We introduce a microscopic model for collinear multiferroics capable of reproducing, as a consequence of magnetic frustration and easy-axis anisotropy, the so-called ``uudd'' (or antiphase) magnetic ordering observed in several type-II multiferroic materials. The crucial role of lattice distortions in the multiferroic character of these materials enters into the model via an indirect magnetoelectric coupling, mediated by elastic degrees of freedom through a pantograph mechanism. Long-range dipolar interactions set electric dipoles in the antiferroelectric order. We investigate this model by means of extensive density matrix renormalization group computations and complementary analytical methods. We show that a lattice dimerization induces a spontaneous ℤ₂ ferrielectric bulk polarization, with a sharp switch off produced by a magnetic field above a critical value. The topological character of the magnetic excitations makes this mechanism robust.Instituto de Física de Líquidos y Sistemas BiológicosInstituto de Física La Plata