Internal redundancy: an approach to improve dynamic parameters of parallel manipulators

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University of New Brunswick
Redundancy in parallel manipulators occurs when the number of active joints is greater than the total degrees of freedom of the manipulator. Redundancy in parallel manipulators has been discussed for the cases of kinematic, actuation, and branch redundancy. Some advantages of these redundant manipulators include the reduction or elimination of some types of kinematic singularities and/ or an increase of their reachable and dexterous workspaces, to name a few. Internal redundancy, first introduced for serial manipulators, refers to the concept of adding redundant masses to some links so as to allow of control the centre of mass and other dynamic properties of some links. This concept has also been referred to as variable geometry. This work investigates the effects of internal redundancy in two different applications. Firstly, the effect of the internal redundancy is studied on the dynamic properties of a planar parallel manipulator while performing a family of trajectories. More specifically, this research investigates the possibility of following a desired trajectory that contains direct kinematic singularity configurations using internal redundancy in parallel manipulators. To illustrate the concept, internal redundancy is first applied to a 2-RPR planar parallel manipulator by adding a redundant mass to each of its two branches. The dynamic model of this internally redundant manipulator is developed using the principle of virtual work. The model is then used to compute the required displacement, velocity, and acceleration of the redundant masses over time as to allow the manipulator to successfully cross singular configurations. Secondly, the 3- RRR planar manipulator, where a redundant mass has been added to the distal link, is allowed to trace trajectories with rounded corners of different radii. The proposed method uses the manipulator's dynamic model to actively optimise the location of the redundant masses at every point along the trajectory to improve the dynamic performance of the manipulator. Numerical examples are presented to support the idea.