Internal redundancy: an approach to improve dynamic parameters of parallel manipulators
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Date
2014
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Publisher
University of New Brunswick
Abstract
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.