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

• The conditions that characterize the singularity set are shortly reviewed.
• The defining equations of the set are formulated in an amenable manner.
• A branch-and-prune method is given to isolate the set independently of its dimension.
• The method can deal with arbitrary planar linkages with revolute/prismatic joints.
• Its performance is illustrated on well-known manipulators and on complex mechanisms.

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.