Skip to main content
SpringerLink
Log in

A Comparison of Algebraic and Iterative Procedures for the Generation of the Workspace of Parallel Robots

  • Conference paper
  • First Online:
Mechanism Design for Robotics (MEDER 2021)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 103))

Included in the following conference series:

Abstract

Computing the workspace of parallel manipulators is critical to characterize their behavior. Usually, workspace is obtained by iterating the robot’s forward kinematics for a discrete range of poses, resulting in a cloud of reachable points. Here we propose an alternative algebraic formulation that is based on a recursive generation of volumes for solids of revolution to evaluate each limb’s workspace. The robot’s workspace is then obtained as the intersection of the limbs’ workspaces. With a practical example on the CaPaMan design and on a 3-UPR architecture, both the numerical and algebraic methods are discussed with their features and limits.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 279.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Tsai, L.W.: Robot Analysis. Wiley, New York (1999)

    Google Scholar 

  2. Ceccarelli, M.: Fundamentals of Mechanics of Robotic Manipulation. Springer, Heidelberg (2004)

    Book  MATH  Google Scholar 

  3. Russo, M., Herrero, S., Altuzarra, O., Ceccarelli, M.: Kinematic analysis and multi-objective optimization of a 3-UPR parallel mechanism for a robotic leg. Mech. Mach. Theor. 120, 192–202 (2018)

    Article  Google Scholar 

  4. Ceccarelli, M.: A formulation for the workspace boundary of general N-revolute manipulators. Mech. Mach. Theor. 31(5), 637–646 (1996)

    Article  Google Scholar 

  5. Gu, H., Ceccarelli, M.: Ring workspace topology of three-revolute manipulators. Int. J. Model. Simul. 31(2), 143–153 (2011)

    Google Scholar 

  6. Li, T., Ceccarelli, M.: A geometric approach for workspace determination of planar n-DOF parallel manipulators. In: 4th International Congress Design and Modeling of Mechanical Systems (2011)

    Google Scholar 

  7. Yahya, S., Moghavvemi, M., Mohamed, H.A.: Geometrical approach of planar hyper-redundant manipulators: inverse kinematics, path planning and workspace. Simul. Model. Pract. Theor. 19(1), 406–422 (2011)

    Article  Google Scholar 

  8. Kim, D.J., Chung, W.K., Youm, Y.: Geometrical approach for the workspace of 6-dof parallel manipulators. Proc. Int Conf. Robot. Autom. 4, 2986–2991 (1997)

    Article  Google Scholar 

  9. Liu, X.J., Wang, J., Oh, K.K., Kim, J.: A new approach to the design of a DELTA robot with a desired workspace. J. Intell. Robot. Syst. 39(2), 209–225 (2004)

    Article  Google Scholar 

  10. Di Gregorio, R., Zanforlin, R.: Workspace analytic determination of two similar translational parallel manipulators. Robotica 21(5), 555 (2003)

    Article  Google Scholar 

  11. Bulca, F., Angeles, J., Zsombor-Murray, P.J.: On the workspace determination of spherical serial and platform mechanisms. Mech. Mach. Theor. 34(3), 497–512 (1999)

    Article  MATH  Google Scholar 

  12. Alamdar, A., Farahmand, F., Behzadipour, S., Mirbagheri, A.: A geometrical approach for configuration and singularity analysis of a new non-symmetric 2DOF 5R spherical parallel manipulator. Mech. Mach. Theor. 147, (2020)

    Article  Google Scholar 

  13. Hu, B., Cui, H., Shi, D., Zhang, D., Wang, A., Wang, Y., Zhang, Q.: Reachable workspace determination for a spatial hyper-redundant manipulator formed by several parallel manipulators. J. Mech. Sci. Technol. 33(2), 869–877 (2019)

    Article  Google Scholar 

  14. Aboulissane, B., El Haiek, D., El Bakkali, L., El Bahaoui, J.: On the workspace optimization of parallel robots based on CAD approach. Procedia Manufact. 32, 1085–1092 (2019)

    Article  Google Scholar 

  15. Ceccarelli, M.: Historical development of CaPaMan, Cassino parallel manipulator. In: New Trends in Mechanism and Machine Science, pp. 749–757. Springer, Dordrecht (2013)

    Google Scholar 

  16. Selvi, Ö., Ceccarelli, M.: Interpretation of earthquake effects on mechanism operation: an experimental approach. J. Naval. Sci. Eng. 8(2), 31–45 (2012)

    Google Scholar 

  17. Ceccarelli, M., Cafolla, D., Russo, M., Carbone, G.: HeritageBot platform for service in cultural heritage frames. Int. J. Adv. Robot. Syst. 15(4), 1729881418790692 (2018)

    Article  Google Scholar 

  18. Ceccarelli, M. et al.: HeritageBot service robot assisting in cultural heritage. In: 2017 First IEEE International Conference on Robotic Computing (IRC), pp. 440–445. IEEE (2017)

    Google Scholar 

  19. Russo, M., Cafolla, D., Ceccarelli, M.: Design and experiments of a novel humanoid robot with parallel architectures. Robotics 7(4), 79 (2018)

    Article  Google Scholar 

  20. Russo, M., Ceccarelli, M., Takeda, Y.: Force transmission and constraint analysis of a 3-SPR parallel manipulator. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 232(23), 4399–4409 (2017)

    Article  Google Scholar 

  21. Chkhartishvili, L.S.: Volume of the intersection of three spheres. Math. Not. 69(3–4), 421–428 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, University of Nottingham, Nottingham, UK

    Matteo Russo

  2. LARM2: Laboratory of Robot Mechatronics, University of Rome “Tor Vergata”, Rome, Italy

    Marco Ceccarelli

Authors
  1. Matteo Russo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco Ceccarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matteo Russo .

Editor information

Editors and Affiliations

  1. SP2MI - Site du Futuroscope, University of Poitiers, Poitiers Cedex 9, France

    Saïd Zeghloul

  2. SP2MI - Site du Futuroscope, University of Poitiers, Poitiers Cedex 9, France

    Med Amine Laribi

  3. SP2MI - Site du Futuroscope, University of Poitiers, Poitiers Cedex 9, France

    Marc Arsicault

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Russo, M., Ceccarelli, M. (2021). A Comparison of Algebraic and Iterative Procedures for the Generation of the Workspace of Parallel Robots. In: Zeghloul, S., Laribi, M.A., Arsicault, M. (eds) Mechanism Design for Robotics. MEDER 2021. Mechanisms and Machine Science, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-030-75271-2_6

Download citation

Publish with us

Policies and ethics

Search

Navigation