The present contribution aims to build chiral Cosserat effective models of architectured media prone to such effects, recoursing to dedicated homogenization methods. In order to develop a method in full generality, the effective Cosserat model is obtained from the degeneration of the micromorphic effective continuum, by projecting the micromorphic kinematic degrees of freedom onto the Cosserat variables. The proposed homogenization method relies on variational principles and a decomposition of the microscopic displacement into a so-called homogeneous part and a periodic fluctuation. The homogeneous contribution to the total microscopic displacement accounts for the postulated effective generalized continuum, and it is corrected by a displacement fluctuation. The energy of the fluctuating displacement is shown to define a measure of the accuracy of the homogenized chiral Cosserat model. Applications of the proposed homogenization framework are done for centrosymmetric and non-centrosymmetric chiral architected media.
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