Small arcs...

[LostL]

There is a method of measuring small arcs from Hexagon floating around using Fixed rad and distance/polar to evaluate radius. The implementation I've seen consisted of measuring the arc with Fixed rad and evaluate the distance from the arc center to points on the radius.
I made this estimate of the result on an incorrect radius and had it verified in CMM:

rad.png

Nominal radius in green measured with 4 points. Red dashed the fixed radius. Blue actual radius. The distance from fixed radius center to a point in the middle of the radius increases when the actual radius is smaller. The distance to points on the edges will decrease slightly. The cooefficient of the function from the distance in between the points and the fixed radius center, to actual radius is nowhere near 1 in this implementation. I can't see any sustantial difference in any implementation I've seen. Am I missing something or is this method broken?

[DAN_M]

I use the small arc method and get good results. But I only attempt this method if I have a little bit of tolerance to work with (where I'm from thats ±0.005" or greater) and if I have 35° or more of the arc to work with.

My procedure for small arc is:

Assuming you're looking down at your part from the Z+ perspective...
1) Make sure I am using Z+ workplane (because a circle is a 2d feature and you want PC DMIS to "see it"). Also make sure I am using an alignment that has all 6 degrees of freedom constrained.
2) Measure the arc using fixed rad. 4 hits. CIR1.
3) Insert new alignment. Make CIR1 X and Y origin.
4) Measure the arc again at X0 and Y0 using leastsquare. 7 hits. CIR2. Use CIR2 for dimensional reporting.

STARTUP =ALIGNMENT/START,RECALL:USE_PART_SETUP,LIST=YES
ALIGNMENT/END
MODE/MANUAL
LOADPROBE/7107_G_4X20
TIP/T1A0B0, SHANKIJK=0, 0, 1, ANGLE=0
PLN_ZP =GENERIC/PLANE,DEPENDENT,CARTESIAN,$
NOM/XYZ,<0,0,0>,$
MEAS/XYZ,<0,0,0>,$
NOM/IJK,<0,0,1>,$
MEAS/IJK,<0,0,1>
PLN_YM =GENERIC/PLANE,DEPENDENT,CARTESIAN,$
NOM/XYZ,<0,0,0>,$
MEAS/XYZ,<0,0,0>,$
NOM/IJK,<0,-1,0>,$
MEAS/IJK,<0,-1,0>
PLN_XM =GENERIC/PLANE,DEPENDENT,CARTESIAN,$
NOM/XYZ,<0,0,0>,$
MEAS/XYZ,<0,0,0>,$
NOM/IJK,<-1,0,0>,$
MEAS/IJK,<-1,0,0>
A1 =ALIGNMENT/START,RECALL:STARTUP,LIST=YES
ALIGNMENT/LEVEL,ZPLUS,PLN_ZP
ALIGNMENT/ROTATE,YMINUS,TO,PLN_YM,ABOUT,ZPLUS
ALIGNMENT/TRANS,XAXIS,PLN_XM
ALIGNMENT/TRANS,YAXIS,PLN_YM
ALIGNMENT/TRANS,ZAXIS,PLN_ZP
ALIGNMENT/END
CIR1 =FEAT/CONTACT/CIRCLE/DEFAULT,CARTESIAN,OUT,FIXED_RAD
THEO/<0.2,0.1,-0.1>,<0,0,1>,0.9885,0
ACTL/<0.2,0.1,-0.1>,<0,0,1>,0.9885,0
TARG/<0.2,0.1,-0.1>,<0,0,1>
START ANG=90,END ANG=450
ANGLE VEC=<1,0,0>
DIRECTION=CCW
SHOW FEATURE PARAMETERS=NO
SHOW CONTACT PARAMETERS=YES
NUMHITS=4,DEPTH=0,PITCH=0
SAMPLE METHOD=SAMPLE_HITS
SAMPLE HITS=0,SPACER=0
AVOIDANCE MOVE=BOTH,DISTANCE=0.3937
FIND HOLE=DISABLED,ONERROR=NO,READ POS=NO
SHOW HITS=NO
A2 =ALIGNMENT/START,RECALL:A1,LIST=YES
ALIGNMENT/TRANS,XAXIS,CIR1
ALIGNMENT/TRANS,YAXIS,CIR1
ALIGNMENT/END
CIR2 =FEAT/CONTACT/CIRCLE/DEFAULT,CARTESIAN,OUT,LEAST_SQR
THEO/<0,0,-0.1>,<0,0,1>,0.9885,0
ACTL/<0,0,-0.1>,<0,0,1>,0.9885,0
TARG/<0,0,-0.1>,<0,0,1>
START ANG=90,END ANG=450
ANGLE VEC=<1,0,0>
DIRECTION=CCW
SHOW FEATURE PARAMETERS=NO
SHOW CONTACT PARAMETERS=YES
NUMHITS=7,DEPTH=0,PITCH=0
SAMPLE METHOD=SAMPLE_HITS
SAMPLE HITS=0,SPACER=0
AVOIDANCE MOVE=BOTH,DISTANCE=0.3937
FIND HOLE=DISABLED,ONERROR=NO,READ POS=NO
SHOW HITS=NO

[LostL]

Yeah, that is similiar to what I do myself. As long as the tolerance is kind and the arc has at least 70-80 degrees it works reasonably well. The difference lies in using a circle or points. It was mostly for the benefit of others as I've noticed that seemingly incorrect instruction still floating around.

[neil.challinor]

The problems people run into with small degrees of arc all ultimately boil down to the mathematical uncertainty of the calculation. The National Physical Laboratory in the UK did a good study on this and published the results in their CMM Measurement Strategies Good Practice Guide #41 which can be downloaded here : https://www.npl.co.uk/special-pages/..._cmm.pdf?ext=.

A better way for designers to control this type of thing would be to use surface profile with a fully constrained datum reference frame. If they boxed the radius in question and it's nominal co-ordinates and then applied a surface profile tolerance that reflected the amount of deviation they were willing to accept, it would be much easier to prove conformance. You would not be reporting an actual radius and location, more proving that the actual shape, size, location & orientation of the defined surface (in this case the radius) was within a certain tolerance band.

[DAN_M]

^^this is what i encourage our imagineers to do whenever possible

[Douglas]

I recently checked some bearing races our engineering dimensioned that way,, .002 profile of a surface on the badic torus... 72° of arc to work with I got good results

[LostL]

I agree it´s generally a better practice , when the engineers can be influenced.

[Nano Vujkovic]

This is from Hexagon

https://support.hexagonmi.com/sfc/servlet.shepherd/document/download/0693z00000AGu1rAAD?operationContext=S1

[LostL]

This is exactly what I'm objecting to. As far as I can see the method is fundamentally matematically unsound.

[Nano Vujkovic]

If I remember correctly, the first time I was introduced to this was by Rob Jenson. If it's good enough for him, it's good enough for me.

[VinniUSMC]

There is a method of measuring small arcs from Hexagon floating around using Fixed rad and distance/polar to evaluate radius. The implementation I've seen consisted of measuring the arc with Fixed rad and evaluate the distance from the arc center to points on the radius.
I made this estimate of the result on an incorrect radius and had it verified in CMM:

Nominal radius in green measured with 4 points. Red dashed the fixed radius. Blue actual radius. The distance from fixed radius center to a point in the middle of the radius increases when the actual radius is smaller. The distance to points on the edges will decrease slightly. The cooefficient of the function from the distance in between the points and the fixed radius center, to actual radius is nowhere near 1 in this implementation. I can't see any sustantial difference in any implementation I've seen. Am I missing something or is this method broken?

I believe the point of this method is to imitate a mating part to use as the origin, because when the radius changes, the center point changes, as you noted. I'm not sure what you're trying to use it for, but the purpose is to measure the radius in a repeatable manner. So, first you align to the "perfect" circle, then you measure it least squares to get the most repeatable feature. The actual center of the feature is the second circle. It would be easy to see physically with radius and pin gages.

Take a .500 pin gage, and look at the difference in the gaps with a 3/8 and a 5/8 radius gage. The 3/8 radius will have a big gap in the center, and the center point of it would be significantly closer to the radius. The 5/8 radius gage would have big gaps on the oustide of the radius, and the center point would be significantly away from the radius.

And the smaller the arc, the more significant the difference. The method isn't broken, I think there's just a misunderstanding about exactly what the method is for.