Method and apparatus for inspecting parts for dimensional accuracy outside a laboratory environment
BACKGROUND OF THE INVENTION 
     This invention relates to the dimensional inspection of parts. 
     The inspection of manufactured parts for dimensional accuracy is often performed by coordinate measuring machines. Such machines typically have a workpiece support and a traveling bridge which supports a workpiece-contacting probe. The probe is movable along three mutually perpendicular axes, and position sensing devices are utilized to determine the locations of the probe when it is in contact with the surface of the workpiece in terms of x, y, and z axes. These locations are recorded and they provide the basis for calculations which indicate the dimensions of the workpiece. 
     Measuring machines are customarily calibrated by using gauge blocks of known dimensions. The gauge block is inspected by the machine being calibrated and the inspection results are compared to the known dimensions of the gauge block. Subsequent measurements from the calibrated machine are adjusted accordingly. 
     Such calibrations are based on the assumptions that the dimensions of a gauge block do not change, and that the errors in a measuring machine are relatively uniform from one point to another throughout the measuring volume. The first of these assumptions is false if the temperature of the gauge block is different from the temperatures at which it was initially gaged, as will usually be the situation on a shop floor where there is no precise temperature control. The second assumption is false because a measuring machine, due to its individual vagaries, will produce errors with magnitudes which vary from one point to another throughout the measuring volume. 
     In the metrology field, it is generally accepted that a coordinate measuring machine must be located in a controlled environment in order to provide accurate measurements. Specially designed measuring laboratories are often constructed so that temperature, air purity, humidity, and other environmental elements are closely controlled to avoid conditions which would adversely affect the accuracy of any measurements. 
     Under current industrial practices, tolerances are stricter than they were in the past, and inventories are minimized due to just-in-time inventory practices. In view of these situations, there is a recognized need to place measuring machines on the shop floor. This would permit inspection of the parts soon after they are manufactured, and the manufacturing conditions can be adjusted quickly when necessary in order to improve the dimensional accuracy of subsequently manufactured parts. Heretofore, efforts to provide accurate measurements on the shop floor have focused on increasing the durability and accuracy of such machines in ways which attempt to overcome environmental problems. 
     As a practical matter, measuring laboratories cannot be located at workstations throughout a factory. A measuring machine in an uncontrolled environment cannot provide measurements which are dimensionally accurate. The sizes and shapes of parts being inspected change in various ways, and the measuring machine itself also changes. Thus, measuring machines remain in the laboratories, and production parts must travel from the shop to the measuring laboratory. This requires extra handling of the parts and inherent delays in detecting problems when they arise. 
     The present invention, aptly called &#34;comparative metrology,&#34; makes it possible to obtain accurate measurements from measuring machines located throughout a factory or elsewhere outside an environmentally controlled measuring laboratory. 
     This invention is untraditional in the respect that it accepts and tolerates the fact that raw dimensional measurements made on the shop floor will be inaccurate. The invention relies on the fact that, despite their inaccuracies, such measurements taken on the shop floor are repeatable within an acceptable range of variations. 
     The rationale behind the present invention is that it is impossible to compensate for everything which may create measurement errors. Rather than trying to overcome environmental problems by modifying the machine or controlling the environment, a reference part of substantially the same size and shape as the eventual production part is inspected in the laboratory so that its dimensions are known as precisely as is possible in the laboratory. This reference part is then taken to another measuring machine which is on the shop floor where there is a less controlled environment to which the reference part and the production parts are exposed. The reference part is inspected by the shop floor machine and a production part is inspected by the shop floor machine. The measurement data is processed to determine, with accuracy comparable to laboratory accuracy, how close the dimensions of the production part are to the specified dimensions. 
     SUMMARY OF THE INVENTION 
     In one respect, the invention is a method for determining the difference between a measured value v P  of a location of an actual data point on a production part and a nominal value v D  of a desired location of the data point on a perfect part. According to this method, a first measuring apparatus at a first site is used to obtain a value v RL  for the location of a data point DP R  on the reference part. A second measuring apparatus at a second site is used to obtain a second value v RS  of the location of the data point DP R  on the reference part. Temperature fluctuations are greater at the second site than at the first site. The production part is inspected by the second measuring apparatus at a data point DP P  which corresponds to the data point on the reference part to obtain a value v P  of the location of the actual data point on the production part. The difference between v RL  and v RS  is then added to one of v D  and v PS  to obtain a given value, and this given value is compared to the other of v D  and v PS  to determine the extent to which the production part deviates from a perfect part. 
     The difference between v RL  and v RS  can be added to v D  to obtain a value which is compared to v PS  to determine the extent to which the production part deviates from a perfect part. Alternatively, the difference between v RL  and v RS  can be added to v PS  to obtain a value which is compared to v D  to determine the extent to which the production part deviates from a perfect part. The invention also pertains to apparatus for determining the difference between a measured value v P  of a location of an actual data point on a production part and a nominal value v D  of the desired location of the data point on a perfect part. At a first site, there is a first measuring means for finding a value v RL  which expresses a location of an actual data point on the reference part. At a second site where temperature fluctuations are greater than at the first site, there is a second measuring machine with means for determining (a) a second value v RS  expressing a location of the actual data point on the reference part, and (b) a value vP of the location of the actual data point on the production part. The apparatus also has a computer or other calculation means for adding the difference between v RL  and v RS  to one of v D  and v PS  to obtain a value which can be compared to the other of v D  and v PS  to determine the extent to which the production part deviates from a perfect part. In one embodiment, the apparatus adds the difference between v RL  and v RS  to v D  to obtain a given value which is compared to v PS  to determine the extent to which the production part deviates from a perfect part. Alternatively, the apparatus is programmed to add the difference between v RL  and v RS  to v PS  to obtain a given value which is compared to v D  to determine the extent to which the production part deviates from a perfect part. 
     The inspection apparatus may be part of a combination which also includes a production part and a reference part, wherein the production part has substantially a same size and shape as the reference part. The second measuring means has means for supporting the production part and the reference part at substantially a same location. 
     The invention is also a method of inspecting parts to determine deviations between locations of (a) data points actually inspected on a production part and (b) corresponding nominal data points specified for a perfect part. This method includes the following steps: 
     a first measuring apparatus is used at a first site to inspect a reference part to obtain a first reference data set which contains coordinate values of data points on the reference part; 
     the coordinate values of the first reference data set are compared to coordinate values of a nominal data set which contains coordinate values of the nominal data points to obtain a first set of deviations which are the differences between the coordinate values of nominal data points and the coordinate values of corresponding data points on the reference part perceived by the first measuring apparatus at the first site; 
     a second measuring apparatus is used at a second site, where temperature fluctuations are greater than at the first site, to reinspect the reference part to obtain a second reference data set which contains coordinate values of the data points on the reference part as perceived by the second measuring apparatus at the second site; 
     the second reference data set is combined with the first set of deviations to obtain a target data set which contains coordinate values of data points on a perfect part as they would be perceived by the second measuring apparatus at the second site; 
     the second measuring apparatus at the second site is used to inspect corresponding data points on a production part to obtain a production part data set which contains coordinate values of data points on the production part actually perceived by the second measuring apparatus at the second site; and, 
     the production part data set is compared to the target data set to determine deviations between the coordinate values of (a) the data points of the production part as perceived at the second site by the second measuring apparatus, and (b) the data points of a perfect part as perceived at the second site by the second measuring apparatus. 
     Preferably the first site is a measuring laboratory and the second site is a manufacturing shop; various values are measured along one two or three axes in an orthogonal coordinate axis system; and, one or both of the measuring apparatuses has a workpiece-contacting probe. The reference part and the production part have substantially the same size and shape, and a plurality of production parts are inspected. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A is a perspective view of a sheet of drawings which illustrate a part which is perfect in the respect that it is precisely identical to specifications. 
     FIG. 1B is an isometric view of a reference part which corresponds substantially in size and shape to the perfect part. 
     FIG. 1C shows one of many production parts which are manufactured in the shop and which have substantially the same size and shape as the parts illustrated in FIGS. 1A and 1B. 
     FIG. 2 is an isometric view a laboratory machine which is used to inspect the reference part shown in FIG. 1B. 
     FIG. 3 shows a shop machine which is used to inspect the reference part of FIG. 1B and a plurality of production parts such as the one shown in FIG. 1C. 
    
    
     DETAILED DESCRIPTION 
     Theoretical Background 
     Three major sources of errors in coordinate measuring machines are (a) temperature changes in the parts being measured, (b) temperature changes in the measuring instrument itself, and (c) peculiarities inherent in any given machine due to nonlinearity of guide rails, inaccuracies in readout scales, and various distortions of the machine&#39;s components. 
     The theoretical underpinnings of the invention are the following principles: 
     When the temperature of a measuring instrument changes, the values of measurements from the instrument also change; but, at any given temperature, the measurements from the instrument are repeatable within an acceptable range of accuracy; 
     Within the measurement volume of a measuring instrument at a given temperature, the machine errors vary from one point to another; 
     These errors are consistent and repeatable for any given point within the measuring volume at a given temperature; 
     The size and shape of a part (&#34;artifact&#34;) change in response to temperature changes; however, at any given temperature, the size and shape of the part are consistent. 
     In this specification, the reference &#34;DP&#34; is used to identify data points; &#34;DS&#34; is used to identify data sets which contain either (1) position-indicating coordinates for many data points, or (2) deviation values Δ; and, &#34;v&#34; is used to represent, in a generic sense, position-indicating values along the x, y and z axes. As to the various subscript characters: 
     - &#34;D&#34; indicates that the drawings 2 is the source of the data; 
     - &#34;R&#34; indicates that the reference part E is the source of the data; 
     - &#34;P&#34; indicates that the production part E is the source of the data; 
     - &#34;L&#34; indicates that the involved data is as perceived actually or theoretically by a measuring machine in the laboratory; and, 
     - &#34;S&#34; indicates that the involved data is as perceived actually or theoretically by a measuring machine in the shop. 
     It should be understood that there are three versions of the part. They are shown in FIGS. 1A, 1B and 1C. All have approximately the same size and shape. The shape is an unconventional geometric shape in the respect that it is not a sphere, cylindrical prism, rectangular prism, annulus or ellipsoid. One is a perfect part D which exists on and is specified by the part drawings 2 shown in FIG. 1A. Another is a reference part E shown in FIG. 1B, and the third is a production part E shown in FIG. 1C. Numerous such production parts will normally be manufactured and measured on the shop floor. The reference part R does not require higher tolerances than the production parts so, in this respect, its function is entirely different from that of a near-perfect part or a gauge block. 
     These parts D, R, and P have corresponding corners DP O  which in this example are arbitrarily selected as benchmarks or data points where the coordinate values of x, y, and z are zero. The parts E and E are inspected by the measuring machines shown in FIGS. 2 and 3. Both of these machines take readings at many data points DP 1 , DP 2 , DP 3 , . . . DP n  which substantially correspond from part-to-part. According to the drawings 2, the corner DP D  of the perfect part is at a data point where x has a value of 60, y has a value of 50, and z has a value of 30. The corresponding point is located at DP R  on the reference part and at DP P  on the production part. 
     FIG. 2 shows a coordinate measuring machine 3 which is used to inspect the reference part R in a controlled laboratory environment. This machine has a horizontal surface 4 which supports the reference part R, and a probe 5 provided with a stylus tip 6 for contacting the surface of a workpiece at any point. The probe may be a hard probe, a touch trigger probe, or an analog probe. These types of probes are well known in the art, and examples of them are shown respectively by U.S. Pat. Nos. 3,840,993, 4,153,998, and 5,154,002. 
     The probe 5 is supported for movement along three mutually perpendicular linear axes. The probe support includes a carriage 7 which travels along a horizontal beam 8 for x-axis movement. The beam is part of a bridge 9 which is supported and guided for y-axis movement. An upright column 10 is movable vertically on the carriage 7 in order to provide the probe with z-axis mobility. The probe is connected to a mount on the lower end of the column 10. The x, y and z movements may be produced manually, or they may be motor driven and computer programmed in order to move along the surface of the workpiece. 
     The laboratory machine 3 has scales 11x, 11y and 11z which are readable visually, optically, inductively, magnetically or otherwise to provide position-indicating signals. A computer 12 receives, processes and stores data read from the scales. Readout devices such as printers and numeric displays are also provided. 
     On the shop floor there is another bridge type coordinate measuring machine 3&#39; which is used to inspect the reference part E and production parts P. This machine 3&#39; can be the same as or different from the laboratory machine 3. It has a support surface 4&#39; a carriage 7&#39; which travels on the beam 8&#39; of a traveling bridge 9&#39;. A vertical column 10&#39; carries a probe 5&#39; provided with a stylus tip 6&#39;. This machine has a computer 12&#39; which is configured so it can share data with the computer 12 via a network or by physical transfer of recording media. It is also possible to have a single computer console which performs the tasks of the two computers 12 and 12&#39;. 
     According to the present invention, the reference part R is first inspected by the laboratory machine 3. The part is positioned on the support surface 4 and the probe 5 is moved so that the stylus tip 6 contacts multiple data points on the surface of the part. The locations of these data points are processed and recorded in order to provide a numerical &#34;picture&#34; of the configuration of the part. 
     When the probe tip 6 is in contact with the reference part at the data point DP R  it provides values x RL , y RL  and z RL  which respectively quantify the x, y and z coordinates of the location of the data point DP R . A wildcard term v RL  is used in this specification to describe any one of the values x RL , y RL  and z RL . As is well known in the art, corrections are introduced to account for the position and diameter of the stylus tip. 
     The reference part is then removed from the laboratory and taken to a second site such as the shop shown in FIG. 3 where the temperature and other environmental conditions fluctuate more than in the laboratory. 
     After the reference part has been in the shop for a period of time sufficient to become acclimated to the environmental conditions there, it is inspected by the shop machine 3&#39; to get a second set of data which contain another &#34;picture&#34; of the reference part in the form of coordinate values v RS  of data points on the reference part actually perceived by the second measuring apparatus 3&#39;. These data are processed and stored in the computer 12&#39;. 
     Since the errors attributable to a particular machine will vary from point-to-point within the measuring volume, the reference part and the production parts should be put at a substantially uniform location on the shop machine so that values from the machine will have the same errors when inspecting the reference part as when inspecting the production parts. Likewise, it is desirable for the reference part and the production parts to have substantially the same size and shape, and for the measurements to be taken at data points which are substantially the same on all parts. Otherwise, the shop machine would be taking measurements at different points within its measurement volume, and these different points may have different errors to skew the results. 
     The invention may be practiced in many ways, two examples of which are presented here. 
     EXAMPLE 1 
     According to this example, a reference part data set (obtained by inspecting the reference part in the laboratory) is compared to a perfect data set (obtained from the drawings of a perfect part). This comparison is used to generate a data set made up of deviation values ΔP which provide comparisons between the perfect part and the reference part. The reference part is inspected in the shop to get a set of values to which the values ΔP are added. This yields target values which are what the shop machine would &#34;see&#34; if it inspected a perfect part. A production part is then measured in the shop to obtain a data set which can then be compared to the target data set to determine if the production part is within tolerances. The steps of this procedure and exemplary coordinate values for one data point are shown in the following Table I. 
     
                                           TABLE I                                 
__________________________________________________________________________
                               DATA ONE    VALUE COORDINATE VALUES        
                         DATA  SET  SELECTED                              
                                           SYMBOL                         
                                                 (SELECTED POINT)         
ROW                      SOURCE                                           
                               NAME POINT  (for x, y, z)                  
                                                 x    y   z               
__________________________________________________________________________
1   Take specified values from drawings                                   
                         Drawings                                         
                               DS.sub.D                                   
                                    DP.sub.D                              
                                           v.sub.D                        
                                                 60   50  70              
    (a &#34;perfect part&#34;)                                                    
2   Inspect the reference part, using the lab                             
                         Lab   DS.sub.RL                                  
                                    DP.sub.R                              
                                           v.sub.RL                       
                                                 58   52  69              
    machine              machine                                          
3   Calculate part-to-part deviations between                             
                         Computer                                         
                               DS.sub.Δ    +02  -02 +01             
    perfect part as specified in the drawings, and                        
    reference part as &#34;seen&#34; by the lab machine                           
    (Row 1 minus Row 2)                                                   
4   Transport the part to the shop, where                                 
    temperatures fluctuate more than in the lab                           
5   Inspect reference part using shop machine                             
                         Shop  DS.sub.RS                                  
                                    DP.sub.R                              
                                           v.sub.RS                       
                                                 60   51  71              
                         Machine                                          
6   Calculate &#34;target&#34; values which the shop                              
                         Computer                                         
                               DS.sub.T                                   
                                    DP.sub.T                              
                                           v.sub.T                        
                                                 62   49  72              
    machine would perceive when inspecting a                              
    perfect part (Row 3 plus Row 5)                                       
7   Inspect a production part, using the shop                             
                         Shop  DS.sub.PS                                  
                                    DP.sub.P                              
                                           v.sub.PS                       
                                                 61   48  68              
    machine              Machine                                          
8   Compare values for a production part with                             
                         Computer                                         
                               DS.sub.P-T  v.sub.P-T                      
                                                 -01  -01 -04             
    target values associated with a perfect part                          
    (Row 7 minus Row 6)                                                   
__________________________________________________________________________
 
    
     As stated in Row 2 of Table I, the reference part R is inspected in the laboratory to get a reference data set DS RL  which includes coordinate values for many data points on the reference part. The columns x, y, and z contain the values v RL  perceived by the laboratory machine for data point DP R  on the reference part R. These values are compared with the specified coordinate values in data set DS D  based on the perfect part as drawn to obtain a set of deviations DS.sub.Δ. These deviations represent, for each of the three axes, the differences between the location of point DP D  on a perfect part and the laboratory-measured location of the corresponding data point DP R  on the reference part. 
     The reference part E is then taken from the laboratory to the shop where temperature fluctuations are greater than those in the laboratory. After the reference part R has been in the shop for a period of time sufficient to become acclimated to shop temperatures, it is measured by the shop machine in the shop&#39;s environmental conditions to provide a data set DS RS  which includes coordinate values for many data points including the values v RS  for data point DP R , i.e. the values of x, y and z which are shown in Row 5 of this table. 
     With the known data sets DS RL  and DS RS  which represent the reference part as seen by the two machines 3 and 3&#39; it is then possible, as will be explained below, to calculate what values would be indicated by the shop machine if it were to inspect the perfect part. 
     According to Row 6, the part-to-part deviation values ΔP (which compare a perfect part to the reference part) are added to the values v RS  obtained when inspecting the reference part in the shop. The sums indicate the values v T  which the shop machine would obtain if it were to inspect the perfect part. These are referred to herein as &#34;target values.&#34; 
     The production part E is then placed at substantially the same location and orientation on the shop machine 3&#39; as had been occupied by the reference part R when it was being inspected. The production part is inspected to produce a data set DS PS  which includes the x, y, and z values for the point DP P  as shown in Row 7. This is compared with the data in Row 6 to determine the extent to which the location of the point DP i , on the production part deviates from the location of the corresponding point DP D  on a perfect part. 
     From another perspective, it will be seen that the values (v RL ) obtained when inspecting the reference part in the laboratory are subtracted in Row 2, and the values (v RS ) obtained when inspecting the reference part in the shop are added in Row 5. The effect of this is that the differences (v RL  -v RS ) between these values are added to the perfect part values (v D  in Row 1) to obtain values (v T , the target values in Row 6) which can be compared to the values obtained when the production part is inspected in the shop. This latter comparison will indicate how far the production part deviates from a perfect part, and whether or not the production part is within allowed tolerances. 
     EXAMPLE 2 
     In this example, a data set (obtained by inspecting the reference part in the laboratory) is compared to a data set (obtained by inspecting the reference part in the shop) to obtain a set of values ΔM which represent machine-to-machine deviations. Adding these deviation values to a data set obtained by inspecting a production part in the shop produces a set of data which represent what the laboratory machine would &#34;see&#34; if it inspected the production part. These data can then be compared to dimensions specified in the drawings 2 to determine if the production part is within tolerances. Table II on the following page illustrates this technique. 
     
                                           TABLE II                                
__________________________________________________________________________
                               DATA ONE    VALUE COORDINATE VALUES        
                         DATA  SET  SELECTED                              
                                           SYMBOL                         
                                                 (SELECTED POINT)         
ROW                      SOURCE                                           
                               NAME POINT  (for x, y, z)                  
                                                 x    y   z               
__________________________________________________________________________
1   Inspect the reference part, using the lab                             
                         Lab   DS.sub.RL                                  
                                    DP.sub.R                              
                                           v.sub.RL                       
                                                 58   52  69              
    machine              Machine                                          
2   Transport the part to the shop, where                                 
    temperatures fluctuate more than in the lab                           
3   Inspect the reference part, using the shop                            
                         Shop  DS.sub.RS                                  
                                    DP.sub.R                              
                                           v.sub.RS                       
                                                 60   51  71              
    machine.             Machine                                          
4   Calculate machine-to-machine deviations                               
                         Computer                                         
                               DS.sub.ΔM   -02  -01 -02             
    ΔM (Row 1 minus Row 3)                                          
5   Inspect production part, using the shop                               
                         Shop  DS.sub.PS                                  
                                    DP.sub.P                              
                                           v.sub.PS                       
                                                 61   48  68              
    machine              Machine                                          
6   Calculate values which the lab                                        
                         Computer                                         
                               DS.sub.PL   v.sub.PL                       
                                                 59   49  66              
    machine would perceive for the production                             
    part (Row 4 plus Row 5)                                               
7   Take specified values from drawings                                   
                         Drawings                                         
                               DS.sub.D                                   
                                    DP.sub.D                              
                                           v.sub.D                        
                                                 60   50  70              
    (a &#34;perfect part&#34;)                                                    
8   Compare &#34;perfect part&#34; values per                                     
                         Computer                                         
                               DS.sub.P-D        -01  -01 -04             
    drawings with values for the production                               
    part (as perceived by lab machine). (Row 6                            
    minus Row 7)                                                          
__________________________________________________________________________
 
    
     Referring to Table II, it will be seen that this procedure commences with the inspection of the reference part R in the laboratory to get a set DS m  of values v RL  which are the coordinate values for many data points on the reference part E, including the point DP R  for which the coordinate values are shown in Row 1 (columns x, y, and z). Then, the reference part is taken to the shop floor where temperature fluctuations are greater than in the laboratory. The reference part is given sufficient time to adjust to the temperatures on the shop floor, and it is inspected by the shop machine to get a data set DS RS  which includes coordinate values v RS  of many points including those for the data point DP R . The latter are shown in columns x, y and z of Row 3. The respective coordinate values in sets DS RL  and DS RS  are compared to get a set of deviation values ΔM which represent the deviations from machine-to-machine (comparing the laboratory machine to the shop machine). Such values for the point DP R   on the reference part R are shown in Row 4. 
     As indicated in Row 5 of this table, a production part P is then measured by the shop machine to get a set DS PS  of data including values v PS  which are the location-indicating coordinates of the data point DP P . The deviations ΔM from Row 4 are added to the values v PS  to obtain a set DS PL  of values v PL  which establish where the laboratory machine would have &#34;seen&#34; the data point DP P . These values in set DS PL  are compared with the specified values v D  (in Row 7) for the location of data point DP D  to find out the extent to which the point DP P  on the production part deviates from the specifications established for the corresponding data point DP D  on the perfect part. The results of this comparison are shown in Row 8. They correspond to and verify those obtained using the procedure of Example 1. 
     From the foregoing, it will be seen that the effect of this procedure is to add A (the difference between the values obtained when inspecting the production part in the lab and in the shop) to the values (v RS ) obtained when inspecting the production part in the shop to obtain a value (v PL ). This value is then compared to the corresponding perfect part value (v D ) to determine the extent to which the production part deviates from a perfect part. 
     OBSERVATIONS AND COMMENTS 
     In cases where extreme accuracy is necessary, or where there are significant temperature fluctuations on the shop floor, the reference part may be reinspected periodically to update the data to provide more accurate values to reflect the current conditions. It is possible to reinspect a reference part prior to each inspection of a production part. Such a procedure is facilitated by the arrangement shown in FIG. 3 where a shuttle table 13 has two jigs which support the reference part E and the production parts P. With this arrangement, the reference part is inspected, a first production part is inspected, the reference part is reinspected, a second production part is inspected, etc, etc. The data is continually updated at each reinspection of the reference part. 
     The invention may be practiced with different types of probes including hard probes, non-contact probes, touch trigger probes, and analog probes. It is most effective to use an analog probe. In an analog probe, the stylus tip is relatively movable with respect to the probe mount, and there are devices for sensing the extent and direction of the relative movement between the tip and mount. 
     Analog probes are particularly well suited to this task because they are able to collect large amounts of data in a short time. Data is storable as &#34;deviation curves&#34; related to the place on the element or feature where they occur. For example, an analog probe can measure an arbitrary circle using 500 data points in about the same length of time it would take a touch trigger probe to touch the circle at five points. Due to the availability of data from a larger number of data points, values obtained from an analog probe are less vulnerable to environmental conditions such as vibrations. If a significant vibration occurs at the instant a touch trigger probe is activated, there are no adjacent measurements to show by comparison that the reading was an aberration. However, when there are many additional readings as are available from an analog probe, the aberration is easily noticed by comparison with the adjacent readings. 
     Because the invention provides highly accurate measurement values in the vicinity of machine tools which are manufacturing parts in the shop, the invention lends itself to a feedback system in which the computer sends signals to the machine tools, indicating the magnitude of errors soon after parts are manufactured. These signals can be processed quickly to change the operation of the machine tools to minimize errors in future parts. 
     Only two embodiments of the invention have been described in detail, but persons familiar with the art will recognize that the invention may be practiced using a wide variety of procedures and machines. Therefore, it is emphasized that the invention is not limited only to the embodiments described above but is embracing of other systems which fall within the spirit of the following claims.