Pseudo-Rigid-Body Models for End-Loaded Heavy Cantilever Beams

Abstract

The large deflection of cantilever beams has been widely studied. A number of models and mathematical techniques have been utilized in predicting the path coordinates and load-deflection relationships of such beams. The Pseudo-Rigid-Body Model (PRBM) is one such method which replaces the elastic beam with rigid links of a parameterized pivot location and torsional spring stiffness. In this paper, the PRBM method is extended to include cases of a constant distributed load combined with a parallel endpoint force. The phase space of the governing differential equations is used to store information relevant to the characterization of the PRBM parameters. Correction factors are also given to decrease the error in the load-deflection relationship and extend the angular range of the model, thereby further aiding compliant mechanism design. Our calculations suggest a simple way of representing the effective torque caused by a distributed load in a PRBM as a function of easily calculated model parameters.