Measuring "closeness" to singularities for parallel manipulators

Singularities of parallel manipulators cause severe problems in the use of such manipulators. Likewise, finding how close the manipulator is to a singularity is key to its operation. This article outlines a new method to define "closeness" to singularities based on constrained optimization and its resulting general eigenvalue problem. This framework joins together many existing techniques into one unified theory. From this framework, the similarities and differences between measures can be easily identified, and new measures (e.g. natural frequency) can be derived.