Analysis of a Fixed Guided Compliant Beam With an Inflection Point Using the Pseudo Rigid Body Model Concept

Abstract

This paper provides an efficient method of analysis for a fixedguided compliant beam with an inflection point, subjected to beam end load or displacement boundary conditions, or a combination thereof. To enable this, such a beam is modeled as a pair of wellestablished pseudorigidbody models (PRBMs) for fixedfree compliant beam segments. The analysis procedure relies on the properties of inflection in developing the necessary set of parametric, static equilibrium and compatibility equations for solution. The paper further discusses the multiplicity of possible solutions, including displacement configurations, for any two specified beam end displacement boundary conditions, depending on the locations and types of the effecting loads on the beam to meet these boundary conditions. A unique solution may exist when a third beam end displacement boundary condition is specified; however, this selection is not unconditional. A concept of characteristic deflection domain is proposed to assist with the selection of the third boundary condition to yield a realistic solution. The analysis method is also used to synthesize a simple, fully compliant mechanism utilizing the fixedguided compliant segments.