Skip to main content

Dynamics of Parallel Robots

  • Living reference work entry
  • First Online:
Encyclopedia of Robotics

Abstract

NA

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

Access this chapter

Institutional subscriptions

Similar content being viewed by others

References

  • Abdellatif H, Heimann B (2009) Computational efficient inverse dynamics of 6-DoF fully parallel manipulators by using the lagrangian formalism. Mech Mach Theory 44(1):192–207

    Article  MATH  Google Scholar 

  • Afroun M, Dequidt A, Vermeiren L (2012) Revisiting the inverse dynamics of the Gough-Stewart platform manipulator with special emphasis on universal-prismatic-spherical leg and internal singularity. Proc Inst Mech Eng Part C: J Mech Eng Sci 226(10):2422–2439

    Article  Google Scholar 

  • Angeles J (2003) Fundamentals of robotic mechanical systems – theory, methods, and algorithms, 2nd edn. Springer Cham Heidelberg New York Dordrecht London

    Book  MATH  Google Scholar 

  • Bhattacharya S, Nenchev D, Uchiyama M (1998) A recursive formula for the inverse of the inertia matrix of a parallel manipulator. Mech Mach Theory 33(7):957–964

    Article  MATH  Google Scholar 

  • Boyer F, Khalil W (1998) An efficient calculation of the flexible manipulator inverse dynamics. Int J Robot Res 17(3):282–293

    Article  Google Scholar 

  • Briot S, Arakelian V (2008) Optimal force generation of parallel manipulators for passing through the singular positions. Int J Robot Res 27(8):967–983

    Article  Google Scholar 

  • Briot S, Gautier M (2015) Global identification of joint drive gains and dynamic parameters of parallel robots. Multibody Syst Dyn 33(1):3–26

    Article  MathSciNet  MATH  Google Scholar 

  • Briot S, Khalil W (2014a) Recursive and symbolic calculation of the elastodynamic model of flexible parallel robots. Int J Robot Res 33(3):469–483

    Article  Google Scholar 

  • Briot S, Khalil W (2014b) Recursive and symbolic calculation of the stiffness and mass matrices of parallel robots. In: Proceedings of the 20-th CISM-IFToMM symposium on theory and practice of robots and manipulators (RoManSy 2014)

    Google Scholar 

  • Briot S, Khalil W (2015) Dynamics of parallel robots: from rigid bodies to flexible elements. Springer, Cham

    Book  MATH  Google Scholar 

  • Carricato M, Gosselin C (2009) On the modeling of leg constraints in the dynamic analysis of Gough/Stewart-type platforms. ASME J Comput Nonlinear Dyn 4(1):1–8

    Google Scholar 

  • Codourey A, Burdet E (1997) A body oriented method for finding a linear form of the dynamic equations of fully parallel robot. In: Proceedings of the 1997 IEEE international conference on robotics and automation (ICRA 1997), Albuquerque, pp 1612–1619

    Google Scholar 

  • Dasgupta B, Choudhury P (1999) A general strategy based on the Newton-Euler approach for the dynamic formulation of parallel manipulators. Mech Mach Theory 34(6):801–824

    Article  MathSciNet  MATH  Google Scholar 

  • De Luca A, Siciliano B (1996) Flexible links, chap. 6. In: Theory of robot control. Springer-Verlag London, pp 219–261

    Google Scholar 

  • Diaz-Rodriguez M, Mata V, Valera A, Page A (2010) A methodology for dynamic parameters identification of 3-DoF parallel robots in terms of relevant parameters. Mech Mach Theory 45:1337–1356

    Article  MATH  Google Scholar 

  • Featherstone R (2008) Rigid body dynamics algorithms. Springer, Boston

    Book  MATH  Google Scholar 

  • Featherstone R, Orin D (2016) Dynamics, chap. 3. In: Handbook of robotics, 2nd edn. Springer-Verlag Berlin Heidelberg, pp 37–66

    Chapter  Google Scholar 

  • Fu S, Yao Y, Wu Y (2007) Comments on “a Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator”. Mech Mach Theory 42(12):1668–1671

    Article  MATH  Google Scholar 

  • Geng Z, Haynes S, Lee J, Carrol R (1992) On the dynamic model and kinematic analysis of a class of Stewart platforms. Robot Auton Syst 9:237–254

    Article  Google Scholar 

  • Gosselin C (1993) Parallel computational algorithms for the kinematics and dynamics of parallel manipulators. In: Proceedings of the 1993 IEEE international conference on robotics and automation, New York, pp 883–889

    Google Scholar 

  • Gosselin C, Angeles J (1990) Singularity analysis of closed-loop kinematic chains. IEEE Trans Robot Autom 6(3):281–290

    Article  Google Scholar 

  • Grotjahn M, Heiman B, Abdellatif H (2004) Identification of friction and rigid-body dynamics of parallel kinematic structures for model-based control. Multibody Syst Dyn 11:273–294

    Article  MathSciNet  MATH  Google Scholar 

  • Guegan S, Khalil W, Lemoine P (2003) Identification of the dynamic parameters of the Orthoglide. In: Proceedings IEEE ICRA, Taipei, pp 3272–3277

    Google Scholar 

  • Hollerbach J, Khalil W, Gautier M (2016) Model identification, chap. 6. In: Handbook of robotics, 2nd edn. Springer-Verlag Berlin Heidelberg, pp 113–138

    Chapter  Google Scholar 

  • Ji Z (1993) Study of the effect of leg inertia in Stewart platform. In: Proceedings of the 1993 IEEE international conference on robotics and automation (ICRA 1993), Atlanta, pp 121–126

    Google Scholar 

  • Khalil W, Dombre E (2002) Modeling, identification and control of robots. Hermes Penton, London

    MATH  Google Scholar 

  • Khalil W, Gautier M (2000) Modeling of mechanical systems with lumped elasticity. In: Proceedings of the IEEE international conference on robotics and automation, San Francisco, pp 3965–3970

    Google Scholar 

  • Khalil W, Guegan S (2004) Inverse and direct dynamic modeling of Gough-Stewart robots. IEEE Trans Robot Automation 20(4):754–762

    Article  Google Scholar 

  • Khalil W, Ibrahim O (2007) General solution for the dynamic modeling of parallel robots. J Intell Robot Syst 49(1):19–37

    Article  Google Scholar 

  • Khalil W, Kleinfinger J (1986) A new geometric notation for open and closed-loop robots. Proceedings of the IEEE international conference on robotics and automation (ICRA1986), San Francisco, pp 1174–1180

    Google Scholar 

  • Khalil W, Kleinfinger J (1987) Minimum operations and minimum parameters of the dynamic model of tree structure robots. IEEE J Robot Autom 3(6):517–526

    Article  Google Scholar 

  • Kruszewski J, Gawronski W, Wittbrodt E, Najbar F, Grabowski S (1975) The rigid finite element method. Arkady, Warszawa

    Google Scholar 

  • Lebret G, Liu G, Lewis F (1993) Dynamic analysis and control of a Stewart platform manipulator. J Robot Syst 10(5):629–655

    Article  MATH  Google Scholar 

  • Lee K, Shah D (1988) Dynamic analysis of a three-degrees-of-freedom in-parallel actuated manipulator. IEEE Trans Robot Autom 4(3):361–368

    Article  Google Scholar 

  • Liu M, Li C, Li C (2000) Dynamics analysis of the Gough-Stewart platform manipulator. IEEE Trans Robot Autom 16(1):94–98

    Article  Google Scholar 

  • Long P, Khalil W, Martinet P (2014) Dynamic modeling of parallel robots with flexible platforms. Mech Mach Theory 81:21–35

    Article  Google Scholar 

  • Luh J, Walker M, Paul R (1980) On-line computational scheme for mechanical manipulators. ASME J Dyn Syst Meas Control 102(2):69–76

    Article  MathSciNet  Google Scholar 

  • Mahboubkhah M, Nategh M, Khadem S (2009) A comprehensive study on the free vibration of machine tools hexapod table. Int J Adv Manuf Technol 40(11–12):1239–1251

    Article  Google Scholar 

  • Merlet J (2006) Parallel robots, 2nd edn. Springer, Dordrecht

    MATH  Google Scholar 

  • Miller K (2004) Optimal design and modeling of spatial parallel manipulators. Int J Robot Res 23(2):127–140

    Article  Google Scholar 

  • Mukherjee P, Dasgupta B, Mallik A (2007) Dynamic stability index and vibration analysis of a flexible Stewart platform. J Sound Vib 307(3):495–512

    Article  Google Scholar 

  • Reboulet C, Berthomieu T (1991) Dynamic models of a six degree of freedom parallel manipulators. In: Proceedings of the international conference on advanced robotics (ICAR 1991), Pisa, pp 1153–1157

    Google Scholar 

  • Shabana A (1990) Dynamics of flexible bodies using generalized Newton-Euler equations. J Dyn Syst Meas Control 112:496–503

    Article  MATH  Google Scholar 

  • Sharf I, Damaren C (1992) Simulation of flexible-link manipulators: basis functions and non-linear terms in the motion equations. In: Proceedings of the IEEE international conference on robotics and automation (ICRA 1992), Nice, pp 1956–1962

    Google Scholar 

  • Six D, Briot S, Chriette A, Martinet P (2017) A controller avoiding dynamic model degeneracy of parallel robots during singularity crossing. ASME J Mech Robot 9(5):051008-1–051008-8

    Google Scholar 

  • Stachera K, Schumacher W (2008) Derivation and calculation of the dynamics of elastic parallel manipulators, chap. 15. In: Automation and robotics. I. Tech. Educ. & Publishing

    Google Scholar 

  • Tsai L (2000) Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work. ASME J Mech Des 122:3–9

    Article  Google Scholar 

  • Vakil M, Pendar H, Zohoor H (2008) Comments on “closed-form dynamic equations of the general Stewart platform through the Newton-Euler approach” and “a Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator”. Mech Mach Theory 43(10):1349–1351

    Article  MATH  Google Scholar 

  • Walker M, Orin D (1982) Efficient dynamic computer simulation of robotics mechanism. ASME J Dyn Syst Meas Control 104:205–211

    Article  MATH  Google Scholar 

  • Wittbrodt E, Adamiec-Wójcik I, Wojciech S (2006) Dynamics of flexible multibody systems. Springer, Berlin/Heidelberg

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sébastien Briot .

Editor information

Editors and Affiliations

Section Editor information

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer-Verlag GmbH Germany, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Briot, S., Khalil, W. (2022). Dynamics of Parallel Robots. In: Ang, M.H., Khatib, O., Siciliano, B. (eds) Encyclopedia of Robotics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41610-1_54-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-41610-1_54-1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41610-1

  • Online ISBN: 978-3-642-41610-1

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics