Investigation of the deficiencies of parallel manipulators in singular configurations through the Jacobian space

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 space 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 unconstrained motion leads directly into a new singular configuration; and 2) for the synthesis of redundant actuation in order to eliminate singular configurations.