How to locate imaginary ball gage inside a cone

[parker.imperl]

Hello, I'm hoping to get some help on what seems to be the most challenging measurement I've come across.
My goal is to measure the distance from a planar datum (perpendicular to the axis of the cone) to the top of an imaginary gage ball that would rest inside of a cone.

I have tried a few things:

• Construct a circle using a cone and picked each of the 3 options I see.

I'm uncertain if I understand correctly what these constructions are doing but this is what I believe they do. I would appreciate feedback if I'm wrong about how they work.

1. I believe the first option was I input at what diameter of the cone I want to read height at.
2. The second option was to determine a "distance" which I presumed to be the distance I'm trying to confirm.
3. The third one looks as if it's asking me what size of ball I want to place into the cone and then it "should" feed back a height. This appears to feed back a diameter instead though.

I've included an image of my problem below:

cmmgageproblem.jpg

[JEFMAN]

some answers here :

https://www.pcdmisforum.com/forum/pc-dmis-enterprise-metrology-software/pc-dmis-for-cmms/32103-how-to-create-a-gage-dia-inside-a-cone

[NinjaBadger]

con1       =feat/contact/cone/default,cartesian,out
            theo/<0,0,0>,<0,0,1>,60,20,25
            actl/<0,0,0>,<0,0,1>,60,20,25
            targ/<0,0,0>,<0,0,1>
            start ang=360,end ang=360
            angle vec=<-1,0,0>
            show feature parameters=no
            show contact parameters=yes
              numhits=9,numlevels=3,depth=0,end offset=0
              sample hits=0,spacer=0.381
              avoidance move=no,distance=25
              onerror=no,read pos=no
            show hits=no
con2       =feat/cone,cartesian,in,ang,no
            theo/<0,0,-21.651>,<0,0,1>,60,25,48.094
            actl/<0,0,-21.651>,<0,0,1>,60,25,48.094
            constr/cone,cast,con1,dependent
a1         =alignment/start,recall:startup,list=yes
            alignment/level,zplus,con2
            alignment/trans,xaxis,con2
            alignment/trans,yaxis,con2
            alignment/trans,zaxis,con2
            alignment/end
            assign/halfang=con1.a/2
            assign/opp=12.7/2
            assign/myhyp=opp/sin(deg2rad(halfang))
f1         =generic/sphere,dependent,cartesian,out,$
            nom/xyz,<0,0,myhyp>,$
            meas/xyz,<0,0,myhyp>,$
            nom/ijk,<0,0,1>,$
            meas/ijk,<0,0,1>,$
            diameter/12.7,12.7
dim loc1= location of sphere f1  units=mm ,$
graph=off  text=off  mult=10.00  output=both  half angle=no
ax    nominal       +tol       -tol       meas        dev     outtol
x        0.000      0.050     -0.050      0.000      0.000      0.000 ----#----
y        0.000      0.050     -0.050      0.000      0.000      0.000 ----#----
z       12.700      0.050     -0.050     12.700      0.000      0.000 ----#----
end of dimension loc1

Steps...

1) Measure cone
2) Create a cast cone from your cone (this is the same cone, but the origin is from the point of the cone not the centroid)
3) Align to the cone (Level to axis and origin on the point
4) from here the trig is simple, your sphere radius is the Opposite side of a right angled triangle, half the cone angle is your angle.
5) Calculate the hypotenuse
6) Construct a generic sphere at 0,0,Hypotenuse with the gauge diameter.

[Jim Poehler]

I would simply measure the bottom. smaller cone and then the cylinder just above it. Now create a circle where these two intersect and looking at it from a side view x or y, call the distance from A to the circle in the z axis. (If your drawing is correct then it seems that this is the dimension you are looking for.)

[VinniUSMC]

https://www.pcdmisforum.com/forum/pc-dmis-enterprise-metrology-software/pc-dmis-for-cmms/435433-projected-circles-from-cones