Summary: In this paper, constructions of triangular norms are investigated. Especially, based on weak negations that are not necessarily involutive, the rotation and the rotation-annihilation constructions are extended. By means of these methods, we can get new families of left-continuous t-norms compatible with the weak negations given. However, not all weak negations are suitable for these generalized constructions. To highlight this, some counterexamples are given.