Skip to main content
SpringerLink
Log in

Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra

  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

A technique for representing large finite rotations in terms of only three independent parameters, the conformal rotation vector, is described and applied to the finite element formulation of 3-D mechanisms problems. A beam finite element that takes into account large finite rotations and various types of rigid joints have been developed. Some test examples which demonstrate the applicability of the proposed technique are presented.

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

  • Agrawal, O. P.; Shabana, A. A. (1986): Application of deformable-body mean axis to flexible multibody system dynamics. Comp. Meth. Appl. Mech. Eng. 56, 217–245

    Article  Google Scholar 

  • Baumgarte, J. (1972): Stabilization of constraints and integrals of motion in dynamical systems. Comp. Meth. Appl. Mech. Eng. 1, 1–16

    Article  MathSciNet  Google Scholar 

  • Bottema, O.; Roth, B. (1979): Theoretical kinematics. Amsterdam: North Holland

    MATH  Google Scholar 

  • Buchet, P.; Geradin M. (1985): Mecano: Répouse dynamique de mécanismes (manuel d'utilisation). LTAS Rpt. IF-69, University of Liege, Belgium

    Google Scholar 

  • Chace, M. (1983): Computer-aided engineering of large displacements dynamic mechanical systems. CAE/CAD/CAM Conference, Salt Lake City, Utah

  • Geradin, M.; Robert, G.; Bernardin (1984): Dynamic modeling of manipulators with flexible members. In: Dauthine, A.; Geradin, M. (eds.): Advanced software in robotics. Amsterdam: North Holland

    Google Scholar 

  • Geradin, M. (1984): Finite element approach to kinematic and dynamic analysis of mechanisms using Euler parameters. In: Taylor, C. (ed.): Numerical methods in nonlinear problems II. Swansea: Pineridge Press

    Google Scholar 

  • Geradin, M.; Robert, G.; Buchet, P. (1986): Kinematic and dynamic analysis of mechanisms: A finite element approach based on Euler parameters. In: Bergan, P. (ed.): Finite element methods for nonlinear problems. Berlin, Heidelberg, New York: Springer

    Google Scholar 

  • Haug, E. J.; Wehage, R.; Barman, N. (1978): Dynamic analysis and design of constrained mechanica systems. Tech. Rpt. Nx 50, Div. of Eng. Univ. of Iowa

  • Hughes, T. J. R. (1983): Analysis of transient algorithms with particular reference to stability problems. In: Belytschko, T.; Hughes, T. J. R. (ed.): Computational methods for transient analysis. Amsterdam: North Holland

    MATH  Google Scholar 

  • Kane, T. R.; Levinson, D. A. (1983): Multibody dynamics. J. Appl. Mech. 50, 1071–1078

    Article  Google Scholar 

  • Milenkovic, V. (1982): Coordinates suitable for angular motion synthesis in robots. Proc. of Robot 6 Conference

  • Milner, H. R. (1981): Accurate finite element analysis of large displacements in skeletal frames. Comput. Struct. 14, 205–210

    Article  Google Scholar 

  • Nikravesh, P. (1984): Spatial kinematics and dynamic analysis with Euler parameters. In: Haug, E. J. (ed.): Computer aided analysis and optimization of mechanical system dynamics. Berlin, Heidelberg, New York: Springer

    Google Scholar 

  • Paul, R. (1981): Robot manipulators, mathematics, programming and control. Cambridge, Mass.: MIT Press

    Google Scholar 

  • Petzold, L.; Lotstedt, P. (1984): Numerical solution of nonlinear differential/algebraic systems from physics and engineering. In: Liu, W.; Belytschko, T.; Park, K. C. (eds.) Innovative methods for nonlinear problems. Swansea: Pineridge Press

    Google Scholar 

  • Rogers, D. F.; Adams, J. A. (1976): Mathematical elements for computer graphics. London: McGraw-Hill

    Google Scholar 

  • Shabana, A. A. (1985): Substructure synthesis methods for dynamic analysis of multi-body systems. Comput. Struct. 20, 359–381

    Article  Google Scholar 

  • Song, J.; Haug, E. J. (1980): Dynamic analysis of mechanisms. Comp. Meth. Appl. Mech. Eng. 24, 359–381

    Article  MathSciNet  Google Scholar 

  • Van Der Werff, L. (1977): Kinematic and dynamic analysis of mechanisms. A finite element approach. PhD Thesis, Delft Univ. Press

  • Van Der Werff, K.; Jonker, J. B. (1982): Dynamics of flexible mechanisms. In: Haug, E. J. (ed.): Computer aided analysis and optimization of mechanical system dynamics. Berlin, Heidelberg, New York: Springer

    Google Scholar 

  • Wehage, R. A.; Haug, E. J. (1982). Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems. J. Mech. Design. 104, 247–255

    Article  Google Scholar 

  • Wehage, R. A. (1984): Quaternions and Euler parameters. A brief exposition. In: Haug, E. J. (ed.): Computer aided analysis and optimization of mechanical system dynamics. Berlin, Heidelberg, New York: Springer

    Google Scholar 

  • Wittenburg, J.: Dynamics of systems of rigid bodies. Stuttgart: Teubner

Download references

Author information

Author notes

  1. M. Geradin

    Present address: Department of Mechanical Engineering and Center for Space Structures and Controls, University of Colorado, Boulder, USA

  2. A. Cardona

    Present address: Becario Externo y Miembro de la Carrera del Investigador del Consejo Nacional de Investigaciones Cientificas y Técnicas de la República Argentina, Argentina

Authors and Affiliations

  1. L.T.A.S., Dynamique des Constructions Mécaniques, Université de Liège, Rue Ernest Solvay, 21, B-4000, Liége, Belgium

    M. Geradin & A. Cardona

Authors
  1. M. Geradin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Cardona
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by S. N. Aduri, June 2, 1987

Rights and permissions

Reprints and permissions

About this article

Cite this article

Geradin, M., Cardona, A. Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra. Computational Mechanics 4, 115–135 (1988). https://doi.org/10.1007/BF00282414

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00282414

Keywords

Search

Navigation