How could least square be larger than minimum circumscribed

I'm running a part on Sunday, main datum is a half external sphere. It measures 5.5mm diam using least squares BF, in tolerance, all is good. All vector pts, lots of them prob 40-50, constructed sphere. I mic it for fun in varying angles and get 5.51mm. Totally acceptable diff being lst sq vs Mic and all the other errors floating around.

So I decide to run it at minimum circumscribed....should be larger than lst sq, no? Welp....i get 5.48mm. How could min cir be less than a lst sq? I'm baffled.

Parents

Neil Challinor over 2 years ago

There is no "maximum circumscribed fit" - it's either minimum circumscribed (smallest diameter sphere that would envelope all of the points) or maximum inscribed (maximum diameter sphere that would fit inside all of the points).

Check that you have selected the correct fit type for the type of sphere you are measuring. If it's an external sphere (ball), you should be using minimum circumscribed, if it's internal (socket) you should be using maximum inscribed. Also, the maximum inscribed / minimum circumscribed are not as mathematically stable or robust as least squares, especially if you have less than a full 360° of arc. For this reason, minimum circumscribed should not be used for any less than 180° or arc and maximum inscribed should not be used for any less than 90° of arc: https://docs.hexagonmi.com/pcdmis/2020.2/en/helpcenter/index.htm?rhcsh=1&rhnewwnd=0#t=mergedProjects%2Fcore%2F16_const_topics%2FBest_Fit_Type_for_Circle.htm
Cancel
Vote Up 0 Vote Down

Sign in to reply

Cancel

Reply

Neil Challinor over 2 years ago

There is no "maximum circumscribed fit" - it's either minimum circumscribed (smallest diameter sphere that would envelope all of the points) or maximum inscribed (maximum diameter sphere that would fit inside all of the points).

Check that you have selected the correct fit type for the type of sphere you are measuring. If it's an external sphere (ball), you should be using minimum circumscribed, if it's internal (socket) you should be using maximum inscribed. Also, the maximum inscribed / minimum circumscribed are not as mathematically stable or robust as least squares, especially if you have less than a full 360° of arc. For this reason, minimum circumscribed should not be used for any less than 180° or arc and maximum inscribed should not be used for any less than 90° of arc: https://docs.hexagonmi.com/pcdmis/2020.2/en/helpcenter/index.htm?rhcsh=1&rhnewwnd=0#t=mergedProjects%2Fcore%2F16_const_topics%2FBest_Fit_Type_for_Circle.htm
Cancel
Vote Up 0 Vote Down

Sign in to reply

Cancel

Children

No Data