A Pseudorigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads

In this paper, a pseudo-rigid-body (PRB) 3R model which consists of four rigid links joined by three revolute joints and three torsion springs is proposed for approximating the de∞ection of a cantilever beam subject to a general tip load. The large de∞ection beam equations are solved through numerical integration. A comprehensive atlas of the tip de∞ection for various load modes is obtained. A three-dimensional search routine has been developed to flnd the optimal set of characteristic radius factors and spring stifiness of the PRB 3R model. Detailed error analysis has been done by comparing with the pre-computed tip de∞ection atlas. Our results show that the approximation error is much less than that of the conventional PBR 1R model. The beneflts of the PRB 3R model include (a) load independence which is critical for analysis/synthesis applications where loads vary signiflcantly, (b) high accuracy for large de∞ection beams, and (c) explicit kinematic and static constraint equations which are simpler to solve compared with the flnite element model. To demonstrate the use of the PRB 3R model, a compliant 4-bar linkage is studied and verifled by a numerical example. The result shows a maximum tip de∞ection error of 1:2% compared with the FEA model.