Vector direction

part two...








Correct part rotation can allow for "Perfect" Vectors

By Richard Clark

"Think of the drive of the axis. If the probe is moving with the drive (positive direction), the vector is one and if the probe is moving opposite the drive (minus direction) the vector is minus one"

In the previous 2 documents concerning Direction Vectors, techniques were discussed to calculate vectors for circular measurements and/or features neither parallel nor perpendicular to an axis. Understanding these concepts is vital to creating stable measurements from the programs used with your CMM, however, a more elementary approach may be the preferred one.

In our first example we can review by using the "90 minus rule" to calculate the direction vector when probing a point located on a feature that is neither parallel nor perpendicular to the X or Y-axes. We can determine from our print specifications that a 210° approach angle would be perpendicular to the surface being measured.

This is clearly illustrated when the Part Coordinate System is viewed using Polar coordinates.

Step #1 – We have a known angle of 210° that rotates from the X-axis.

Step #2 – Using the “90 minus rule” we can determine the unknown angle to be -120° and since we are in the XY plane the angle rotation is from the Y-axis.

Step #3 – Calculate the I-J-K vectors using the Cosine of the angles.
I = -0.86603 (The Cosine of our 210° X angle)
J = -0.50000 (The Cosine of our -120° Y angle)
K= 0 (Our probe is not moving along the Z axis)


In my short history of writing CMM part programs I have found that vector points are usually needed to construct a plane or line feature on a part. Most DCC CMM software has auto-measure plane and auto-measure line macros built within the software, which various geometric data about the feature can be entered and the software and CMM take off and measure the feature. If your software has this you should do 2 things: First, get very comfortable using it, because it will be very beneficial. Second, get comfortable not using it because if you haven't ran across an application, part, or fixture where this won't work, you are very lucky. The only sure thing I know about luck is that it always runs out.

To illustrate how easy this process can become we will use the earlier example part, rotate about an axis and create the "perfect" vectors needed to probe points for a line measurement. The first step is to rotate the part coordinate system in such a way that our line feature is "true" with an axis line. Since the part angle rotation from the X-axis is -60° and the Y-axis is 30°, we can rotate about the Z-axis (-60°), which "clocks" our part and aligns the feature with the X-axis.



Now our part is "true" to the X axis. Here is where it gets really cool. This is where the angle rotation from the axis, and 90 minus rule, need not be used. A direction vector that is needed to probe a feature aligned with an axis will always be calculated by the cosine of 90°, which equals 1.

Mr. Jerry Guffy, CMM software trainer from Mitutoyo, told me a rule of thumb that I'll always use and never forget. "Think of the drive of the axis. If the probe is moving with the drive (positive direction), the vector is 1 and if the probe is moving opposite the drive (minus direction) the vector is minus 1."




For our probe to contact our line at a correct vector we use:
I = 0.0000
J = -1.0000
K = 0.0000

We do not want the probe to move along the X or Z-axes but we do want it to move in a Y minus direction. J is the Y vector, so it equals -1.

So here's how it works (at combat speed). We program a movement or series of movements to place our probe on the Y positive side of our line at the desired clearance from the part and the desired Z-axis elevation. We used the comp point, go meas, meas direction feature, which basically tells the probe to move until contact.

MEAS/CPOINT,F(CPT_1),1,AXDIR
MEAS_DIR/I-J-K,0.000,-1.000,0.000

After the point is taken we can use a CMM goto movement (relative) to move the probe a certain distance only along the X-axis.

GOTO/INCR,CART,3.00000,0.00000,0.00000

Now we can copy and paste the 3 lines and change the designation of the point label (red text) to probe the desired number of points along the line. We'll use 3 for simplicity only.

MEAS/CPOINT,F(CPT_1),1,AXDIR
MEAS_DIR/I-J-K,0.000,-1.000,0.000
GOTO/INCR,CART,3.00000,0.00000,0.00000

MEAS/CPOINT,F(CPT_2),1,AXDIR
MEAS_DIR/I-J-K,0.000,-1.000,0.000
GOTO/INCR,CART,3.00000,0.00000,0.00000

MEAS/CPOINT,F(CPT_3),1,AXDIR
MEAS_DIR/I-J-K,0.000,-1.000,0.000
GOTO/INCR,CART,3.00000,0.00000,0.00000

Now we can construct the line from the 3 data points.

MEAS/LINE,F(LINE2),3
CONSTPT/FA(CPT_1)
CONSTPT/FA(CPT_2)
CONSTPT/FA(CPT_3)
ENDMES

And that’s all there is to it. Read the print carefully and rotate your part correctly. All of your vectors will be as easy as counting to one.

Richard Clark works as a Metrology Consultant and CMM operator in Portland Indiana, to receive a freeware version of his “Vector Direction Calculator 4.02” e-mail feedback to rcmetrology@yahoo.com

Techniques described is this document are derived from the book "DCC CMM Programming - Part Alignment and Vector Points" by Scott C. Beavers. To obtain a copy of this book, contact CMM Resources (513) 535-0870.

part two...








Correct part rotation can allow for "Perfect" Vectors

By Richard Clark

"Think of the drive of the axis. If the probe is moving with the drive (positive direction), the vector is one and if the probe is moving opposite the drive (minus direction) the vector is minus one"

In the previous 2 documents concerning Direction Vectors, techniques were discussed to calculate vectors for circular measurements and/or features neither parallel nor perpendicular to an axis. Understanding these concepts is vital to creating stable measurements from the programs used with your CMM, however, a more elementary approach may be the preferred one.

In our first example we can review by using the "90 minus rule" to calculate the direction vector when probing a point located on a feature that is neither parallel nor perpendicular to the X or Y-axes. We can determine from our print specifications that a 210° approach angle would be perpendicular to the surface being measured.

This is clearly illustrated when the Part Coordinate System is viewed using Polar coordinates.

Step #1 – We have a known angle of 210° that rotates from the X-axis.

Step #2 – Using the “90 minus rule” we can determine the unknown angle to be -120° and since we are in the XY plane the angle rotation is from the Y-axis.

Step #3 – Calculate the I-J-K vectors using the Cosine of the angles.
I = -0.86603 (The Cosine of our 210° X angle)
J = -0.50000 (The Cosine of our -120° Y angle)
K= 0 (Our probe is not moving along the Z axis)


In my short history of writing CMM part programs I have found that vector points are usually needed to construct a plane or line feature on a part. Most DCC CMM software has auto-measure plane and auto-measure line macros built within the software, which various geometric data about the feature can be entered and the software and CMM take off and measure the feature. If your software has this you should do 2 things: First, get very comfortable using it, because it will be very beneficial. Second, get comfortable not using it because if you haven't ran across an application, part, or fixture where this won't work, you are very lucky. The only sure thing I know about luck is that it always runs out.

To illustrate how easy this process can become we will use the earlier example part, rotate about an axis and create the "perfect" vectors needed to probe points for a line measurement. The first step is to rotate the part coordinate system in such a way that our line feature is "true" with an axis line. Since the part angle rotation from the X-axis is -60° and the Y-axis is 30°, we can rotate about the Z-axis (-60°), which "clocks" our part and aligns the feature with the X-axis.



Now our part is "true" to the X axis. Here is where it gets really cool. This is where the angle rotation from the axis, and 90 minus rule, need not be used. A direction vector that is needed to probe a feature aligned with an axis will always be calculated by the cosine of 90°, which equals 1.

Mr. Jerry Guffy, CMM software trainer from Mitutoyo, told me a rule of thumb that I'll always use and never forget. "Think of the drive of the axis. If the probe is moving with the drive (positive direction), the vector is 1 and if the probe is moving opposite the drive (minus direction) the vector is minus 1."




For our probe to contact our line at a correct vector we use:
I = 0.0000
J = -1.0000
K = 0.0000

We do not want the probe to move along the X or Z-axes but we do want it to move in a Y minus direction. J is the Y vector, so it equals -1.

So here's how it works (at combat speed). We program a movement or series of movements to place our probe on the Y positive side of our line at the desired clearance from the part and the desired Z-axis elevation. We used the comp point, go meas, meas direction feature, which basically tells the probe to move until contact.

MEAS/CPOINT,F(CPT_1),1,AXDIR
MEAS_DIR/I-J-K,0.000,-1.000,0.000

After the point is taken we can use a CMM goto movement (relative) to move the probe a certain distance only along the X-axis.

GOTO/INCR,CART,3.00000,0.00000,0.00000

Now we can copy and paste the 3 lines and change the designation of the point label (red text) to probe the desired number of points along the line. We'll use 3 for simplicity only.

MEAS/CPOINT,F(CPT_1),1,AXDIR
MEAS_DIR/I-J-K,0.000,-1.000,0.000
GOTO/INCR,CART,3.00000,0.00000,0.00000

MEAS/CPOINT,F(CPT_2),1,AXDIR
MEAS_DIR/I-J-K,0.000,-1.000,0.000
GOTO/INCR,CART,3.00000,0.00000,0.00000

MEAS/CPOINT,F(CPT_3),1,AXDIR
MEAS_DIR/I-J-K,0.000,-1.000,0.000
GOTO/INCR,CART,3.00000,0.00000,0.00000

Now we can construct the line from the 3 data points.

MEAS/LINE,F(LINE2),3
CONSTPT/FA(CPT_1)
CONSTPT/FA(CPT_2)
CONSTPT/FA(CPT_3)
ENDMES

And that’s all there is to it. Read the print carefully and rotate your part correctly. All of your vectors will be as easy as counting to one.

Richard Clark works as a Metrology Consultant and CMM operator in Portland Indiana, to receive a freeware version of his “Vector Direction Calculator 4.02” e-mail feedback to rcmetrology@yahoo.com

Techniques described is this document are derived from the book "DCC CMM Programming - Part Alignment and Vector Points" by Scott C. Beavers. To obtain a copy of this book, contact CMM Resources (513) 535-0870.