A NUMERICAL-METHOD FOR STABILITY ANALYSIS OF PINNED FLEXIBLE MECHANISMS

A technique is presented to investigate the stability of mechanisms wi th pin-jointed flexible members. The method relies on a special floati ng frame from which elastic link co-ordinates are defined. Energies ar e easily developed for use in a Lagrange equation formulation, leading to a set of non-linear and mixed ordinary differential-algebraic equa tions of motion with constraints. Stability and bifurcation analysis i s handled using a numerical procedure (generalized co-ordinate partiti oning) that avoids the tedious and difficult task of analytically redu cing the system of equations to a number equalling the system degrees of freedom. The proposed method was then applied to (1) a slider-crank mechanism with a flexible connecting rod and crank of constant rotati onal speed, and (2) a four-bar linkage with a flexible coupler with a constant speed crank. In both cases, a single pinned-pinned beam bendi ng mode is employed to develop resonance curves and stability boundari es in the crank length-crank speed parameter plane. Flip and fold bifu rcations are common occurrences in both mechanisms. The accuracy of th e proposed method was also verified by comparison with previous experi mental results [1]. (C) 1996 Academic Press Limited