On the shaking force balancing of compliant mechanisms

This paper is a first approach in finding design principles for the design of shaking force balanced compliant mechanisms. Shaking force balance means that the motions of the mechanism do not create any resultant dynamic reaction forces on the base, eliminating base vibrations.It is found that for a single balanced rotatable flexible link two stiffness related balance conditions exist in addition to the balance condition known for a rigid link. With these conditions the shaking force balance of a planar parallelogram mechanism with flexible links is considered. The case with fully compliant hinges is applied to a planar translator and the results are compared with the case in which the hinges are real revolute joints. Simulations show perfect force balance for the model with revolute joints and a reduced shaking force of 67% for the model with flexible joints. Prototypes of both mechanisms were developed and experimentally tested, showing shaking force reductions of 93% and 97.5%, respectively.