I deleted Constraint83 and recreated it, and it made FreeCAD hang for less than a minute, then I got an error message saying (translating from French) "Editing this value is forbidden because the sketch contains conflicting constraints".
I've been unable to repeat that delay.
I only had a quick look but your sketch contains at least two redundant constraints that are not mentioned by the solver: Constraint3 which is a point on object between the far right circle's center and the horizontal axis. It is unnecessary since you have a symmetric constraint with the far left circle. Deleting it produces a conflicting constraint error listing a whole bunch of possible constraints to remove.
Same case for Constraint41 which is redundant because of Constraint44.
yoshimitsuspeed wrote:I would wait 5 minutes for it to resolve the sketch or would even throw over constrained errors when none were deserved.
Are you sure? Maybe your flange sketch has redundant constraints similar to what I pointed out.
OS: Ubuntu 12.04.3 LTS
Version: 0.14.2542 (Git)
Python version: 2.7.3
Qt version: 4.8.1
Coin version: 3.1.3
SoQt version: 1.5.0
OCC version: 6.5.0