Method and apparatus for determining shapes of countersunk holes

• US 6,154,279 A
• Filed: 04/09/1998
• Issued: 11/28/2000
• Est. Priority Date: 04/09/1998
• Status: Expired due to Fees

• Current Assignee: John W. Newman
• Original Assignee: John W. Newman
• Inventors: Thayer, Stephen W.
• Primary Examiner(s): Rosenberger, Richard A.
• Application Number:
  US09/057,706
• Time in Patent Office: 964 Days
• Field of Search: 356/376
• US Class Current: 356/602
• CPC Class Codes: G01B 11/22 for measuring depth
• CPC Class Codes: G01B 11/24 for measuring contours or curvatures

Abstract

The dimensions of a countersunk hole, or of a fastener head, are determined accurately and rapidly by a nondestructive measurement system. At least one laser projects spots of light onto the surface being analyzed. From knowledge of the projection angle, and of the lateral displacement of the spots of light caused by variations in the depth of the surface, one can calculate an actual depth of each point on the surface. A set of parameters defining a mathematical model of the hole or fastener head are fitted to a set of measured coordinates of points on the surface being analyzed, using conventional numerical techniques. The optimized parameters define the dimensions of the countersunk hole or fastener head. The present invention operates independently of the coordinate system used to perform the measurements, so the invention eliminates errors caused by misalignment of optical components. The invention can also provide automatic warnings when the dimensions of a particular countersunk hole or fastener heads exceed predetermined tolerances.

Claims

1. A method of determining an orientation of a camera used to observe a countersunk hole, the method comprising the steps of:

a) electronically measuring coordinates of a plurality of points on a countersunk hole, the countersunk hole having an axis and an apex, and storing said coordinates in a memory of a computer, said coordinates of each of said plurality of points being designated by (x_i, y_i, z_i),

b) deriving two distinct expressions for a radius of the countersunk hole corresponding to each of said points, wherein said expressions are functions of x₀, y₀, z₀, x₁, y₁, and φ

, where (x₀, y₀, z₀) is the apex of the countersunk hole, (x₁, y₁, z₁) is a point at which the axis of the countersunk hole intersects a reference plane z=z₁ =0, and φ

is an angle between the axis of the countersunk hole and a line connecting the apex of the countersunk hole and one of the points (x_i, y_i, z_i),

c) selecting values of parameters x₀, y₀, z₀, x₁, y₁, and φ

so as to minimize an error function comprising a comparison of said two distinct expressions,

d) determining an orientation of vector V defined by

space="preserve" listing-type="equation">V=(x.sub.1 -x.sub.0)i+(y.sub.1 -y.sub.0)j+(z.sub.1 -z.sub.0)k

wherein the orientation of V corresponds to an orientation of the camera with respect to the countersunk hole.

2. The method of claim 1, wherein the expressions derived in step (b) are computed to be:

space="preserve" listing-type="equation">r.sub.i =s.sub.i tan φ

=(B(A·

B)/(B·

B))tan φ

and

space="preserve" listing-type="equation">r.sub.i '"'"'=D(C·

D)/(D·

D)tan [cos .sup.-1 ((C·

D)/|C| |D|)]

where A is a vector extending from the apex of the countersunk hole to one of said points (x_i, y_i, z_i), B is a vector extending from the apex of the countersunk hole to the point (x₁, y₁, z₁), C is a vector from the point (x₁, y₁, z₁) to one of said points (x_i, y_i, z_i), and D is a vector from the point (x₁, y₁, z₁) to the apex of the countersunk hole.

3. A method of determining an orientation of a countersunk hole relative to a surrounding surface, the method comprising the steps of:

a) using a camera to measure coordinates of a plurality of points on a countersunk hole, the countersunk hole having an axis and an apex, and storing said coordinates in a memory of a computer, said coordinates of each of said plurality of points being designated by (x_i, y_i, z_i),

b) deriving two distinct expressions for a radius of the countersunk hole corresponding to each of said points, wherein said expressions are functions of x₀, y₀, z₀, x₁, y₁, and φ

, where (x₀, y₀, z₀) is the apex of the countersunk hole, (x₁, y₁, z₁) is a point at which the axis of the countersunk hole intersects a reference plane z=z₁ =0, and φ

is an angle between the axis of the countersunk hole and a line connecting the apex of the countersunk hole and one of the points (x_i, y_i, z_i),

c) selecting values of parameters x₀, y₀, z₀, x₁, y₁, and φ

so as to minimize an error function comprising a comparison of said two distinct expressions,

d) determining an orientation of vector V defined by

space="preserve" listing-type="equation">V=(x.sub.1 -x.sub.0)i+(y.sub.1 -y.sub.0)j+(z.sub.1 -z.sub.0)k

wherein the orientation of V corresponds to an orientation of the camera with respect to the countersunk hole,

e) repeating step (a) to determine a second plurality of points on a surrounding surface of the countersunk hole, and using said second plurality of points to determine a surface normal vector V'"'"', and

f) using a difference between V and V'"'"' to calculate an angle at which the countersunk hole was drilled relative to the surrounding surface.

4. The method of claim 3, wherein the expressions derived in step (b) are computed to be:

space="preserve" listing-type="equation">r.sub.i '"'"'=s.sub.i tan φ

=(B(A·

B)/(B·

B))tan φ

and

space="preserve" listing-type="equation">r.sub.i '"'"'=D(C·

D)/(D·

D)tan [cos .sup.-1 ((C·

D)/|C| |D|)]

where A is a vector extending from the apex of the countersunk hole to one of said points (x_i, y_i, z_i), B is a vector extending from the apex of the countersunk hole to the point (x₁, y₁, z₁), C is a vector from the point (x₁, y₁, z₁) to one of said points (x_i, y_i, z_i), and D is a vector from the point (x₁, y₁, z₁) to the apex of the countersunk hole.

5. An apparatus for determining an orientation of a camera used to observe a countersunk hole, comprising:

a) means for electronically measuring coordinates of a plurality of points on a countersunk hole, the countersunk hole having an axis and an apex, and for storing said coordinates in a memory of a computer, said coordinates of each of said plurality of points being designated by (x_i, y_i, z_i),

b) means for deriving two distinct expressions for a radius of the countersunk hole corresponding to each of said points, wherein said expressions are functions of x₀, y₀, z₀, x₁, y₁, and φ

, where (x₀, y₀, z₀) is the apex of the countersunk hole, (x₁, y₁, z₁) is a point at which the axis of the countersunk hole intersects a reference plane z=z₁ =0, and φ

is an angle between the axis of the countersunk hole and a line connecting the apex of the countersunk hole and one of the points (x_i, y_i, z_i),

c) means for selecting values of parameters x₀, y₀, z₀, x₁, y₁, and so as to minimize an error function comprising a comparison of said two distinct expressions,

d) means for determining an orientation of vector V defined by

space="preserve" listing-type="equation">V=(x.sub.1 -x.sub.0)i+(y.sub.1 -y.sub.0)j+(z.sub.1 -z.sub.0)k

wherein the orientation of V corresponds to an orientation of the camera with respect to the countersunk hole.

6. The apparatus of claim 5, wherein the means for deriving includes means for computing said expressions by the formulas:

space="preserve" listing-type="equation">r.sub.i =s.sub.i tan Φ

=(B(A·

B)/(B·

B))tan φ

and

space="preserve" listing-type="equation">r.sub.i =D(C·

D)/(D·

D)tan [cos .sup.-1 ((C·

D)/|C| |D|)]

where A is a vector extending from the apex of the countersunk hole to one of said points (x_i, y_i, z_i), B is a vector extending from the apex of the countersunk hole to the point (x₁, y₁, z₁), C is a vector from the point (x₁, y₁, z₁) to one of said points (x_i, y_i, z_i), and D is a vector from the point (x₁, y₁, z₁) to the apex of the countersunk hole.

7. An apparatus for determining an orientation of a countersunk hole relative to a surrounding surface, comprising:

a) means for manipulating a camera so as to measure coordinates of a plurality of points on a countersunk hole, the countersunk hole having an axis and an apex, and means for storing said coordinates in a memory of a computer, said coordinates of each of said plurality of points being designated by (x_i, y_i, z_i),

b) means for deriving two distinct expressions for a radius of the countersunk hole corresponding to each of said points, wherein said expressions are functions of x₀, y₀, z₀, x₁, y₁, and φ

, where (x₀, y₀, z₀) is the apex of the countersunk hole, (x₁, y₁, z₁) is a point at which the axis of the countersunk hole intersects a reference plane z=z₁ =0, and φ

is an angle between the axis of the countersunk hole and a line connecting the apex of the countersunk hole and one of the points (x_i, y_i, z_i),

c) means for selecting values of parameters x₀, y₀, z₀, x₁, y₁, and so as to minimize an error function comprising a comparison of said two distinct expressions,

d) means for determining an orientation of vector V defined by

space="preserve" listing-type="equation">V=(x.sub.1 -x.sub.0)i+(y.sub.1 -y.sub.0)j+(z.sub.1 -z.sub.0)k

wherein the orientation of V corresponds to an orientation of the camera with respect to the countersunk hole,

e) means for determining a vector V'"'"' representing an orientation of a surrounding surface of the countersunk hole, and

f) means for calculating a difference between V and V'"'"' and for using said difference to determine an angle at which the countersunk hole was drilled relative to the surrounding surface.

8. The apparatus of claim 7, wherein the means for deriving include means for computing said expressions by the formulas:

space="preserve" listing-type="equation">r.sub.i =s.sub.i tan φ

=(B(A·

B)/(B·

B))tan φ

and

space="preserve" listing-type="equation">r.sub.1 '"'"'=D(C·

D)/(D·

D)tan [cos.sup.-1 ((C·

D)/|C| |D|)]

where A is a vector extending from the apex of the countersunk hole to one of said points (x_i, y_i, z_i), B is a vector extending from the apex of the countersunk hole to the point (x₁, y₁, z₁), C is a vector from the point (x₁, y₁, z₁) to one of said points (x_i, y_i, z_i), and D is a vector from the point (x₁, y₁, z₁) to the apex of the countersunk hole.