Mass equivalent triads

In this paper it is shown how a general 3-DoF triad can be designed mass equivalent to a general (1-DoF) link element. This is useful in the synthesis of shaking force balanced and statically balanced mechanisms, for instance to add or remove a number of DoFs of a balanced mechanism maintaining its balance. Also it can be used as a simple approach for synthesis of complex balanced mechanisms. To obtain the parameters for mass equivalence, a mass equivalent model with real and virtual equivalent masses is used. The characteristics of this model are explained and the properties of a mass equivalent triad are shown. Subsequently the parameters of a mass equivalent triad are derived with the method of rotations about the principal points (RAPP) and application examples are il-lustrated and discussed.