Overarching framework for measuring closeness to singularities of parallel manipulators

Singular configurations where a parallel manipulator can lose stiffness are well documented and studied in literature. There exist many proposed measures on how close a pose is to these singularities. This paper develops a framework which unites many of the existing measures, provides further understanding for others, and creates new ones. The framework originates from a physical understanding of singularities with a natural progression to a constrained optimization problem. The solution to the optimization problem is a simple general eigenvalue problem of constant matrices. The power of this new framework is that it is easy to compare existing measures and develop new ones. Several examples of measures within the framework are given.