Why is a robotic manipulator's inertia matrix non-invertible at certain joint angles?

[Sed]

Hello,

What could be wrong when the total inertia matrix of a robotic manipulator is non invertible when under certain values of the joint angles?

Thank you

 

[Dr.D]

You would be more likely to get useful help if you showed us what your robot looks like and how the inertia matrix was developed.

 

[Sed]

The model is for a dynamically equivalent manipulator (fixed base with spherical passive joint). The model was developed in the attached paper.
I checked all the steps, everything seems fine except for the resulting inertia matrix.
The whole matrix is non invertible but if i divide it into small matrices where the upper right 3 by 3 matrix represents the spherical joint inertia and the lower right n by n matrix represent the rest of the manipulator. Then the manipulator matrix is always invertible and the spherical joint one is not.

If you have just an idea about what might cause the problem, i realize it's a long process to got through all the equation.

Thank you