Nonlinear Analysis of Flexible Four Linkage Mechanism

Abstract

This paper was discretizing numerically the links of the mechanism using finite element to develop model of unconstrained flexible mechanisms considering both axial and transverse deformations. The augmented Lagrange equations were used to drive the global governing equations. The equations of motion were solved for mechanisms with frequently varying mass, gyroscopic and stiffness matrices to compute the eigenvalues of the mechanism. The model of the mechanism was combination of flexible links connected by rotational pairs. The critical running speeds were calculated based on stability criterion method. The methods for determining critical operating speeds of linkage mechanisms with all links assumed as elastic members were applied in this work. Contribution/ Originality: This study is one of very few studies which have investigated the equation of motion of flexible mechanism considering gyroscopic matrix in computing the eigenvalues of the mechanism.