Non-slipping Conditions of Endless-Cable Driven Parallel Robot by New Interpretations of the Euler-Eytelwein’s Formula

  • Takashi HaradaEmail author
  • Koki Hirosato
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 74)


Non-slipping conditions of endless-cable driven parallel robot (E-CDPR) which enables unlimited rotation of the hand are discussed in this paper. Instead of fixing the end of the cable to the pulley and the winch, endless-cable (loop-cable) is turned around the endless-pulley and the endless-winch. Because friction forces between the cable and the drum transfer the cable tension, slipping of the cable which is dominated by the well-known Euler-Eytelwein’s formula is taking into consideration of the statics of the E-CDPR. In this paper, a new interpretation of the Euler-Eytelwein’s formula is proposed by using a graph that the non-slipping condition is expressed as an area in the cable tensions. Equations of the statics of the endless-pulley and the endless-winch are superimposed on the graph, then the non-slipping conditions of the E-CDPR are derived.


endless-Cable friction drive the Euler-Eytelwein’s formula statics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by JSPS KAKENHI Grant Number 18K04068.


  1. 1.
    Pott, A.: Cable-Driven Parallel Robots, Theory and Application. Springer, (2018). Scholar
  2. 2.
    Cable-Driven Parallel Robots, Mechanisms and Machine Science 13, Editors, Bruckmann, T., Pott, A., Springer (2013). Scholar
  3. 3.
    Cable-Driven Parallel Robots, Mechanisms and Machine Science 53, Editors, Goselin, C., Cardou, P., Bruckmann, T, Springer (2017). Scholar
  4. 4.
    Fortin-Côté, A., Faure, C., Bouyer, L., McFadyen, B.J., Mercier, C., Bonenfant, M., Laurendeau, D., Cardou, P., Gosselin, C.: On the Design of a Novel Cable-Driven Parallel Robot Capable of Large Rotation About One Axis. in Cable-Driven Parallel Robots, Mechanisms and Machine Science 53, pp. 390-401, Springer (2017).
  5. 5.
    Miermeister, P., Pott, A.: Design of Cable-Driven Parallel Robots with Multiple Platforms and Endless Rotating Axes. Interdisciplinary Applications of Kinematics, Mechanisms and Machine Science 26, pp. 21-29 Springer, (2015). Scholar
  6. 6.
    Pott, A., Miermeister, P: Workspace and Interference Analysis of Cable-Driven Parallel Robots with an Unlimited Rotation Axis. in Advances in Robot Kinematics, pp. 341-350 Springer, (2018). Scholar
  7. 7.
    Makino, T., Harada, T.: Cable Collision Avoidance of a Pulley Embedded Cable-Driven Parallel Robot by Kinematic Redundancy. 4th International Conference on Control, Mechatronics and Automation, pp. 117-120, Barcelona (2016).
  8. 8.
    Meriam, J.J, Kraige, L.G.: Engineering Mechanics, Statics (Seventh Edition). pp. 377-378, John Wiley & Sons (2006). ISBN:978-0-470-61473-0.Google Scholar
  9. 9.
    Popov, V.L.: Contact Mechanics and Friction, Physical Principles and Applications. pp. 148-149, Springer (2010). Scholar
  10. 10.
    Zitzewitz, J.V., Fehlberg, L., Bruckmann, T., Vallery, H.: Use of Passively Guided Deflection Units and Energy-Storing Elements to Increase the Application Range of Wire Robots. Cable-Driven Parallel Robots, Mechanisms and Machine Science 12, pp. 167-184, Springer (2013). Scholar
  11. 11.
    Gouttefarde, M., Gosselin, C.: L., Analysis of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms. IEEE Transactions on Robotics, VOL. 22, No. 3, pp. 434-445 (2006). Scholar
  12. 12.
    Loloei, A.Z., Taghirad, H.D.: Controllable Workspace of Cable-Driven Redundant Parallel Manipulators by Fundamental Wrench Analysis. Transactions of the Canadian Society for Mechanical Engineering, Vol. 36, No. 3, pp. 297-314 (2012).CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Kindai UniversityHigashiosaka, OsakaJapan
  2. 2.Kindai University, Graduate School of Science and Engineering ResearchHigashiosaka, OsakaJapan

Personalised recommendations