On the Kinematic, Kinetostatic and Dynamic Properties of Parallel Manipulators in the Presence of Singularity

Introduction Over the past decades, with the large development of parallel structures, more attention has been paid to their kinematic, kinetostatic and dynamic properties, and in particular, to their singularities. Several papers deal with singularity analysis of parallel manipulators [111]. Most of them present the analysis of singular configurations from a kinematic point of view [1-5]. Algebraically, a singularity analysis is based on the degeneracy of Jacobian matrices of the mechanical structure, or of the system of reciprocal screws (wrenches) applied to the platform by the legs. However, it is also known that, when parallel manipulators have Type 2 singularities [1], they lose their stiffness and their quality of motion transmission, as a result, their payload capability. Therefore, the singularity zones in the workspace of manipulators may be analysed not only in terms of kinematic criterions, from the theoretically perfect model of manipulators, but also in terms of kinetostatic approaches [6-8]. However, the proposed criterions are difficult to use, above all when applied to manipulators involving both translational and rotational degrees of freedom (DOF). Moreover, while it is demonstrated using the kinetostatic approach that, when subjected to Type 2 singularities parallel manipulator lock up, it has been shown experimentally that, via optimal dynamic control of manipulators, it is possible to pass through these singular zones [9-11]. Thus, singular configurations should also be examined in terms of dynamic aspects. In this paper, we present an overview of our recent works on the kinematic, kinetostatic and dynamic aspects of singularities. As an application of our works, the singular configurations of a new manipulator developed at the INSA of Rennes (PAMINSA: PArallel Manipulator of the INSA [12]) are studied from kinematic, kinetostatic and dynamic points of