Projective Synthesis of Compliant Mechanisms With Equivalent Kinetostatics

In the last years, many research efforts have been made to develop suitable synthesis methods for compliant mechanisms, generally focused at the mechanism level. Recently, projective geometry has been exploited for designing compliant systems, both at the mechanism and at the output port levels. At the mechanism level, the projective synthesis method starts from the load-displacement requirement, and consists of a top-down procedure based on series and parallel decompositions of ellipses of elasticity. The decompositions are performed by exploiting the self-polar triangles associated to the conics that relate the primary ellipse to a pair of secondary ellipses. Eventually, the lowest-level ellipses are materialized into elastic elements, or flexures. Different decompositions lead to the design of different compliant systems, characterized by specific topologies. In this paper, the method is applied to the synthesis of compliant mechanisms that are kinetostatically equivalent at the output port, that is the rigid link interacting with the external environment. Since the top-down procedure is not unique, infinite equivalent mechanisms can be obtained. In particular, two different closed-chain mechanisms, characterized by a non-symmetric and by a symmetric structure, are designed. The kinetostatic equivalence of the systems predicted by the theory is compared to the numerical results of finite element simulations, considering several load conditions.