The deterministic front-ratchet effect, namely, the unidirectional transport of the bistable fronts (BFs) under the additive zero-mean ac forcing, is considered within the piecewise-linear model of the bistable system. Two different mechanisms underlying the front ratchet, two cases of the broken symmetry of (i) the rate function, and/or (ii) the external zero-mean ac forcing are analyzed. Types of unidirectional motion, some versions of the "unforced" migration of BFs, are found in both cases of the travelling (initially propagating) and the static (motionless) fronts. We show that symmetry breaking in the front ratchet could produce progressive, regressive, and reversal types of the unidirectional motion of traveling BFs. By tuning the parameters of the rate function the propagation direction of BF exhibits reversal, as a function of the amplitude of the applied ac forcing. The static BFs, which stay initially at rest, can gain the dc motion discussed if the symmetry of either the rate function or the applied ac forcing is broken. The adiabatic approximation is used. To perform a rigorous analytic treatment for the arbitrary strengths of the driving force we assume that the frequency of the applied ac forcing is small, if compared to the characteristic relaxation rates in the system.