Abstract
The aim of this paper is to present kinematical and dynamical models of a system of flexible bodies in a compact form suitable for modeling, identification or control. Use of a Taylor series expansion of the body deformation in the kinematical model presents a way to refine the deformation description by increasing the expansion order. Including the definition of augmented bodies in the model permits us to write the equations of motion in a more compact form. It also gives a formulation of the dynamical model of the system that is linear in terms of the mass parameters. Then it a priori gathers the mass parameters in groups that have independent influences to the dynamical model. These properties are particularly appreciated when the purpose of modeling is to identify the multibody system.
Similar content being viewed by others
References
Fisette, P., Samin, J.C. and Willems, P.Y, ‘Contribution to symbolic analysis of deformable multibody systems’, Internat. J. Numer. Methods Engrg. 32, 1991, 621–1635.
Fisette, P. and Samin, J.C., ‘A fully symbolic generation of the equations of motion of multibody systems containing flexible beams’, Comput. Methods Appl. Mech. Engrg. 142, 1997, 123–152.
Khorrami, F., Jain, S. and Tzes, A., ‘Experimental results on adaptive nonlinear control and input preshaping for multi-link flexible manipulators’, Automatica . 31(1), 1995, 83–97.
Oliviers, M. and Campion, G., ‘A contribution to identification of robot with flexible arms’, Technical report, Université Catholique de Louvain, 1996.
Piedboeuf, J.-C., ‘The Jacobian matrix for a flexible manipulator’, J. Robotic Syst. 12(11), 1995, 709–726.
Piedboeuf, J.-C., ‘Symbolic modeling of flexible manipulators’, in Proceedings of the AAS/AIAA Astrodynamics Conferences, Halifax, Nova Scotia, Canada, August 14–17, 1995, AAS 95–357.
Raucent, B. and Samin, J.C., ‘Minimal parameterization of robot dynamic models’, Mech. Structures Mach. 22(3), 1994, 371–396.
Renaud, M., ‘Quasi-minimal computation of the dynamic model of a robot manipulator utilizing the Newton–Euler formalism and the notion of augmented body’, in Proceedings of the IEEE International Conference on Robotics and Automation, Raleigh, NC, 1987, 1677–1682.
Wittenburg, J., Dynamics of Systems of Rigid Bodies, B.G. Teubner, Stuttgart, 1977.
Rights and permissions
About this article
Cite this article
Oliviers, M., Campion, G. & Samin, J. Nonlinear Dynamic Model of a System of Flexible Bodies Using Augmented Bodies. Multibody System Dynamics 2, 25–48 (1998). https://doi.org/10.1023/A:1009778206326
Issue Date:
DOI: https://doi.org/10.1023/A:1009778206326