Design and analysis of closed-chain principal vector linkages for dynamic balance with a new method for mass equivalent modeling

Succeeding the already studied open-chain principal vector linkages, this paper introduces the design and analysis of closed-chain principal vector linkages with two approaches. With the proposed open-chain method solutions are obtained by simply closing the chain of an open-chain principal vector linkage. With the proposed method of the mass equivalent principal chain less complex solutions are obtained with consideration of the loop closure relations. Then an open-chain principal vector linkage is closed with an additional element which, with a general mass distribution, is modeled mass equivalently in a new way with two real equivalent masses and one virtual equivalent mass. The results are validated with a dynamic simulation and a grasper mechanism with payload balanced together is shown as application example.