A direct derivation of the equations of motion for 3D-flexible mechanical systems

Abstract

Equations of motion for rigid bodies with the body-fixed co-ordinate system placed at or away from the centre of mass are derived in a clear and direct way by making use of the two basic equations of mechanics (Newton's second law and the corresponding law of angular momentum). The dynamic equations for flexible mechanical systems are derived using the principle of virtual work, which introduces inertia in a straightforward manner, because this principle treats inertia as a force. The flexible formulation is exemplified by the use of circular beam elements and some basic matrices are derived in a direct way using skew-symmetric matrices. The capabilities of the formulation are demonstrated through examples. Results are compared with and verified by examples from the literature. Derivations throughout the paper are simplified by means of skew-symmetric matrices.

Comparison and Implementation of a Rigid and a Flexible Multibody Planetary Gearbox Model

“…Pedersen and Pedersen (1998);Shabana (1989). Another description of exibility eects in multibody systems is given in e.g.…”

Control of Flexible Manipulators. Theory and Practice

“…Some examples are: (De Luca & Siciliano, 1991) for planar manipulators, (Pedersen & Pedersen, 1998) for 3 degree of freedom manipulators and (Schwertassek et al, 1999), in which the election of shape functions is discussed. The deflections are calculated from the following expression:…”