Dynamic balancing of mechanisms with flexible links

The dynamic balancing of flexible mechanisms, that is, the reduction or elimination of shaking forces and shaking moments on the support structure, is considered. Two approaches are pursued: one uses similarity and the other modal balancing. A single rotating link can be balanced by a properly scaled countermass, for which balancing criteria are given. If all balancing conditions are satisfied, shaking force balance can even be achieved if geometric non-linearities are taken into account. This single link can be extended to a translator. Owing to the unscaled pitch of the translator and the asymmetric driving motor, no perfect shaking force balance is achieved, but the results can be considered satisfactory. Then, the dynamic balancing of a four-bar mechanism with a flexible coupler by means of modal balancing is shown. If the coupler is supported at the nodes of the first free vibration mode, this mode can be suppressed in the shaking force and shaking moment response. By supporting the coupler at four points with two whippletree mechanisms, the contribution of the first three symmetric vibration modes can be significantly reduced.