Four-bar linkages, elliptic functions, and flexible polyhedra

Abstract We revisit Darboux' parametrization of the configuration space of a quadrilateral with fixed side lengths by elliptic functions, remind how it implies Darboux' folding porism, and relate it to Bottema's zigzag porism. Further, we review some mechanical applications of this parametrization giving rise to overconstrained linkages and polyhedra.