A Novel Kinematically Redundant Planar Parallel Robot Manipulator With Full Rotatability

Abstract

This paper presents a novel kinematically redundant planar parallel robot manipulator, which has full rotatability. The proposed robot manipulator has an architecture that corresponds to a fundamental truss, meaning that it does not contain internal rigid structures when the actuators are locked. This also implies that its rigidity is not inherited from more general architectures or resulting from the combination of other fundamental structures. The introduced topology is a departure from the standard 3-RPR (or 3-RRR) mechanism on which most kinematically redundant planar parallel robot manipulators are based. The robot manipulator consists of a moving platform that is connected to the base via two RRR legs and connected to a ternary link, which is joined to the base by a passive revolute joint, via two other RRR legs. The resulting robot mechanism is kinematically redundant, being able to avoid the production of singularities and having unlimited rotational capability. The inverse and forward kinematics analyses of this novel robot manipulator are derived using distance-based techniques, and the singularity analysis is performed using a geometric method based on the properties of instantaneous centers of rotation. An example robot mechanism is analyzed numerically and physically tested; and a test trajectory where the end effector completes a full cycle rotation is reported. A link to an online video recording of such a capability, along with the avoidance of singularities and a potential application, is also provided.

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

“…The geometric conditions for this instance to occur are that if the line which passes through leg 3 of the manipulator is rotated by δ in the clockwise direction, and the result is a collinearity with the line which passes through leg 4. In addition to computing the rank of the corresponding rigidity matrix, it is also possible to verify that this configuration is non-singular by performing the singularity analysis via instantaneous centres of rotation [10], [22], [23]. This analysis is not conducted here for the sake of brevity, however the reader is referred to [10] for the method of performing the analysis on the same architecture as that in example 1, but with RRR instead of RPR legs.…”

“…In addition to computing the rank of the corresponding rigidity matrix, it is also possible to verify that this configuration is non-singular by performing the singularity analysis via instantaneous centres of rotation [10], [22], [23]. This analysis is not conducted here for the sake of brevity, however the reader is referred to [10] for the method of performing the analysis on the same architecture as that in example 1, but with RRR instead of RPR legs. The result is that, when in the configuration detailed in example 1, the instantaneous centres of rotation between the platform and the base, for each of the four equivalent mechanisms where all but one of the actuators are locked, are all determinable and do not coincide with one another, indicating that the robot is not in a singularity.…”

“…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.…”

“…There are two different ways to obtain kinematically redundant architectures; the first is to take a non-redundant architecture and add extra actuated joints in the kinematic chains (limbs) connecting the end-effector to the base, such that there now exists actuated joints connected in series [12]. The second is to develop architectures where two or more of the limbs are interconnected between the base and the platform such that none of the actuators are connected in series [13], [10]. We refer to these two types of kinematically redundant architectures as those with serially connected actuators and those with non-serially connected actuators, respectively.…”

A Geometric Method of Singularity Avoidance for Kinematically Redundant Planar Parallel Robots

“…In this paper, a simple, geometric method of singularity avoidance for kinematically redundant planar parallel robots is proposed. Kinematically redundant parallel robots are architectures with more actuators than required by the task workspace, but which all contribute to make the robot rigid when locked without serially connected subsets [6,7]. The suggested method, which is based on the properties of instantaneous centres of rotation, has a direct geometric interpretation, providing a physical insight of the robot's proximity to a singularity.…”