Investigation of the Deficiencies of Parallel Manipulators in Singular Configurations Through the Jacobian Nullspace

It is well known that parallel manipulators may encounter singular configurations that can result in a loss of full constraint. The nature of the kinematic deficiency at such a singular configuration can be analyzed by calculating the nullspace of the Jacobian matrix at that configuration. The result is a set of one or more screws, called the EE deficiency twists, representing the unconstrained instantaneous motion of the end-effector that cannot be controlled through the actuators. This article discusses the importance of the EE deficiency twists (1) to identify singular configurations whose unconstrainable motion leads directly into a new singular configuration; (2) for the synthesis of redundant actuation in order to eliminate singular configurations.