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Mechanical Sciences An open-access journal for theoretical and applied mechanics
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Volume 7, issue 1
Mech. Sci., 7, 31-38, 2016
https://doi.org/10.5194/ms-7-31-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Mech. Sci., 7, 31-38, 2016
https://doi.org/10.5194/ms-7-31-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 21 Jan 2016

Research article | 21 Jan 2016

Guaranteed detection of the singularities of 3R robotic manipulators

R. Benoit1, N. Delanoue1, S. Lagrange1, and P. Wenger2 R. Benoit et al.
  • 1Laboratoire Angevin de Recherche en Ingénierie des Systèmes (LARIS), 62 avenue Notre Dame du Lac, 49000 Angers, France
  • 2Institut de Recherche en Communications et Cybernétique de Nantes (IRCyN), 1 rue la Noë, 44321 Nantes CEDEX 03, France

Abstract. The design of new manipulators requires the knowledge of their kinematic behaviour. Important kinematic properties can be characterized by the determination of certain points of interest. Important points of interest are cusps and nodes, which are special singular points responsible for the non-singular posture changing ability and for the existence of voids in the workspace, respectively. In practice, numerical errors should be properly tackled when calculating these points. This paper proposes an interval analysis based approach for the design of a numerical algorithm that finds enclosures of points of interest in the workspace and joint space of the studied robot. The algorithm is applied on 3R manipulators with mutually orthogonal joint axes. A pre-processing collision detection algorithm is also proposed, allowing, for instance, to check for the accessibility of a manipulator to its points of interest. Through the two proposed complementary algorithms, based on interval analysis, this paper aims to provide a guaranteed way to obtain a broad characterisation of robotic manipulators.

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We propose two Interval Analysis based methods to characterize novel robots. Interval analysis theory allows us to consider intervals instead of values, making it possible to use computer algorithms, without the drawback of rounding errors. The first proposed method can isolate chosen interest points and is applied to the characteristic cusp and node points of 3R orthogonal manipulators. The second method encloses the robot available postures, giving complementary information on the novel robot.
We propose two Interval Analysis based methods to characterize novel robots. Interval analysis...
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