Apparatus and method for determining a center and measuring with reference thereto

• US 5,151,870 A
• Filed: 11/17/1989
• Issued: 09/29/1992
• Est. Priority Date: 11/17/1989
• Status: Expired due to Term

• Current Assignee: Micro-Poise Measurement Systems LLC (Ametek Incorporated)
• Original Assignee: Illinois Tool Works Inc.
• Inventors: Lees, David W. Sr., Beebe, James C., Cargould, Barry D.
• Primary Examiner(s): LALL, PARSHOTAM S
• Application Number:
  US07/439,231
• Time in Patent Office: 1,047 Days
• Field of Search: 364/556, 364/560, 33/501.6, 33/543, 33/546, 33/548, 33/550, 33/551, 33/552, 33/553, 33/554, 33/555, 33/555.1, 33/644, 33/203, 33/600, 33/545, 33/547, 382/8, 356/384, 356/386, 356/387, 250/492.1
• US Class Current: 702/168
• CPC Class Codes: G01B 5/201 for measuring roundness
• CPC Class Codes: G01B 5/252 for measuring eccentricity, i.e. lateral shift between two parallel axes
• CPC Class Codes: G01B 7/282 for measuring roundness
• CPC Class Codes: G01B 7/30 for measuring angles or tapers; for testing the alignment of axes

Abstract

An object is positioned in fixed relation to a measuring axis without regard to centering the object on the axis and at least one series of data samples correlated to the distance between the measuring axis and a series of points located at angularly spaced intervals on at least one surface feature of the object are generated and stored. To determine the center of a first surface feature, the corresponding series of samples is analyzed to identify samples therein corresponding to points lying on a maximum inscribed circle whose center corresponds to that of the surface feature. To measure a second surface feature of an object with reference to the center of a first surface feature thereof, a first signal and a second signal correlated to the distance between the measuring axis and points on the first surface feature and second surface feature, respectively are generated. The center of the first surface feature is then determined to define a vector indicating the positional offset between the measuring axis and that center. The second signal is then adjusted in accordance with that vector to provide a coordinate-corrected signal to be used as a basis for a centered measurement.

Claims

1. A method for determining a center of a surface feature of an object, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating signals correlated to the distance between a point on said measuring axis and points located on said surface feature;

(b) effecting relative movement between said object and said distance measuring device in order to generate a series of said signals, each of which is correlated to the distance between said point on said measuring axis and one of a corresponding series of said points located on said surface feature;

(c) processing said signals to repetitively;

(i) identify ones of said series of points incapable of lying on a maximum inscribed circle of said surface feature, and

(ii) effectively discard said ones of said points until only a predetermined number of said points remain in said series of points, said predetermined number of points specifying said maximum inscribed circle, and

(d) calculating the center of said maximum inscribed circle specified by said predetermined number of points, said center corresponding to a center of said surface feature of the object.

2. A method for measuring the effective size of a surface feature of an object, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating at least one signal correlated to the distance between a point on said measuring axis and points located said surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said signal in order to generate series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and one of a corresponding series of said points located on said surface feature;

(c) processing said series of data samples to repetitively;

(i) identify ones of said data samples in said series incapable of corresponding to points on a maximum inscribed circle of said surface feature, and

(ii) effectively discard said ones of said data samples from said series until only a predetermined number of said data samples remain therein, said predetermined number of data samples specifying said maximum inscribed circle, and

(d) calculating the diameter of said maximum inscribed circle specified by said predetermined number of data samples as a measure of the effective size of the surface feature.

3. A method for measuring the out-of-roundness of a surface feature of an object, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating at least one signal correlated to the distance between a point on said measuring axis and points located on said surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said signal in order to generate a series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and one of a corresponding series of said points located on said surface feature;

(c) processing said series of data samples to repetitively;

(i) identify ones of said data samples in said series incapable of corresponding to points on a maximum inscribed circle of said surface feature, and

(ii) effectively discard said ones of said data samples from said series until only a predetermined number of said data samples remain therein, said predetermined number of data samples specifying said maximum inscribed circle;

(d) calculating the radius and center of said maximum inscribed circle specified by said predetermined number of data samples;

(e) calculating the maximum distance between said center and any of said points in said series of points, and

(f) subtracting said radius from said maximum distance to obtain a measurement of the out-of-roundness of said surface feature.

4. A method for measuring the total indicated runout (TIR) of a surface feature of an object, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating at least one signal correlated to the distance between a point on said measuring axis and points on said surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said signal in order to generate a series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and one of a corresponding series of said points located on said surface feature;

(c) processing said series of data samples to repetitively;

(i) identify ones of said data samples in said series incapable of corresponding to points on a maximum inscribed circle of said surface feature, and

(ii) effectively discard said ones of said data samples from said series until only a predetermined number of said data samples remain therein, said predetermined number of data samples specifying said maximum inscribed circle;

(d) calculating the center of said maximum inscribed circle specified by said predetermined number of data samples;

(e) calculating both the maximum distance from said center to any point in said series of points and the minimum distance from said center to any point in said series of points, and the minimum distance from said center to any point in said series of points, and

(f) calculating the difference between said maximum distance and said minimum distance to obtain a measurement of the total indicated runout (TIR) of said surface feature.

5. A method for measuring the eccentricity between a first surface feature and a second surface feature of an object, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating a first signal correlated to the distance between a point on said measuring axis and points located on said first surface feature and a second signal correlated to the distance between said point on said measuring axis and points located on said second surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said first signal in order to generate a first series of data samples, each data sample in said first series of data samples being correlated to the distance between said point on a measuring axis and a corresponding one of said points located on said first surface feature;

(c) repetitively;

(i) identifying ones of said data samples in said first series of data samples incapable of corresponding to points lying on a first maximum inscribed circle of said first surface feature, and

(ii) effectively discarding said ones of said data samples from said first series of data samples until only a predetermined number of said data samples specifying said first maximum inscribed circle of said first surface feature remain in said first series of data samples;

(d) calculating the center of said first maximum inscribed circle;

(e) effecting relative movement between said object and said distance measuring device and using said second signal in order to generate a second series of data samples, each data sample in said second series of data samples being correlated to the distance between said point on said measuring axis and a corresponding one of said points located on said second surface feature;

(f) repetitively;

(i) identifying ones of said data samples in said second series of data samples incapable of corresponding to points lying on a second maximum inscribed circle of said second surface feature, and

(ii) effectively discarding said ones of said data samples from said second series of data samples until only a predetermined number of said data samples specifying said second maximum inscribed circle of said second surface feature remain in said second series of data samples;

(g) calculating the center of said second maximum inscribed circle; and

(h) calculating the distance between said centers of said first and second maximum inscribed circles as a measure of the eccentricity between said first and second surface features.

6. A method for determining a center of a first surface feature of an object and measuring the total indicated runout (TIR) of a second surface feature of the object with reference to that center, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating a first signal correlated to the distance between a point on said measuring axis and points located on said first surface feature and a second signal correlated to the distance between said point on said measuring axis and points located on said second surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said first signal in order to generate a first series of data samples, each data sample in said first series of data samples being correlated to the distance between said point on a measuring axis and a corresponding one of said points located on said first surface feature;

(c) effecting relative movement between said object and said distance measuring device and using said second signal in order to generate a second series of data samples, each data sample in said second series of data samples being correlated to the distance between said point on said measuring axis and a corresponding one of said points located on said second surface feature;

(d) repetitively;

(i) identifying ones of said data samples in said first series of data samples incapable of corresponding to points lying on a first maximum inscribed circle of said first surface feature, and

(ii) effectively discarding said ones of said data samples from said first series of data samples until only a predetermined number of said data samples specifying said first maximum inscribed circle of said first surface feature remain in said first series of data samples;

(e) determining the center of said first surface feature by calculating the location of the center of a circle which intersects each point on said first surface feature represented by each of said predetermined number of data samples from said first series;

(f) calculating both the maximum distance from said center to any point in said second series of points and the minimum distance from said center to any point in said second series of points, and

(g) calculating the difference between said maximum distance and said minimum distance to obtain a measurement of the total indicated runout (TIR) of the second surface feature with respect to the center of the first surface feature.

7. In a method for determining the eccentricity between a first surface feature and a second surface feature of an object, said surface features having respective first and second centers, the improvement comprising determining said respective center of at least one of said surface features in accordance with the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating a signal correlated to the distance between a point on said measuring axis and points located on said least one surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said signal in order to generate a series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and a corresponding one of said points located on said at least one surface feature;

(c) processing said series of data samples to repetitively;

(i) identify ones of said data samples in said series incapable of corresponding to points on a maximum inscribed circle of said at least one surface feature, and

(ii) effectively discard said ones of said data samples from said series until only a predetermined number of said data samples remain therein, said predetermined number of data samples specifying said maximum inscribed circle, and

(d) calculating the center of said maximum inscribed circle specified by said predetermined number of data samples, said center corresponding to the center of said at least one surface feature of the object.

8. A method for determining a center of a surface feature of an object, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating a signal correlated to the distance between a point on said measuring axis and points located on said surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said signal in order to generate a series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and a corresponding one of said points located on said surface feature;

(c) for each set of three of said data samples remaining in said series corresponding to a group of three adjacent ones of said points on said surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(d) reducing said series of data samples by eliminating therefrom the data sample remaining therein which corresponds to that vertex the distance between which and its associated fourth point is the smallest;

(e) repeating steps (c) and (d) to further reduce said series of data samples until only a predetermined number of data samples representing particular ones of said points on said surface feature remain therein, and

(f) calculating the location of the center of a circle which intersects each of said particular ones of said points to determine the center of said surface feature.

9. The method of claim 8 wherein step (d) thereof further comprises the steps of determining whether any of said data samples defines a concavity of a polygon defined by said series of data samples and, if so, deferring elimination of each data sample defining a said concavity of said polygon.

10. The method of claim 9 wherein said deferring step includes the step of assigning an arbitrarily large value to a number representing said distance between each fourth point associated with a data sample defining a said concavity and the vertex associated with said fourth point.

11. The method of claim 8 wherein said predetermined number is three.

12. A method for measuring the effective size of a surface feature of an object, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating a signal correlated to the distance between a point on said measuring axis and a series of points located on said surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said signal in order to generate a series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and a corresponding one of said series of points located on said surface feature;

(c) for each set of three of said data samples in said series corresponding to a group of three adjacent ones of said points on said surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(d) reducing said series of data samples by eliminating therefrom the data sample remaining therein which corresponds to that vertex the distance between which and its associated fourth point is the smallest;

(e) repeating steps (c) and (d) to further reduce said series of data samples until only a predetermined number of data samples representing particular ones of said points on said surface feature remain in said series of data samples, and

(f) calculating the diameter of the circle which intersects each of said particular ones of said points as a measure of the effective size of said surface feature.

13. The method of claim 12 wherein step (d) thereof further comprises the steps of determining whether any of said data samples defines a concavity of a polygon defined by said series of points and, if so, deferring elimination of each data sample defining a said concavity of said polygon.

14. The method of claim 13 wherein said deferring step including the step of assigning an arbitrarily large value to a number representing said distance between each fourth point associated with a data sample defining a said concavity and the vertex associated with said fourth point.

15. The method of claim 12 wherein said predetermined number is three.

16. A method for measuring the out-of-roundness of a surface feature of an object, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating a signal correlated to the distance between a point on said measuring axis and a series of points located on said surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said signal in order to generate a series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and a corresponding one of said series of points located on said surface feature;

(c) for each set of three of said data samples in said series corresponding to a group of three adjacent ones of said points on said surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(d) reducing said series of data samples by eliminating the remaining data sample in said series corresponding to that vertex the distance between which and its corresponding fourth point is the smallest;

(e) repeating steps (c) and (d) to further reduce said series of data samples until only a predetermined number of data samples representing particular ones of said points on said surface feature remain in said series of data samples, and

(f) calculating the maximum distance between any of said points represented by said series of data samples prior to reduction thereof and the nearest point thereto on a circle intersecting each of said particular ones of said points as a measure of the out-of-roundness of said surface feature.

17. A method for measuring the total indicated runout (TIR) of a surface feature of an object, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating a signal correlated to the distance between a point on said measuring axis and a series of points located on said surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said signal in order to generate a series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and a corresponding one of said series of points located on said surface feature;

(c) for each set of three of said data samples remaining in said series corresponding to a group of three adjacent ones of said points on said surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(d) reducing said series of data samples by eliminating therefrom the data sample remaining therein which corresponds to that vertex the distance between which and its associated fourth point is the smallest;

(e) repeating steps (c) and (d) to further reduce said series of data samples until only a predetermined number of data samples representing particular ones of said points on said surface feature remain in said series of data samples, and

(f) calculating the location of the center of a circle which intersects said particular ones of said points to determine the center of said surface feature;

(g) calculating both the maximum distance from said center to any point present in said series of points prior to carrying out said reducing step and the minimum distance from said center to any point present in said series of points prior to carrying out said reducing step, and

(h) calculating the difference between the maximum distance and said minimum distance as a measure of the total indicated runout (TIR) of said surface feature.

18. The method of claim 17 wherein said steps of generating said first and second series of data samples are carried out substantially simultaneously by effecting relative rotational movement about said measuring axis between said object and (i) a first probe mounted for sensing a parameter correlated to the distance between said measuring axis and said first surface feature and (ii) a second probe mounted for sensing a parameter correlated to the distance between said measuring axis and said second surface feature.

19. A method for determining the center of a first surface feature of an object and measuring the total indicated runout (TIR) of a second surface feature of the object with respect to that center, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating a first signal correlated to the distance between a point on said measuring axis and a first series of points located on said first surface feature and a second signal correlated to the distance between said point on said measuring axis and a second series of points located on said second surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said first signal in order to generate a first series of data samples, each data sample in said first series of data samples being correlated to the distance between said point on said measuring axis and a corresponding point in said first series of points located on said surface feature;

(c) effecting relative movement between said object and said distance measuring device and using said second signal in order to generate a second series of data samples, each data sample in said second series of data samples being correlated to the distance between said point on said measuring axis and a corresponding point in said second series of points located on said second surface feature;

(d) for each set of three of said data samples remaining in said first series corresponding to a group of three adjacent ones of said points on said first surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(e) reducing said first series of data samples by eliminating therefrom the remaining data sample corresponding to that vertex the distance between which and its corresponding fourth point is the smallest;

(f) repeating steps (d) and (e) to further reduce said first series of data samples until only a predetermined number of data samples representing particular ones of said points on said first surface feature remain in said first series of data samples;

(g) determining the center of said first surface feature by calculating the location of the center of a circle which intersects each of said particular ones of said points on said first surface feature;

(h) calculating both the maximum distance from said center to any point present in said second series of points prior to carrying out said reducing step and the minimum distance from said center to any point present in said second series of points prior to carrying out said reducing step, and

(i) calculating the difference between said maximum distance and said minimum distance as a measure of the total indicated runout (TIR) between said first surface feature and said second surface feature.

20. The method of claim 19 wherein said steps of generating said first and second series of data samples are carried out substantially simultaneously by effecting relative rotational movement about said measuring axis between said object and (i) a first probe associated with said distance measuring device and mounted for sensing a parameter correlated to the distance between said measuring axis and said first surface feature and (ii) a second probe associated with said distance measuring device and mounted for sensing a parameter correlated to the distance between said measuring axis and said second surface feature.

21. A method for measuring the eccentricity between a first surface feature and a second surface feature of an object, said method comprising the steps of:

(a) positioning the object in fixed relation to a measuring axis of a machine which includes at least one distance measuring device for generating a first signal correlated to the distance between a point on said measuring axis and a first series of points located on said first surface feature and a second signal correlated to the distance between said point on said measuring axis and a second series of points located on said second surface feature;

(b) effecting relative movement between said object and said distance measuring device and using said first signal in order to generate a first series of data samples, each data sample in said first series of data samples being correlated to the distance between said point on said measuring axis and a corresponding point in said first series of points located on said first surface feature;

(c) effecting relative movement between said object and said distance measuring device and using said second signal in order to generate a second series of data samples, each data sample in said second series of data samples being correlated to the distance between said point on said measuring axis and a corresponding point in said second series of points located on said second surface feature;

(d) for each set of three data samples remaining in said first series corresponding to a group of three adjacent ones of said points on said first surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(e) reducing said first series of data samples by eliminating therefrom the data sample remaining therein which corresponds to that vertex the distance between which and its associated fourth point is the smallest;

(f) repeating steps (d) and (e) to further reduce said first series of data samples until only a first predetermined number of data samples representing particular ones of said points on said first surface feature remain in said first series of data samples;

(g) determining the center of said first surface feature by calculating the location of the center of a circle which intersects each of said particular ones of said points on said first series of points;

(h) for each set of three data samples remaining in said second series corresponding to a group of three adjacent ones of said points on said second surface feature, each said group having a vertex separating two endpoints, calculating a fifth point defined by the intersection of the perpendicular bisectors of a third line and a fourth line, said third line connecting said vertex with one of said endpoints, said fourth line connecting said vertex with the other one of said endpoints;

(i) reducing said second series of data samples by eliminating therefrom the data sample remaining therein which corresponds to that vertex the distance between which and its corresponding fifth point is the smallest;

(j) repeating steps (h) and (i) to further reduce said second series of data samples until only a second predetermined number of data samples representing particular ones of said points on said second surface feature remain in said second series of data samples;

(k) determining the center of said second surface feature by calculating the location of the center of a second circle which intersects each of said particular ones of said points in said second series of points, and

(l) calculating the distance between said centers of said first and second surface features, respectively as a measure of the eccentricity between said first and second surface features.

22. The method of claim 21 wherein said steps of generating said first and second series of data samples are carried out substantially simultaneously by effecting relative rotational movement about said measuring axis between said object and (i) a first probe mounted for sensing a parameter correlated to the distance between said measuring axis and said first series of points and (ii) a second probe mounted for sensing a parameter correlated to the distance between said measuring axis and said second series of points.

23. An apparatus for determining the center of a surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means for generating a signal correlated to the distance between a point on said measuring axis and each of a series of points on the surface feature, said probe means and the surface feature being movable with respect to one another, and

(c) computer means coupled to said probe means for;

(i) processing said signal to repetitively;

(1) identify ones of said points incapable of lying on a maximum inscribed circle of said surface feature and

(2) effectively discard said ones of said points until only a predetermined number of said points remain in said series of points, said predetermined number of points specifying said maximum inscribed circle, and

(ii) calculating the center of said maximum inscribed circle, said center corresponding to the center of said surface feature of the object.

24. An apparatus for determining the center of a surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means for generating a signal correlated to the distance between a point on said measuring axis and each of a series of points on the surface feature, said probe means and the surface feature being movable with respect to one another while said position of the object is maintained fixed with respect to said measuring axis, and

(c) computer means coupled to said probe means for;

(i) sampling said signal and storing a series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and one of a corresponding series of points located at angularly spaced intervals on said surface feature;

(ii) processing said series of data samples to repetitively;

(1) identify ones of said data samples corresponding to points incapable of lying on a maximum inscribed circle of said surface feature, and

(2) effectively discard said ones of data samples until only a predetermined number of said data samples remain in said series of data samples, said remaining data samples corresponding to points lying on said maximum inscribed circle, and for

(iii) calculating the center of said maximum inscribed circle, said center corresponding to the center of said surface feature of the object.

25. An apparatus for measuring the effective size of a surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means for generating a signal correlated to the distance between a point on said measuring axis and each of a series of points on the surface feature, said probe means and the surface feature being movable with respect to one another, and

(c) computer means coupled to said probe means for;

(i) sampling said signal and storing a series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and one of a corresponding series of points located at angularly spaced intervals on said surface feature;

(ii) processing said series of data samples to repetitively;

(1) identify ones of said data samples corresponding to points incapable of lying on a maximum inscribed circle of said surface feature, and

(2) effectively discard said ones of data samples until only a predetermined number of said data samples remain in said series of data samples, said remaining data samples corresponding to points lying on said maximum inscribed circle, and for

(iii) calculating the diameter of said maximum inscribed circle as a measure of the effective size of the surface feature.

26. An apparatus for measuring the out-of-roundness of a surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the object fixed in relation to a measuring axis;

(b) probe means for generating a signal correlated to the distance between a point on said measuring axis and each of a series of points on the surface feature, said probe means and the surface feature being movable with respect to one another, and

(c) computer means coupled to said probe means for;

(i) sampling said signal and storing a series of data samples, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and one of a corresponding series of points located at angularly spaced intervals on said surface feature;

(ii) processing said series of data samples to repetitively;

(1) identify ones of said data samples corresponding to points incapable of lying on a maximum inscribed circle of said surface feature, and

(2) effectively discard said ones of data samples until only a predetermined number of said data samples remain in said series of data samples, said remaining data samples corresponding to points lying on said maximum inscribed circle;

(iii) calculating the radius and center of said maximum inscribed circle;

(iv) determining the maximum distance between said center and any of said points in said series of points, and for

(v) subtracting said radius from said maximum distance as a measure of the out-of-roundness of said surface feature.

27. An apparatus for measuring the total indicated runout (TIR) of a surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means for generating a signal correlated to the distance between a point on said measuring axis and each of a series of points on the surface feature, said probe means and the surface feature being movable with respect to one another while said position of the object is maintained fixed with respect to said measuring axis, and

(c) computer means coupled to said probe means for;

(i) storing a series of data samples of said signal, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and one of a corresponding series of points located at angularly spaced intervals on said surface feature;

(ii) processing said series of data samples to repetitively;

(1) identify ones of said data samples corresponding to points incapable of lying on a maximum inscribed circle of said surface feature, and

(2) effectively discard said ones of data samples until only a predetermined number of said data samples remain in said series of data samples, said remaining data samples corresponding to points lying on said maximum inscribed circle;

(iii) calculating the center of said maximum inscribed circle;

(iv) calculating both the maximum distance from said center to any point in said series of points and the minimum distance from said center to any point in said series of points, and for

(v) calculating the difference between said maximum distance and said minimum distance as a measure of the total indicated runout (TIR) of said surface feature.

28. An apparatus for measuring the eccentricity between a first surface feature and a second surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means movable with respect to the object for generating both a first signal correlated to the distance between a point on said measuring axis and each of a first series of first points on the first surface feature and a second signal correlated to the distance between said point on said measuring axis and each of a second series of second points on the second surface feature, and

(c) computer means coupled to said probe means for;

(i) storing a first series of data samples of said first signal, each data sample in said first series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said first series of points;

(ii) processing said first series of data samples to repetitively;

(1) identify ones of said data samples corresponding to points incapable of lying on a first maximum inscribed circle of said first surface feature, and

(2) effectively discard said ones of said data samples from said first series of data samples until only a predetermined number of said data samples remain in said first series of data samples, said remaining data samples in said first series specifying said first maximum inscribed circle;

(iii) calculating the center of said first maximum inscribed circle;

(iv) storing a second series of data samples of said second signal, each data sample in said second series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said second series of points;

(v) processing said second series of data samples to repetitively;

(1) identify ones of said data samples therein corresponding to points incapable of lying on a second maximum inscribed circle of said second surface feature, and

(2) effectively discard said ones of said data samples from said second series of data samples until only a predetermined number of said data samples remain in said second series of data samples, said remaining data samples in said second series of data samples specifying said second maximum inscribed circle;

(vi) calculating the center of said second maximum inscribed circle, and for

(vii) calculating the distance between said centers of said first and second maximum inscribed circles as a measure of the eccentricity between said first and second surface features.

29. An apparatus for determining the center of a first surface feature of an object and measuring the total indicated runout (TIR) of a second surface feature of the object with reference to that center, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means movable with respect to the object for generating both a first signal correlated to the distance between a point on said measuring axis and each of a first series of first points on the first surface feature and a second signal correlated to the distance between said point on said measuring axis and each of a second series of second points on the second surface feature, and

(c) computer means coupled to said probe means for;

(i) storing a first series of data samples of said first signal, each data sample in said first series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said first series of points;

(ii) processing said first series of data samples to repetitively;

(1) identify ones of said data samples therein corresponding to points incapable of lying on a maximum inscribed circle of said first surface feature, and

(2) effectively discard said ones of said data samples from said first series of data samples until only a predetermined number of said data samples remain in said first series of data samples;

(iii) determining the center of said first surface feature by calculating the location of the center of a circle which intersects each of said ones of said first points represented by said data samples remaining in said first series of data samples;

(iv) calculating both the maximum distance from said center to any said second point in said second series of second points and the minimum distance from said center to any second point in said second series of second points, and for

(v) calculating the difference between said maximum distance and said minimum distance to obtain a measurement of the total indicated runout (TIR) of the second surface feature with respect to the center of the first surface feature.

30. An apparatus for determining the center of a surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means for generating a signal correlated to the distance between a point on said measuring axis and each of a series of points on the surface feature, said probe means and the surface feature being movable with respect to one another, and

(c) computer means coupled to said probe means for;

(i) storing a series of data samples of said signal, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said series of said points;

(ii) for each set of three data samples remaining in said series of data samples corresponding to a group of three adjacent ones of said points on said surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(iii) reducing said series of data samples by eliminating therefrom the data sample remaining therein which corresponds to that vertex the distance between which and its associated fourth point is the smallest;

(iv) repeating steps (ii) and (iii) to further reduce said series of data samples until only a predetermined number of samples representing particular ones of said points in said series of points remain therein, and for

(v) calculating the location of the center of a circle which intersects each of said particular ones of said points to determine the center of said surface feature.

31. An apparatus for measuring the effective size of a surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means for generating a signal correlated to the distance between a point on said measuring axis and each of a series of points on the surface feature, said probe means and the surface feature being movable with respect to one another, and

(c) computer means coupled to said probe means for;

(i) storing a series of data samples of said signal, each data sample in said series of data samples being correlated to the distance between a point on said measuring axis and one of said points in said series of points;

(ii) for each set of three data samples in said series of data samples corresponding to a group of three adjacent ones of said points on said surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(iii) reducing series of data samples by eliminating therefrom the data sample remaining therein which corresponds to that vertex the distance between which and its associated fourth point is the smallest;

(iv) repeating steps (ii) and (iii) to further reduce said series of data samples until only a predetermined number of samples representing particular ones of said points in said series of points remain in said series of data samples, and for

(v) calculating the diameter of the circle which intersects each of said particular ones of said points as a measure of the effective size of said surface feature.

32. An apparatus for measuring the out-of-roundness of a surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means for generating a signal correlated to the distance between a point on said measuring axis and each of a series of points on the surface feature, said probe means and the surface feature being movable with respect to one another, and

(c) computer means coupled to said probe means for;

(i) storing a series of data samples of said signal, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said series of points;

(ii) for each set of three data samples in said series of data samples corresponding to a group of three adjacent ones of said points on said surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(iii) reducing said series of data samples by eliminating the remaining data sample in said series corresponding to that vertex the distance between which and its corresponding fourth point is the smallest;

(iv) repeating steps (ii) and (iii) to further reduce said series of data samples until only a predetermined number of samples representing particular ones of said points in said series of points remain in said series of data samples;

(v) calculating the radius and center of a circle intersecting each of said particular ones of said points;

(vi) calculating the maximum distance between said center and any of said points in said series of points, and for

(vii) subtracting said radius from said maximum distance to obtain a measurement of the out-of-roundness of said surface feature.

33. An apparatus for measuring the total indicated runout (TIR) of a surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means for generating a signal correlated to the distance between a point on said measuring axis and each of a series of points on the surface feature, said probe means and the surface feature being movable with respect to one another, and

(c) computer means coupled to said probe means for;

(i) storing a series of data samples of said signal, each data sample in said series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said series of said points;

(ii) for each set of three data samples remaining in said series of data samples corresponding to a group of three adjacent ones of said points on said surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(iii) reducing said series of data samples by eliminating therefrom the data sample remaining therein which corresponds to that vertex the distance between which and its associated fourth point is the smallest;

(iv) repeating steps (ii) and (iii) to further reduce said series of data samples until only a predetermined number of samples representing particular ones of said points in said series of points remain in said series of data samples;

(v) calculating the location of the center of a circle which intersects said particular ones of said points to determine the center of said surface feature;

(vi) calculating both the maximum distance from said center to any point in said series of points and the minimum distance from said center to any point in said series of points, and for

(vii) calculating the difference between said maximum distance and said minimum distance to obtain a measurement of the total indicated runout (TIR) of said surface feature.

34. An apparatus for determining the center of a first surface feature of an object and measuring the total indicated runout (TIR) of a second surface feature of the object with respect to that center, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means movable with respect to the object for generating both a first signal correlated to the distance between a point on said measuring axis and each of a first series of first points on the first surface feature and a second signal correlated to the distance between said point on said measuring axis and each of a second series of second points on the second surface feature, and

(c) computer means coupled to said probe means for;

(i) storing a first series of data samples of said first signal, each data sample in said first series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said first series of points;

(ii) for each set of three data samples remaining in said first series of data samples corresponding to a group of three adjacent ones of said points on said first surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(iii) reducing said first series of data samples by eliminating therefrom the remaining data sample corresponding to that vertex the distance between which and its corresponding fourth point is the smallest;

(iv) repeating steps (ii) and (iii) to further reduce said first series of data samples until only a predetermined number of data samples representing particular ones of said points in said first series of points remain in said first series of data samples;

(v) determining the center of said first surface feature by calculating the location of the center of a circle which intersects each of said samples of predetermined number;

(vi) calculating both the maximum distance from said center to any point in said second series of points and the minimum distance from said center to any point in said second series of points, and for

(vii) calculating the difference between said maximum distance and said minimum distance to obtain a measurement of the total indicated runout (TIR) of the second surface feature with respect to the center of the first surface feature.

35. An apparatus for measuring the eccentricity between a first surface feature and a second surface feature of an object, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means movable with respect to the object for generating a first signal correlated to the distance between a point on said measuring axis and each of a first series of first points on the first surface feature and a second signal correlated to the distance between said point on said measuring axis and each of a second series of second points on the second surface feature, and

(c) computer means coupled to said probe means for;

(i) storing a first series of data samples of said first signal, each data sample in said first series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said first series of points;

(ii) storing a second series of data samples of said second signal, each data sample in said second series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said second series of points;

(iii) for each set of three data samples remaining in said first series of data samples corresponding to a group of three adjacent ones of said points on said first surface feature, each said group having a vertex separating two endpoints, calculating a fourth point defined by the intersection of the perpendicular bisectors of a first line and a second line, said first line connecting said vertex with one of said endpoints, said second line connecting said vertex with the other one of said endpoints;

(iv) reducing said first series of data samples by eliminating therefrom the data sample remaining therein which corresponds to that vertex the distance between which and its associated fourth point is the smallest;

(v) repeating steps (iii) and (iv) to further reduce said first series of data samples until only a first predetermined number of data samples representing particular ones of said points in said first series of points remain in said first series of data samples;

(vi) determining the center of said first surface feature by calculating the location of the center of a first circle which intersects each of said samples of said first predetermined number;

(vii) for each set of three data samples remaining in said second series of data samples corresponding to a group of three adjacent ones of said points on said second surface feature, each said group having a vertex separating two endpoints, calculating a fifth point defined by the intersection of the perpendicular bisectors of a third line and a fourth line, said third line connecting said vertex with one of said endpoints, said fourth line connecting said vertex with the other one of said endpoints;

(viii) reducing said second series of data samples by eliminating therefrom the data sample remaining therein which corresponds to that vertex the distance between which and its corresponding fifth point is the smallest;

(ix) repeating steps (vii) and (viii) to further reduce said second series of data samples until only a second predetermined number of samples representing particular ones of said points in said second series of points remain in said second series of data samples;

(x) determining the center of said second surface feature by calculating the location of the center of a second circle which intersects each of said samples of said second predetermined number, and for

(xi) calculating the distance between said centers of said first and second surface features, respectively as a measure of the eccentricity between said first and second surface features.

36. An apparatus for measuring a second surface feature of an object with respect to the center of a first surface feature of the same object without requiring the center to be physically aligned with a measuring reference, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means movable with respect to the object for generating both a first signal correlated to the distance between a point on said measuring axis and each of a first series of first points on the first surface feature as well as a second signal correlated to the distance between said point on said measuring axis and each of a second series of second points on the second surface feature, and

(c) computer means coupled to said probe means for;

(i) storing a first series of data samples of said first signal, each data sample in said first series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said first series of points;

(ii) storing a second series of data samples of said second signal, each data sample in said second series of data samples being correlated to the distance between said point on said measuring axis and one of said points in said second series of points;

(iii) calculating the coordinates of the center of said first surface feature using said first series of data samples;

(iv) calculating the coordinates of each point in said second series of points;

(v) generating and storing a coordinate-corrected representation of said second series of points in accordance with the magnitude and angle of a vector relating said coordinates of said center to said point on said measuring axis, and for

(vi) calculating at least one measurement figure using said coordinate-corrected representation.

37. A method of measuring a second surface feature of an object with respect to the center of a first surface feature of the same object without requiring the center to be physically aligned with a measuring reference, said method comprising the steps of:

(a) mounting the object on a machine in fixed relation to a measuring axis of said machine, said machine including first and second probes for generating respective first and second signals;

(b) effecting relative movement between said object and said first probe in order to generate said first signal, said first signal being correlated to the distance between the first surface feature and said point on said measuring axis;

(c) effecting relative movement between said object and said second probe in order to generate said second signal, said second signal being correlated to the distance between the second surface feature and said point on said measuring axis;

(d) storing a first series of data samples of said first signal, each sample in said first series being correlated to the distance between said point on said measuring axis and one of a corresponding first series of points located at angularly spaced intervals on said first surface feature;

(e) storing a second series of data samples of said second signal, each sample in said second series being correlated to the distance between said point on said measuring axis and one of a corresponding second series of points located at angularly spaced intervals on said second surface feature;

(f) calculating the coordinates of the center of said first surface feature using said first series of data samples;

(g) calculating the coordinates of each point in said first series of points;

(h) generating and storing a coordinate-corrected representation of said second series of points in accordance with the magnitude and angle of a vector relating said coordinates of said center to said point on said measuring axis, and

(i) calculating at least one measurement figure using said coordinate-corrected representation.

38. An apparatus for measuring a second surface feature of an object with respect to the center of a first surface feature of the same object without requiring the center to be physically aligned with a measuring reference, said apparatus comprising:

(a) positioning means for maintaining the position of the object fixed in relation to a measuring axis;

(b) probe means for generating both a first signal correlated to the distance between a point on said measuring axis and each of a first series of first points on the first surface feature as well as a second signal correlated to the distance between said point on said measuring axis and each of a second series of second points on the second surface feature, and

(c) computer means connected to said probe means for;

(i) generating using said first signal a third signal indicating the magnitude and angle of the positional offset between the said measuring axis and the center of said first surface feature;

(ii) combining said third signal with said second signal to form a coordinate-corrected signal, and

(iii) calculating at least one measurement figure using said coordinate-corrected signal.

39. A method of measuring a second surface feature of an object with respect to the center of a first surface feature of the same object without requiring the center to be physically aligned with a measuring reference, said method comprising the steps of:

(a) mounting the object on a machine in fixed relation to a measuring axis of said machine, said machine including first and second probes for generating respective first and second signals;

(b) effecting relative movement between said object and said first probe in order to generate said first signal, said first signal being correlated to the distance between the first surface feature and said point on said measuring axis;

(c) effecting relative movement between said object and said second probe in order to generate said second signal, said second signal being correlated to the distance between the second surface feature and said point on said measuring axis;

(d) generating using said first signal a third signal indicating the magnitude and angle of the positional offset between the said measuring axis and the center of said first surface feature;

(e) combining said third signal with said second signal to form a coordinate-corrected signal, and

(f) calculating at least one measurement figure using said coordinate-corrected signal.

40. An apparatus for measuring wheels of the type having a pilot hole bounded by an interior edge and at least one surface feature surrounding the pilot hole, said apparatus comprising:

(a) fixture means for holding the wheel in fixed relation to a measuring axis;

(b) first probe means for generating a first signal correlated to the distance between said edge and said axis, said first probe means having a member mounted in distance-sensing relation with said edge;

(c) second probe means for generating a second signal correlated to the distance between said edge and said axis, said second probe means having a member mounted in distance-sensing relation with said surface feature;

(d) drive means connected to said fixture means for effecting relative rotation about said axis between the wheel and at least said first probe means;

(e) center determining means connected to said first probe means for determining based on said first signal the positional offset between said measuring axis and the center of said pilot hole;

(f) correcting means for adjusting said second signal in accordance with said positional offset to generate a corrected second signal, and

(g) calculating means for calculating at least one measurement figure based on said corrected second signal.

41. The apparatus of claim 40 wherein said first probe means comprises:

(a) an electromechanical transducer including a first member mounted in a fixed position with respect to said measuring axis and a second member movable with respect to said measuring axis and means for generating said first signal in accordance with the distance between said first and second members, and

(b) biasing means for maintaining mechanical contact between said second member and said edge while said relative rotation takes place.

42. The apparatus of claim 41 further comprising retraction means for selectively retracting said second member.

43. The apparatus of claim 41 wherein said electromechanical transducer comprises a differential transformer.

44. The apparatus of claim 41 wherein said biasing means comprises a pneumatic cylinder having a movable member mechanically coupled to said second member.