A Numerical and Experimental Analysis of a Chain of Flexible Bodies

Abstract

A flexible multi-body dynamics approach is described. It uses an equivalent rigid link system from which are measured small displacements. The equations of motion are obtained by direct application of the principle of virtual work. Some terms in the virtual and real components have been neglected by virtue of the small displacement assumption. The use of sensitivity coefficients allows one to obtain a formulation which can be easily interfaced with any kinematic solution algorithm. It also enables one to check the correctness of the chosen equivalent rigid link system. The theory is then employed to reproduce numerically the experimental recordings obtained from a flexible linkage. Agreement between experimental and numerical data is good.

Accurate Modelling of a Flexible-Link Planar Mechanism by Means of a Linearized Model in the State-Space Form for Design of a Vibration Controller

“…A more detailed explanation is contained in reference [32]. Now, nodal elastic virtual displacements u and virtual displacements of the ERLS r are completely independent with each other.…”

“…The accuracy of such a model has been proved by experimental tests, the results of which are presented in the same paper [32]. Each #exible link of the mechanism is subdivided into "nite elements, and an ERLS is de"ned so that the elastic displacements with respect to it can be considered.…”

“…It is now required to linearize the non-linear system (35) about an equilibrium point x C , v C , i.e., a point for which, recalling equation (32)…”

“…The dynamic model of a #exible-link mechanism used in this work is based on the theory proposed by Giovagnoni [32] and is summarized here. The accuracy of such a model has been proved by experimental tests, the results of which are presented in the same paper [32].…”

“…The mechanism links are modelled by beam elements according to the "nite elements method. The overall motion of the mechanism is decomposed into the rigid motion of a suitably de"ned equivalent rigid link mechanism (ERLS) and an overlapped elastic motion, following the ideas set forward by Turcic and Midha [28}30], Chang and Hamilton [31] and Giovagnoni [32]. The equations of motion for the #exible mechanism can then be written by direct application of the virtual work principle.…”