Synthesis of Dynamically Balanced Mechanisms by Using Counter-Rotary Countermass Balanced Double Pendula

Complete dynamic balancing principles still cannot avoid a substantial increase in mass and inertia. In addition, the conditions for dynamic balance and inertia equations can be complicated to derive. This article shows how a double pendulum, which is fully dynamically balanced using counter-rotary countermasses (CRCMs) for reduced additional mass and inertia, can be used as a building element in the synthesis of dynamically balanced mechanisms. It is also shown that for these mechanisms, the balancing conditions and inertia equations can be derived quickly. For constrained mechanisms, the procedure is to first write down the known balancing conditions and inertia equations for the balanced double pendula and subsequently substitute the kinematic relations. In addition, new CRCM configurations were derived that have low inertia, a single CRCM, or all CRCMs near the base.