Point Synthesis in Compliant Four-Bar Mechanisms

In the last decades, many different methods have been proposed for the synthesis of compliant mechanisms. These methods generally define a compliant structure according to specific design requirements. On the other hand, the synthesis problem can be addressed, from a different point of view, at the output port level. In fact, the load-displacement requirements can be met by a compliant mechanism with an already defined structure, by exploiting the field of displacements of its rigid body that interacts with the external environment, that is the output port. In this scenario, the point compliance synthesis method, proposed for planar systems, focuses on the relation between the force and the consequent displacement at the same point. The kinetostatics of the elastic suspension is modeled by the ellipse of elasticity theory, that reduces the complexity of the compliant mechanism to a unique parameter, i.e. the eccentricity of the ellipse. Spectral analysis is performed to characterize the compliance of the points of the plane associated to the output port. On this basis, the point compliance synthesis consists of finding the points that satisfy the assigned load-displacement requirements by solving an algebraic system. The solutions, expressed in closed form, always exist and can be used for any compliant mechanism. The method is applied to the coupler of a compliant four-bar linkage to meet the requirements assigned in terms of orientation and ratio of the point principal compliances. Numerical simulations are performed to verify the proposed approach.