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Computing the Safe Working Zone of a 3-RRS Parallel Manipulator

Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 43)

Abstract

Determination of the safe working zone (SWZ) of a parallel manipulator is a one-time computational task with several permanent benefits. As this subspace of the workspace of the manipulator is free of both the loss- and gain-type singularities, link interference, as well as physical joint limits, the manipulator can move freely in this space. Moreover, if the natural choice of a convex-shaped SWZ is adhered to, then point-to-point path planning inside the SWZ always has a trivial solution, namely, a segment joining the two points, which is guaranteed to be inside the workspace. In this paper, the SWZ of the 3-RRS existing in the İzmir Institute of Technology has been computed. Starting with the geometry of the manipulator, the loop-closure constraint equations have been derived. The singularity conditions are obtained based on the singularity of certain Jacobian matrices associated with the constraint functions. The interference between the links are detected by first encapsulating the links in rectangular parallelepipeds, which are then discretized into triangles, and subjected to collision tests between the relevant pairs of triangles. Using these theoretical developments, the SWZ is computed. The numerical results are depicted graphically.

Keywords

Parallel manipulator 3-RRS Singularity Safe working zone 

References

  1. 1.
    Devillers, O., Guigue, P.: Faster triangle-triangle intersection tests. Tech. Rep. RR-4488, INRIA (2002). https://hal.inria.fr/inria-00072100
  2. 2.
    Itul, T., Pisla, D.: 446. On the kinematics and dynamics of 3-dof parallel robots with triangle platform. J. Vibroeng. 11(1) (2009)Google Scholar
  3. 3.
    Perrin, N., Stasse, O., Lamiraux, F., Kim, Y.J., Manocha, D.: Real-time footstep planning for humanoid robots among 3d obstacles using a hybrid bounding box. In: 2012 IEEE International Conference on Robotics and Automation (ICRA), pp. 977–982. IEEE (2012)Google Scholar
  4. 4.
    Srivatsan, R.A., Bandyopadhyay, S.: Computational Kinematics: Proceedings of the 6th International Workshop on Computational Kinematics (CK2013), Chap. Determination of the Safe Working Zone of a Parallel Manipulator, pp. 201–208. Springer, Netherlands, Dordrecht (2014)Google Scholar
  5. 5.
    Tetik, H., Kalla, R., Kiper, G., Bandyopadhyay, S.: Position Kinematics of a 3-\(\underline{{\rm {R}}}\)RS Parallel Manipulator. Accepted for Presentation at the 21st CISM-IFToMM Symposium on Robot Design, Dynamics, and Control, ROMANSY (2016)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Indian Institute of TechnologyMadrasIndia
  2. 2.İzmir Institute of TechnologyİzmirTurkey

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