A Family of Kinematically Redundant Planar Parallel Manipulators

Abstract

Parallel manipulators feature relatively high payload and accuracy capabilities compared to their serial counterparts. However, they suffer from small workspace and low maneuverability. Kinematic redundancy for parallel manipulators can improve both of these characteristics. This paper presents a family of new kinematically redundant planar parallel manipulators with six actuated-joint degrees of freedom based on a 3-PṞRR architecture obtained by adding an active prismatic joint at the base of each limb of the 3-ṞRR manipulator. First, the inverse displacement of the manipulators is explained, then their reachable and dexterous workspaces are obtained. Comparing the proposed redundant manipulators to the original 3-ṞRR nonredundant manipulator, both reachable and dexterous workspaces are substantially larger. Next, the Jacobian matrices of the manipulators are derived, and different types of singularities are analyzed and demonstrated. It is shown that the vast majority of singularities can be avoided by using kinematic redundancy.

Design of mechanical presses driven by multi-servomotor

“…For parallel mechanisms, there are a few researches dealing with the issue [20][21][22]. In general, the kinematic redundancy can be implemented by adding extra active joints and links to limbs.…”

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

“…The redundant output variable,ṗ3,5, is then eliminated by substituting (11) into (12). By expanding the velocity vectors, we obtain Fig.…”

“…The advantage of kinematically redundant architectures is that they do not suffer from the generation of internal forces or moments due to the mechanism being over-constrained. 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].…”

Overall Motion Planning for Kinematically Redundant Parallel Manipulators

“…Kinematic redundancy increases the mobility and results in an infinite number of solutions for the inverse displacement problem (IDP). Adding kinematic redundancy has various advantages such as avoiding most kinematic singularities and enlarging the workspace [11].…”