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.
M. Leu and D. K. Pai, "Genericity and Singularities of Robot Manipulators," IEEE Transactions on Robotics and Automation, Institute of Electrical and Electronics Engineers (IEEE), Jan 1992.
The definitive version is available at https://doi.org/10.1109/70.163780
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)
Article - Journal
© 1992 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.