Originally applied to the accurate, passive positioning of submillimetric devices, recent works proved capillary self-alignment as effective also for larger components and relatively large initial offsets. In this paper, we describe an analytic quasi-static model of 1D capillary restoring forces that generalizes existing geometrical models and extends the validity to large displacements from equilibrium. The piece-wise nature of the model accounts for contact line unpinning singularities ensuing from large perturbations of the liquid meniscus and dewetting of the bounding surfaces. The superior accuracy of the generalized model across the extended displacement range, and particularly beyond the elastic regime as compared to purely elastic models, is supported by finite element simulations and recent experimental evidence. Limits of the model are discussed in relation to the aspect ratio of the meniscus, contact angle hysteresis, tilting and self-alignment dynamics.