Abstract:
An apparatus and a method are presented for finding positional relationships and geometrical changes of at least one rotating part attached to or forming part of a machine when the part is in a rotating mode. In the apparatus and method, geometrical changes of the part caused by its state of production and use, determine any locations on the rotating part which exhibit contaminants, and subsequently remove or compensate effects of such contaminants present on the rotating part.

Description:
BACKGROUND OF THE INVENTION 
     Description of the Related Art 
     The present invention relates to the field of technical arrangements and methods for determining positions and changes for determining positional deviation and changes that has occurred in the course of a mechanical machining operation or a mechanical control activity. 
     Further, the invention relates to a quality control touch probing method for enabling a position of a quality control tool in the form of a touch probe to be related to position of a rotating part. 
     In order to simplify this disclosure by uniquely identifying important parts related to a typical machine system, which may be a system for mechanical quality control, the following explains the use of some general terms. 
     The term “machine” denotes any production or quality control machine, such as machining centers for milling, drilling, turning, grinding, polishing, cutting, bending, forming, etc., an EDM (Electrical Discharge Machine), a CMM (Coordinate Measuring Machine), a touch probe and stylus position sensing machine, a computer vision system, even a simple mechanical support structure, or similar. 
     “Work piece” denotes a part to be machined or to be subjected to quality control. The actual area on the work piece that has been machined, or quality controlled, is denoted “work area”. 
     The part or device that is performing the actual machining or quality control of the work area is denoted “work tool”. The work tool can be a machining tool (for milling, turning, drilling, etc.), a spark erosion tool (EDM tool), a touch probe or stylus position sensor, an optical imaging sensor, an electromagnetic sensor, or similar. 
     All the mechanical parts of a machine including different support structures, work pieces, work tools, work holders, and parts of the apparatus of the present invention, are called “machine part”. 
     The “position” of the work tool, or other different parts of a machine, etc., shall, unless otherwise stated, in this document typically mean the position, orientation, or both of the aforementioned, relative to another part. 
     The term “contaminant” will in this context represent non permanent material resting on a machine part, such material being one or more of oil, water, chip residues, and other material with similar properties. 
     The term “buildup” is defined as material that sticks to the part on a more permanent basis. 
     The term “wear” relates to machine part dimensional changes due to use. 
     To find position, or counteract the fact that unaccountable positional and geometrical changes may occur, several techniques are in common use such as: mechanical touch probe and stylus sensing, macroscope and microscope viewing, laser beam obstruction sensing, and pressure transducer sensing, see “Modern Machine Shop&#39;s Handbook for the Metalworking Industries”; Editor Woodrow Chapman, ISBN: 1-56990-345-X; 2002, 2368 pages, (Publisher: Hanser Gardner) and “Modern Machine Shops Guide to Machining Operations”; Woodrow Chapman; ISBN: 1-56990-357-3, 2004, 968 pages (Publisher: Hanser Gardner). 
     In many cases there is no time to slow down the rotation of a machine part to control its position in a static or nearly static condition. Except for the laser beam obstruction the mentioned techniques do not have the capability, and sufficient temporal resolution, to control rotating tools at high speed. The touch probe determines the position of the static work piece by use of a position sensing stylus tip. However, if a machining tool is made to slowly rotate in the reverse direction a variant of the touch probe approach can be used. In that case the touch probe “tip” is a plane surface against which the machining tool is rotating. 
     For the non contact position control of rotating work tools, running at their full speed, the work tool can be made to approach a focused laser beam and apply means to read the degree of beam obstruction. To find the geometry of a rotating machine part, specifically a work tool tip, repeated recordings of a laser beam obstruction is not sufficiently reliable. In theory a laser obstruction unit might be able to do the job. However such a technique would be time consuming and would have difficulty in discriminating between part contaminants, wear, and buildup, thereby reporting unreliable position data. 
     One of the inventors of the present invention describes in PCT/NO2005/000336 how so called fiducial patterns can be combined with optical techniques to accurately relate positions of machine parts to each others. That invention does not account for the position control of machine parts rotating at high speeds. 
     OBJECTIVES OF THE INVENTION 
     The objective of the present invention is to overcome all or part of the aforementioned limitations and shortcomings, by improvements of the overall position reading precision and speed, and the machine part handling reliability of machines. The present invention is therefore intended to be used to improve the machining and quality control position accuracy of any machine by finding the positions of the work tool and different machine parts, remove the effect of contaminations, and characterize buildup, wear, and tear thereon. In particular, the apparatus of the invention is useful for application on rotating work tools. 
     SUMMARY OF THE INVENTION 
     The present invention provides an apparatus for finding part positional relationships of parts of mechanical and opto-mechanical machining and quality control systems, for removing the effect of contaminants on rotating parts, for characterizing machine parts wear and tear, as well as buildup of machining material on rotating parts. 
     The present invention provides a method for finding positional relationships and geometrical changes of parts of a machine, of parts of apparatus made according to the present invention, and for removing the effect of contaminants. 
     The present invention relies on optical contactless sensing technology and aims at providing an in-the-process quality control technique that regularly and automatically can provide updates of position information for key rotating machine parts without having to rely on external quality control and calibration means. 
     The present invention determines the position and size of parts rotating at high speeds, even when the parts are contaminated by residues of oil, water, machining chips, etc. Especially, the invention determines the position and size of part details called fiducial patterns. It is also able to cause removal of the effects of contaminants and determines geometrical changes of the rotating parts by applying fiducial pattern models. It ensures high position accuracy by carefully discriminating between fiducial pattern models and fiducial pattern image models. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the drawings, which are not necessarily drawn to scale, like numerals describe substantially similar components throughout the several views. Like numerals having different letter suffixes represent different instances of substantially similar components. The drawings illustrate generally, by way of example, but not by way of limitation, various embodiments discussed in the present disclosure. 
         FIGS. 1   a - c  illustrate generally a first example of the inventive apparatus for use on a machine having rotary parts in operation. 
         FIGS. 2   a - c  illustrate generally a second example of the inventive apparatus for use on a machine having rotary parts in operation. 
         FIGS. 3   a - c  illustrate generally a third example of the inventive apparatus for use on a machine having rotary parts in operation. 
         FIGS. 4   a - c  illustrate generally a fourth example of the inventive apparatus for use on a machine having rotary parts in operation. 
         FIGS. 5   a - b  illustrate generally a fifth example of the inventive apparatus for use on a machine having rotary parts in operation, the apparatus having two pairs of illuminators and optical detectors. 
         FIGS. 6   a - c  illustrate that the same arrangement that is used for controlling rotating work tools can easily be adapted to study static work tools, like an unloaded touch probe of this figure. 
         FIGS. 7   a - b  illustrate that the same arrangement that is used for controlling rotating work tools can easily be adapted to study nearly static work tools, like the trigger position control of a touch probe of this figure. 
     
    
    
     The invention is now firstly to be described with reference to  FIG. 1 .  FIGS. 1-5  schematically exemplifies machines covered by the present invention where  34  exemplifies fiducial patterns integrated with rotating parts within these machines. These fiducial patterns  34  can be geometrical part details or part surface structure. 
       FIG. 1  shows a functional diagram that illustrates key ideas of the present invention. An optical detector  24  and illuminator  42  are fastened to a machine part  16 . The illuminator  42  illuminates the rotating machine part  22  along an optical path  56 A and the optical detector  24  observes the same machine part along an optical path  56 B. On the basis of a request  50  to a part position finder  44 , containing reference to a fiducial pattern model  36  or a fiducial pattern image model  52  of the rotating machine part  22 , the part position finder  44  defines control  54  of the illuminator  42 . The illuminator  42  provides pulsed illumination onto the rotating machine part  22  to optically reduce rotation blur and make it possible to reconstruct image exposure timing. Images from the optical detector  24  are controlled by a timer  38 , the light pulses from illuminator  42  are controlled by a timer  40 , and for improved performance the timers are synchronized  76 . Images of fiducial patterns  34 , that form parts of the machine part  22 , are detected by means of the optical detector  24 , converted to fiducial pattern images  58 , and recorded by the part position finder  44 . On the basis of part change constraints  68  the part position finder  44  determines the machine part changes  72  that are computed from fiducial pattern image  58  changes relative to the fiducial pattern image model  52 . To derive machine part changes  72  the part position finder  44  applies knowledge about the part geometry relations  70  where the machine position data  60  are taken into account. 
       FIG. 1  is a schematic drawing illustrating generally one example of a machine, representing any machine such as a milling machine, turning machine, drilling machine, Die sinking EDM (Electrical Discharge Machine), CMM, etc. Note that for clarity the optical assembly  26  has been turned ninety degrees around the z-axis, i.e. the work tool  22  should rather be translating through the open gap, a detection zone  78 , of the optical assembly  26 . The figure illustrates the position control of a milling tool  22  that is rotating at full speed. The magnified work tool tip  FIG. 1   c  shows a milling tool that may contain contaminants  62 , such as oil, water, and machining chip residues. The tool might also be affected by wear  66  and buildup  64  that needs to be reliably characterized. 
       FIG. 2  is a schematic drawing illustrating generally one example of a machine, representing any machine such as a milling machine, turning machine, drilling machine, Die sinking EDM (Electrical Discharge Machine), CMM, a calibration jig, etc. The figure illustrates how the position control of a rotating calibration pin  22  can help calibrating alignment and control of the optical detector  24  and the optical assembly  26  relative to the machine. 
       FIG. 3  is a schematic drawing illustrating generally one example of a machine, representing any machine such as a milling machine, turning machine, drilling machine, Die sinking EDM (Electrical Discharge Machine), CMM, etc. The figure illustrates the position control of a rotating work tool  22 . The magnified illustration of  FIG. 1   b - c  show a bar shaped EDM die  22 . The dashed line indicates the fiducial pattern model  36  and the fully drawn line indicates the outline of a worn die. Images of the fiducial patterns  34 A,  34 B, are recorded in one rotation scan, while images of the fiducial patterns  34 E,  34 F are recorded in another rotation scan. In  FIGS. 3   b - c  the size of the field of view  74  is indicated with rectangles. 
       FIG. 4  is a schematic drawing illustrating generally one example of a machine, representing any machine such as a milling machine, turning machine, drilling machine, Die sinking EDM (Electrical Discharge Machine), CMM, etc. The figure illustrates the position control of a rotating work tool  22  where the tool is observed by reflected light from its surface. For simplicity the magnified illustration in  FIG. 4   b - c  show a bar shaped EDM die  22 . Images of the fiducial patterns  34 A,  34 B, are recorded in one rotation scan, while images of the fiducial patterns  34 E,  34 F, are recorded in another rotation scan. The fiducial patterns are surface structure  34  in the die. In  FIGS. 4   b - c  the size of the field of view  74  is indicated with rectangles. 
       FIG. 5  shows a combination of two illuminator  42 —optical detector  24  arrangements similar to the ones illustrated elsewhere. The combination of the optical path between the illuminator  42 A and optical detector  24 A, and between the illuminator  42 B and optical detector  24 B helps triangulate full 3D data about the rotating work tool  22 . The illuminator-detector combinations need not be arranged into one optical assembly  26  as illustrated. Depending on space requirements they can be placed separately inside the machine. 
       FIG. 6  illustrates that the same arrangement that is used for controlling rotating work tools  22  can easily be adapted to find the position of static work tools, like the unloaded touch probe  22  of this figure. I.e. a machine tool and quality control tool can be made to refer to exactly the same position in space. 
       FIG. 7  illustrates that the same arrangement that is used for controlling rotating work tools  22  can easily be adapted to find the position of nearly static work tools, like the trigger position control of the touch probe  22  of this figure. The illustration indicates that by pneumatically introducing a glass cube  100  into the field of view, against which the touch probe can trigger, the trigger position can be found. To find this trigger position a transparent frosted glass sheet  34  is attached to the glass cube  100 . To make space for a machine tool the glass cube is pulled out of the detection zone by means of a pneumatic control. 
     DETAILED DESCRIPTION OF THE INVENTION 
     In the following detailed description, reference is made to the accompanying drawings which form a part hereof, disclosing by way of illustration specific, yet merely amplifying embodiments of how the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is to be understood that two or more of the embodiments may be combined, or that structural, logical and electrical changes may be made to arrive at other embodiments, however without departing from the concepts of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims and their technical equivalents. 
     The term “fiducial pattern” of a machine part is any geometric characteristics, including the surface structure itself, of that part. The “fiducial pattern image” is the image of that fiducial pattern as presented by the optical detector. The “fiducial pattern image model” is a mathematical model describing the image geometrical characteristics of the fiducial pattern as they appear in the optical detector 2D image projection, including image distortion, etc. The “fiducial pattern model” is a mathematical model describing 2D and 3D geometry of the fiducial pattern as it is given, or by reverse projection appears to be given in space. I.e. the fiducial pattern model is a mathematical model that is geometrically mapped to the fiducial pattern image model through mathematical image descriptions. 
     In the following examples, a reference coordinate frame position, or simply a frame, represents the position, including orientation, of a component, or a part of a larger structure, relative to another component, or part of a larger structure. The specification of a frame position may both represent nominal and measured positions. The term “frame relations” represents frame positions and the fact that components or parts are mechanically or optically interlinked, or that parts of a larger structure are mechanically interlinked. In one of its simplest form, the frame relations may only describe four frames that for example represent a machine support structure, a moving part inside a machine, a part fastened to the moving part, and an optical detector fastened to the support structure. Then the position of the part fastened to the moving part may be determined from data provided by the optical detector. In other cases, the reference frame relations may represent a more complicated mechanical structure. Basic principles of the application of frames within the applications covered by the present document are described in PCT/NO2005/000336. 
     EXAMPLE 1 
       FIG. 1   a  is a schematic drawing illustrating, by way of example, a machine that may represent any machine such as a milling machine, drilling machine, turning machine, Die sinking EDM, Wire EDM, CMM, or similar. These machines can be equipped with a range of different mechanical configurations, but all can be equipped with an apparatus according to the present invention. We indicate some key elements of these machines as a work piece carrier  28  (performing movements like two orthogonal translations x, y and rotations around the same axes), a work tool carrier  10  (in this example performing two translations, in the x and z directions), a work tool chuck  12 , position encoders  14 A,  14 B,  14 C, and a support structure  16 . The support structure is in this example indicated to include a base support  16 , a machine support link  18 , and a work tool support  20 . The purpose of this machine configuration and example is to find the cutter edge positions of a work tool  22  relative to the position of the optical detector  24 . The optical detector  24  is via the optical assembly  26  fastened to the base support  16 . In this example the work tool  22  is fastened to the work tool chuck  12 , and the work tool  22  is a milling tool with four cutters equally distributed around the rotation circumference. Moving the milling tool  22  relative to the optical assembly  26  and base support  16 , by means of the work tool carrier  10 , work tool support  20 , and the work piece carrier  28 , performs displacements necessary for the position and geometry measurement to take place. During process the position of these carriers is read at the locations of the position encoders  14 A,  14 B, and  14 C. Note that for ease of illustration the optical assembly  26  has been rotated  90  degrees around the z-axis. 
       FIGS. 1   a - c  show a milling tool  22  that is a production tool for the machining of a work piece  30 . At the tip of the milling tool  22  there are cutters  32  that actually perform the machining/cutting action. The present example illustrates how to find the cutter edge positions, relative to other machine parts, while a small diameter milling tool  22  is rotating at a high speed, e.g. at 27000 rpm (revolutions per minute). We assume that the milling tool  22  is new and has four clean cutter edges  34 , and that a parametric fiducial pattern model  36  is used. We also assume that the timer  38  of the optical detector  24  and the timer  40  of the illuminator  42  are not exchanging synchronization signals  76 . In the present example we shall find the radius distance and lengths of each of the cutter edges  34  individually. When the tool is measured, the position of the position encoders  14 B, and  14 C are also read. Those positions represent the machine position  60 . 
     The present example is illustrated in  FIG. 1   a - c . The part position finder  44  can be embodied as process within a computer, personal computer, dedicated processor, or similar. In this example we shall assume that part position finder  44  processes are carried out by means of two computers, a machine NC (Numerical Control) computer  46  together with an additional computer  48  dedicated to the control and monitor of the optical assembly  26 . 
     A request  50  is entered from another computer (not shown in  FIG. 1   a - c ) telling that the machine part is a rotating milling tool  22 . The request  50  defines parametrically the milling tool  22  type (e.g. bull nose, flat end, milling head with cutter tips, etc), number of cutters, nominal dimensions, and that a nominal internal fiducial pattern model  36  should be built and applied on the basic of this information. The NC computer  46  adds to the request  50  that the rotation speed is e.g. 27000 rpm. Note that we discriminate between a fiducial pattern model  36  and a fiducial pattern image model  52 . The fiducial pattern model  36  is a description of the 2D/3D model characteristics in space. The fiducial pattern image model  52  is the 2D projection image of that model that includes image distortion, etc. The part position finder  44  is able to derive the geometrical data of one model from the other. The request  50  may also define the measurement quality needed. An illuminator  42  receives the control data  54  from a computer  48  necessary for the illuminator  42  to create pulsed illumination of the fiducial pattern  34  along the optical path  56 A. 
     To create a predictable optical detector  24  exposure timing, and optically freeze the rotation movement, the illuminator  42  includes in the present example a dedicated electronic circuit running with an internal timer  40  at a repetition rate of e.g. 1 microsecond. The optical detector  24  is free running with a timer  38  rate of 60 images per second. It records along the optical path  56 B fiducial pattern images  58  of the fiducial patterns  34 , the cutter edges, while the milling tool rotates at the speed of 27000 rpm. The images are relayed to the computer  48 . A magnified and rotated view of the milling tool  22  and its cutter edges  34  is shown in  FIGS. 1   b - c . The coordinate axes of  FIGS. 1   a - b  indicate the orientation of the different views. The cutter edge  34  is back illuminated by the illuminator  42  and the fiducial pattern images  58  are shadow images of the cutter edges  34  in different angular orientations. On the basis of input request  50  from the NC computer  46 , the computer  48  calculates an optimum number of fiducial pattern images  58  to be recorded. The computer  48  might also base its illumination calculation on a standard number of images that from experience is known to work well. Assume that this number is 100 images. With equally distributed images around the circumference the 100 images results in one image per 360/100=3.6 degrees. 
     Then the computer  48  calculates the pulse width and repetition rate that enables the illuminator  42  to illuminate the full circumference of the cutter edges  34  with 100 nearly equally spaced images. 27000 rpm is equal to 450 rotations per second. In order to cover the full circumference in 1.66 seconds (100 images at a rate of 60 images per second) this would give an illumination pulse rate of 450 (100/101)=445.5 pulses per second. In order to optically freeze the rotation movement the pulse width should be less than the passing time of an 100&#39;th of a rotation cycle, i.e. less than 1/(450*100)=0.0000222 seconds (22.2 microseconds). These illumination parameters are transmitted from the computer  48  to the illuminator  42  as a control  54  signal. The illuminator  42  contains an dedicated electronic circuit that on the basis of the control  54  is able to produce the calculated illumination pulses by means of e.g. a LED (Light Emitting Diode). 
     The fiducial pattern images  58  are by known means converted/digitized and will be available for computer  48  operations. The computer  48  saves these 100 images in 1.66 seconds. Without delay the milling tool  22  machine positions  60 , represented by the positions of the encoders  14 B and  14 C, are recorded by the NC computer  46 . The optical detector  24  is a 2D (two-dimensional) array camera. Both the illuminator  42  and the optical detector  24  are, by means of the optical assembly  26 , fastened to the base support  16 . 
     Since the series of images were recorded at an arbitrary angular starting position in the rotation cycle, the computer  48  has at first to refer each of the fiducial pattern images  58  to their correct angular position. To do that it creates a function of the extreme +y-cutter edge positions of those images as a function of image number. From this function it calculates the angular positions of the maxima relative to the images. With four cutter edges this creates four function maxima. There will also be a nearest neighbor image to each of those four maxima. These images will be marked as the primary fiducial images  58  of the cutter edge  34 . We assume that the rotation axis is located close to the image center and that the milling tool diameter is less than optical detector  24  field width. This means that the computer  48  can repeat the above calculations also in the −y-direction, creating in effect two primary fiducial images  58  per cutter. 
     The fiducial pattern model  36  is in  FIG. 1   c  indicated with a dashed line. For clarity it is shifted slightly to the right compared to the fully drawn line that represents the shadow outline of one of the cutter edge  34 . The present example assumes that the cutter edges  34  are new and clean, i.e. the contaminants  62  are assumed to be small and the edges do not have accumulated buildup  64  or started to wear  66 , i.e. it this example the shadow image resembles more like the magnified illustration in  FIG. 1   b . In the present example the part change constraints  68  are defined by the cutter edge positions that are allowed to shift in the y- and z-directions. The part change constraints  68  are predefined and stored in the computer  48 . The shift might be due to the positioning of the milling tool  22  inside the chuck  12 , or due to the fact that the position of the cutter edges  34  are manufactured slightly different from the nominal model  36  position. 
     The NC computer  46  handles the machine positions  60 . In the present example they are relayed to the computer  48  for frame loop evaluations that involve the machine positions  60 . The position encoder  14 B data are added to the position of the frame  10 , representing the work tool carrier  10  position relative to the work tool support  20 . The position encoder  14 C data are added to the position of the frame  20 , representing its position relative to the machine support link  18 . 
     The part position finder  44  initial conditions are defined by part geometry relations  70  that have been earlier calibrated and stored in the computer  48 , in the part position finder  44 . At the time of optical assembly  26  alignment and calibration the optical assembly  26  relevant part geometry relations  70  has been created. See e.g. Example 4. This ensures that the initial part geometry relations  70 , where the optical detector  24  includes the fiducial part image model  52 , and the milling tool  22  includes the fiducial pattern model  36 , are consistent with each others, i.e. for example all coordinate frames reproduce correctly any spatial position within the geometry, and especially that the calculation of a position through any closed loop of the part geometry relations  70  of  FIG. 1   a  replicates itself. 
     The primary fiducial pattern images  58  of the cutter edges  34 , angular distances of those images from the maximum positions mentioned above, and the corresponding machine position data  60 , are taken care of by updating the part geometry relations  70  of the computer  48  (In the simplest case the machine position data  60  need not be transferred from the NC computer  46  to the computer  48 . The computer  48  may assume a fixed set of machine position data  60 , and when the NC computer  46  receives the part change data  72  it takes the machine position data  60  into account). The computer  48  first calculates a raw data version of the fiducial pattern image  58  and then rotates those data into the maximum position. The raw data are found by means of conventional image processing edge finding routines. Optionally the computer  48  adapts a mathematical spline to those data in a least square sense (by iteratively deforming the spline and finding the minimum of the least square sum of distances between the spline and the raw data). We shall call this spline the adapted fiducial pattern image model  52 A. 
     The computer  48  calculates the y- and z-displacement of the fiducial pattern image model  52  that best fit the rotated raw data positions calculated above. The computer  48  first creates a mathematical spline function describing the fiducial pattern image model  52 . It then iteratively displaces this image model in the y- and z-directions to best fit the rotated raw data, where the y-positions represent radius distances from the rotation center and z-positions represent tool cutter lengths. The spline displacements are calculated by iteratively translating the image model spline in the y- and z-direction and finding the minimum of the least square sum of distances between the spline and raw data. Alternatively, these displacements can be found by finding the y- and z-extrema of the adapted fiducial pattern image model  52 A and the fiducial pattern image model  52 , respectively and subtract those values from each others. The above calculations are repeated for all four cutter edges  34 . 
     Note that the adapted spline function  52 A, describing the rotated cutter edge image  58 , can be transformed into a new fiducial pattern image model  52 , specifically representing the geometry of this identified cutter edge. This new model makes it possible to later check the wear and buildup of this specific cutter edge relative to its present condition. 
     As illustrated in  FIG. 1   a  the cutter edge  34  is mechanically interlinked to the optical detector  24  via the cutter  32 , milling tool  22 , work tool chuck  12 , work tool carrier  10 , work tool support  20 , machine support link  18 , and the optical assembly  26 . The cutter edge  34  is also optically interlinked to the optical detector  24 . This creates what we call the frame loop ( 24 - 32 - 22 - 12 - 10 - 20 - 18 - 26 - 24 ). The part position finder  44  receives a request  50  to find cutter edge radii-(y) and length (z)-positions. The computer  48  finds the cutter edge positions by translating the fiducial pattern model  36  in the y- and z-directions to obtain that all the frame positions in this loop become consistent with each other. By starting with a given position, and calculating the positions mapped through the closed loop, we know that we should come back to the same position. I.e. one key purpose of the part position finder  44  of this invention is to ensure that, when positions are mapped through the whole loop, all positions that are members of a given closed loop should map back on to themselves. Now when the cutter edge might be in another position relative to the initial fiducial pattern model  36  then the frame positions of the loop ( 24 - 32 - 22 - 12 - 10 - 20 - 18 - 26 - 24 ) are not longer consistent with each other. The part position finder  44  then applies the part change constraint  68  that only the frame representing the fiducial pattern model  36  is allowed to translate in the y- and z-directions. Except for the carrier  14 B and  14 C displacements, taken care of by the machine positions  60 , all other frames are assumed to have not moved relative to each others. 
     PCT/NO2005/000336 describes a range of mathematical methods that can be used to solve a loop inconsistency. Here we assume that the mathematical problem of restoring consistency is obtained by solving a set of linear equations, describing the transforms between the different frames. This can be accomplished by use of 4×4 matrices describing the 3D (three-dimensional translation and rotation by means of so called homogenous coordinates. In the present example the y-z translations between the original fiducial pattern image model  52  position and the new position are two known values (found by means of the above spline least square calculation), and the y-z-translations of the fiducial pattern model  36 , the searched part change  72 , are two unknown values. By this means, the part position finder  44  calculates the fiducial pattern model  36  translations and thereby also the cutter edge positions. 
     If the fiducial pattern image model  52  is shifted, a major fraction of the optical detector  24  size, optical distortion may affect accuracy. In that case, the fiducial pattern image model  52  comparison with the fiducial pattern image  58  may have to be found by an unlinear mathematical method. One such approach is to map positions in the initial fiducial pattern image model  52  to its fiducial pattern model  36  counterparts, then change the position of the fiducial pattern model  36 , and finally map positions back from the fiducial pattern model  36  to the fiducial pattern image model  52 . This process might have to be repeated iteratively, but not necessarily. The final step can be based on the linear approach described above. By this approach, as the fiducial pattern image model  52  is shifting it is also changing shape to compensate for optical distortion, and the comparison with the fiducial pattern image  59  will be more accurate. The end result of this (iterative) mapping approach will be both the new searched position and shape of the fiducial pattern image model  52 , and the new position of the fiducial pattern model  36 . The searched part change  72  is given by this fiducial pattern model  36  position change. 
     Earlier we saw how to create a new fiducial pattern image model  52 A by adapting a mathematical function, a spline, to the recorded geometry. Alternatively, we may take the shifted fiducial pattern models  36  for each of the cutter edges  34  to represent an alternative best fit adaptation to this milling tool  22 . We assume that the tool is clean. Therefore, this new model can also be saved as a new fiducial pattern model  36  describing this specific milling tool  22  together with its ID, and making it possible to later check wear and buildup from this initial state. 
     EXAMPLE 2 
     This example is similar to Example 1, but the milling tool  22  is diameter is larger and rotating at a slower speed of e.q. 7200 rpm (rotations per minute). The illuminator pulses are synchronized  76  with the optical detector image timing. The edges  34  in the present example might be contaminated by residues of oil, water, machining chips, etc. The milling tool  22  is a tool with ID (Identification Number). A fiducial pattern image model  52 , specifically made for this identified tool, is applied. Example 1 shows how such a model can be made. 
     The present example is illustrated in  FIGS. 1   a - c . The part position finder  44  can be embodied as process within a computer, personal computer, dedicated processor, or similar. In this example, we shall assume that part position finder  44  processes are carried out by means of a computer that takes care of both the machine NC (Numerical Control) together with processes dedicated to the control and monitor of the optical assembly  26 . The request  50  is entered from a keyboard telling that the machine part is a rotating milling tool  22 , rotating at the speed of e.g. 7200 rpm. The request  50  specifies the milling tool  22  ID, and that a previously made fiducial pattern image model  52  should be used. The request may also define the measurement quality needed in terms of angular rotation resolution, e.g. 3.6 degrees. An illuminator  42  receives the control  54  from the position finder  44  to create pulsed illumination of the fiducial pattern  34  along the optical path  56 A. 
     To optically freeze the rotation movement, and obtain a predictable fiducial pattern image  58  exposure and exposure timing, the illuminator  42  is in the present example a dedicated electronic circuit running with an internal timer  40  at the repetition rate of e.g. 0.1 microseconds. An optical detector  24  is free running at a timing rate of 45 images per second provided by the timer  38 . It records along the optical path  58 B fiducial pattern images  58  of the fiducial pattern  34 , the cutter edges, while the milling tools rotates at the speed of 7200 rpm. The images are relayed to the part position finder  44 . 
     A magnified and rotated view of the milling tool  22  and its cutter edges  34  is shown in the magnified illustrations of  FIGS. 1   b - c . The coordinate axes of  FIGS. 1   a - b  indicate the orientation of the different views. In  FIG. 1   c  contaminants  62 , due to oil, water, and machining chip residues, are indicated. In the present example we do not assume that cutter edges contain buildup  64  or wear  66 . The cutter edge  34  is back illuminated by the illuminator  42  and the fiducial pattern images  58  are shadow images of the cutter edges  34  in different angular orientations. 
     When the milling tool rotates at the speed of 7200/60=120 rotations per second, and the optical detector  24  operates with 45 images per second, there will be a non-integer number of edge passing per image. I.e. if the illumination pulses were created as a continuous series of equally spaced pulses the fiducial pattern images  58  would flicker in brightness and the center time of the exposure would vary in a slightly unpredictable manner. To come around that problem, in the present example, we assume that the illuminator pulse timing is synchronized  76  to the optical detector timing  38 , within the 0.1 microsecond precision of the illuminator timer  40 . The part position finder  44  calculates an illumination pulse train that gives the same number of pulses per image, and where the exact exposure center time of those pulses results in a predictable, but slightly uneven, angular spacing recording around the milling tool circumference. In the present example the number of pulses per image is truncated down to 2. On the basis of defining the 7200 rpm tool rotation speed, and the input request 3.6 degrees angular rotation resolution, the part position finder  44  calculates the pulse width and pulse distance within each image. 7200 rpm is equal to 120 rotations per second. In order to cover the full circumference in 2.22 seconds (360/3.6=100 images at a rate of 45 images per second) this would within each image give an illumination pulse distance equal to 1/120 seconds. In order to optically freeze the rotation movement the pulse width should be less than the passing time of the angular resolution width, i.e. less than ( 1/120)*(3.6/360)=0.000083 (83 microseconds). 
     These illumination parameters are given to the illuminator  42  as the control  54  signal from the part position finder  44 . The internal pulse calculations of the part position finder  44  ensure that no pulse is made in the neighborhood of the image shifts (“blanking” period). The full tool circumference is divided into 100 angular positions (100 images). The part position finder  44  also ensures that the timing of the pulse train of each image refers to the same angular position, and that the next image refers to another angular position around the tool circumference, until all 100 positions are covered with nearly equally spaced recordings. If the rotation speed is slower than the image rate this calculation may rely on jumping a prime number, smaller than 100, of angular position between each image. The fiducial pattern images  58  are by known means converted/digitized and will be available for part position finder  44  operations. The part position finder  44  saves these 100 images in the given 2.22 seconds. Without delay the milling tool  22  position, represented by the positions of the encoders  14 B and  14 C, the machine positions  60 , are recorded by the part position finder  44 . 
     An idea of the present invention is that the optical detector  24  timer  38  and/or illuminator  42  timer  40  need not be synchronized to the tool  22  rotation, i.e. no tachometer reading is necessary. Since the series of images were recorded at an arbitrary angular starting position in the rotation cycle, the part position finder  44  first have to refer each fiducial pattern image  58  to an identified angular position. To do that the part position finder  44  creates a function of the extreme +y-cutter edge positions of all images as a function of image number. From this function it calculates the angular positions of the maxima relative to these images. With four cutter edges this creates four function maxima. There will also be a nearest neighbor image to each of those four maxima. These images will be marked as the primary fiducial pattern images  58  of the cutter edge  34 . We assume that the tool diameter is so large that the rotation axis is located outside the optical detector  24  field of view and that the extreme +y-positions of the cutter edges are placed close to the image center. With the tool in this position four primary edge images are recorded. 
     Then, in order to record the four images on the other side the machine would have move the milling tool its own diameter in the y-direction, before another series is recorded and analyzed. For these one-sided radius position measurements the position of the rotation axis needs to be known. We assume that the rotation axis position has been earlier calibrated into the part position finder  44 , otherwise look at Example 4 that amongst others describes an example of that kind of calibration. The fiducial pattern model  36  is in  FIG. 1   c  indicated with a dashed line. For clarity it is shifted slightly to the right compared to the fully drawn line that represents one of the primary fiducial pattern images  58 . The present example assumes that the cutter edges  34  include contaminants  62 . In the present example the part change constraints  68  are defined by the cutter edge positions that are allowed to shift radially, in the y- and z-directions. This shift might be due to the positioning of the milling tool  22  inside the chuck  12 , or due to the fact that the positions of the cutter edges  34  are manufactured slightly different from the nominal model. 
     As described earlier the machine position data  60  are added to the corresponding frame positions. The part position finder  44  initial conditions are defined by part geometry relations  70  that have been earlier calibrated into the part position finder  44 . At the time of the optical assembly  26  alignment and calibration the optical assembly  26  part geometry relations  70  are created. See e.g. Example 4. This ensures that the initial part geometry relations  70  of  FIG. 1   a , where the optical detector  24  includes—the fiducial part image model  52 , and the milling tool  22  includes the fiducial pattern model  36 , are consistent with each others. In this example the fiducial pattern image model  52  is placed in the center of the field of view and made to make all coordinate frames reproduce correctly any spatial position within the geometry, and especially that the calculation of a position through any closed loop of the part geometry relations  70  of  FIG. 1   a  replicates itself. 
     The primary fiducial pattern images  58  of the cutter edges  34 , the image angular distance from the maximum positions mentioned above, and the corresponding machine position data  60 , are fed into the part geometry relations  70  of the part position finder  44 . The part position finder  44  first calculates a raw data version of the primary fiducial pattern image  58  and rotates those data into the maximum position. The raw data are found by means of conventional image processing edge finding routines. The part position finder  44  then calculates the y- and z-displacements of the fiducial pattern image model  52  that best fit the rotated raw data positions calculated above. The part position finder  44  creates a mathematical spline function describing the fiducial pattern image model  52 . It then iteratively displaces this image model in the y- and z-directions to best fit the rotated raw data. The spline displacements are calculated by iteratively translating the model spline in the y- and z-direction and finding the minimum of the least square sum of distances between the spline and raw data. 
     To remove the effect of contaminants  62  the part position finder  44  then removes all raw data that both are smaller than a certain length along the spline and outside a certain threshold distance from the image model  52 . In order to improve the accuracy it may repeat this removal process several times. The end result is a slightly displaced fiducial pattern image model  52 . 
     Optionally the part position finder  44  adapts a mathematical spline to the remaining raw data in a least square sense by iteratively deforming the spline and finding the minimum of the least square sum of distances between the spline and the raw data. We shall call this spline the adapted fiducial pattern image model  52 A. Alternatively the displacements can then be found by finding the y- and z-extrema of respectively the adapted fiducial pattern image model  52 A and the fiducial pattern image model  52  spline and subtract those values from each others. The above calculations are repeated for all four cutter edges. Note that the adapted fiducial pattern image spline function  52 A, describing the rotated cutter edge image  58 , and where the effect of the contaminants  62  are removed, can be transformed into a new fiducial pattern image model  52  specifically representing the geometry of the identified cutter edge. This new model makes it possible to later check the wear and buildup of this specific cutter edge. Note that, instead of all the spline calculations in the present example, a number of other smooth adaptation functions could do the job. 
     As illustrated in  FIG. 1   a  the cutter edge  34  is mechanically interlinked to the optical detector  24  via cutter  32 , milling tool  22 , work tool chuck  12 , work tool carrier  10 , work tool support  20 , machine support link  18 , and the optical assembly  26 . The fiducial pattern  34  is also optically interlinked to the optical detector  24 . This creates what we call the frame loop ( 24 - 32 - 22 - 12 - 10 - 20 - 18 - 26 - 24 ). The part position finder  44  receives or issues a request  50  to find cutter edge radii-(y) and length (z)-positions. As a result of the image displacement of the fiducial pattern image model  52 , the part position finder  44  finds the cutter edge positions  34  by translating the fiducial pattern model  36  in the y- and z-directions, and by ensuring that all the frame positions in this loop again become consistent with each others. If the cutter edge is translated relative to the initial fiducial pattern image model  52  then the frame positions of the loop ( 24 - 32 - 22 - 12 - 10 - 20 - 18 - 26 - 24 ) are no longer consistent with each other. The part position finder  44  then applies the part change constraint  68  that only the frame representing the fiducial pattern model  36  is allowed to translate in the y- and z-directions. Except for the carrier displacements  14 B and  14 C, taken care of by the machine positions  60 , all other frames are assumed to have not moved relative to each others. 
     We apply the previous 4×4 matrices describing the 3 dimensional translation and rotation by means of so called homogenous coordinates. In the present example the y-z translations to fit fiducial pattern image model  52  to the fiducial pattern image  58  are two know values (found by means of the above spline least square calculation), and the y-z-translations of the fiducial pattern model  36 , the searched part change  72 , are two unknown values. By this means the part position finder  44  calculates the fiducial pattern model  36  translations and thereby also the cutter edge position. 
     Earlier we explained how we could create a new fiducial pattern image model  52  by adapting the geometry of a mathematical function, a spline. Alternatively we may take the shifted fiducial pattern models  36  for each of the cutter edges  34  to represent an alternative best fit adaptation to an identified milling tool  22 . We have removed the effect of contaminants  62 . Therefore, this new model can be saved as a fiducial pattern model  36  describing this specific milling tool  22  that may even carry contaminants, but still making it possible to later check wear and buildup of the tool. 
     EXAMPLE 3 
     This example is similar to Examples 1 and 2, but the timing of the optical detector  24  is synchronized  76  by the illuminator  42 , and the milling tool  22  is a used tool with seven cutters  32 . I.e. in addition to the fact that the cutter edges might be contaminated by residues of oil, water, machining chips, etc., the cutter edge geometry might be distorted due to buildup  64  and wear  66 . The present example also demonstrates how a fiducial pattern image model  52 , adapted from the geometry of the same tool in a previous stage, helps characterizing this used tool. 
     The present example is illustrated in  FIGS. 1   a - c . The part position finder  44  can be embodied as process within a computer, personal computer, dedicated processor, or similar. In this example we shall assume that part position finder  44  processes are carried out by means of two computers that exchange messages, where one computer takes care of the machine NC (Numerical Control)  46  while the other  48  controls processes dedicated to the control and monitor of the optical assembly  26 . The request  50  is entered from a keyboard telling that the machine part is a rotating milling tool  22 . The NC computer controls the rotation speed to be e.g. 5000 rpm. The request  50  identifies the milling tool  22  with its ID, and that an earlier defined ID fiducial pattern image model  52  should be used. That earlier defined model might originally have come from a CAD drawing or from measurements similar to the ones outlined by e.g. Examples 1 and 2. The request may define the measurement quality needed in terms of angular rotation resolution, e.g. 1.8 degrees; otherwise internal parameters of the part position finder are used. 
     An illuminator  42  receives the control  54  from the position finder  44  to create pulsed illumination of the fiducial pattern  34  along the optical path  56 A. To optically freeze the rotation movement and obtain correct image exposure timing the illuminator  42  is in the present example a dedicated electronic circuit running with an internal timer  40  at the repetition rate of e.g. 1.6 microsecond. In the present example the optical detector  24  has an input to synchronize its timer  38  to a down conversion of the illuminator internal timer  40 , to create 50 images per second. The optical detector  24  records along the optical path  56 B fiducial pattern images  58  of the fiducial pattern  34 , the cutter edges, while the milling tools rotates at the speed of 5000 rpm. The images are relayed to the part position finder  44 . A magnified and rotated view of the milling tool  9  and its cutter edges  34  is shown in  FIG. 1   c . The coordinate axes of  FIGS. 1   a - c  indicate the orientation of the different views. In  FIG. 1   c  contaminants  62 , possibly due to oil, water, and machining chip residues, is indicated. The same illustration schematically shows buildup  64  and wear  66 . The cutter edge  34  is back illuminated by the illuminator  42 , and the fiducial pattern images  58  are shadow images of the cutter edges  34  in different angular orientations. 
     When the milling tool rotates at the speed of 5000/60=83.33 rotations per second, and the optical detector  22  operates with 50 images per second, there will be a non integer number of edge passing per image. I.e. if the illumination pulses were created as a continuous series of equally spaced pulses the detector  22  images would flicker in brightness and the mean time of the exposure would vary in an unpredictable manner. To come around that problem, in the present example, we assume that the optical detector timer  38  is synchronized  76  to the illuminator timer  40 . Then the part position finder  44  calculates an illumination pulse train that gives the same number of pulses per image, and where the exact mean exposure of those pulses results in a predictable, but slightly uneven, image reference to angular spacing around the milling tool circumference. However this slight variation is controlled and taken into account by the part position finder  44 . In the present example the number of pulses per image is truncated down to 1. On the basis of the input request defining the 5000 rpm tool rotation speed, and the 1.8 degrees angular rotation resolution, the part position finder  44  calculates the pulse width and pulse position within each image. 5000 rpm is equal to 83.33 rotations per second. In order to cover the full circumference in 4 seconds (360/1.8=200 images at a rate of 50 images per second) this would give an illumination pulse rate close to 83.33 pulses per second. In order to optically freeze the rotation movement the pulse width should typically be less than the passing time that corresponds to the part (1.8/360) of one rotation cycle, i.e. less than (1/88.33)*(1.8/360)=0.000056 (56 microseconds). 
     These illumination parameters are given to the illuminator  42  as the control  54  signal from the part position finder  44 . The internal pulse calculations of the part position finder  44  ensure that no pulse is made in the neighborhood of the image shifts (“blanking” period). The full tool circumference is divided into 200 angular positions (200 images). The part position finder  44  also ensures that the next image refers to the next angular position around the tool circumference, until all 200 positions are covered. If the rotation speed is slower than the image rate this calculation may rely on jumping a prime number of angular position between each image that is less than 200. The fiducial pattern images  58  are by known means converted/digitized and will be available for part position finder  44  operations. The part position finder stores these 200 images in 4 seconds. Without delay the milling tool  22  machine positions  60 , represented by the positions of the encoders  14 B and  14 C, are recorded by the part position finder  44 . 
     Since the series of images were recorded at an arbitrary angular starting position in the rotation cycle, the part position finder  44  first have to refer each fiducial pattern image  58  to an identified angular position. To do that the part position finder  44  creates a function of the extreme +y-cutter edge positions of those images as a function of image number. From this function it calculates the angular positions of the maxima relative to the images. With seven cutter edges this creates seven function maxima. There will also be a nearest neighbor image to each of those seven maxima. However, since these data may contain the effects of contaminant  62  and buildup  64 , first the part position finder  44  calculates a raw data version of the fiducial pattern images  58  (the raw data can be calculated by means of conventional edge finding routines). In order to find reliable maximum positions of the image edge projections it then, for all images, remove the effect of the contaminants  62  and buildup  64  by searching for local protrusions along the image periphery. To aid this process it also creates a smooth mathematical spline function that adapts itself to the periphery raw data in a least square distance sense, and removes those raw data that protrude a certain threshold outside the spline, like the process described in Example 2. Then the extreme +y-cutter edge positions can be found. Those images closest to the found maxima will be marked as the primary fiducial images  58  of the cutter edge  34 . 
     We assume that the tool diameter is so large that the rotation axis is located outside the optical detector  24  field of view and that the extreme +y-positions of the cutter edges are placed close to the image center. With the tool in this position seven primary edge images are recorded. Then, in order to record the seven primary images on the other side the machine moves the milling tool its own diameter in the y-direction, before another series is recorded and analyzed. For these one-sided radius position measurements the position of the rotation axis needs to be known. In this example the rotation axis position has been earlier calibrated into the part position finder  44  or calculated from these two-sided measurements. Example 4 describes an example of that kind of calibration. The fiducial pattern model  36  is in  FIG. 1   c  indicated with a dashed line. For clarity it is shifted slightly to the right compared to the fully drawn line that represents one of the primary fiducial pattern images  58 . The present example assumes that the cutter edges  34  possibly include contaminants  62 , buildup  64 , and wear  66 . In the present example the part change constraints  68  are defined by the cutter edge positions that are allowed to shift in the y- and z-directions. This shift might be due to the positioning of the milling tool  22  inside the chuck  12 , due to the fact that the positions of the cutter edges are manufactured slightly different from the model, or a range of other possible causes. 
     As described earlier the machine positions  60  are added to the corresponding frame positions. On the basis of exact distortion calibration the fiducial pattern image model  52  and the fiducial pattern model  36  are made to map each others. For simplicity the fiducial pattern image model  52  is placed in the center of the field of view. This ensures that the initial part geometry relations  70 , where the optical detector  24  includes the fiducial part image model  52 , and the milling tool  22  includes the fiducial part model  36 , are consistent with each others, and especially that the calculation of a position through any closed loop of the part geometry relations  70  replicates itself. 
     To find the fiducial pattern image shift the calculations follows pretty much the same procedure as in e.g. Example 2. The end result is a displaced ID fiducial pattern image model  52 . This model is now used to characterize buildup  64  and wear  66 . Those raw data that protrude outside the image model are identified as possible buildup  64 , and the position finder  44  characterize them by measures like the number of protrusions, position of protrusion, the maximum protrusion distance from model, area of protrusion, length of protrusion, etc. Those raw data that go inside the model are identified as possible wear  66 , and the position finder  44  characterize them by measures like the number of wears, position of wear, the maximum wear distance from model, area of wear, length of wear, etc. Note as earlier that, instead of all the spline calculations in the present example, a number of smooth adaptation functions could equally well do the job. 
     To find the fiducial pattern model shift that corresponds to the fiducial pattern image shift, the calculations of the present example follow pretty much the same procedure as in e.g. Example 2. The frame loop is identified, part change constrains  68  are applied, and those fiducial pattern model  36  shifts that creates the previously found image shifts are calculated. By such means the part position finder  44  calculates the fiducial pattern model  36  translations, and thereby also the cutter edge position. In addition, by reverse imaging, the part position finder  44  calculates dimensions of the possible buildup  64  and wear  66 , and add that information to the part change  72  data. 
     EXAMPLE 4 
       FIGS. 2   a - c  is a schematic drawing illustrating, by way of example, a machine that may represent any machine such as a milling machine, drilling machine, turning machine, die sinking EDM, Wire EDM, CMM, or simply a fixed alignment/calibration jig. The purpose of this machine configuration and example is to help align and/or initialize/calibrate the optical detector  24  position and the position (axis of orientation) of the optical path  56 B, relative to the position of the machine. In this example the work tool  22  is a calibration pin. This present example illustrates how to control the y- and z-position, and tilt around the x- and y-axis, of the optical assembly  26  relative to the machine position, at the time of installation, recalibration, or service. This is done by use of a calibration pin  22  whose length has been pre calibrated. This example also illustrates how position and geometry of rotating work tools with more complicated shapes can be controlled. As illustrated in the  FIGS. 2   b - c  the pin tip is made asymmetrical to help include the calibration of tilt around the z-axis. This pin could have had a range of different shapes but in the present example it consists essentially of two blades,  22 ′ and  22 ″, separated at a distance close to the optical depth of field. This is indicated by the two projections illustration of  FIGS. 2   b - c . The blade edges are parallel and have essentially the same lengths relative to the pin stem  22 ″′. Their lengths have been measured (pre calibrated) to a high accuracy. The calibration pin  22  is mounted in the tool chuck  12  and made to position itself in the z-direction by use of some mechanical locator points on the chuck and pin base, or by means of a flange to flange mechanical contact. The pin is made to rotate at a given speed of 3610 rpm. If the calibration takes place in a calibration rig, an EDM, or CMM machine the rotation speed could be much slower, e.g. in the range of 60 rpm. 
     The present example is illustrated in  FIGS. 2   a - c . The part position finder  44  can be embodied as process within a computer, personal computer, dedicated processor, or similar. In this example the part position finder  44  processes are carried out by means of one computer  48  that receives controls from the machine NC (Numerical Control)  46 , and that the computer controls and monitors the optical assembly  26 . The two computers are connected through a local network. This connection handles the request  50 . Alternatively the request  50  can be entered to the part position finder  44  by means of a keyboard. The part geometry relations  70  and the part change constraints  68  have been loaded into the part position finder  44  at an earlier stage. The request  50  identifies the calibration pin  22  and specifies a rotation speed of e.g. 3610 rpm (around the z-axis). We assume that a pre calibrated internal fiducial pattern image model  52 , describing the 3D (three-dimensional) pin tip geometry, has been earlier calibrated and saved in the part position finder  44 . The calibration pin  22  position is found by recording 360 images of the fiducial pattern  34 , in this case the rotating pin tip geometry. An illuminator  42  receives the control  54  from the position finder  44  to create a pulsed illumination of the fiducial pattern  34  along the optical path  56 A. 
     To create sharp images, optically freeze the movement, the illuminator  42  pulse generation is in this case a real time kernel inside the same computer  48  that monitors the fiducial pattern images  58 . The optical detector  24  is free running with a timer rate of 60 images per second provided by the timer  38 . It records along the optical path  56 B fiducial pattern images  58  of the fiducial pattern  34 , the calibration pin tip, while the pin rotates at the speed of 3610 rpm. The images are relayed to the part position finder  44 . The pin tip  34  is back illuminated by the illuminator light source  80 , e.g. a LED, and the fiducial pattern images  58  represent shadow images of the pin tip  34  in different angular orientations (for ease of drawing  FIG. 2   a  the light source  80  is drawn outside the illuminator  42 , even if it is a part of the illuminator  42 ). 
     When the calibration pin  22  rotates at the speed of 3610/60=60.1667 rotations per second, and the camera operates with 60 images per second, the recording position will shift the fraction 1/360 of the circumference per image. To assure that the illuminator  42  pulses are synchronized to the optical detector timer  38  we assume that the real time kernel of the part position finder synchronizes illuminator  42  pulses to the received fiducial pattern images  58 . On the basis of the input request defining the 3610 rpm tool rotation speed, and the 360/360=1 degrees angular rotation resolution, the part position finder  44  calculates the pulse width and pulse distance within each image. 3610 rpm is equal to 60.1667 rotations per second. The full circumference is covered in 6 seconds (360 images at a rate of 60 images per second). In order to optically freeze the rotation movement the pulse width should be less than the passing time of the angular resolution distance, i.e. less than ( 1/60)*( 1/360)=0.000046 (46 microseconds). These illumination parameters are given to the illuminator  42  as the control  54  signal (not shown in  FIG. 1   a ) from the part position finder  44 . The internal pulse calculations of the part position finder  44  ensure that no pulse is made in the neighborhood of the image shifts (“blanking” period). The full tool circumference is divided into 360 (360 images) equally spaced angular positions. 
     Two magnified views of the fiducial pattern  34  are shown in  FIGS. 2   b - c . The coordinate axes of  FIGS. 2   a - c  indicate the orientation of the different views. In most cases, for example if the calibration pin  22  is fastened to the tool chuck  12  from a tool changer, its initial orientation around the z-axis is unknown. The rotation makes it possible to record a series of images and later select the optimal ones. The two views of  FIG. 1   b - c  indicate the most interesting orientation. If the optical axis of the observation path  56 B is mounted to result in an offset tilt around the y-axis, the fiducial pattern image  58  will display the two edges with different z-heights, as shown by the illustration of  FIG. 2   c . In the same view the mean z-positions of the  22 ′ and  22 ″ edges give the z-position. By collecting data from all rotation angles the spindle axis orientation around the x-axis, and its run out, can be found from the orientation of the calibration pin stem  22 ″′. The stem  22 ″′ is cylindrical. 
     Since the series of images might be recorded at an arbitrary angular starting position in the rotation cycle, the part position finder  44  first have to refer each fiducial pattern image  58  to an identified angular position. To do that the part position finder  44  creates a function of the y-distance between the  22 ′ and  22 ″ blades. From this function it calculates the angular position when the distance is equal to a pre calibrated value, corresponding to the orientation of the views of the  FIGS. 2   b - c  magnified illustrations. There will be two nearest neighbor image to these positions. These images will be marked as the primary fiducial pattern images  58  of the pin tip  34 . 
     We assume that the pin diameter is so small that it fits inside the optical detector  24  field of view. In the present example the part change constraints  68  are defined by the pin tip positions that are allowed to shift in the y- and z-directions, and rotate around the x- and y-axes. This shift is due to the y- and z-positioning of the calibration pin  22  inside the field of view. The rotations are due to the fact that the optical detector  24  orientation around the x-axis, and the observation path  56 B tilt around the y-axis relative to the machine, is not perfectly aligned. 
     The initialization that ensures frame loop consistency follow the general outline described earlier. The primary fiducial pattern images  58  of the pin tip  34 , the image angular distance from the given  22 ′- 22 ″ blade y-distance described above, and the corresponding machine position data  60 , are fed into the part geometry relations  70  of the part position finder  44 . The part position finder  44  first calculates a raw data version of the primary fiducial pattern images  58  and rotates those data into the orientation of the given positions. The part position finder  44  then calculates the y- and z-displacements, the mean and difference z-positions of the blades  22 ′ and  22 ″, and the angular orientation of the pin stem  22 ″′ of the fiducial pattern image model  52 , that best fit the rotated raw data positions calculated above. The part position finder  44  creates a mathematical spline function describing a fiducial pattern image model  52  that contain three separate sub elements. To best fit the raw data it first iteratively displaces the whole image model in the y- and z-directions, and around the x-axis. It then fine tunes the position of the sub elements by repeating the iterative process for each of them. The spline displacements are calculated by iteratively translating the model spline in the y- and z-direction, rotating around the x-axis, and finding the minimum of the least square sum of distances between the spline and raw data. The process is repeated for each of the two primary fiducial pattern images that are separated with a rotation around the z-axis with 180 degrees. 
     In an alternative, the iterative approach, by mapping positions between the models described in the end of Example 1 can be used. Then the-sub elements are shifted as a group, not individually. 
     As illustrated in  FIG. 2   a  the calibration pin  22  is mechanically interlinked to the optical detector  24  via work tool chuck  12 , work tool carrier  10 , work tool support  20 , machine support link  18 , and the optical assembly  26 . The fiducial pattern  34  is also optically interlinked to the optical detector  24 . This creates what we call the loop ( 24 - 22 - 12 - 10 - 20 - 18 - 26 - 24 ). The part position finder  44  receives a request  50  to find the y- and z-displacements, and x- and y-rotations, of the calibration pin  22 . The sub elements of the fiducial pattern image model  52  are displaced from the position of its initial conditions. The part position finder  44  finds the calibration pin  22  new position by shifting the assembled fiducial pattern model  36  (not the sub elements separately) in 3D in the y- and z-directions, and rotating around the x- and y-axis, to obtain that all the frame positions in this loop become consistent with each other again. By starting with a given position, and calculating the positions mapped through a certain closed loop we know that we should come back to the same positions. I.e. the part position finder  44  of this invention ensures that, when positions are mapped through the whole loop, all positions that are members of a given closed loop should map back on to themselves. If the fiducial pattern image  58  is translated, rotated and distorted relative to the initial fiducial pattern image model  52 , then the frame positions of the loop ( 24 - 22 - 12 - 10 - 20 - 18 - 26 - 24 ) are no longer consistent with each other. The part position finder  44  then applies the part change constraint  68  that only the frame representing the fiducial pattern model  36  is allowed to translate in the y- and z-directions, and rotate around the x- and y-axis. Except for the carrier  14 B and  14 C displacements, taken care of by the machine position  60 , all other frames are assumed to have not moved relative to each others. 
     The mathematical problem of restoring loop consistency is obtained by solving a set of linear equations, describing the transforms between the different frames. This can be accomplished by use of 4×4 matrices describing the 3 dimensional translation and rotation by means of so called homogenous coordinates. In the present example the y-translation and x-rotation of the stem  22 ″′ sub element, the z-shift of the blade  22 ′ sub-element, the z-shift of the blade  22 ″ sub element, between the fiducial pattern image model  52  and the fiducial pattern image  58 , are four know values (found by means of the above spline least square calculations). The 3D(imentional) y- and z-translation, and x- and y-rotations of the fiducial pattern model  36 , the searched part change  72 , are four unknown values. By such means the part position finder  44  calculates the fiducial pattern model  36  displacement and thereby also the calibration pin  22  position. The above process is completed for both data sets that originated from the two primary fiducial pattern images  58 . From the found values the mean x-rotations represent the rotation axis angle, the mean y-translation the rotation axis y-position, and the mean z-translations the calibration pin  34  length. The mean y-rotation angle represents the rotation of the optical axis relative to the machine. The part position finder  44  output all these data as part change  72  to e.g. a monitor as a feedback to an operator that works with production, alignment, or service alignment of the optical assembly  26 . The final data are saved as a part of the part geometry relations  70 . The new position of the fiducial pattern model  36  of this calibration pin  22  can also be saved for later reference, alignment, calibration, and control. 
     EXAMPLE 5 
     This example describes how to control the position and wear of an EDM die  22  that might be contaminated with residues. In comparison to cutter tool and touch probe tips an EDM die can have a complicated shape without a defined radius position. The illustrations of  FIGS. 3   b - c  indicate the shadow image of a simple die  22  in two given rotation angles. For the purpose of illustration we have selected two positions of rotation out of many, indicating two fiducial pattern  34 A and  34 B that are part of the die  22  control in one rotation scan, and two other fiducial patterns  34 E and  34 F that are part of the die control in another rotation scan. The fully drawn line shows a die  22  with wear, and the dashed line shows the geometry of a fiducial pattern model  36 . The fiducial pattern model  36  might come from a CAD drawing or a previous recording of the same die without wear. The die rotates at a speed of e.g. 70 rpm. 
     The present example is illustrated in  FIGS. 3   a - c . The part position finder  44  can be embodied as process within a computer, personal computer, dedicated processor, or similar. In this example we shall assume that part position finder  44  processes are carried out by means of two computers, the machine NC computer  46 , and the computer  48  that controls and monitors the optical assembly  26 . The two computers are connected through a local network. This connection handles the request  50  and the resulting part change  72  data. The part geometry relations  70  have been loaded into the part position finder  44  at an earlier stage. The request  50  identifies the die  22  and specifies a rotation speed of e.g. 70 rpm (around the z-axis). We assume that a fiducial pattern model  36 , describing the 3D(imentional) die geometry, is loaded into the computer  48  as a part of the request  50  (from the fiducial pattern model  36  the part position finder  44  derives the fiducial pattern image model  52 ). 
     To describe the control principles in simple terms, in the present example an x-y-plane cross section with a prism shaped die  22  makes a quadrate, and that four fiducial patterns  34  around the circumference, representing four corners with equal radii distances from the rotation center, will be studied. 
     In  FIGS. 3   b  and  3   c  the patterns  34 A and  34 B illustrates two of those four patterns  34 A,  34 B,  34 C, and  34 D. Since the die  22  rotates around the z-axis all fiducial patterns refer to the same z-height, as indicated by  34 A and  34 B. The size of the field of view  74  is shown by the small rectangles in  FIGS. 3   b - c . If the die  22  is a cylinder, i.e. the cross section is a circle, the full circumference of patterns, like for example 360 patterns around the circle, could be studied. An illuminator  42  receives the control  54  from the position finder  44  to create a pulsed illumination of the fiducial patterns  34 A,  34 B,  34 C, and  34 D along the optical path  56 A. To create sharp images, to optically freeze the movement, the illuminator  42  is in this case an electronic circuit that modulates a light source. An optical detector  24  is free running at a timing rate of 60 images per second provided by the timer  38 . It records along the optical path  56 B fiducial pattern images  58  of the fiducial patterns  34 , corners of the die  22 , while the die rotates at the speed of 70 rpm. 360 images are recorded. 
     The images are relayed to the part position finder  44 . The die  22  is back illuminated by the illuminator  42  and the fiducial pattern images  58  represent shadow images of the die in different angular orientations. When the die  22  rotates at the speed of 70/60=1.1667 rotations per second, and the optical detector operates with 60 images per second, the recording position will shift the fraction 7/360 of the circumference per image. To fill the whole circumference with a series of images the nominator of this fraction should always be a prime number, like the seven in this example, and the total number of images divided by this prime number should not be an integer. The illuminator  42  pulses are synchronized as indicated by numeral  76  with the optical detector timer  38 . On the basis of the input request defining the 70 rpm tool rotation speed, and the 360/360=1 degrees angular rotation resolution, the part position finder  44  calculates the pulse width and pulse distance. 60 rpm is equal to 1.1667 rotations per second. The full circumference is covered in 6 seconds (360 images at a rate of 60 images per second). In order to optically freeze the rotation movement the pulse width should be less than the passing time of the angular resolution distance, i.e. less than ( 1/60)*( 1/360)=0.000046 (46 microseconds). 
     These illumination parameters are given to the illuminator  42  as the control  54  signal from the part position finder  44 . The internal pulse calculations of the part position finder  44  ensure that no pulse is made in the neighborhood of the image shifts (“blanking” period). The full tool circumference is divided into 360 (360 images) equally spaced angular positions. The fiducial pattern images  58  are by known means converted/digitized and will be available for part position finder  44  operations. The part position finder saves these 360 images in 6 seconds. Without delay the die  22  machine positions  60  are recorded by the part position finder  44 . 
     Two views of the fiducial pattern  34  are shown in  FIGS. 3   b - c . The coordinate axes of  FIGS. 3   a - c  indicate the orientation of the different views. The views of  FIGS. 3   a  and  3   b  represent two of the 360 images that are recorded. The rotation makes it possible to record a series of images and later select the ones of most interest. The two views of  FIGS. 3   b  and  3   c  indicate the selected orientations for the detection of the fiducial patterns  34 A and  34 B corners.  34 C and  34 D, representing the orientation of the other two corners, are not shown. Since the series of images may be recorded at an arbitrary angular starting position in the rotation cycle, the part position finder  44  first have to find the correct angular position of each fiducial pattern images  58 . To do that the part position finder  44  creates a truncated function of the extreme +y-shadow distances. A proper truncation can be calculated from the 3D fiducial pattern model  36 . It then calculates the similar +y distances from the fiducial pattern images  58 . These functions are shifted to find the best overlap. By use of the found shift the part position finder  44  calculates the angular orientation of the recorded images  58 . The shift might not coincide with an image, but there will be a nearest neighbor image to each of the four corner positions, and a corresponding angular distance from those corner positions. These four images will be marked as the primary fiducial pattern images  58  of the patterns  34 A,  34 B,  34 C, and  34 D. In the present example the part change constraints  68  are defined by each of the die corner model  36  positions that are allowed to shift radially in the y- and z-directions. This shift is due to the y- and z-die wear  66 . 
     As described earlier the machine position data  60  are added to the corresponding frame positions. On the basis of exact distortion calibration the fiducial pattern image model  52  and the fiducial pattern model  36  are made to map each others. For simplicity the fiducial pattern image model  52  is placed in the center of the field of view. This ensures that the initial part geometry relations  70 , where the optical detector  24  includes the fiducial part image model  52 , and the die  22  includes the fiducial part model  36 , are consistent with each others, and especially that the calculation of a position through any closed loop of the part geometry relations  70  of  FIG. 2   a  replicates itself. 
     The primary fiducial pattern images  58  of the corners, the angular distance of the distances from the ideal orientation mentioned above, and the corresponding machine encoder positions  60 , are fed into the part geometry relations  70  of the part position finder  44 . The part position finder  44  first calculates a raw data version of the primary fiducial pattern images  58  and rotates those data into the angular orientation of the ideal positions. The raw data are found by means of conventional image processing edge finding routines. The part position finder  44  then calculates the individual y- and z-displacements of the fiducial pattern image model  52  corner elements that best fit the rotated raw data positions calculated above. The part position finder  44  creates a mathematical spline function describing a fiducial pattern image model  52  that contain four separate sub elements. It then fine tunes the position of the sub elements by repeating an iterative process for each of them. The spline displacements are calculated by iteratively translating the model spline in the y- and z-direction and finding the minimum of the least square sum of distances between the spline and raw data. The process is repeated for each of the primary fiducial pattern images  58 . 
     As illustrated in  FIG. 3   a  the die  22  is mechanically interlinked to the optical detector  24  via work tool chuck  21 , work tool carrier  10 , work tool support  20 , machine support link  18 , and the optical assembly  26 . The fiducial pattern  34  is also optically interlinked to the optical detector  24 . This creates what we call the frame loop ( 24 - 22 - 21 - 10 - 20 - 18 - 26 - 24 ). The part position finder  44  receives a request  50  to find the y- and z-wear of the die corners  34 . The sub-elements of the fiducial pattern image model  52  are displaced. The part position finder  44  finds the corner  34  new positions by shifting the individual fiducial pattern model  36  corner positions in 3D in a plane whose normal is parallel to the direction of observation, and by ensuring that all the frame positions in this loop become consistent with each other. By starting with a given position, and calculating the positions mapped through a certain closed loop in  FIG. 3   a , we know that we should come back to the same positions. I.e. one purpose of the part position finder  44  of this invention is to ensure that, when positions are mapped through the whole loop, all positions that are members of a given closed loop should map back on to themselves. If the fiducial pattern image  58  is translated relative to the initial fiducial pattern image model  52 , then the frame positions of the frame loop ( 24 - 22 - 21 - 10 - 20 - 18 - 26 - 24 ) are no longer consistent with each other. The part position finder  44  then applies the part change constraint  72  that only the frame representing the individual corners of the fiducial pattern model  36  is allowed to translate in the y- and z-directions. 
     The mathematical problem of restoring loop consistency is obtained by solving a set of linear equations, describing the transforms between the different frames. This can be accomplished by use of 4×4 matrices describing the 3D (three-dimensional) translation and rotation by means of so called homogenous coordinates. In the present example the y-z-translation of each of the corner sub element, between the fiducial pattern image model  52  sub elements and the fiducial pattern images  58 , are four pairs of know values (found by means of the above spline least square calculations). The effectively 2D translation of four pairs of the fiducial pattern model  36  sub elements, the searched part change  72 , are four pairs of unknown values. By this means the part position finder  44  calculates the fiducial pattern model  36  sub elements displacement and thereby also the die  22  wear. The computer  48  output all these data as part change  72  to the NC computer  46  to allow the NC computer to make a decision whether the wear is acceptable or not. The part changes  72  are saved as a part of the part geometry relations  70 . The new position of the fiducial pattern model  36  of this die  22  can also be stored for later reference. 
     The present example describes the recording of the fiducial patterns  34 A-D. By moving the die  22  in the z-direction, shifting the rotation axis position in the y-direction, and repeating the rotation process, other fiducial patterns can be recorded, as indicated by the fiducial patterns  34 E-F in  FIG. 3   a . If needed this rotation process can be repeated many times across the die  22 . 
     EXAMPLE 6 
     This example is illustrated in  FIGS. 4   a - c . The purpose is to control the die position after it has been taken out of the machine and been put back in. From the point of recording this example is otherwise similar to Example 5, but here the EDM die  22  is illuminated and observed in reflection geometry, rather than the shadow arrangement of Example 5. The fiducial patterns  34 A-D is the surface structure of the die itself. The fiducial pattern image models  52  are actually images of the surface structures  34 A-D, before the die  22  is taken out. The fiducial pattern images  58  are then recorded after the die has been put back in. Techniques for finding fiducial pattern image model shifts, such as shifts of e.g.  52 , are described in PCT/NO2005/000336. In comparison to Example 5, where the model sub-elements were allowed to move independently, the fiducial pattern model  36  is in this case translated and rotated as a whole in 3D to find the new six degrees of freedom of the die position. 
     For both examples 5 and 6 the EDM die rotation speed is smaller than for the rotating milling tools. This makes it possible to rotate the die and record fiducial pattern images  58  in a step and repeat fashion. If the die is sitting in a chuck, that defines its z-rotation angle precisely, then the above descriptions of how to refer the fiducial pattern images  58  to the correct z-angular position of rotation is made simpler. 
     EXAMPLE 7 
     Examples 1-6 describe arrangements according to the present invention where essentially one illuminator  42  and one optical detector  24  is used. In order to obtain a full 3D control, not only the image y-z-positions need to be recorded. This is indicated in  FIG. 5  where a combination of two illuminator  42 A-optical detector  24  arrangements is illustrated as illuminator  42 A-optical detector  24 A and illuminator  42 B-optical detector  24 B. The illuminator-detector combinations need not be arranged into one optical assembly  26  as illustrated. Depending on space requirements they can be placed separately.  FIG. 5   b  shows the optical arrangement in  FIG. 5   a  from a different direction of view, as indicated by the accompanying coordinate axes.  54 A and  54 B denote links between the detectors  24 A and  24 B, respectively, and the part position finder  44 .  58 A and  58 B denote links between the part position finder  44  and the detectors  24 A and  24 B, respectively. 
     Quality Control Tool Positions Versus Rotating Tool Positions 
     A touch probe is suitably used inside machines to do quality control. By combining the invention of PCT/NO2005/000336 with the present invention the position of a quality control tool can be related to the position of a rotating machining tool. During position control the touch probe  22  is held by the tool chuck  12  in a static position.  FIG. 6  illustrates an example where the milling tool  22  of  FIG. 1  is replaced with a touch probe  22 . The touch probe  22  finds positions on a work piece  30  by touching the work piece  30  surfaces with a certain force until an internal process triggers that a specific state of contact is obtained, then the machine movement stops. The touch probe tip is a sphere of a hard material, e.g. ruby. At the time of trigger the position of the position encoders  14 B and  14 C are read. Those positions represent the touch probe tip  34  position. The unloaded position of the touch probe  34  tip is different from the position at the time of trigger.  FIG. 7  indicates a modification of an arrangement as disclosed in said PCT/NO2005/000336 and which can be used to find the touch probe unloaded position. 
       FIG. 7  illustrates how the touch probe trigger position can be found. In order to test the trigger position of the touch probe  22  the pneumatic rod  102  brings a glass cube  100 , with a fiducial pattern  34 A attached to it, into the optical detector  24  field of view. The touch probe moves against the glass cube until it triggers, and then stops. The glass cube  100  position can be then be found in a manner as e.g. disclosed in said PCT/NO2005/000336. 
     If we assume that the distance between unloaded and trigger positions of the touch probe  22  do not change much over time, we may not need to repeat the trigger touch probe calibration of  FIG. 7  each time the touch probe is used. Since we have now been able to calibrate the position of the touch probe  22  while it is triggering, and been able to reliably refer that position to the position of the optical detector  24 , we can later simplify touch probe  22  position calibrations. To finish a full touch probe calibration we only need to record an image  58  of the touch probe tip and by image processing calculate its position relative to the optical detector  24 . To do that the pneumatic rod  102  is pulled back so that glass cube  100  and the fiducial pattern  34 A are out of the optical detector  24  field of view. By use of the machine we bring the unloaded touch probe  22  into the field of view, as indicated by  FIG. 6 . Later, unless the touch probe  22  is exchanged with another one, or gone out of calibration, we may read the position of the unloaded touch probe  22  add the trigger offsets, and use those data for touch probe position calibration. It should be noted that in the touch probing method, the finding of the trigger position includes using one of a transparent, frosted glass plate attached to the glass cube, and frosting the glass cube itself. 
     It is conceivable to let the apparatus of the invention be adapted to be supported by a fiducial pattern cleaning device that cleans the fiducial pattern of the rotating part by means of air blowing, or blowing of a detergent agent followed by air blowing. Further, it is conceivable that the part position finder  44 , the part change constraints  68 , the part geometry relations  70 , and the request  50  inputs are distributed on different units of equipment elected from the group of: computers, electronic processors, embedded processors, and hard wired electronics, said units capable of exchanging data for the purpose of finding the part change  72 .