Singularity-Free Kinematically Redundant Planar Parallel Mechanisms With Unlimited Rotational Capability

Abstract

This paper introduces a novel family of singularityfree kinematically redundant planar parallel mechanisms that have unlimited rotational capabilities. The proposed mechanisms are akin to conventional three-degree-of-freedom planar parallel mechanisms. By introducing a novel kinematically redundant arrangement, four-degree-of-freedom parallel mechanisms are obtained that can completely alleviate singularities and provide unlimited rotational capabilities. The kinematics of the mechanisms are derived, and the Jacobian matrices are obtained. It is shown that the singularities of this type of mechanism are governed by the orientation of a passive link connecting the redundant leg to the platform and that the latter orientation is easily controlled using the kinematic redundancy, thereby alleviating all direct kinematic singularities. An example mechanism is proposed, and a prototype is demonstrated. Example trajectories that include full cycle rotations are shown. The prototype also illustrates the use of the kinematic redundancy for an auxiliary task, namely grasping.Index Terms-Kinematic redundancy, parallel mechanisms, parallel robots, planar mechanisms, singularity. 1552-3098

On the False Positives and False Negatives of the Jacobian Matrix in Kinematically Redundant Parallel Mechanisms

“…Redundancy has been traditionally included in closed-loop manipulators to overcome one of the major limitations of these robots, namely their limited workspaces and rotational capabilities due to the existence of singularities [5], [6]; it was indeed a highly active research topic in the late 1990s and early 2000s (e.g., [7], [8]). The use of redundancy in parallel robots has regained popularity in recent years as it is useful for obtaining architectures able to complete full rotations of the end-effector [9], [10]. Just as for non-redundant robots, the Jacobian is frequently used to perform the singularity analysis of redundant parallel mechanisms.…”

“…It can be said that there exists two types of redundant parallel mechanisms: those that are redundantly actuated, and those that are kinematically redundant [9]. Kinematically redundant architectures correspond to mechanisms for which the number of actuated joints exceeds the task space of the end-effector, but all of which are required to be locked in order for the entire system to become rigid.…”

“…We refer to these two types of kinematically redundant architectures as those with serially connected actuators and those with non-serially connected actuators, respectively. Herein, our focus is directed at the latter category of architectures, as it has been shown that some of these systems have exhibited unlimited rotational capabilities (e.g., [9]), an impossible task with other parallel architectures, and have become fairly popular recently.…”

“…Several kinematically redundant architectures with non-serially connected actuators have been indeed proposed in the literature in the last five years. When conducting the kinematic analysis of these mechanisms, it is commonplace to formulate the so-called forward kinematic Jacobian by eliminating the additional passive joint velocity which describes the kinematically redundant degree of freedom-see for instance [9], [13], [14]. However, there are problems associated with this method which, to the authors' knowledge, have yet to be discussed in the literature.…”

Increasing the energy efficiency of parallel manipulators by means of kinematic redundancy and Model Predictive Control

“…As a consequence, the workspace of PKMs is rather limited imposing an important drawback. To overcome this, some researchers have explored the use of redundancy for reducing the singular configurations (KOTLARSKI; HEIMANN; ORTMAIER, 2012), (CHA;LASKY;VELINSKY, 2007), LALIBERTé;VEILLETTE, 2015). Besides the enlargement of the workspace due to the reduction of the singularity loci, the addition of redundancy might also provide higher accuracy (KOTLARSKI; HEIMANN; ORTMAIER, 2011), better motion/force transmissibility (XIE; LIU; WANG, 2011) and improved dynamic performance (ZHAO; GAO, 2009), (FONTES;SILVA, 2016).…”