In NX, there is a command for displaying the unconstrained DOF(s) of a given part in an assembly. In other less capable CAD packages, the unconstrained DOF(s) can be detected by simply attempting to move the part. If unconstrained, the part will move / rotatate in the unconstrained DOFs and when all 6 are constrained, a pop up message will notify the user that the part is fully constrained. Does NX have that type of DOF query method?
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