however, when importing just the physical model with the three inputs it has unconnected, Mathematica complains the model is unbalanced and and nothing can be done

Many properties and SystemModel functions relay on the model building to be able to compute results. In some cases this is necessary (e.g. when simulating) but in some cases we do have some room for improvement where building would not be necessary in principle.

However, when importing with just a Const.k =0 connected to the models inputs, it can simulate the model, but the outputs and inputs appear empty and it refuses to give a statespacemodel that has any inputs or outputs..

I don't have your model, but let me show you what I think may be happening with one of the Modelica library examples in this domain. If you compute

SystemModelLinearize["Modelica.Mechanics.MultiBody.Examples.Elementary.ForceAndTorque"]

you'll find that there are no inputs or outputs in the resulting state space model. This is because sources are explicitly being provided to the would-be inputs and there are no top-level real outputs either. If you duplicate this model and you replace either the component torque or the component force, for a 3D array of "Modelica.Blocks.Interfaces.RealInput", then linearization will detect these inputs. Similarly, you can add a sensor from "Modelica.Mechanics.MultiBody.Sensors" to a frame in the model, connected to a top level output ("Modelica.Blocks.Interfaces.RealOutput"), and then linearization will detect them as outputs. Hope this helps.

Thank you for such a quick reply, and your tips, in fact the error was using the three revolute joints...once switching to a Sphericaljoint as you suggested the problem went away, I can now simulate and test as I please....Though I am now having another problem, I would like to import the model into Mathematica to derive some control values and experiment there...however, when importing just the physical model with the three inputs it has unconnected, Mathematica complains the model is unbalanced and and nothing can be done.

However, when importing with just a Const.k =0 connected to the models inputs, it can simulate the model, but the outputs and inputs appear empty and it refuses to give a statespacemodel that has any inputs or outputs...(outputs I expect to be around 15 and inputs 3...should I ask a new question or are you aware if models have to be specially designed for inputs and outputs when importing to Mathematica?

Thank you again for the initial help!

Thanks for posting a very nicely illustrated question. I am on the System Modeler development team, and very interested in understanding what we can do better to help users "debug" this sort of problems. Of course, I also wish things were simple enough that one would never need to reach out for help, but I am well aware that this is not always the case when working with MultiBody models.

Some observations to start with:

• Your model has a sequence of three revolute joints to give the cube its three degrees of freedom. However, such a configuration has the danger of ending up in singular configurations. Maybe you are aware of this and can make sure you don't end up there, but a Spherical joint typically solves this problem in a better way.
• It surprises me that the only nonlinear system seen in the equation browser has been reduced by tearing to just a single angular variable. I mean, the symmetry of the problem's three degrees of freedom suggests to me that none of the angles should be possible to solve before any of the others, and since the three angles are not algebraically constrained, the nonlinear system where one angle is solved shouldn't be possible to tear to size 1. However, maybe the physical symmetry is lost in the sequence of revolute joints, so I could be wrong about this.
• My gut feeling is that one could expect angles to be computed by integration of angular velocities rather than being solved from nonlinear systems of equations. Have you checked whether the selection of states looks sensible?