R. Vidoni, A. Gasparetto, M. Giovagnoni, P. Boscariol
Dynamic analysis and simulation of spatial flexible-link manipulators by means of a novel Equivalent Rigid Link System approach
Atti del XX Congresso Nazionale AIMETA, Bologna, 12-15 settembre 2011

Abstract: In this paper, a novel approach for modeling the dynamics of 3-D flexible-link multi-body mechanisms featuring large displacements and small deformations is discussed. The novel 3-D method is based on an Equivalent Rigid Link System (ERLS), concept introduced in [1, 2], on the use of finite element techniques (in this work the Euler-Bernoulli model for a spatial beam has been considered) and on the extensive use of the Jacobian Matrix and the 1st and 2nd order differential kinematics. These terms allow to obtain a general formulation and to explicitly express infinitesimal displacements of the ERLS versus infinitesimal displacements of its generalized coordinates. Thus, if known the rigid-body kinematic solution, it can be directly used in the flexible multi-body analysis. As a result, the approach leads to a non decoupled formulation and the motion of the Equivalent Rigid-Link System is not independent from vibration. Moreover, the novel 3-D ERLS approach allows to decouple the kinematic equations of the ERLS from the compatibility equations of the displacements at the joints without neglecting the mutual influence between rigid body motion and vibration. The dynamic equations of motion for the flexible-links multibody systems are obtained and formulated by applying the principle of virtual work, imposing the kinematic constraints (i.e. the compatibility equations at the joints that are here written and included considering only the elastic displacements) and introducing some damping for simulating practical applications. The proposed novel approach has been compared with respect to the Floating Frame of Reference (FFR) formulation, at today the most used and adopted method [3] for dynamic modeling of multibody rigid-flexible-link mechanisms. The overall 3D formulation has been implemented in a generic software developed in MatlabTM and the dynamics of different spatial benchmark mechanisms have been simulated and compared with respect to Adams-FlexTM software, where the flexible mechanisms are modeled by means of a component mode synthesis (CMS) technique based on the Craig-Bampton method [4] and the FFR approach [3], showing a good agreement and the validity of the approach.

Area: Vibrazioni Meccaniche

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