station ST 3 , and the transposing mechanism  82  is disposed intermediate the third processing work station ST 3  and the fourth or final processing work station ST 4 ) and pivot about the axes  84 ,  86 ,  88 ,  90 , respectively, which are perpendicular to the plane containing the four axes of rotation of the spherical objects O. The axes  84 ,  86 ,  88 ,  90  are equidistant from adjacent work stations and positioned so that the spherical object O will come to rest in the lower cup of two adjacent workstations when the associated transposing mechanism is at each end of its 90 degree pivotal arc. 
     FIG. 9   b  depicts a side view of a single transposing mechanism  76  made up of a mechanical gripper  76   G  that is pneumatically operated and a pair of gripper pads  96 ,  96   a  made from low durometer polyurethane or rubber to prevent the spherical object O from moving relative to the gripper  76   G  when the spherical object O is conveyed through the fixed arc of 90 degrees. The centerline of the gripper  76   G  moves in the same plane as that of the rotational axes of the adjacent stations (see, e.g., axes Z 2  and Z 3  in  FIG. 1 ). 
     FIG. 10  is a block diagram showing the calculating unit  130  for the present invention. An image acquisition or “frame-grabbing” unit  98 , which is operative for the purpose of acquiring the image from the line sensor camera  34 , is connected to a processing unit  100 . The processing unit  100  performs image processing and calculations to determine the Euler angles necessary to position the spherical object O at each processing work station ST 2 , ST 3 , ST 4  as discussed above. The processing unit  100  is also connected to a pulse generating unit  106  that is operative to generates pulses that activate the stepper motor drivers  114  to rotate the stepper motors  64 ,  112 ,  120 ,  126 , and concomitantly, the corresponding spherical objects O, through predetermined angles (for this described embodiment, the predetermined angles of rotation are controlled by the number of generated pulses). 
   Operation: The operation of the preferred embodiment described above will now be described. Initially, a randomly oriented spherical object O, with an existing reference indicium I, is supplied to the apparatus  53  at the pickup station ST 0 . The spherical object O is picked from the starting cup  60  at the first station ST 0  by the first transposing mechanism  76 . This transposing mechanism  76  grips the spherical object O and then pivots it through a fixed 90 degree arc resulting in the spherical object O being placed on the bottom cup  62  of the first processing, i.e., “locating”, work station ST 1 . The upper cup  66  is then operated to physically engage the spherical object O to hold it securely in the bottom cup  62 . The transposing mechanism  76  releases the spherical object O and then rotates back to a vertical position midway between the two adjacent work stations ST 0 , ST 1 . The bottom cup  62  and spherical object O are then rotated about an axis (see axis Z 1  in  FIG. 2 ) that passes through the center of the spherical object O by the motor means  64 . The line sensor camera means  34  (see  FIG. 4  or  8 —one skilled in the art will also appreciate that the dual line sensor configuration depicted in  FIG. 2  could also be used) images the spherical object O while it is rotated at least one complete revolution at the first locating work station ST 1 . The processing unit  100  then manipulates the scanned line image  32  to determine the position and two-dimensional orientation of the reference indicium I on the spherical object O (see reference numeral  22  in  FIG. 2 ). 
   In the preferred embodiment the existing manufacturer&#39;s trade name indicium (see, e.g.,  FIGS. 1 ,  2 ) is used as a reference mark to define the target point on the surface of the spherical object where additional processing is to occur, i.e., printing of a custom insignia. Because there are usually two trade names or indicia on the spherical object, their relationship to any additional manufacturer&#39;s indicia, for example the marking showing the ball type, is used to determine which trade name to use as the reference indicium. If the trade name is identified by the computer means then the spherical object O is rotated about its axis in order to place the centroid of said trade name on a circle defined by the intersection of the spherical object with the plane that includes the axis of rotation and is perpendicular to the X reference axis (see discussion above with respect to reference numeral  24  in  FIG. 2  and the first locating work station ST 1 ). 
   If the trade name is not detected then an attempt is made to extrapolate its position from the reference indicia that are visible. The extrapolated position of the trade name is then moved to a point on the circle. If the position of the trade name cannot be determined from the data in the image then the assumption is made that the trade name is located under either the bottom or upper cup  62 ,  66  and no move is made because the surface area obscured by these cups will end up on or near the equator when the spherical object O is conveyed to the second locating work station ST 2 . 
   The spherical object O is “released” at the first locating work station ST 1  by retracting the upper cup  66  holding the spherical object O in the bottom cup  62 , and then conveyed from the first locating work station ST 1  to the second locating work station ST 2  by means of the second transposing mechanism  78  located between the first locating work station ST 1  and the second locating work station ST 2 , i.e., by pivoting the transposing mechanism  78  and the spherical object O together through a fixed arc of 90 degrees resulting in the spherical objected O being placed on the bottom cup  108  of the second locating work station ST 2  of the apparatus  53  (see discussion above with respect to  FIG. 7  and the first and second locating work stations ST 1 , ST 2 ). The axis of rotation of the second locating work station ST 2  now passes through the center of the spherical object O at an angle that is perpendicular to the line where the axis of rotation of the first locating work station ST 1  passed through it. The upper cup  110  is then operated to physically engage the spherical object O to hold it securely in the bottom cup  108 . The second transposing mechanism  78  releases the spherical object O and then rotates back to a vertical position midway between the first and second locating work stations ST 1 , ST 2 . The reference indicium I is now located near the equator of the spherical object O due to the coarse positioning done at the first locating work station ST 1  (see discussion above with respect to reference numerals  22 ,  24  at the first locating work station ST 1  in  FIG. 2 ). 
   The bottom cup  108  is then rotated about an axis that passes through the center of the spherical object O by the motor means  112 , which is operative to control the amount of rotation of the spherical object O, at the second locating work station ST 2 . The line sensor camera means  34  images the spherical object O while it is rotated at least one complete revolution. The entire reference indicium I is now visible in the ST 2  image  33  without being truncated by the edge of the image (see  FIG. 4 ; see also discussion above with respect to  FIGS. 3 ,  4 ). The processing unit  100  is then operated to manipulate the ST 2  image  33  to locate and define the position and two-dimensional orientation of the reference indicium I on the surface of the spherical object O. The center of the reference indicium I is calculated as well as the angle thereof from the X reference axis, i.e., the two-dimensional orientation of the reference indicium I. From this information the processing unit  100  calculates the three Euler angles .phi, .theta, .psi necessary to rotate the spherical object O for orientation thereof so that the reference indicium I is located at a predetermined final position (with a predetermined final two-dimensional orientation), i.e., so that the target point of the spherical object O is aligned or prepositioned for additional processing such as printing, inspection, or some other type of operation (see discussion above with respect to  FIG. 2  and the second locating work station ST 2 —see also  FIG. 4 ). 
   Once the reference indicium is located as described in the preceding paragraphs, and the Euler angles phi, theta, and psi have been determined, the second processing work station ST 2  then functions as the first orienting work station ST 2 . The motor means  112  is then operative to rotate the spherical object O about the same axis used to image it (see axis Z 2  in  FIGS. 1 ,  2 ) to move the reference indicium I through the predetermined angle phi to the first reference position  12  (see discussion above with respect to  FIG. 1  and the first orienting work station ST 2 ). This results in movement of the reference indicium I from the defined position  11  to the first reference position  12 , which is located on the circle C on the surface of the spherical object O defined by the plane that contains the axis of rotation Z 2  and which is perpendicular to the X axis of the reference coordinate system (see  FIG. 1 ). 
   The spherical object O is then transported from the first orienting work station ST 2  to the second orienting work station ST 3  by retracting the upper cup  110  to “release” the spherical object O at the first orienting work station ST 2  and transposing it with the transposing mechanism  80  disposed between the first orienting work station ST 2  and the second orienting work station ST 3 , i.e., by pivoting the transposing mechanism  80  and the spherical object O together through a fixed arc of 90 degrees resulting in the spherical object O being placed on the bottom cup  116  of the second orienting work station ST 3  of the apparatus  53 . In this position at the second orienting work station ST 3 , the reference indicium I of the spherical object O is now located at the second reference position  14  illustrated in  FIG. 1 . The axis of rotation Z 3  of the second orienting work station ST 3  now passes through the center of the spherical object O at an angle that is perpendicular to the line where the axis of rotation of station ST 2  passed through it (see axis Z 3  in  FIG. 1 ). The upper cup  118  is then operated to physically engage the spherical object O to hold it securely in the bottom cup  116 . The transposing mechanism  80  releases the spherical object O and then pivots back to a vertical position midway between the first and second orienting work stations ST 2 , ST 3 . The center of the reference indicium I at the second reference position  14  is now located on the equator (or circle C) of the spherical object O due to the positioning done at the first orienting work station ST 2  (see  FIG. 1 ). The bottom cup  116  is then rotated about an axis Z 3  that passes through the center of the spherical object O by the motor means  120 . The angle that the spherical object O is rotated through is the predetermined angle .theta. calculated from the image that was acquired when the spherical object O was at the second locating work station ST 2 . An additional rotation of 90 degrees is added to the predetermined angle .theta so that the reference indicium I ends up at the third reference position  16  that lies on the plane defined by the axes of rotation of the second and third orienting work stations ST 3 , ST 4  (see reference numeral  16  in  FIG. 1  and the discussion relating thereto). 
   The spherical object O is then transported to the third or final orienting work station ST 4  by retracting the upper cup  118  to “release” the spherical object O at the second orienting work station ST 3  and then transposing it with the transposing mechanism  82  disposed between the second and third orienting work station ST 3 , ST 4 , i.e., by pivoting the transposing mechanism  82  and the spherical object O together through a fixed arc of 90 degrees resulting in the spherical object O being placed on the bottom cup  122  of the third or final orienting work station ST 4  of the apparatus  53 . The axis of rotation of the final orienting work station ST 4  now passes through the center of the spherical object O at an angle that is perpendicular to the line where the axis of rotation of the second orienting work station ST 3  passed through it (see axis Z 4  in  FIG. 1 ). The upper cup  124  is then operated to physically engage the spherical object O to hold it securely in the bottom cup  122 . The transposing mechanism  82  is operated to release the spherical object O and then rotates back to a vertical position midway between the second and third orienting work stations ST 3 , ST 4 . The reference indicium I is now located at the fourth or final reference position  18 , i.e., the top pole, of the spherical object O (see reference numeral  18  in  FIG. 1  and discussion above relating thereto). The bottom cup  122  is then rotated about an axis that passes through the center of the spherical object by the motor means  126  (see axis Z 4  in  FIG. 1 ). The predetermined angle that the spherical object O is rotated through at the third orienting work station ST 4  is the predetermined angle .psi calculated from the image that was acquired when the spherical object O was at the second locating work station ST 2 . 
   The spherical object O at the third orienting work station ST 4  is now disposed so that the reference indicium I is in the final reference position with the final two-dimensional orientation (see reference numeral  20  in  FIG. 1  and discussion above relating thereto) that results in the target point TP being in the aligned or prepositioned for additional processing (see  FIG. 1 ). The spherical object O can now be moved by a similar transposing mechanism or other means onto a conveyor, or the like, that maintains the reference indicium in the predetermined final position and two-dimensional orientation while performing additional process on the spherical object O through a printer, or performing some other operation on the properly oriented spherical object, e.g. inspection. 
   Another embodiment of the spherical object orienting system according to the present invention would be to use the dimple pattern of a spherical object such as a golf ball as the reference indicium for spatially orientating the spherical object utilizing the apparatus and method of the present invention described above. 
   Another embodiment of the spherical object orienting system according to the present invention would be to use a time-delay integration line sensor camera to image the surface of the spherical object. This would allow the spherical object to be rotated faster with the same amount of light, or rotated at the same speed with less light, as the plurality of data lines representing the image of the spherical object is acquired. 
   Another embodiment of the spherical object orienting system according to the present invention would be to use a camera means at the final orienting work station ST 4  to verify that the spherical object was successfully spatially orientated. 
   A variety of modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that, within the scope of the appended claims, the present invention may be practiced other than as specifically described above.