Singularity free assembly mode change of parallel manipulators
Singularity free assembly mode change of parallel manipulators
Abstract: Non singular assembly mode change of parallel manipulators has
been
discussed for a while within the robotics community. This term means
that a parallel
robot can pass from one solution of the direct kinematics into another
without crossing a singularity. In this presentation we will show that
opposed
to the accepted opinion all general planar 3-RPR parallel manipulators have
this ability. Using geometric properties of the singularity surface of this
manipulator we will give a rigorous mathematical proof for this proposition.
This proof will use the fact that the singularity surface is a fourth order
surface having only very special singularities. A secondary result of this
proof will be the first proof for the widespread used property that the
singularity surface divides the workspace of the manipulator into two
aspects
that are path connected. For the first time we give a simple technique
how to
construct singularity free paths that join all assembly modes of one
aspect to
the other.