In this paper a new nite element formulation for slender beams is suggested that is valid for large rotations and de ections. Traditional formulations such as the oating frame approach and the incremental method are limited to small de ections, which restricts the scope of their applicability to small accelerations. In the local frame formulation no simplifying assumptions are made in accounting for the inertia forces. As the formalism remains consistent with large de ections it can be used for accurate evaluation of deformations caused by inertia forces at large accelerations. The paper is concerned with multibeam plane motions. The new formulation is implemented as a computer algebra tool that generates dynamic equations of exible multibody systems from speci cations. A number of case studies related to high-speed machinery are presented.

This paper presents a heuristic algorithm to solve the linear coordinate reduction problem. If Cartesian coordinates are chosen in the initial formulation the algorithm eliminates two-thirds of dependent coordinates in the planar case and one-half in the spatial case for mechanisms composed of spherical, revolute and universal joints. For an open-loop system composed of spherical joints it eliminates all dependent coordinates. A computer algebra-based implementation in the Maple language is presented. The proposed technique is demonstrated by application to the dynamic analysis of a Peaucellier mechanism.