On the Elastodynamic Behaviour of Balanced Closed-Loop Mechanisms: Numerical Analysis of a Four-Bar Linkage

The purpose of this research is the analysis of the effects produced by different techniques of static balancing, e.g. mass redistribution and elastic compensation, on the dynamic behaviour of closed-loop mechanisms. In particular, this contribution focuses on the study of a planar four-bar linkage – considered as the simplest example of closed-loop mechanism. For comparison purposes, three models are studied: an unbalanced, a mass-balanced and an elastically-compensated linkage. The elastodynamic analysis is performed via a commercial multibody software. In particular, the flexibility of the links is modelled by the finite element method, whereas lumped parameters are employed to describe the compliance of the mechanical driving transmission. The modal analysis of the three models is carried out, the natural frequencies and the mode shapes being computed for several positions of the mechanisms. Furthermore, the kineto-elastodynamic simulation is performed, the driving torque and the constraint reactions being derived for different input velocities. The effects of the different balancing techniques are investigated and discussed. The performed simulations provide some interesting results, which justify the extension of the research to more complex closed-loop mechanisms.