The study of mechanism singularities has traditionally focused on holonomic systems. On the other hand many robotic systems are characterized by non-holonomic constraints, such as mobile platforms and manipulators driven by non-holonomic joints, and a general concept of singularities seems in order. In this paper a possible generalization of the singularity concept is proposed that equally accounts for holonomic and non-holonomic kinematic systems. The central object is the associated kinematic control problem. Singularities are identified as those configurations where the iteration depth of Lie brackets required to compute the accessibility Lie algebra changes. This notion of singularities is applied to serial manipulator and to non-holonomic mobile platforms. It is shown for holonomic manipulators that this is equivalent to the usual Jacobian rank condition. As example the condition is discussed for a Scara manipulator, a 6R manipulator, and for a kinematic car with one or two trailers.
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ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 12–15, 2012
Chicago, Illinois, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-4503-5
PROCEEDINGS PAPER
A Proposal for a Unified Concept of Kinematic Singularities for Holonomic and Non-Holonomic Mechanisms Available to Purchase
Andreas Müller
Andreas Müller
Institute of Mechatronics, Chemnitz, Germany
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Andreas Müller
Institute of Mechatronics, Chemnitz, Germany
Paper No:
DETC2012-70649, pp. 1543-1552; 10 pages
Published Online:
September 9, 2013
Citation
Müller, A. "A Proposal for a Unified Concept of Kinematic Singularities for Holonomic and Non-Holonomic Mechanisms." Proceedings of the ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B. Chicago, Illinois, USA. August 12–15, 2012. pp. 1543-1552. ASME. https://doi.org/10.1115/DETC2012-70649
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