Determination of the magnitudes and directions of the constraints of a mechanical system can be achieved by finding the basis of the system's characteristics compliance matrix. When little is known about the geometry of the system, conventional methods cannot be used to calculate the system's compliance matrix. A new method has been developed that uses experimental data to calculate a passive system's compliance matrix,and an eigenvalue decomposition to extract the directions and magnitudes of the system constraints. The data were wrenches applied to the system and the mechanism's resulting displacement from equilibrium. Computer simulations suggest that the method reliably finds eigenscrew pitches, compliances and directions for well-conditioned matrices. Eigenscrew pitches and compliances can be found for ill-conditioned matrices. This analytical technique can be used to evaluate the static behaviour of a system. It may prove valuable as a design and analysis tool for biomechanics, robotics and automation.