Abstract
In this paper, a broadly applicable approach for numerically obtaining
the workspace and the singularity curves of a planar RRRRR-type manipulator
is presented. The workspace generation is formulated as a direct
kinematic problem involving only two branches which are mathematically
defined and related with the manipulator's assembly configurations.
For solving that problem, the analytical solution of two simple quadratic
equations is found. A simple existence criterion is also obtained
to detect the set of points forming the manipulator's workspace.
On the other hand, the singularity curves are composed of sets of
singular points. In order to obtain the singular points, the properties
of the Jacobian matrix are used. The complete method has been implemented
and tested, as illustrated with examples for different geometrical
properties of the manipulator. For each of these examples, the corresponding
singularity curves are graphically generated to obtain the practical
manipulator's workspace. This feature is a very powerful design tool
which is indispensable in visualizing and analyzing the kinematic
working capability of the manipulator. (C) 2000 Elsevier Science
Ltd. All rights reserved.
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