The Stability and Response of a Flexible Rod in a Quick Return Mechanism: Large Crank Case

Abstract

The response and stability of a flexible rod, rigid crank quick return mechanism is investigated without a small crank restriction. A Galerkin's approach was found to be too computationally intensive, due to the moving boundary and complex mode shapes, and thus unsuitable for monodromy based parametric resonance stability investigations. A simple set of polynomial modes were developed. Although requiring more modes than the Galerkin method to obtain the same accuracy, polynomial modes require less computation time for stability investigations. A free-free (time independent) mode method was used to obtain non-linear dynamical and constraint equations. The method was found to be the most accurate and least computationally expensive for response; however, these equations were non-linear and not suitable for stability investigations.