The singularities of the differential kinematic map, i.e. of the manipulator Jacobian, are considered. The authors first examine the notion of a generic kinematic map, whose singularities form smooth manifolds of prescribed dimension in the joint space of the manipulator. For three-joint robots, an equivalent condition for genericity using determinants is derived. The condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators, i.e. manipulators that an be separated into a three-joint translating part and a three-joint orienting part. The results are illustrated by analyzing the singularities of two classes of three-joint positioning robots.

Meeting Name

1989 IEEE International Conference on Robotics and Automation, 1989


Mechanical and Aerospace Engineering

Keywords and Phrases

Differential Kinematic Map; Kinematics; Manipulator Jacobian; Robot Manipulators; Robots; Singularities; Smooth Manifolds; Three-Joint Positioning Robots; Three-Joint Robots

Document Type

Article - Conference proceedings

Document Version

Final Version

File Type





© 1989 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 1989