[Olivier]

Not every robot brands have the same tolerances with singularities.

RoboDK can solve the IK inside a singularity because it is a simulation, but in real life your controller will stop the robot before going there.

However, RoboDK can predict singularities given the correct tolerances.
You can modify the singularity tolerances in RoboDK in Tools->Options->Motion (see picture) to match your Mecademic robot behavior.