Skip to main content
SpringerLink
Log in

Hyper-Jerk Analysis of Robot Manipulators

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

In this work the hyper-jerk analysis of robot manipulators is addressed by means of the theory of screws. The reduced hyper-jerk state of a rigid body as observed from another body or reference frame is obtained as a six-dimensional vector by applying the concept of helicoidal vector field. Moreover, this contribution demonstrates that the reduced hyper-jerk state of a rigid body can be considered, similar to the velocity state, as a twist about a screw. Furthermore, the reduced hyper-jerk state is systematically obtained in pure screw form. Finally, a case study, which is verified with the aid of commercially available software, that consists of solving the kinematics, up to the hyper-jerk analysis, of a zero-torsion parallel manipulator is included in order to show the application of the method of kinematic analysis.

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

Similar content being viewed by others

References

  1. Ball, R.S.: A Treatise on the Theory of Screws. Cambridge University Press, Cambridge (1900, reprinted 1998)

    MATH  Google Scholar 

  2. Brand, L.: Vector and Tensor Analysis. Wiley, New York (1947)

    MATH  Google Scholar 

  3. Rico, J.M., Duffy, J.: An application of screw algebra to the acceleration analysis of serial chains. Mech. Mach. Theory 31, 445–457 (1996)

    Article  Google Scholar 

  4. Rico, J.M., Gallardo, J., Duffy, J.: A determination of singular configurations of serial non-redundant manipulators, and their escapement from singularities using Lie products. In: Merlet, J.-P., Ravani, B. (eds.) Computational Kinematics ’95, pp. 143–152. Kluwer, Dordrecht (1995)

  5. Rico, J.M., Gallardo, J.: Acceleration analysis, via screw theory and characterization of singularities of closed chains. In: Lenarčič, J., Parenti-Castelli, V. (eds.) Recent Advances in Robot Kinematics, pp. 139–148. Kluwer, Dordretch (1996)

    Chapter  Google Scholar 

  6. Gallardo-Alvarado, J., Orozco-Mendoza, H., Rodríguez-Castro, R., Rico-Martínez, J.M.: Kinematics of a class of parallel manipulators which generates structures with three limbs. Multibody Syst. Dyn. 17, 27–46 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gallardo, J., Orozco, H., Rico, J.M.: Kinematics of 3-RPS parallel manipulators by means of screw theory. Int. J. Adv. Manuf. Tech. 36, 598–605 (2008)

    Article  Google Scholar 

  8. Gallardo-Alvarado, J., Alici, G., Pérez-González, L.P.: A new family of constrained redundant parallel manipulators. Multibody Syst. Dyn. 23, 57–75 (2010)

    Article  MATH  Google Scholar 

  9. Rico, J.M., Gallardo, J. and Duffy, J.: Screw theory and higher order kinematic analysis of open serial and closed chains. Mech. Mach. Theory 34, 559–586 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gallardo-Alvarado, J., Rico-Martinez, J.M.: Jerk influence coefficients, via screw theory, of closed chains. Meccanica 36, 213–228 (2001)

    Article  MATH  Google Scholar 

  11. Gallardo-Alvarado, J.: Jerk distribution of a 6-3 Gough-Stewart platform. Proc. Instn. Mech. Engrs. Part K: J. Multi-body Dyn. 217, 77–84 (2003)

    Article  Google Scholar 

  12. Gallardo-Alvarado, J.: Jerk analysis of a six-degrees-of-freedom three-legged parallel manipulator. Robot. Cim-Int Manuf. 28, 220–226 (2012)

    Article  Google Scholar 

  13. Lipkin, H.: Time derivatives of screws with applications to dynamic and stiffness. Mech. Mach. Theory 4, 259–273 (2005)

    Article  Google Scholar 

  14. Viviani, P., Schneider, R.: A developmental study of the relationship between geometry and kinematics in drawing movements. J. Exp. Psychol. Hum. Percept. Perform. 17, 198–218 (1991)

    Article  Google Scholar 

  15. Balasubramaniam, R., Wing, A.M., Daffertshofer, A.: Keeping with the beat: movement trajectories contribute to movement timing. Exp. Brain Res. 159, 129–134 (2004)

    Google Scholar 

  16. Fradet, L., Lee, G., Dounskaia, N.: Origins of submovements in movements of elderly adults. J. NeuroEngineering Rehabil. 5, 28 (2008)

    Article  Google Scholar 

  17. Safronov, V.A.: Chaotic and ordered processes mediating the knee-jerk reflex. Hum. Physiology 35, 306–315 (2009)

    Article  Google Scholar 

  18. Piazzi, A., Visioli, A.: Global-minimum-jerk trajectory planning of robot manipulators. IEEE Trans. Ind. Electron. 47, 140–149 (2000)

    Article  Google Scholar 

  19. Bruijnen, D., van Helvoort, J., van de Molengraft, R.: Realtime motion path generation using subtargets in a rapidly changing environment. Robot. Auton. Syst. 55, 470–479 (2007)

    Article  Google Scholar 

  20. Gasparetto, A., Zanotto, V.: A new method for smooth trajectory planning of robot manipulators. Mech. Mach. Theory 42, 455–471 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  21. Bagci, C.: Synthesis of double-crank (drag-link) driven mechanisms with adjustable motion and dwell time ratios. Mech. Mach. Theory 12, 619–638 (1977)

    Article  Google Scholar 

  22. Barre, P.-J, Bearee, R., Borne, P., Dumetz, E.: Influence of a jerk controlled movement law on the vibratory behaviour of high-dynamics systems. J. Intell. Robot. Syst. 42, 275–293 (2005)

    Article  Google Scholar 

  23. Naskar, T.K., Acharyya, S.: Measuring cam-follower performance. Mech. Mach. Theory 45, 678–691 (2010)

    Article  MATH  Google Scholar 

  24. Macfarlane, S., Croft, E.: Jerk-bounded manipulator trajectory planning: design for real-time applications. IEEE Trans. Robot. Autom. 19, 42–52 (2003)

    Article  Google Scholar 

  25. Dumetz, E., Dieulot, J.-Y., Barre, P.-J., Colas, F., Delplace, T.: Control of an industrial robot using acceleration feedback. J. Intell. Robot. Syst. 46, 111–128 (2006)

    Article  Google Scholar 

  26. Boryga, M., Grabos, A.: Planning of manipulator motion trajectory with higher-degree polynomials use. Mech. Mach. Theory 44, 1400–1419 (2009)

    Article  MATH  Google Scholar 

  27. Bearee, R., Barre, P.-J., Bloch, S.: Influence of high-speed machine tool control parameters on the contouring accuracy. Application to linear and circular interpolation. J. Intell. Robot. Syst. 40, 321–341 (2004)

    Google Scholar 

  28. Xu, R.Z., Xie, L., Li, C.X., Du, D.S.: Adaptive parametric interpolation scheme with limited acceleration and jerk values for NC machining. Int. J. Adv. Manuf. Tech. 36, 343–354 (2008)

    Google Scholar 

  29. Wan, D., Wang, S.L., Zhu, C.C., Meng, F.: Feedrate scheduling and jerk control algorithm for high-speed CNC machining. Int. J. Adv. Manuf. Manag. 17, 216–231 (2009)

    Google Scholar 

  30. Sugimoto, K., Duffy, J.: Application of linear algebra to screw systems. Mech. Mach. Theory 17, 73–83 (1982)

    Article  Google Scholar 

  31. Hunt, K.H.: Structural kinematics of in-parallel-actuated robot arms. ASME J. Mech. Trans. Aut. Des. 105, 705–712 (1983)

    Article  Google Scholar 

  32. Lee, K.M., Shah, D.K.: Kinematic analysis of a three-degree-of-freedom in-parallel actuated manipulator. IEEE J. Robot. Autom. 4, 354–360 (1988)

    Article  Google Scholar 

  33. Huang, Z., Fang, Y.F.: Kinematic characteristics analysis of 3 DOF in-parallel actuated pyramid mechanism. Mech. Mach. Theory 31, 1009–1018 (1996)

    Article  Google Scholar 

  34. Kim, H.S., Tsai, L.-W.: Kinematic synthesis of a spatial 3-RPS parallel manipulator. ASME J. Mech. Des. 125, 92–97 (2003)

    Article  Google Scholar 

  35. Liu, C.H., Cheng, S.: Direct singular positions of 3RPS parallel manipulators. ASME J. Mech. Des. 126, 1006–1016 (2004)

    Article  Google Scholar 

  36. Rao, N.M., Rao, K.M.: Multi-position dimensional synthesis of a spatial 3-RPS parallel manipulator. ASME J. Mech. Des., Technical Brief 128, 815–819 (2006)

    Article  Google Scholar 

  37. Sokolov, A., Xirouchakis, P.: Singularity analysis of a 3-DOF parallel manipulator with R-P-S joint structure. Robotica 24, 131–142 (2006)

    Article  Google Scholar 

  38. Huang, Z., Mu, D., Zeng, D.: The screw motion simulation on 3-RPS parallel pyramid mechanism. In: Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation, pp. 2860–2864. Harbin, China (2007)

  39. Bonev, I.A.: Direct kinematics of zero-torsion parallel mechanisms. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 3851–3856. Pasadena, California (2008)

  40. Rad, C.-R, Manic, M., Balan, R., Stan, S.-D.: Real time evaluation of inverse kinematics for a 3-RPS medical parallel robot usind dSpace platform. In: IEEE Proceedins 3rd Conference on Human System Interactions (HSI), pp. 48–53 (2010)

  41. Yu, L., Zhang, L., Zhang, N., Yang, S., Wang, D.: Kinematics simulation and Analysis of 3-RPS parallel robot on SimMechanics. In: Proceedings of the 2010 IEEE International Conference on Information and Automation, pp. 2363–2367. Harbin, China (2010)

  42. Gallardo, J., Lesso, R., Rico, J.M., Alici, G.: The kinematics of modular spatial hyper-redundant manipulators formed from RPS-type limbs. Robot. Autonomous Syst. 59, 12–21 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Instituto Tecnológico de Celaya, Av. Tecnológico y A. García Cubas, 38010, Celaya, Gto., México

    Jaime Gallardo-Alvarado

Authors
  1. Jaime Gallardo-Alvarado
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jaime Gallardo-Alvarado.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gallardo-Alvarado, J. Hyper-Jerk Analysis of Robot Manipulators. J Intell Robot Syst 74, 625–641 (2014). https://doi.org/10.1007/s10846-013-9849-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-013-9849-z

Keywords

Search

Navigation