measuring a countersink

There's an error in the previous post, it' an ASIN and not an ATAN !!!!!


Then the radius of the contact point are :

The height of contact point are :


The a 2D line (H=a R + b) should give :



The upper diameter of the countersick is done when H=0, so when R=-B/A



Hope this helps...

This is absolutely beautiful, thank you so much for your help, i was actually able to follow your steps to match my needs, I will need help now assigning those variables to a generic feature to dimension it , I would assume I need to create a generic cone to then intersected to the top surface? Is that correct? Could you please review my code to make sure I'm doing it right? How do i used the results from the variables to do that? Thanks in advance.

ASSIGN/V10=PROBEDATA("diam","T1_3X20")/2+PROBEDATA("prbrdv","T1_3X20")
              ASSIGN/V11=PROBEDATA("diam","T6_5X20")/2+PROBEDATA("prbrdv","T6_5X20")
              ASSIGN/V12=RAD2DEG(ASIN(PT2.Z-PT1.Z)/(V11-V10))
              ASSIGN/R1=V10*SIN(DEG2RAD(V12))
              ASSIGN/R2=V11*SIN(RAD2DEG(V12))
              ASSIGN/H1=PT1.Z-V10*COS(DEG2RAD(V12))
              ASSIGN/H2=PT2.Z-V11*COS(DEG2RAD(V12))
              ASSIGN/A=(H2-H1)/(R2-R1)
              ASSIGN/B=(H2-A*R2)
              ASSIGN/DIAM=2*(-B/A)
CS_X34.5     =GENERIC/CIRCLE,DEPENDENT,CARTESIAN,OUT,$
              NOM/XYZ,<0,0,-0.29311>,$
              MEAS/XYZ,<0,0,-0.29311>,$
              NOM/IJK,<0,0,1>,$
              MEAS/IJK,<0,0,1>,$
              RADIUS/0,0

The dimension depends on the blue print.
The top diameter can be created by a generic circle :


Creating a cone is also possible, I'm not at the cmm to check...
I think the XYZ values are the vertex coordinates

The cone angle (half value is V3)​
The length of the cone depends on the diameter of the threaded hole

ASSIGN/ANGLE_AXIS=ACOS(DOT(UNIT(PT2.XYZ-PT1.XYZ,PL1.IJK))) i must have a syntax error on this line, is highlighted red, also my center .z is .00009 , is that enough to worry? most of the assignments are returning 0 values working offline but on a program that already ran online is that normal?,thanks in advance , you are keeping me awake the entire weekend , user like you make this forum a really valuable and unlimited learning source, thanks for sharing.

I forgot a bracket in the assignment
ASSIGN/ANGLE_AXIS=ACOS(DOT(UNIT(PT2.XYZ-PT1.XYZ),PL1.IJK))
The result of a dot product between two vectors is the product of the length of both vectors by the cosine of the angle between them.
So if you use UNIT, the length is 1, a vector using .IJK is 1, so the dot product gives the cosine. ACOS gives the angle.

Could you share values of center ball, so that I can check all the assignments.
Even if 0.00009 is very small, it should be zero, so maybe I'm wrong in an assignment (I wrote this from my memory, I wasn't at the cmm... !)

the values for the center ball are 34.42939,.000457,.00009 , one thing i didn`t mention ,i used 3mm and 5mm as 4 was not available until this week, could be that my problem? thank you so much , i tried that bracket and it turned blue but i was not sure if it was correct, oh god this is intense thanks for double checking.

ASSIGN/R1=V10*SIN(DEG2RAD(V12)) result is 0
ASSIGN/R2=V11*SIN(RAD2DEG(V12)) result is 0
ASSIGN/H1=PT1.Z-V10*COS(DEG2RAD(V12)) result is .10652
ASSIGN/H2=PT2.Z-V11*COS(DEG2RAD(V12)) result is 1.89691
ASSIGN/A=(H2-H1)/(R2-R1) result is 99999999999999
ASSIGN/B=H2-A*R2 result is 1.89691
ASSIGN/DIAM=2*(-B/A) result is 0
ASSIGN/DIST1=DOT(PT1.XYZ-PLN1.XYZ,PLN1.IJK) result is .10652
ASSIGN/ANGLE_AXIS=ACOS(DOT(UNIT(PT2.XYZ-PT1.XYZ),PL1.IJK)) result is .04216
ASSIGN/CENTER=PT1.XYZ+(DIST1/COS(ANGLE_AXIS))*UNIT(PT2.XYZ-PT1.XYZ) result is 34.42939,.000457,.00009
ASSIGN/VECT=UNIT(PT2.XYZ-PT1.XYZ) result is .04144,.00562,-.99913​

ASSIGN/V12=RAD2DEG(ASIN(PT2.Z-PT1.Z)/(V11-V10))....... here, I wrote RAD2DEG to give a result in degrees. If you don't use degrees, just write /V12=ASIN((PT2.Z-PT1.Z)/(V11-V10))
ASSIGN/R1=V10*SIN(DEG2RAD(V12)).............so here R1=V10*SIN(V12)
ASSIGN/R2=V11*SIN(RAD2DEG(V12)).............so here R2=V11*SIN(V12)
and :
ASSIGN/H1=PT1.Z-V10*COS(V12)
ASSIGN/H2=PT2.Z-V11*COS(V12)

Other results should change... ​​

If you want to play with, there's here an excel sheet which makes the job
autocenter cone.zip

you just have to change values in green cells.
Hope this helps.

nothing but respect to your skills in both ,Pcdmis and Math ,thank you so much for sharing, of course i will try , this is keeping me awake since i started ,have learned so much but i fell i will never stop learning , i will be taking official training in 2 weeks ,super excited thank you thank you thank you.