Skip to main content
SpringerLink
Log in

The kinematic effects of simplifications in the analysis of linear translational parallel robots

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

Universal joints are required to achieve linear motion in the design of linear-translational-parallel-robots (LTPR). A usual practice among researchers is to assume that the angular velocity of a link attached to a universal joint is perpendicular to it. Although this assumption is intuitive, this research proves analytically and experimentally the existence of a component of the angular velocity in the direction of the link. Thus, proving that the angular velocity of a link attached to a U-joint is not perpendicular to it. Then, a new methodology is proposed to compute the exact value of the angular velocity and acceleration of links attached to universal joints, obtaining a reliable tool to analyze LTPR or robots with universal joints.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Lin J, Luo C-H, Lin K-H (2015) Design and implementation of a new delta parallel robot in robotics competitions. Int J Adv Robotic Syst 12(10):153

    Article  Google Scholar 

  2. Ur-Rehman R, Caro S, Chablat D, Wenger P (2009) Kinematic and dynamic analysis of the 2-dof spherical wrist of orthoglide 5-axis arXiv preprint arXiv:0904.0145

  3. Zeng Q, Ehmann KF, Cao J (2014) Tri-pyramid robot: design and kinematic analysis of a 3-dof translational parallel manipulator. Robotics Computer Integr Manuf 30(6):648–657. https://doi.org/10.1016/j.rcim.2014.06.002

    Article  Google Scholar 

  4. Lee S, Zeng Q, Ehmann KF (2017) Error modeling for sensitivity analysis and calibration of the tri-pyramid parallel robot. Int J Adv Manuf Technol 93(1–4):1319–1332

    Article  Google Scholar 

  5. Islam MR, Assad-Uz-Zaman M, Rahman MH (2020) Design and control of an ergonomic robotic shoulder for wearable exoskeleton robot for rehabilitation. Int J Dyn Control 8(1):312–325

    Article  Google Scholar 

  6. Briot S, Bonev I (2009) Pantopteron: a new fully decoupled 3dof translational parallel robot for pick-and-place applications. J Mech Robotics 1(2):021001

    Article  Google Scholar 

  7. Cardou P, Laurendeau D, Beaulieu L, Bélanger L, Carette A (2010) The dimensional synthesis of the linear delta robot for a force-feedback device. In: ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp 829–838 American Society of Mechanical Engineers

  8. Höppner H, Grebenstein M, van der Smagt P (2015) Two-dimensional orthoglide mechanism for revealing areflexive human arm mechanical properties In: Intelligent Robots and Systems (IROS), 2015 IEEE/RSJ International Conference On, pp 1178–1185 IEEE

  9. Martini A, Troncossi M, Carricato M, Rivola A (2015) Static balancing of a parallel kinematics machine with linear-delta architecture: theory, design and numerical investigation. Mech Mach Theory 90:128–141

    Article  Google Scholar 

  10. Fernández Yánez LA, Sotomayor Reinoso LF (2016) Análisis cinemático inverso y directo del robot paralelo Master’s thesis, Quito, 2016

  11. Carricato M, Parenti-Castelli V (2003) A family of 3-dof translational parallel manipulators. J Mech Design 125(2):302–307

    Article  Google Scholar 

  12. Caro S, Wenger P, Bennis F, Chablat D (2006) Sensitivity analysis of the orthoglide: a three-dof translational parallel kinematic machine. J Mech Design 128(2):392–402

    Article  Google Scholar 

  13. Zeng Q, Ehmann KF, Cao J (2016) Tri-pyramid robot: stiffness modeling of a 3-dof translational parallel manipulator. Robotica 34(2):383–402

    Article  Google Scholar 

  14. Pedrammehr S, Danaei B, Abdi H, Masouleh MT, Nahavandi S (2018) Dynamic analysis of hexarot: axis-symmetric parallel manipulator. Robotica 36(2):225–240

    Article  Google Scholar 

  15. Qi Y, Song Y (2018) Coupled kinematic and dynamic analysis of parallel mechanism flying in space. Mech Mach Theory 124:104-117

  16. Zarei M, Aflakian A, Kalhor A, Masouleh MT (2018) Oscillation damping of nonlinear control systems based on the phase trajectory length concept: an experimental case study on a cable-driven parallel robot. Mech Mach Theory 126:377–396

    Article  Google Scholar 

  17. Carricato M, Gosselin C (2009) On the modeling of leg constraints in the dynamic analysis of gough/stewart-type platforms. J Comput Nonlinear Dyn 4(1):011008

    Article  Google Scholar 

  18. Arian A, Danaei B, Abdi H, Nahavandi S (2017) Kinematic and dynamic analysis of the gantry-tau, a 3-dof translational parallel manipulator. Appl Math Model 51:217–231

    Article  MathSciNet  Google Scholar 

  19. Lu S, Li Y (2015) Dynamic analysis of a 3-dof 3-puu parallel manipulator based on the principle of virtual work In: 2015 IEEE International Conference on Advanced Intelligent Mechatronics (AIM), pp 1445–1450 IEEE

  20. Herrero S, Pinto C, Altuzarra O, Diez M (2018) Analysis of the 2pru-1prs 3dof parallel manipulator: kinematics, singularities and dynamics. Robotics Computer Integr Manuf 51:63–72

    Article  Google Scholar 

  21. Zarrin A, Azizi S, Aliasghary M (2020) A novel inverse kinematics scheme for the design and fabrication of a five degree of freedom arm robot. Int J Dyn Control 8(2):604–614

    Article  Google Scholar 

  22. Malayjerdi M, Akbarzadeh A (2019) Analytical modeling of a 3-d snake robot based on sidewinding locomotion. Int J Dyn Control 7(1):83–93

    Article  Google Scholar 

  23. Klein J, Spencer S, Allington J, Bobrow JE, Reinkensmeyer DJ (2010) Optimization of a parallel shoulder mechanism to achieve a high-force, low-mass, robotic-arm exoskeleton. IEEE Transactions Robotics 26(4):710–715

    Article  Google Scholar 

  24. Hasan S, Dhingra AK (2020) 8 degrees of freedom human lower extremity kinematic and dynamic model development and control for exoskeleton robot based physical therapy. Int J Dyn Control 8(3):867–886

    Article  Google Scholar 

  25. Brahmi B, Rahman MH, El-Bayeh C, Laraki MH (2021) A new tracking walking adaptive control of uncertain biped robot by state feedback and output feedback Int J Dyn Control 1–17. https://doi.org/10.1007/s40435-021-00791-7

  26. Kali Y, Saad M, Boland J-F, Fortin J, Girardeau V (2021) Walking task space control using time delay estimation based sliding mode of position controlled nao biped robot. Int J Dyn Control 9(2):679–688

    Article  MathSciNet  Google Scholar 

  27. Forouhar M, Abedin-Nasab MH, Liu G (2020) Introducing gyrosym: a single-wheel robot. Int J Dyn Control 8(2):404–417

    Article  MathSciNet  Google Scholar 

  28. Sanjuan J, Serje D, Pacheco J (2018) Closed form solution for direct and inverse kinematics of a us-rs-rps 2-dof parallel robot. Scientia Iranica. Transaction B Mechanical Eng 25(4):2144–2154

    Google Scholar 

  29. Life performance research: 9-axis bluetooth IMU LPMS-B2 series - LP-research https://lp-research.com/9-axis-bluetooth-imu-lpmsb2-series/ Accessed: 2021-11-14

  30. Han C, Kim J, Kim J, Park FC (2002) Kinematic sensitivity analysis of the 3-upu parallel mechanism. Mech Mach Theory 37(8):787–798

  31. Zhang H, Fang H, Zhang D, Zou Q, Luo X (2020) Trajectory tracking control study of a new parallel mechanism with redundant actuation Int J Aerospace Eng 2020. https://doi.org/10.1155/2020/7178103

Download references

Funding

There was no funding.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI, USA

    Javier Sanjuan, Elias Muñoz, Miguel Padilla & Mohammad Rahman

  2. Department of Mechanical Engineering, Universidad del Norte, Barranquilla, Colombia

    Javier Sanjuan

Authors
  1. Javier Sanjuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elias Muñoz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Miguel Padilla
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohammad Rahman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Javier Sanjuan.

Ethics declarations

Conflict of interest

I declare that there is no conflict of interest in the publication of this article, and that there is no conflict of interest with any other author or institution for the publication of this article.

Ethical Statements

I hereby declare that this manuscript is the result of my independent creation under the reviewers’ comments. Except for the quoted contents, this manuscript does not contain any research achievements that have been published or written by other individuals or groups. I am the only author of this manuscript. The legal responsibility of this statement shall be borne by me.

Data Availability

Not applicable.

Code Availability

Not applicable.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sanjuan, J., Muñoz, E., Padilla, M. et al. The kinematic effects of simplifications in the analysis of linear translational parallel robots. Int. J. Dynam. Control 10, 1424–1441 (2022). https://doi.org/10.1007/s40435-021-00897-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-021-00897-y

Keywords

Search

Navigation