  This paper proposes a classification of three-revolute orthogonal
manipulators that have at least one of their DH parameters equal to zero. This
classification is based on the topology of their workspace. The workspace is
characterized in a half-cross section by the singular curves. The workspace
topology is defined by the number of cusps and nodes that appear on these
singular curves. The manipulators are classified into different types with
similar kinematic properties. Each type is evaluated according to interesting
kinematic properties such as, whether the workspace is fully reachable with
four inverse kinematic solutions or not, the existence of voids, and the
feasibility of continuous trajectories in the workspace. It is found that
several orthogonal manipulators have a "well-connected" workspace, that is,
their workspace is fully accessible with four inverse kinematic solutions and
any continuous trajectory is feasible. This result is of interest for the
design of alternative manipulator geometries.
