Synthesis of Path Generating Compliant Mechanisms Using Initially Curved Frame Elements

Initially curved frame elements are used in this paper within an optimization-based framework for the systematic synthesis of compliant mechanisms (CMs) that can trace nonlinear paths. These elements exhibit a significantly wider range of mechanical responses to applied loads than the initially straight frame elements, which have been widely used in the past for the synthesis of CMs. As a consequence, fewer elements are required in the design discretization to obtain a CM with a desired mechanical response. The initial slopes at the two nodes of each element are treated as design variables that influence not only the shape of the members in a CM, but also the mechanical response of the latter. Building on our prior work, the proposed synthesis approach uses genetic algorithms with both binary (i.e., 0/1) and continuous design variables in conjunction with a co-rotational total Lagrangian finite element formulation and a Fourier shape descriptors-based objective function. This objective function is chosen for its ability to provide a robust comparison between the actual path traced by a candidate CM design and the desired path. Two synthesis examples are presented to demonstrate the synthesis procedure. The resulting designs are fabricated as is, without any postprocessing, and tested. The fabricated prototypes show good agreement with the design intent.