Abstract:
A method for correcting errors in a coordinate measuring machine having a measuring head which is adapted to move in at least two different spatial directions. Measuring scales and measuring lines are assigned to each spatial direction. The measuring lines of different spatial directions intersect, and correction values are determined along the measuring lines at predetermined values of the scales in order to correct for elastic and/or geometric errors of the scales and/or of the guiding mechanism for moving the measuring head. According to one aspect of the invention, the correction values determined along a measuring line of a first spatial direction are modified such that the modified correction value of this measuring line assumes a predetermined value at the point of intersection with a first measuring line of a second spatial direction.

Description:
REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is a continuation of international patent application PCT/EP03/00217, filed on Jan. 13, 2003 and published as WO 03/081168 in German language, which claims priority under the Paris convention from German patent application DE 102 14 490.7 filed on Mar. 26, 2002.  
       BACKGROUND OF THE INVENTION  
       [0002]     The invention relates to a method and a device for correcting errors in a coordinate measuring machine having a movable measuring head and elements for guiding the measuring head in at least two different spatial directions.  
         [0003]     According to DE 33 34 460 A1, a position of a measuring head of a coordinate measuring machine is determined interferometrically. The interferometrical value is compared by means of an evaluation device with values are supplied by a scaling, such as an optically and/or electrically scannable sequence of mechanical marks. Deviations between values supplied from the scales and the values provided by the interferometric acquisition are stored and are used in the operation of the coordinate measuring machine to correct the values supplied from the scales.  
         [0004]     So-called guiding errors can be corrected in this way during operation of the coordinate measuring machine. Such guiding errors can be determined not only interferometrically, but also using other measuring means, such as mechanical calibrating apparatuses. A guiding error is understood as a deviation of the true coordinates of the measuring head from the coordinates which are supplied by the scales in this position. The true coordinates are dependant on the position of the guides in this case.  
         [0005]     In the case of ideally stiff guides, such deviations between desired and actual positions can be caused by geometrical errors of the guides and/or of the scales. For example, a guide which guides a translational movement of the measuring head can have a manufacturing-induced corrugation that leads to transverse deviations of the measuring head position relative to the direction of the translation.  
         [0006]     As an example, in order to correct for these errors, there might be defined a single measuring line (standard line) along each axis of the coordinate measuring machine, with interferometric correction values, for example, being determined in relation to this measuring line (standard method). Correction values at points which are situated in measuring volumes remote from the standard measuring lines are produced in the case of stiff guides by computational interpolation based on measured correction values of the individual standard measuring lines.  
         [0007]     However, real coordinate measuring machines have guides which are not ideally stiff. These guides have an elasticity which is dependent on the materials and structures used. This elasticity leads to deformations of the coordinate measuring machine which cause deviations between the actual coordinates and the coordinates supplied by the elastically deformed scales, and which are therefore noticed as errors. In the case of a measuring head which is fitted at the end of a measuring arm which can be extended transverse to the direction of gravity, a flexure of the measuring arm which grows with increasing extension length will occur, for example. Such a flexure causes an elastically caused positional error of the measuring head in the direction of the flexure.  
         [0008]     Such elastically caused errors overlap with the geometrically caused guiding errors. It is problematic here that the elastically caused errors and the geometrically caused errors can generally be a function of various influences and axes or spatial directions. The above-described standard method is directed toward the correction of geometrically caused errors, and it is therefore generally not optimal for correcting elastically caused errors. However, raising the accuracy of coordinate measuring machines also requires a correction of elastically caused errors.  
         [0009]     DE 195 18 268 A1 discloses a method for measuring coordinates at workpieces, in the case of which the elastic bending behaviour of coordinate measuring machines is simulated by a deformation matrix. This known method delivers a good correction quality, but requires a high outlay on measuring and computing in order to determine the coefficients of the deformation matrix.  
       SUMMARY OF THE INVENTION  
       [0010]     Against this background, it is the object of the invention to provide a high-quality correction even for measuring errors which are caused by elastic deformations of the measuring apparatus. It is another object to keep the required measurement outlay relatively low in order to permit the correction to be used within industrial manufacturing of coordinate measuring machines.  
         [0011]     According to one aspect of the invention, these and other objects are achieved by correction values of a measuring line of a first spatial direction being modified such that the correction value of this measuring line assumes a predetermined value at the point of intersection with a measuring line of another spatial direction.  
         [0012]     A consequence of this approach is that the modified correction values along the measuring line of the first spatial direction reflect only relative deviations with reference to the predetermined value, while the absolute value information is lost by the modification. Under some circumstances, the absolute value also included an unknown offset resulting from the measuring operation, and it was additionally affected by influences of errors of the second spatial direction. Modifying the correction values such that a predetermined value is set at the point of intersection results in the advantage that these undesired influences from the other spatial direction and from the offset are eliminated such that the remaining, modified correction values of the first spatial direction are no longer dependent on these influences.  
         [0013]     In this way, a certain relationship is built up between intersecting measuring lines, and this relationship then consequently permits a relationship between measuring lines running in parallel which are intersected by a transverse measuring line. This relationship between parallel measuring lines constitutes a precondition of the inventive correction of elastically caused errors with the aid of parallel measuring lines.  
         [0014]     In accordance with an advantageous refinement, the modification of the correction values is performed by combination with an additive offset.  
         [0015]     This procedure is advantageous due to an exceptionally low computational outlay.  
         [0016]     In accordance with a further refinement, the predetermined value is equal to zero.  
         [0017]     A very low requirement for storage space results as an advantage from the fact that there is a need to store only deviations from zero.  
         [0018]     According to a further refinement, the first spatial direction is assigned a number of measuring lines which run along this spatial direction.  
         [0019]     The use of a number of measuring lines in one spatial direction, in conjunction with the inventive reference to a predetermined value, permits a quantitative acquisition of elastic influences transverse to the first spatial direction  
         [0020]     A further refinement of the invention comprises a further modification of the correction values as a function of a second measuring line of the second spatial direction.  
         [0021]     This refinement permits a compensation of effects which are caused by undesired deviations of the measuring line directions from desired directions while recording the associated errors or correction values.  
         [0022]     One embodiment of this refinement is characterized by the fact that a curve which joins the correction values of the measuring line, which runs in the first spatial direction, is manipulated such that after the manipulation the correction value of this measuring line assumes a predetermined value at the point of intersection with the second measuring line of the second spatial direction.  
         [0023]     This embodiment advantageously permits the above-mentioned undesired effects to be compensated easily by computation.  
         [0024]     According to a further embodiment of this refinement, the predetermined value is equal to zero. In accordance with a further embodiment, the curve is manipulated outside a fixed point which is formed by the predetermined value of the modified correction value of this measuring line at the point of intersection with the first measuring line of the second spatial direction.  
         [0025]     Such a manipulation can be obtained, for example, from the equation fg(xi)=f(xi)−(h/xh)*xi, with f(xi) representing a sequence of correction values about points xi of a measuring line of a first spatial direction, and h specifying the distance of the correction value f(xh) from the value of zero at the point of intersection of this measuring line with the second measuring line of the second spatial direction. The result of this is a manipulation of the curve f(xi) about the zero point.  
         [0026]     These embodiments are likewise characterized by a simple computational implementation.  
         [0027]     In accordance with a further refinement of the invention, the measuring lines of the first spatial direction are additionally subjected to a rectangularity measurement with reference to a normal to the plane which is defined by a number of measuring lines of the first spatial direction. A deviation in the rectangularity of each single measuring line from a common reference value is formed and there follows a manipulation of the curves of the correction values of the individual measuring lines, the extent of the manipulation being determined by the said deviation.  
         [0028]     This embodiment advantageously permits compensation of deviations of the measuring line directions from a desired value which deviations lead out of the plane of the measuring lines.  
         [0029]     Computationally simple compensation of this effect results according to a further embodiment by virtue of the fact that the extent of the manipulation is proportional to said deviation. Here, the term manipulation respectively defines, for example, a correction of the curve by subtraction of a straight line.  
         [0030]     In accordance with a further advantageous refinement, the correction values of a predetermined measuring line from a multiple spectrum of measuring lines running along the first spatial direction are subtracted from the associated correction values of these measuring lines.  
         [0031]     The effect of this subtraction is that the remaining relative corrections or errors of parallel measuring lines are related to the corresponding values of a standard line. Since the geometrical errors of the parallel measuring lines under consideration are equal, this subtraction advantageously results in elimination of these geometrical errors, with the result that the remaining values are determined solely by elastically caused errors.  
         [0032]     The data obtained in this way for an elastic correction or for the elastically caused error which is to be corrected are therefore independent of the geometrical guiding errors, and can be either kept constant for a type of coordinate measuring machine, or be adapted by means of simple measurements.  
         [0033]     It is to be seen as a further advantage that these data include only long-period components for elastic correction, and can therefore advantageously be smoothed by means of filters of known type.  
         [0034]     Consequently, for each individual machine of a series of machines, guiding errors need only be measured by means of a standard procedure. In other words, there is no need to redetermine errors from elastic deformations for each individual coordinate measuring machine.  
         [0035]     A further advantage is to be seen in that the origin of the correction data can be accomplished in accordance with the separation indicated, and can be visualized separately.  
         [0036]     This also provides the possibility of individual corrections being excluded or introduced in a simple way (elastic and geometric fashion for individual machines, elastic fashion for type series).  
         [0037]     Furthermore, the order of the correction of guiding errors of individual machines and elastic errors typical for type series can also be selected as desired in the case of a two-stage correction.  
         [0038]     To this end, it is advantageous for the correction values of the predetermined measuring line (standard line) running along the first spatial direction to be stored as first correction values in a correction value memory.  
         [0039]     These first correction values are advantageously determined individually for an individual coordinate measuring machine and stored. They include the geometrical guiding errors of individual machines and the components of the elastic errors for individual machines.  
         [0040]     A further embodiment provides that the results obtained from the subtraction are stored as second correction values in the correction value memory.  
         [0041]     These second correction values include components of elastically caused errors which are typical of type series and are therefore not tied to individual machines. These second correction values are advantageously determined in the case of an individual coordinate measuring machine of a specific type, and stored in correction value memories of other measuring machines of the same type. Accompanying this is the particularly great advantage that the measurements which go beyond the standard procedure need not be undertaken for each individual machine. Rather, it is sufficient for these measurements to be recorded for an individual machine of a series type as representative of the other machines of the series type.  
         [0042]     In accordance with one refinement of the invention, guiding errors of coordinate measuring machines are corrected during operation of the coordinate measuring machines on the basis of the first and the second correction values. This type of correction permits correction both of the geometrical errors and elastic errors of individual machines, on the one hand, and of the elastic errors typical of series type, on the other hand. This correction can be supplemented by absolute error information obtained when recording standard lines.  
         [0043]     In accordance with a further refinement of the invention, correction values for points which are not situated on the measuring lines are determined by means of interpolation of correction values from at least two measuring lines.  
         [0044]     The interpolation permits a restriction of the number of measuring lines to be recorded, since it permits correction values to be obtained between the measuring lines by means of a computational method. As already remarked above, this interpolation presupposes a common relationship between the measuring lines.  
         [0045]     The interpolation can be based on a two-dimensional interpolation method or a three-dimensional interpolation method.  
         [0046]     A typical coordinate measuring machine suitable for using the said method is a horizontal arm measuring machine, which has a column which can move in the X direction and supports a horizontal arm, the arm being movable in the Y direction and in the Z direction, and having a measuring head. Because of the elastic deformations occurring upon extension of the horizontal arm, the above-mentioned advantages result in particular extend for such a coordinate measuring machine.  
         [0047]     The application of the invention is not, however, limited to such a horizontal arm measuring machine, but can be applied to every coordinate measuring machine in which elastic deformations occur. An example of a further coordinate measuring machine is a so-called gantry machine which has a gantry, movable in the Y direction, and a carriage, which can move on the gantry in the X direction and which supports a center sleeve which is movable in the Z direction, with a measuring head. Coordinate measuring machines of cantilever design or having any desired other kinematic chains constitute further exemplary embodiments.  
         [0048]     Further advantages follow from the description and attached figures.  
         [0049]     It goes without saying that the above-named features and the following ones still to be explained can be used not only in the combination respectively specified, but also in other combinations or on their own, without departing from the scope of the present invention.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0050]     Exemplary embodiments of the invention are illustrated in the drawing and explained in more detail in the following description. In the drawing:  
         [0051]      FIG. 1  shows a horizontal arm measuring machine as an example of a coordinate measuring machine;  
         [0052]      FIG. 2  shows the structure of an evaluation apparatus from  FIG. 1 ;  
         [0053]      FIG. 3  shows an illustration for explaining translational errors;  
         [0054]      FIG. 4  shows an illustration for explaining rotational errors;  
         [0055]      FIG. 5  shows the profile of a rotation error related to the X axis in the case of various movements of the measuring head of the horizontal arm measuring machine from  FIG. 1 ;  
         [0056]      FIG. 6  shows a laser measuring machine for recording the translational and rotational errors;  
         [0057]      FIG. 7  shows a schematic representation for explaining a measurement of straightness;  
         [0058]      FIG. 8  shows two profiles, related to the Y axis, of rotational errors with different error components;  
         [0059]      FIG. 9  shows angular errors in the recording of measured values along specific measuring lines;  
         [0060]      FIG. 10  shows effects of these angular errors;  
         [0061]      FIG. 11  shows results of a correction of these angular errors;  
         [0062]      FIG. 12  shows a multiple spectrum of measuring lines with a standard line and two additional multiple lines;  
         [0063]      FIG. 13  shows a qualitative representation of remaining errors after removal of the offset;  
         [0064]      FIG. 14  shows a qualitative representation of remaining errors after normalization of the multiple lines from  FIG. 12  to the standard line of  FIG. 12 ;  
         [0065]      FIG. 15  shows geometrical relationships relating to a two-dimensional interpolation method;  
         [0066]      FIG. 16  and  
         [0067]      FIG. 17  show alternatives to the recording of measuring lines with the aid of mechanical calibration apparatuses instead of the laser measuring machines of  FIG. 6 . 
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0068]     An overall view of a horizontal arm measuring machine as an example of a coordinate measuring machine is denoted by numeral  10  in  FIG. 1 . The horizontal arm measuring machine  10  has a reference plane  12  on which a column  14  can move along an X direction  16 . The reference plane  12  is, for example, a measuring table or as flat as possible a surface in space. The position of the column  14  can be read off an X scale  18 . The column  14  supports horizontal arm  20  which can move in the Y direction  22  and Z direction  24 . The Y position of the horizontal arm  20  and its Z position can be read off on a Y scale  26  and a Z scale  28 , respectively. The horizontal arm  20  supports a measuring head  30  with the aid of which workpiece positions or components can be approached. The X, Y and Z positions reached by the measuring head  30  when touching the components can be read off on the said scales, and/or acquired by suitable sensor systems and transmitted to an evaluation apparatus  32  for further processing.  
         [0069]      FIG. 2  illustrates the structure of such an evaluation apparatus  32 . Accordingly, a central processing unit  34  switches between input sections and output sections of an input and output device  36  in accordance with programs stored in a program memory  38  and by using data stored in a correction value memory  40 .  
         [0070]      FIG. 3  illustrates translational errors such as occur during operation of the coordinate measuring machine and of the horizontal arm measuring machine  10 . In this case, the numeral  42  denotes a non-errored position of the measuring head  30 . Numeral  44 , by contrast, denotes a position of the measuring head  30  which differs from the non-errored position by a distance xTx. Here, the first x (on the left) denotes the direction of movement of the measuring head, the letter T indicates that the movement is a translation, and the second x (on the right) specifies the direction of the error represented. Consequently, xTx corresponds to a positional error in the X direction which occurs on a translation in the X direction. A typical cause for such an error would be an inaccuracy of the X scale  18 .  
         [0071]     Numeral  46  denotes the position of the measuring head  30  with a positional error in the Y direction. This error is noted here as xTy. Thus, xTy represents some sort of a linearity deviation. Such an error is caused, for example, by a waviness of the X guide, which leads to a transverse deviation y in the case of a translation in the direction of the X axis.  
         [0072]     The numeral  48  denotes the position of the measuring head  30  with a positional error xTz in the Z direction. Here, as well, the notation is based on a translatory movement in the X direction, something which is expressed by the first two letters x and T. The transverse deviation in the Z direction typically results, as also does the previously described transverse deviation in the Y direction, due to a waviness (lack of straightness) of the X guide.  
         [0073]      FIG. 3  shows that X, Y and Z translational errors for movements in the direction of the X axis. X, Y and Z errors occur analogously upon movement in the direction of the Y axis and upon movement in the direction of the Z axis, the result being a total of 3×3=9 possible translational errors.  
         [0074]      FIG. 4  illustrates three possible rotational errors for movements of the measuring head  30  in the direction of the X axis. Here, the error xRx denotes rotations about the X axis for movement in the direction of the X axis, and thus a so-called rolling of the measuring head  30 . A rotation about the Y axis upon movement in the direction of the X axis is denoted as pitching, and a rotation about the Z axis upon movement in the direction of the X axis is denoted as yawing.  
         [0075]      FIG. 4  therefore represents three possible rotational errors for movement in the direction of the X axis. Rolling, pitching and/or yawing can also occur analogously in the case of movements in the direction of the Y axis as well as for movements in the direction of the Z axis, and so 3×3=9 possible errors also result in the case of rotation.  
         [0076]      FIG. 5  illustrates possible profiles of rotations about the X axis (Rx) for various movements of the measuring head  30 . The curves over the parallel measuring lines  49  correspond to xRx errors, and the curve over the straight line connecting the points y 1  and y 2  corresponds to a yRx error. The tendency to be seen here is that the Rx error becomes larger with increasing y (y 2 &gt;y 1 ). This is a typical effect such as is to be expected in the case of a horizontal arm measuring machine  10  where there is addition of geometrical and elastically caused errors (these errors can, however, also be of different sign and are then subtracted). The further the horizontal arm  20  is extended, the larger is the resulting torque about the X axis, and this is absorbed by an elastic deformation of the column  14  and of the horizontal arm  20 . The elastic deformations result in the trend in the Rx values which rises from left to right in  FIG. 5 . The short wave minima and maxima which are expressed on the profiles illustrated in  FIG. 5  typically result from the geometrical guiding errors of the X and Y guides.  
         [0077]      FIG. 6  shows a laser measuring device  50  with the aid of which it is possible to record the profiles illustrated in  FIG. 5 . The numeral  52  denotes a base which supports four lasers  54 ,  56 ,  58  and  60 , for example laser diodes, together with a focussing unit. The base  52  is, for example, connected to the reference plane  12  of the horizontal arm measuring machine  10  in a defined fashion. A reflector arrangement  62  with reflectors  64 ,  66 ,  68  and  70  is connected to the measuring head  30 . The light emitted by the lasers  54 ,  56 ,  58  and  60  is reflected by the reflectors  64 ,  66 ,  68  and  70  and recorded by photodetectors  80 ,  82 ,  84  and  86 . The measuring head is moved with the reflector arrangement  62  in the direction of the laser beams. Rotations and translatory displacements which occur lead in this case to changes in the intensity, recorded by the photodetectors  80 ,  82 ,  84  and  86 , of the reflected laser beams. The profiles illustrated in  FIG. 5  can be produced from these changes in intensity.  
         [0078]     Thus, for example, the interferometer  72  can be used to determine positional errors in the direction of movement of the measuring head and consequently of the reflector arrangement  62 . The laser beam emitted by the laser  56  is split at the interface between the prisms  74  and  78  into a measuring beam and a reference beam. The reference beam is directed onto photodetectors  80  with the aid of the prism  76  and the boundary surface between the prisms  74  and  78 . The reference beam therefore has a defined length. The measuring beam leaves the prism  78  and is reflected by the reflector  66 , for example a silvered cube corner. The prisms  74  and  78  direct the reflected beam onto the photodetectors  80  such that the reference beam and reflected beam are superimposed. The reflected beam or measuring beam has a variable length which is a function of the spacing of the reflector arrangement  62  from the base  52 . Depending on the path difference between the reference beam and measuring beam, interference after the union of the beams results in amplification or extinction. The movement of the reflector arrangement  62  results in a sequence of brightness maxima and minima at the spacing of half wavelengths. A linear measure with the fineness of half a wavelength, for example, is yielded by counting the maxima. Thus, the result for a wavelength of 600 nm, for example, is an accuracy of the order of magnitude of tenths of a micrometre. It is thereby possible when the measuring head is moved in the direction of the X axis to determine positional errors with this accuracy in this direction (xTx).  
         [0079]     The light emanating from the laser  58  is reflected by a flat mirror  68  on the photodetector  84 . Yawing and pitching movements of the reflector arrangement  62  are therefore imaged directly in the intensity distribution on the photodetector  84 . Rotational pitching and yawing errors can therefore be determined by evaluating this intensity distribution.  
         [0080]     Rolling movements can be determined by evaluating the signals of the photodetectors  82  and  86 . A single photodetector  82  or  86  can be used firstly to determine transverse displacements of the reflector arrangement  62 . This is illustrated by  FIG. 7 . The reflector  64  can be implemented, for example, as a silvered cube corner and has the property of retroreflecting incident light parallel to the direction of incidence. In the position denoted by  64 , for example, the reflector  64  reflects the incident beam  90  onto the photodetector  82  as reflected beam  94 . The numeral  88  denotes the reflector  64  in a position displaced transverse to the incident laser beam by the amount a opposite to the Z direction. In this case, the light incident on the reflector  64  is reflected as light beam  92 . As may be seen from the figure, the light beam  92  is incident on the photodetector  82  at the spacing  2  * a from the light beam  94 . Transverse displacements a can therefore be detected by evaluating the intensity distribution on the photodetector  82 . In the illustration of  FIG. 6 , the simultaneous occurrence of a transverse movement of the reflector  64  out of the plane of the drawing and a transverse movement of the reflector  70  into the plane of the drawing (or vice versa) corresponds to a rolling movement about the X axis. It is therefore also possible for a rolling movement to be detected and acquired quantitatively with the aid of the laser arrangement shown.  
         [0081]     In order to detect the various translational and rotational errors, the signals of the photodetectors  80 ,  82 ,  84  and  86  can, for example, be fed to the evaluation apparatus  32 .  FIG. 8  shows rotational errors Ry such as can be acquired with the aid of the laser measuring device  50  described above. Here, numerals  49  denote measuring lines which run in the Z spatial direction and have been measured at a first Y position y 1  and a second Y position y 2 . The numerals  96  and  102  denote the associated zRy profiles. The errors zRy 1  (numeral  96 ) include two constant components  98 ,  100  and a variable remainder.  
         [0082]     The constant error component  98  can result, for example, from a geometrical guiding error of the Y guide at the position y 1 . This geometrical error component then remains constant for the illustrated movement along the Z axis with constant y 1 .  
         [0083]     The constant error component  100  can correspond to a measuring error (offset) which is caused by the adjustment of the laser base  52  or of the reflector arrangement  62 , and remains constant during movement of the measuring head  30  with the reflector  64  along the Z spatial direction.  
         [0084]     In an entirely analogous way, the curve  102 , that is to say the profile of the error zRy at the position y 2  has a constant error component  104  as geometrical guiding error of the Y guide, and a constant measuring error  106  (offset).  
         [0085]     Since the laser measuring device  50  was newly mounted and adjusted in each case for the recording of the error curves  96  and  102 , the offset errors  100  and  106  resulting from these mountings are generally not equal. This holds analogously for the errors  98  and  104  of the Y guide, which are generally different at different points y 1 , y 2 . Because of the different magnitudes of the constant error components, the absolute values of the zRy error curves  96  and  102  cannot be directly compared. This is problematical, in particular, whenever the aim is to interpolate between the lines. The error curves  96  and  102  need to have the same absolute relationship for a correct interpolation. For the reasons illustrated, this is not automatically the case when simply measuring a number of individual lines.  
         [0086]     According to the invention, the profiles of rotational errors (here zRy 1 , zRy 2 ) at defined positions are set to a predetermined value. Such positions are defined, for example, by points of intersection of the measuring line  49  of the first spatial direction with a measuring line of a second spatial direction. In the illustration of  FIG. 8 , the connection of the points y 1  and y 2  could form a measuring line of a second spatial direction. In this case, the error curves  96  and  102  each are additively displaced until they assume the value zero at their respective point of intersection with the join of the points y 1  and y 2 . A common relationship is thereby produced between the rotations zRy 1 , zRy 2  and, if appropriate, yRy. The residual errors remaining after the displacement over the measuring lines  49  specify the relative changes in errors or corrections respectively for movements along the Z spatial direction.  
         [0087]     This eliminates the problem of the initially lacking relationship between the rotation error curves. Further problems arise from the fact that the direction of the measuring lines which are defined by the laser beam direction deviates from the desired direction. This plays a role, in particular, in the acquisition of translational errors.  
         [0088]     Such deviations in direction or angular errors in the case of recordings of measured values are illustrated by  FIG. 9 .  FIG. 9  shows a ZY plane with a vertical line  117 . Numeral  116  denotes the desired direction, and thus the ideal position of measuring lines. The numeral  108  denotes a measuring line of a first spatial direction which is admittedly situated in the YZ plane but deviates in this plane from the desired direction  116  by an angular deviation  120 . The numeral  110  correspondingly denotes a measuring line of a first spatial direction which deviates from the desired direction  116  by an angular deviation  118 , this deviation being directed such that it leads out of the YZ plane. The numeral  112  denotes a first measuring line of a second spatial direction, and the numeral  114  denotes a second measuring line, parallel thereto, of the second spatial direction. The first measuring line  112  serves to define points of intersection for producing the relationships between different error curves, as was explained in conjunction with  FIG. 8 . The second measuring line  114  represents some sort of an auxiliary transverse line which can be used to compensate the effects of the angular errors illustrated. This will be explained below.  
         [0089]      FIG. 10  shows a typical profile of a curve of correction values which are recorded with an angular error of a measuring line. On the left side, the curve has been displaced to the zero point, as was explained in conjunction with  FIG. 8 . The profile rising to the right results from an angular error  118  or  120 . The directional errors illustrated in  FIG. 9  give rise during the measurement operation to apparent transverse deviations which are not present in reality and therefore undesirably falsify the measurement results. With increasing spacing, these apparent transverse deviations grow such that the defective profile of the curve  122  illustrated in  FIG. 10  can result. In this case, the curve  122  is defined by virtue of the fact that it joins different measured errors or correction values corresponding thereto. According to the invention, this error is compensated by manipulating the curve  122  computationally about its left-hand origin until its right-hand end reaches a predetermined value, preferably the value zero. In this case, the right-hand end coincides with the point of intersection of the measuring line  116  and the auxiliary transverse line  114 . The auxiliary transverse line  114 , which was also denoted above as a second measuring line of the second spatial direction therefore serves to compensate angular errors  118 ,  120 . The curve  124  in  FIG. 11  shows the result of the inventive manipulation of the curve  122 .  
         [0090]     It was described above how a common reference for individually recorded rotational error curves can be produced, and how directional errors in translational error curves can be removed. The error values left over after the described conditioning of the acquired values still include elastically caused and geometrically caused error components. Explained below is a further refinement of the invention, which permits a far reaching, if still not complete, separation of elastically caused guiding errors and geometrically caused guiding errors.  
         [0091]      FIG. 12  shows a multiple spectrum  126  of measuring lines  128 ,  130  and  132 , which extend in the Y, Z plane along the Z direction as first spatial direction. Plotted over these measuring lines are rotations about the Y axis in the case of movement in the Z direction, that is to say the zRy errors, or else the correction values for compensating precisely these errors. The measuring lines  128 ,  130  and  132  are intersected by a first measuring line  134  of a second spatial direction (y here). This measuring line arrangement can be used to acquire elastically caused modifications of rotational errors with reference to the Y axis in the case of movements in the direction of the Z axis.  
         [0092]     Consideration is firstly given to the horizontal arm measuring machine  10  from  FIG. 1  in order to illustrate such influences. Extension of the horizontal arm  20  naturally results in elastic flexures which are a function of the extension length, that is to say of the values y 1 , y 2  and y 3  in the image of  FIG. 12 . These elastic flexures are superimposed with a geometrical guiding error which occurs as rotation along the Y guide. The superimposition of the geometrically caused rotation of the horizontal arm  20  with its elastic flexure corresponds physically to a rotation of an arcuate beam. During the rotation of an arcuate beam, the deepest line end of the arcuate beam is rotated out of its deepest position. As a consequence of gravity, this rotation out of the deepest position necessarily gives rise to restoring torque which leads to an elastic torsion of the beam.  
         [0093]     This elastic torsion is superimposed with the geometrically caused rotation. Finally, the result of the superimposition is measured. Different flexures, and thus different restoring torques and therefore different torsions occur depending on extension length (y 1 , y 2 , y 3 ). The result of this is elastically caused influences differing in strength depending on the Y position (y 1 , y 2 , y 3 ), on rotations about the Y axis for movements along the Z axis.  
         [0094]     Similar effects also occur in other spatial directions, for example a zRx guiding error can occur in the X direction. The measuring line arrangement illustrated in  FIG. 12  is therefore to be appraised only as an example.  
         [0095]     Error profiles zRy 1 , zRy 2 , zRy 3  or correction values referred to these errors, are plotted along the measuring lines  128 ,  130 ,  132  in the way described above. Furthermore, the relationship is produced between these zRy curves and the yRy curves over the measuring line  134  of second spatial direction by additively displacing the zRy curves, as was described in conjunction with  FIG. 8 . If appropriate, an angular correction is further performed by manipulation of the curves, as was described in conjunction with FIGS.  9  to  11 . This manipulation or angular correction is important in the case of translations, and can be omitted if appropriate when considering rotations. In qualitative terms, the zRy values remaining after these corrections have the composition in  FIG. 13 . Here, the zRy profiles are illustrated as being essentially constant for reasons of clarity.  
         [0096]     The zRy profile  136  over the measuring line  128  has, for example, a geometrically caused component  140  and an elastically caused component  138 . Analogously, the zRy profile  142  over the measuring line  130  has a geometrical component  146  and an elastically caused component  144  with a negative sign. In the same way, the zRy profile  148  over the measuring line  132  has an elastically caused component  150  and a geometrically caused component  152 .  
         [0097]     As regards the geometrically caused components, it is important here that different geometrically caused errors resulting from different Y positions have already been subtracted in the case of the displacement of zRy curves in accordance with  FIG. 8 . The geometrically caused error components now still remaining in  FIG. 13  therefore result from geometrical influences of the guide in the Z direction.  
         [0098]     These influences are the same for the three measuring lines  128 ,  130  and  132 . It results therefrom as an important conclusion that the remaining geometrical influences can be eliminated by a further subtraction.  
         [0099]     According to the invention, one of the measuring lines  128 ,  130 ,  132  of the multiple spectrum  126  is selected as reference line. This is typically, but not necessarily, the standard line  128  (SL(y 2 )) situated in the middle of the measuring range. Inaccuracies which increase with the spacing are minimized by the middle position. The zRy values of this standard line  128  are subtracted from the corresponding zRy values of the remaining parallel measuring lines  130  and  132 . As illustrated in  FIG. 14 , this results in zRy values which no longer include geometrical components of any sort.  
         [0100]     Physically, these remaining values correspond to the changes in the elastic influences upon transition from the standard line  128  to a line which is parallel thereto. According to the invention, a far reaching, if not complete separation of elastically caused errors and geometrically caused errors is achieved in this way. Separation is far reaching to the extent that the remaining zRy values over the measuring lines  130  and  132  no longer include geometrically caused components of any sort. On the other hand, the separation is not complete, because the zRy values of the curve  136  over the standard measuring line  128  still have geometrically caused components  140  and elastically caused components  138 .  
         [0101]     The far-reaching separation, achieved according to the invention, of the elastically caused influences from the geometrically caused influences is greatly advantageous. Thus, for example, the remaining elastically caused influences, which represent elastically caused changes by comparison with the values of the standard line, are largely constant for coordinate measuring machines of a specific type. In particular, they are not influenced by geometrical guiding errors of individual machines. These geometrically caused guiding errors of individual machines can be acquired for each machine by measuring a few standard lines. By contrast, in the case of an individual coordinate measuring machine the additional elastically caused changes can be recorded by way of representation of the entire type series of these coordinate measuring machines. These values can then simply be stored in a correction value memory for individual machines in addition to the standard lines recorded for the individual machines.  
         [0102]     In this way, the invention also permits a correction of elastically caused guiding errors in conjunction with a low outlay which, when consideration is given to a single machine, does not exceed the outlay previously expended for recording the standard lines.  
         [0103]      FIG. 15  shows an interpolation method for determining and/or correcting errors of any desired points P in the measurement volume of a coordinate measuring machine. Here, the measuring line ML(zTy 2 ) corresponds, for example, to a standard line for whose points B and D associated correction values F(B) and F(D) are stored in the correction value memory as first correction values. The measuring line ML(zTy 1 ) corresponds to a measuring line parallel to the standard line such as was measured by way of presentation for the associated type series of the coordinate measuring machines in the case of an individual coordinate measuring machine. The correction value memory  40  correspondingly contains for the points C and A of this line the changes in the elastically caused errors/corrections by comparison with the values of the points B and D of the standard line. The correction values/errors F(A) and F(C) can then be determined from the values F(T), F(B) and the changes for the points C and A. The error/correction value of any desired point P can then be determined for the four values F(A), F(B), F(C), F(D) by the interpolation illustrated in  FIG. 15 . According to this selfexplanatory representation, the error F(P) at the point P has, for example, a value, weighted with the area (1-dy)*(1-dz) of the error/correction value of the point A, as well as the error/correction value, weighted with (1-dz)*dy, of the point B, the error/ correction value, weighted with dz*(1-dy) at the point C, and the error/correction value, weighted with dz*dy at the point D.  
         [0104]     It was explained in conjunction with FIGS.  9  to  11 , how a directional relationship can be established between different measuring lines. As an alternative to the method described in conjunction with FIGS.  9  to  11 , it is also possible in the case of Z translations to align the Z translations parallel to the direction of gravity by means of high-precision electronic inclination scales in the same horizontal position, and thus to establish the directional relationship. Since the measuring lines must always be recorded with reference to the reference plane of the coordinate measuring machine, which reference plane can also tilt as the coordinate measuring machine moves, it is particularly advantageous for this purpose to align the Z translations with the difference of two electronic inclination scales, in which case, for example, one set of inclination scales is mounted directly on the reference plane of the coordinate measuring machine, and the other is mounted on the laser measuring device for the Tz measurement.  
         [0105]     Furthermore, translations can be aligned by measuring suitable points on a large calibrated plate. The measurement and evaluation are performed in this case in the direction of the translations. In the case of X translations, it is possible, for example, to use a reference plane, calibrated in the X direction, of the coordinate measuring machine for the purpose of producing the directional relationships. Such a calibrated Z,Y plane with measuring points  160  calibrated in the X direction is illustrated in  FIG. 16 . Directional relationships of all the translations can also be produced by measuring a ball plate having balls calibrated in all directions.  
         [0106]     Also of particular advantage is a large plate with straightness standards  162  permanently clamped on and aligned, as illustrated in  FIG. 17 . These straightness standards can be used to determine all required translations (for example zTx and zTy in the case of Z multiple lines) directly and with directional relationship simply by scanning the straightness standards.