The kinematic singularities of robot manipulators are studied from the point of view of the theory of singularities. The notion of a "generic'' kinematic map, whose singularities form smooth manifolds of prescribed dimension in the joint space of the manipulator, is examined. For three-joint robots, an equivalent algebraic condition for genericity using the Jacobian determinants is derived. This condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators. Orientation and translation singularities of manipulators are studied in detail. A complete characterization of orientation singularities of robots with any number of joints is given. The translation singularities of the eight possible topologies of three-joint robots are studied and the conditions on the link parameters for nongenericity are determined.


Mechanical and Aerospace Engineering

Keywords and Phrases

Jacobian Determinants; Equivalent Algebraic Condition; Generic Maps; Genericity; Joint Space; Kinematic Singularities; Kinematics; Manipulators; Orientation Singularities; Robots; Symbol Manipulation; Symbolic Computation; Three-Joint Robots; Topology; Translation Singularities

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 1992 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 1992