Singularities and self-motions of equiform platforms

In this contribution we discuss singular positions and self-motions of a sp ecial class of planar parallel manipulators, where the platform is similar to the base. We describe all singular positions of such a manipulator and s how that it has no self-motions unless it is architecturally singular even if it has a large variety of singularities. For an architecturally singular manipulator of this type we show that it is always movable in the algebrai c sense - the direct kinematics of this manipulator always has infinite num ber of solutions. We show that it can happen that from this infinite number of solutions only finite many are real. A parallel manipulator in such a p osition is stiff in spite of the fact that it is architecturally singular - which means that any infinitesimal motion leads the manipulator again into a singular position. (C) 2001 Elsevier Science Ltd. All rights reserved.