Transactions of the Korean Society of Machine Tool Engineers (한국공작기계학회논문집)

The Korean Society of Manufacturing Technology Engineers (한국생산제조학회)
권호 표지

An Implementation Method of Linearized Equations of Motion for Multibody Systems with Closed Loops

  • Bae, D.S. (Dept. of Mechanical Engineering, Hanyang University)
  • Published : 2003.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

This research proposes an implementation method of linearized equations of motion for multibody systems with closed loops. The null space of the constraint Jacobian is first pre-multiplied to the equations of motion to eliminate the Lagrange multiplier and the equations of motion are reduced down to a minimum set of ordinary differential equations. The resulting differential equations are functions of all relative coordinates, velocities, and accelerations. Since the variables are tightly coupled by the position, velocity, and acceleration level coordinates, direct substitution of the relationships among these variables yields very complicated equations to be implemented. As a consequence, the reduced equations of motion are perturbed with respect to the variations of all variables, which are coupled by the constraints. The position velocity and acceleration level constraints are also perturbed to obtain the relationships between the variations of all relative coordinates, velocities, and accelerations and variations of the independent ones. The Perturbed constraint equations are then simultaneously solved for variations of all variables only in terms of the variations of the independent variables. Finally, the relationships between the variations of all variables and these of the independent ones are substituted into the variational equations of motion to obtain the linearized equations of motion only in terms of the independent variables variations.

Keywords

References

  1. ASME. Journal of Mechanism v.108 Automatic Linearization of Constrained Dynamical Models Sohoni, V. N.;Whitesel, J.
  2. IEEE Transactions on System v.SMC-14 no.6 Linearization and Sensitivity Functions of Dynamic Robot Models Neuman, C. P.;Murray, J. J.
  3. IEEE Journal of Robotics and Automation v.RA-2 no.3 Recursive Evaluation of Linearized Dynamic Robot Models Balafoutis, C. A.;Misra, P.;Patel, R. V.
  4. Computers & Structures v.57 no.2 Lagrangian Formulation and Linearization of Multibody System Equations Goniter, C.;Li, Y. https://doi.org/10.1016/0045-7949(94)00599-X
  5. Mech. Struct. and Machines v.15 no.3 A Recursive Formulation for Constrained Mechanial System Dynamics: Part Ⅰ, Open Loop Systems Bae, D. S.;Haug, E. J. https://doi.org/10.1080/08905458708905124
  6. Mech. Struct. and Machines v.15 no.4 A Recursive Formulation for Constrained Mechanical System Dynamics: Part Ⅱ, Closed Loop Systems Bae, D. S.;Haug, E. J. https://doi.org/10.1080/08905458708905130
  7. Mech. Struct. and Machines v.27 no.3 A Generalized Recursive Formulation for Constrained Mechanical System Dynamics Bae, D. S.;Han, J. M.;Yoo, H. H. https://doi.org/10.1080/08905459908915700
  8. Computer Methods in Applied Mechanics adn Engineering v.187 An Explict Integration Method for Realtime Simulation of Multibody Vehicle Models Bae, D. S.;Lee, J. K.;Cho, H. J.;Yae, H. https://doi.org/10.1016/S0045-7825(99)00138-3
  9. International Journal for Numerical Methods in Engineering v.50 A Generalized Recursive Formulation for Constrained Flexible Multibody Dynamics Bae, D. S.;Han, J. M.;Choi, J. H.;Yang, S. M. https://doi.org/10.1002/nme.97
  10. International Journal for Numerical Methods in Engineering v.48 A Compliant Track Link Model for High-Speed, High-Mobility Tracked Vehicles Ryu, H. S.;Bae, D. S.;Choi, J. H.;Shabana, A. A. https://doi.org/10.1002/1097-0207(20000810)48:10<1481::AID-NME959>3.0.CO;2-P
  11. Computer Methods in Applied Mechanics and Engineering v.190 Configuration Design Sensitivity Analysis of Dynamics for Constrained Mechanical Systems Kim, H. W.;Bae, D. S.;Choi, K. K. https://doi.org/10.1016/S0045-7825(00)00372-8
  12. B. G. Teubner Stuttgart Dynamics of Systems of Rigid Bodies Wittenburg, J.
  13. British A.R.C. Reports and Memoranda no.766 The Free Transverse Vibration of Airscrew Blades Southwell, R.;Gough, F.
  14. RecurDyn User's Manual