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Dual-quaternion on simple scissor-like elements

  • Juan G. GrijalvaEmail author
  • Edson R. De Pieri
  • Daniel Martins
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

Assembles of scissor-like elements have plenty of links and joints leading into complex kinematic analysis. By using dual-quaternions in this paper is presented a novel approach to deal with. Forward, inverse kinematics analysis is developed on simple scissor-like element assembles. Aiming to improve the computational efficiency, dual-quaternion exponentiation is applied too. The various steps to compute the work-space, by using an algorithm, are discussed. Finallly, a numerical example is presented where is applied this novel approach.

Keywords

computational kinematics dual-quaternion scissor-like element 

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Notes

Acknowledgments

This research was supported by the Ecuadorian Council of Science Technology and Innovation (SENESCYT) and by the Coordination for the Improvement of Higher Education Personne (CAPES).

References

  1. 1.
    Aydın, Y., and Kucuk, S. (2006, July). Quaternion based inverse kinematics for industrial robot manipulators with Euler wrist. In IEEE International Conference on Mechatronics, vol. July (pp. 3-5).Google Scholar
  2. 2.
    Casement, S., Flannery, M., Glassman, T., Lo, A. (2012, September). Starshade design driven by stray light from edge scatter. In Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave (Vol. 8442, p. 84424H). International Society for Optics and Photonics.Google Scholar
  3. 3.
    Chevallier, D. P. (1991). Lie algebras, modules, dual quaternions and algebraic methods in kinematics. Mechanism and Machine Theory, 26(6), 613-627.Google Scholar
  4. 4.
    Farrugia, Pierre. (2008). Kinematic analysis of foldable structures. Doctoral dissertation. University of Surrey (United Kingdom).Google Scholar
  5. 5.
    Gonzalez, D. J., and Asada, H. H. (2017). Design and Analysis of 6-DOF Triple Scissor Extender Robots With Applications in Aircraft Assembly. IEEE Robotics and Automation Letters, 2(3), 1420-1427.Google Scholar
  6. 6.
    Radavelli, L. A., Martins, D., De Pieri, E. R., and Simoni, R. (2015). Cinemática posicional de robôs via iteração e quatérnios. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 3(1).Google Scholar
  7. 7.
    Radavelli, L., Simoni, R., De Pieri, E., and Martins, D. (2012). A comparative study of the kinematics of robots manipulators by Denavit-Hartenberg and dual quaternion. Mecánica Computacional, Multi-Body Systems, 31(15), 2833-2848.Google Scholar
  8. 8.
    Radavelli, L. A., De Pieri, E. R., Martins, D., and Simoni, R. (2014). A screw dual quaternion operator for serial robot kinematics. Proceedings of PACAM XIV, Santiago, 27-38.Google Scholar
  9. 9.
    Sun, Y., Wang, S., Mills, J. K., and Zhi, C. (2014). Kinematics and dynamics of deployable structures with scissor-like-elements based on screw theory. Chinese Journal of Mechanical Engineering, 27(4), 655-662.Google Scholar
  10. 10.
    You, Z., and Chen, Y. (2014). Motion structures: deployable structural assemblies of mechanisms. Crc Press.Google Scholar
  11. 11.
    Zhao, J. S., Wang, J. Y., Chu, F., Feng, Z. J., and Dai, J. S. (2011). Structure synthesis and statics analysis of a foldable stair. Mechanism and Machine Theory, 46(7), 998-1015.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Juan G. Grijalva
    • 1
    Email author
  • Edson R. De Pieri
    • 2
  • Daniel Martins
    • 2
  1. 1.Control and Automation Laboratory (LCA-DAS), Department of Automation and SystemsFederal University of Santa CatarinaFlorianopolisBrazil
  2. 2.Department of Mechanical EngineeringRaul Guenther Robotics Laboratory (LRRG-EMC)FlorianopolisBrazil

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