Single-point synthesis of compliant mechanisms

In the last decades, several methods have been developed for the synthesis of compliant mechanisms. Generally, the proposed approaches work at the mechanism level, leading to the definition of a compliant structure starting from specific design requirements and constraints. In this paper, a novel point compliance synthesis method for planar systems is presented. The method relies on a different perspective, namely, at the output port level. It starts from the requirements on an already defined compliant structure, modeled as a two-port system, and leads to the design of the suspended body, that serves both as input and output port. The kinetostatics of the elastic suspension is described by resorting to the ellipse of elasticity theory, under the assumptions of linear deflections and linear elastic material. Then, the point compliance synthesis, based on spectral analysis, targets the field of displacements of the suspended body to define the points meeting the design requirements. The synthesis problem is formulated as a non-dimensional algebraic system that always admits real solutions. In particular, the obtained closed-form expressions hold in the general case, for every compliant mechanism. The method is applied to two case studies, at the element and at the mechanism levels, and finite element simulations are performed to test the theoretical results.