Elastodynamic behavior of balanced closed-loop mechanisms: numerical analysis of a four-bar linkage

This paper investigates the influence of two common techniques of static balancing on the dynamic performance of closed-chain linkages, by taking into account the flexibility of the mechanism components. The long-term goal of the research consists in enhancing the operation of parallel spatial robots by means of optimal balancing strategies. This contribution is primarily meant to provide the analysis method of the research and, for this purpose, it focuses on the planar four-bar linkage, intended as the simplest example of closed-chain mechanism. Firstly an original approach for the static balancing of planar linkages by means of constant-force generators is proposed. The implemented formulation, which permits to compute the balancing parameters of both counter-weights and/or springs, is adopted for deriving a mass balanced and an elastically compensated variant of the studied four-bar linkage, respectively. Then the operation of the unbalanced linkage and its two balanced variants is numerically studied. The natural frequencies and mode shapes of these mechanisms are estimated by modal analysis, whereas the dynamic performance at different operating regimes is assessed by kineto-elastodynamic investigation and finally discussed.