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Transitions between Multiple Solutions of the Direct Kinematic Problem

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Advances in Robot Kinematics: Analysis and Design

Abstract

The direct kinematic problem in parallel manipulators has multiple solutions that are traditionally called assembly modes. Non-singular transitions between some of these solutions have been detected and shown in the past. Cusp points have been defined as special points on the projection of the singularity curve onto the joint space that have the property of allowing such a non-singular transitions when encircling them. In this paper the authors will show that the condition for such a transition is more general. Authors also argue about the need for a differentiation between the concept of assembly mode and solution of the direct kinematic problem.

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References

  1. Bamberger, H., Wolf, A., Shoham M., Assembly mode changing in parallel mechanisms. IEEE Transactions on Robotics, submitted (2008).

    Google Scholar 

  2. Chablat, D., Wenger, Ph., Working modes and aspects in fully parallel manipulator. In Pro-ceedings IEEE International Conference on Robotics and Automation, pp. 1970-1976 (1998).

    Google Scholar 

  3. Chablat, D., Wenger, Ph., Séparation des solutions aux modèles géométriques direct et inverse pour les manipulateurs pleinement parallèles. Mechanism and Machine Theory 36(6), 763-783 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  4. Chablat, D., Wenger, Ph., The kinematic analysis of a symmetrical three-degree-of-freedom planar parallel manipulator. CISM-IFToMM Symposium on Robot Design, Dynamics and Control, Montréal (2004).

    Google Scholar 

  5. Hunt, K.H., Primrose, E.J.F., Assembly configurations of some in-parallel-actuated manipulators. Mechanism and Machine Theory 28(1), 31-42 (1993).

    Article  Google Scholar 

  6. Innocenti, C., Parenti-Castelli, V., Singularity-free evolution from one configuration to an-other in serial and fully-parallel manipulators. Journal of Mechanical Design 120(1), 73-79 (1998).

    Article  Google Scholar 

  7. Macho, E., Altuzarra, O., Pinto, C., Hernandez, A., Singularity free change change of assembly mode in parallel manipulators. Application to the 3-RPR planar platform. In Proceedings of 12th World Congress in Mechanism and Machine Science, IFToMM 2007, Besançon, France (2007).

    Google Scholar 

  8. Macho, E., Altuzarra, O., Pinto, C., Hernandez, A., Workspaces associated to assembly modes of the 5R planar parallel manipulator. Robotica, in press (2008).

    Google Scholar 

  9. McAree, P.R., Daniel, R.W., An explanation of never-special assembly changing motions for 3-3 parallel manipulators. The International Journal of Robotics Research 18(6), 556-574 (1999).

    Article  Google Scholar 

  10. Wenger, Ph., Chablat, D., Workspace and assembly modes in fully-parallel manipulators: A descriptive study. In Advances in Robot Kinematics: Analysis and Control, J. Lenar či č and M.L. Husty (Eds.), pp. 117-126. Kluwer Academic Publishers (1998).

    Google Scholar 

  11. Wenger, Ph., Chablat, D., Zein, M., Degeneracy study of the forward kinematics of planar 3-RPR parallel manipulators. Journal of Mechanical Design 129(12) (2007).

    Google Scholar 

  12. Zein, M.,Wenger, Ph., Chablat, D., Singular curves and cusp points in the joint space of 3-RPR parallel manipulators. In Proceedings of the 2006 IEEE International Conference on Robotics and Automation, Orlando, USA (2006).

    Google Scholar 

  13. Zein, M., Wenger, Ph., Chablat, D., Non-singular assembly mode changing motions for 3-RPR parallel manipulators. Mechanism and Machine Theory 43(4), 480-490 (2008).

    Article  MATH  Google Scholar 

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Macho, E., Altuzarra, O., Pinto, C., Hernandez, A. (2008). Transitions between Multiple Solutions of the Direct Kinematic Problem. In: Lenarčič, J., Wenger, P. (eds) Advances in Robot Kinematics: Analysis and Design. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8600-7_32

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  • DOI: https://doi.org/10.1007/978-1-4020-8600-7_32

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-8599-4

  • Online ISBN: 978-1-4020-8600-7

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