  A classification of a family of 3-revolute (3R) positioning manipulators is
established. This classification is based on the topology of their workspace.
The workspace is characterized in a half-cross section by the singular curves
of the manipulator. The workspace topology is defined by the number of cusps
and nodes that appear on these singular curves. The design parameters space is
shown to be partitioned into nine subspaces of distinct workspace topologies.
Each separating surface is given as an explicit expression in the
DH-parameters.
