I have a mechanical / geometrical system that is defined by certain equations. For some variables, I know that they are known, some of them are constant. I would like to have a software (freeware) that allows me to evaluate the degrees of freedom (better: the positivity of the equation system) and that lets me play with some of the variables to see how they affect others. I know that Matlab (with the Symbolic_Toolbox) would be capable of doing such things (Mathematica most probably as well), but since I am at work here and I don't have the license I would need a freeware solution.
EDIT: I have the basic Matlab License. But I am not sure how to create an equation system and how to get information about how well it is determined without the symbolic toolbox.
EDIT 2:
What I am trying to solve:
I have a system that is running in X-Direction between two not ideal rails. Purpose of the system is to dertermine the track error of the two rails.
The system is spring-susbended on respectively two rolls on top and bottom which allows not only for the intended X-Movement but also a translation in Y direction and a rotation around any point within the rectangle defined by the four rolls. In addition to the four lengths that are measured here (L1 - L4) I have a relative X position given by a Sensor pointing in X direction (not marked).
In addition to that I have another set of four sensors that are on the same position of L1 - L4 a fixed distance above (Z direction).
To be honest, I think I don't even know what I exactly want myself. I am trying to get all the equations possible out of the system to see how underdetermined it is and what additional information (e.g. an angle sensor) the most useful would be.