Analysis of configuration space singularities of closed-loop mechanisms and parallel manipulators

A parallel manipulator or a closed-loop mechanism may gain or loose one or more degree-of-freedom at a singular point, and in this paper, we study the singularity associated with the gain of one or more degrees-of-freedom. We analyze the constraint forces associated with the kinematic constraints inherent in a closed-loop mechanism or a parallel manipulator, and characterize the gain singularities from the degeneracy of these constraint forces. Several special phenomena associated with gain singularity, such as locking of the actuators have been studied, and analytical criteria for these have been derived. We also present the necessary condition for finite self-motion and finite dwell of the passive links by analyzing second-order properties of the constraint equations. The results are illustrated with the help of several closed-loop mechanisms.