Singularities of non-redundant manipulators: A short account and a method for their computation in the planar case

The study of the singularity set is of utmost utility in understanding the local and global behavior of a manipulator. After reviewing the mathematical conditions that characterize this set, and their kinematic and geometric interpretation, this paper shows how these conditions can be formulated in an amenable manner in planar manipulators, allowing the definition of a conceptually-simple method for isolating the set exhaustively, even in higher-dimensional cases. As a result, the method delivers a collection of boxes bounding the location of all points of the set, whose accuracy can be adjusted through a threshold parameter. Such boxes can then be projected to the input or output coordinate spaces, obtaining informative diagrams, or portraits, on the global motion capabilities of the manipulator. Examples are included that show the application of the method to simple manipulators, and to a complex mechanism that would be difficult to analyze using common-practice procedures.