Singularities and self-motions of equiform platforms

In this contribution we discuss singular positions and self-motions of a special class of planar parallel manipulators, where the platform is similar to the base. We describe all singular positions of such a manipulator and show 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 algebraic sense – the direct kinematics of this manipulator always has infinite number 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 position 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.